Hydraulic-fractures-How-far-can-they-go-_2012
Modeling Ithaca’s natural hydraulic fractures
1INRODUCTIONHydraulic fractures occur naturally in the Earth’s crust. These range in size from mm as small pres-sure partings to km as magmatic dike intrusions. Ithaca, New York, which lies in the heart of the Fin-ger Lakes region, is a great place to see intermedi-ate-scale natural hydraulic fractures. Glaciation and erosion have led to large outcrops of middle and up-per Devonian clastic rocks. These rocks have ex-perienced two major orogenic events in addition to uplift and erosion all of which have left a pattern of brittle fracture in the rocks as seen today. A brief geological history of the area is necessary to set the stage for the discussion of natural hydraulic frac-tures in these rocks.Outcrops within the Finger Lakes are part of the Devonian Catskill Delta Complex, a clastic wedge that is more than 2 km thick in the Finger Lakes re-gion. The complex was deposited on a continental shelf with an open sea to the south and consists of layers of black shales, gray shales, silstones and sandstones, and an occasional limestone. Uplift ac-companying the Acadian orogeny to the east pro-vided a large source of sediment for the clastic wedge that was prograding into the Appalachian Ba-sin. Deposition rates reached 170m per Ma. At the close of the Paleozoic, during the Pennsylvanian and Permian, the Alleghanian orogeny caused wide-spread folding, faulting and jointing in eastern North America. This was the last major orogeny to affect this part of the continent.Engelder and others (see Engelder et al. 2000) have studied the joints and other geologic features within the Catskill Delta Complex for many years. There is an abundance of evidence that indicates that many of these joints developed as natural hydraulic fractures caused by abnormally high fluid pressures. The Alleghanian orogeny also left a unique imprint as many joints show a clockwise sequence in re-sponse to the reorientation of stress as the African continent collided with North America.There is a significant body of literature that de-scribes the joints and tries to interpret their origin and formation (e.g. Pollard & Aydin 1988). How-ever, there have been few numerical simulations to illustrate the theorized processes. The aim of this paper is to examine various components of these joints using numerical simulations to determine whether current formation theories are reasonable or valid.2GEOLOGIC EVIDENCE OF NATURAL HYDRAULIC FRACTURES AND STRESS ROTATIONSThe current theories of joint formation in the Cats-kill Delta Complex depend upon visual inspection of many joints and joint sets (Engelder et al. 2000). The first bit of evidence comes from the surface morphology of many of the joint surfaces in the silt-stone.Modeling Ithaca’s natural hydraulic fracturesB.J. Carter & A.R. IngraffeaCornell University, Ithaca, NY, USAT. EngelderPenn State University, University Park, PA, USAABSTRACT: Joints within the Catskill Delta complex are believed to be natural hydraulic fractures and abundant indirect evidence supports this claim. The indirect evidence is based on many observations of joint surface morphology and joint spacing among other features. The Alleghanian orogeny left a unique imprint on the joint surfaces also, indicating a rotating horizontal compressive stress field. Numerical simulations il-lustrate that the formation and propagation of the joints can be described by hydraulic fracturing mechanisms. The numerical simulations include hydraulic fracture propagation from sedimentary structures at layer inter-faces and fracture twisting in response to the reorientation of the remote stress field after initial joint propaga-tion.Cracks tend to start at points of higher stress con-centration (McConaughy & Engelder 2000). In the case of sedimentary beds, the largest stress concen-trations are in the form of concretions, fossils, rip-ples, groove casts, and similar features. Figure 1 shows a joint surface in the Ithaca Formation silt-stone that starts at a groove cast, a location where the siltstone penetrates the shale layer, formed dur-ing erosion of the muddy substrate and deposition of the silt. The figure also shows the plumose surface morphology of the joint surface. The plumose struc-tures and the related arrest lines are well described by Bahat & Engelder (1984). Barbs, the darkened lines in Figure 1, radiate from the plume axis and indicate the direction of fracture growth. Arrest lines mark the termination of crack propagation in-crements. Natural hydraulic fractures do not have a steady supply of fluid (Lacazette & Engelder 1992). As the crack propagates, the pressure decays and the crack arrests until the pressure builds up again.Figure 1. Plumose joint surface starting from a groove cast.It can also be seen in Figure 1 that the fracture initially stays within the siltstone layer. It has been found that in sedimentary basins where the horizon-tal stress is less than the vertical, the shale layers have a higher horizontal stress than the siltstones (Evans et al. 1989, Warpinski 1989). Assuming that the pore pressure is the same in both the shale and siltstone layers, then the fractures would form in the siltstones first. This will be more evident in the next figure.The difference in horizontal stress leads to joint-ing in the siltstones followed by jointing in the shale. Joints in the shale beds usually start at the edges of existing joints in the siltstone; the joints act as con-duits for the pore fluid. If there is no rotation of the principal horizontal stresses, joints will develop in the shale in plane with those in the sandstone. How-ever, if the horizontal stress does rotate, then en-echelon or fringe cracks will develop (Pollard et al. 1982). Figure 2 shows a set of fringe cracks that start at the interface between the siltstone and shale. These fractures propagate downward. The numer-ous small cracks at the immediate interface reduce to a few large cracks as propagation continues.Figure 2. Multiple en-echelon cracks propagate down from the siltstone-shale interface and are rotated from the parent joint.There are many more features of the joints that offer indirect evidence of natural hydraulic fractures, including joint spacing, slip on open joints, crosscut-ting and abutting relationships, and evidence of a pressure seal that could have led to over-pressurization of the formation. However, it is be-yond the scope of this paper to discuss all of this evidence. Instead, numerical simulations are used to illustrate that natural hydraulic fracturing processes can explain some of the features described herein.3HYDRAULIC FRACTURING SOFTWARE The 3D numerical simulations that are described in the following sections are performed using HY-FRANC3D and accompanying software (Carter et al. 2000a,b). In addition, ANSYS (ANSYS 2000) and FRANC2D (CFG 2000) are used for some 2D analyses.The 3D software consists of OSM, FRANC3D, HYFRANC3D, and BES. OSM is used to create the initial geometric models. FRANC3D is a fracture analysis code with pre- and post-processing capabili-ties. HYFRANC3D builds upon FRANC3D by add-ing a fluid flow module that couples the elastic structural response with fluid flowing in the fracture. BES is a linear elastic boundary element program. BES provides an elastic influence matrix that re-lates the set of unit pressures (p) at the nodes on the crack surface to the elastic displacements (w). The fluid flow formulation is based on the elasticity, lu-brication and continuity equations. For a Newtonian fluid, the stress ahead of the crack front has a 1/3 singularity, as does the fluid pressure inside thecrack (Carter et al. 2000b). Physically, the fluid pressure cannot be singular, thus, a fluid lag must develop at the crack front (Figure 3). The finite ele-ment formulation in HYFRANC3D combines an analytical solution for the pressure and crack open-ing displacement at the crack front with a standard finite element formulation of the lubrication equa-tion for the bulk of the fracture. The analytical solu-tion at the crack front provides an elegant way to overcome the singular behavior and limits the re-quired number of elements at the crack front. Hy-draulic fracture simulation proceeds as a series of crack advance increments, requiring an elastic solu-tion and coupled flow analysis at each step.Figure 3. Crack front region with fluid lag; p is pressure, w is crack opening displacement, V is crack front velocity, σ3 is clo-sure stress and x is the local coordinate axis along the crack.4SIMULATION OF HYDRAULIC FRACTURE PROPAGATION FROM A GROOVE CASTCracks tend to start at pre-existing flaws and points of high stress concentration. The groove cast in Fig-ure 1 is modeled to evaluate the stress intensification and to determine the hydraulic fracture propagation behavior from this location. The intent of these simulations is to show that hydraulic fracture is a plausible mechanism; thus, realistic boundary condi-tions are necessary, but accurate values are not es-sential to provide qualitative results.The numerical model consists of the siltstone layer only. McConaughy & Engelder (2000) de-scribe the difficulties in determining and modeling the correct boundary conditions. They conclude that the interface between the shale and siltstone must al-low slip. To simplify the 3D model, the upper and lower shale layers are notmodeled; a vertical con-straint is applied to the upper surface. A far-field compressive stress is applied in the horizontal direc-tion only; the vertical stress is neglected. The com-pressive stress perpendicular to the crack surface is 50 MPa and the stress parallel to the crack plane is 100 MPa. The elastic modulus is set to 14 GPa and the Poisson’s ratio is set to 0.1.The initial plane strain ANSYS stress analysis clearly shows that the groove cast alters the horizon-tal stress (Fig. 4). A tensile stress is induced at the groove cast. An initial crack is nucleated in the 3D numerical model at this location and hydraulic frac-ture propagation is simulated.Figure 4. ANSYS contours of maximum principal stress around a groove cast in a siltstone layer; tension is positive and values are in MPa.Figure 5 shows the shape of the hydraulic fracture after 17 steps of propagation. The fluid boundary conditions consist of a crack mouth flow rate equal to 1.0e-6 m3/s and zero flow rate at the crack front. These boundary conditions do not match the pre-sumed conditions of periodic fluidpressure build-up, but it is assumed that this will only affect the fracturing time and the surface features. The shape of the fracture to this stage matches that seen in the field reasonably well, although the barbs and arrest lines cannot be reproduced. The simulation can be continued such that the fracture breaks through the upper surface of the silt layer, but this is not com-plete yet.Figure 5. Shape of a hydraulic fracture from a groove cast af-ter 17 steps of propagation.5SIMULATION OF HYDRAULIC FRACTURE IN A ROTATING STRESS FIELDHydraulic fractures in these brittle rocks tend to grow perpendicular to the direction of maximum tension (or minimum compression). If an initial crack is subjected to a rotated stress field, the crack will kink out of the original plane to align itself with the new stress field. The rotation of the stress field induces different modes of deformation on different parts of the crack front. The kinking behavior de-pends on the pressure distribution inside the crack, the geometry of the crack, and the stress and stiff-ness contrasts in the rock layers (Carter et al. 1999). As a simple example, an initial elongated radial crack (emanating from a horizontal borehole) is ori-ented 70°from the maximum horizontal compres-sive stress (Fig. 6). The crack is nucleated in a single layer model with an elastic modulus of 27.6 GPa and a Poisson’s ratio of 0.25. The vertical stress is 69 MPa, the maximum horizontal stress is 62 MPa, and the minimum horizontal stress is 48 MPa. The crack mouth flow rate is set to 0.0795 m3/s.Figure 6. The initial crack shape is 9 m long and 0.3 m deep; σHmax is aligned with the x-axis (not to scale).Hydraulic fracture is simulated and stress inten-sity factors (SIF’s) are computed. Figure 7 shows the distribution of SIF’s along the initial crack front. The mode I values are highest, but there is a signifi-cant mode III component; mode II is significant only at the ends of the crack front. Pollard et al. (1982) provide a relationship between the mode III/I ratio and the number and spacing of en-echelon cracks that form along the crack front. Germanovich (2000) is conducting experiments on glass and brittle plastic to further characterize these relationships.The combination of all three modes is studied less well. However, the HYFRANC3D software allows the crack to propagate while ignoring the mode III SIF. Under these circumstances, the crack front does not break up, although, it quickly shows that it should. Figure 8 shows that the ends of the crack turn to align with σHmax. Most of the crack front is not aligned with σHmax. Instead, “large” ripples can be seen. The ripples are a result of the numerical propagation procedure, which only accounts for modes I and II. As the fracture propagates, the mode II and mode III SIFs increase rather than decrease. Due to the elongated shape, more effort is required to turn the entire crack front as compared to a more circular shape crack (Carter et al, 1999). As the crack front does not break, the combination of modes I and II produces initially minor oscillations in the crack front. These escalate as the crack con-tinues to grow, leading to the ripples.The mode III SIF value in the middle of the crack front reaches 10 MPa⋅√m at the final stage (15th step of propagation) while the mode I value remains rela-tively constant for each step, ranging from 20 to 25 MPa⋅√m along the crack front. Rotation and break up of the crack front is seen in many locations in the Ithaca area; Figure 9 shows a typical example.Figure 7. Mode I, II, and III SIF’s along the crack front; values are in MPa⋅√m.Figure 8. Ignoring mode III SIF during propagation leads to “large” ripples in the crack front indicating it should break up. The ends of the crack turn to align with the stress field.Figure 9. Joint in a siltstone indicating a rotated stress field as the crack surface shows obvious breaks; this might be seen as a set of en-echelon cracks when looking from above.6SIMULATION OF MULTIPLE HYDRAULIC FRACTURESMultiple parallel cracks tend to reduce in number and increase in spacing as they propagate. It is often assumed that the length to spacing ratio should be about 1.0 for a stable system of parallel cracks (Hwang, 1999). Figure 2 shows an example of a large number of closely spaced fractures at the shale-siltstone interface. As the cracks propagate down into the shale, most of the cracks arrest very quickly. Only a few, relatively widely spaced cracks remain at the base of the shale layer. Based on this figure, the length to spacing ratio is significantly greater than 1.0. Hwang (1999) has studied systems of parallel cracks, although not for 3D hydraulic fractures. Both 3D hydraulic fracture simulations and 2D simulations will be performed here.A set of three hydraulic fractures is used to gain insight into the behavior of a system of many paral-lel hydraulic fractures. The initial model is shown in Figure 10. The model is symmetrically constrained. The initial cracks are 1 mm deep and 6.35 mm apart. The crack mouth flow rate is 1.0e-6 m3/s and the material properties are the same as in section 4. In reality, more cracks should be modeled, but the simulations become quite time consuming as more cracks are added; three cracks should provide ade-quate insight.HYFRAN3D computes pressure distributions and crack opening displacements in the 3D fractures along with SIF distributions along the crack front. The usual procedure for growing multiples cracks is to scale the crack growth for all cracks based on the relative values of the stress intensity factors. Using this technique, the 3D hydraulic fractures are propa-gated for 10 steps. Although the mode I SIF for the center crack is slightly less than that for the two outer cracks (14.5 versus 15.2 MPa⋅√m for the initial crack), it continues to propagate. At step 10, the crack length is 10.5 mm. The length to spacing ratio is 1.7 and the center crack shows no signs of arrest-ing based on the relative mode I SIF values, 3.4 ver-sus 3.5 MPa⋅√m for the center and outer cracks re-spectively. Based on Figure 2, one might expect that the length to spacing ratio could be much higher than this. To verify that the crack growth is still sta-ble, 2D simulations are performed.FRANC2D is able to compute SIF’s, energy re-lease rates, and rates of energy release rates. The lat-ter allows the program to decide whether crack growth is stable and to decide which of the cracks are arrested. Although FRANC2D does not simulate fluid flow, a static pressure distribution of arbitrary shape can be applied to the crack surfaces (edges). It was shown previously (Carter et al, 1999) that if the correct pressure distribution, based on the 3D fluid flow analysis in HYFRANC3D, is applied to the crack surfaces of the 2D model, the correct hydrau-lic fracture behavior is captured. Thus, the pressure profile through the middle of each 3D crack is ap-plied to the 2D cracks to evaluate the rates of energy release rates.Figure 10. Initial 3D model of multiple parallel cracks.The initial FRANC2D analysis predicts that the center crack has a slightly lower rate of energy re-lease rate than the two outer cracks. The values are presented in matrix form in Table 1. The off-diagonal terms define the interaction between neighboring cracks. The negative values indicatethat crack growth is stable for all cracks. The influ-ence of neighboring cracks is relatively small, indi-cating a weak interaction.Table 1. Matrix of rates of energy release rate for 1 mm cracks.Crack 1 Crack 2 Crack 3 Crack 1 -0.6537E-01 -0.8141E-02 -0.2088E-02 Crack 2 -0.8141E-02 -0.6184E-01 -0.8141E-02 Crack 3 -0.2088E-02 -0.8141E-02 -0.6537E-01FRANC2D simulations corresponding to steps 5 and 10 of the 3D model are performed to examine the change in the rates as the cracks grow. The pres-sure profiles from the corresponding 3D HF simula-tions are used in the 2D simulations. The rates of energy release rate are provided in Tables 2-3. It is evident that the rate for the center crack is much less than the rate for the outer cracks at step 10, almost an order of magnitude. Also, the interaction between neighboring cracks is much stronger than for the ini-tial configuration. However, the rate is still non-zero and crack growth is still stable. The simulations are being continued to determine the final length to spacing ratio at which the center crack arrests.Table 2. Matrix of rates of energy release rate at 3.7 mm.Crack 1 Crack 2 Crack 3 Crack 1 -0.2531E-01 -0.5444E-02 -0.2027E-02 Crack 2 -0.5444E-02 -0.1514E-01 -0.5443E-02 Crack 3 -0.2027E-02 -0.5443E-02 -0.2534E-01Table 3. Matrix of rates of energy release rate at 10.7 mm.Crack 1 Crack 2 Crack 3 Crack 1 -0.1474E-01 -0.7807E-02 -0.4911E-02 Crack 2 -0.7807E-02 -0.2951E-02 -0.7807E-02 Crack 3 -0.4911E-02 -0.7807E-02 -0.1473E-017SIMULATION OF EN-ECHELON CRACKSEn-echelon cracks are often the result of crack front break up due to high mode III stress intensity fac-tors. The model in section 5 shows that the mode III stress intensity factor should not be ignored during propagation. Crack front break up is difficult to model, however, and is still not well understood.A simplified approach is taken here to examine crack front break up under a mode III loading. The model is shown in Figure 11. A single edge crack in a unit cube is subjected to a shear force while the crack faces are prevented from overlapping by the inclusion of a static fluid pressure. The elastic modulus is 10 GPa and Poisson’s ratio is set to zero. The SIFs are shown in Figure 12, which indicates the relatively high mode II and mode III SIF.Figure 11. Single edge crack subjected to mode III shear.Figure 12. SIF’s for single edge crack under torsion. Pollard et al. (1982) provide the following rela-tionship between the mode III/I ratio and the en-echelon crack orientation:()21tan211>−=−IIIIIKKKνβ(1)The inequality ensures an open crack. The equa-tion defines the orientation of a plane in front of the parent crack that has zero shear stress and the maximum tensile stress. If the mode III SIF is zero, the crack grows in its own plane. Based on the val-ues in Figure 12, β is –21° in the middle portion of the crack front. The initial spacing of the en-echeloncracks is less well defined and Germanovich (2000) continues to work on this.The initial crack front break up is modeled by manually creating a set of three small en-echelon “petal” cracks at the crack front as described by Germanovich (2000). Figures 13 and 14 show the side and plan views of the crack configurations. They are spaced 0.05 units apart with a radius of 0.02 units.Figure 13. Side view of 3 en-echelon cracks simulating the crack front break up.Figure 14. Plan view of 3 en-echelon cracks simulating the crack front break up.The initial stress analysis was performed without computing the elastic influence matrix. The maxi-mum principal stress is concentrated at the intersec-tion of the main and “petal” cracks (Figure 15). Ef-forts to define the crack growth criterion and propagation behavior for this crack configuration are continuing and further results will be presented elsewhere.Figure 15. Maximum principal stress is concentrated at the in-tersection of the main and “petal” cracks.8CONCLUSIONSThe indirect evidence for natural hydraulic fractures is abundant in the Ithaca, NY region. The proof might depend upon the interpretation, however. Numerical hydraulic fracture simulations lend addi-tional insight to the natural processes. Hydraulic fracture simulation from a sedimentary interface is modeled to examine the influence of natural stress concentrations, the propagation of multiple frac-tures, and the re-orientation of fractures in a rotating stress field.The simulations are not complete yet, but they do indicate that hydraulic fracturing is a plausible mechanism for describing the joints seen in the rocks in the Ithaca, NY region. The simulations are continuing and the final results will be presented later.ACKNOWLEDGEMENTSThe authors would like to acknowledge the past and present financial support of the NSF (EIA-9972853; EIA-9726388; CMS-9625406). This research was conducted using the resources of the Cornell Theory Center, which receives funding from Cornell Uni-versity, New York State, federal agencies, and cor-porate partners. Penn State’s Seal Evaluation Con-sortium (SEC) supported the fieldwork.REFERENCESANSYS 2000. /.Bahat, D. & T. Engelder 1984. Surface morphology on cross-fold joints of the Appalachian Plateau, New York and Pennsylvania, Tectonophysics 104:299-313.Carter, B.J., X. Weng, J. Desroches & A.R. Ingraffea, 1999.Hydraulic Fracture Reorientation: Influence of 3D Geome-try, Hydraulic Fracture Workshop, 37th US Rock Mechan-ics Symposium, Vail, CO.Carter, B.J., P.A Wawrzynek & A.R. Ingraffea 2000a. Auto-mated 3D Crack Growth Simulation, Gallagher Special Is-sue Int. J. Num. Meth. Engng. 47:229-253.Carter, B.J., J. Desroches, A.R. Ingraffea & Wawrzynek, P.A.2000b. Simulating fully 3d hydraulic fracturing. In M.Zaman, G. Gioda & Booker, J. (eds), Modeling in Geome-chanics, 525-557, Wiley Publishers.Engelder, T. & students 2000. The Catskill Delta Complex: Analog for modern continental shelf and delta sequences containing overpressured sections. SEC Report, Dept. of Geosciences, Penn State University.Evans, K., G. Oertel, T. Engelder 1989. Appalachian Stress Study 2: Analysis of Devonian shale core: some implica-tions for the nature of contemporary stress variations and Alleghanian deformation in Devonian rocks. J. Geophys.Res. 94:1755-1770.FRANC2D 2000. /software/. Germanovich, L. 2000. Pers. Comm.Hwang, C. 1999. Virtual crack extension method for calculat-ing rates of energy release rate and numerical simulation of crack growth in two and three dimensions. PhD Thesis, Cornell University, Ithaca, NY.Lacazette, A., & Engelder, T. 1992. Fluid-driven cyclic propa-gation of a joint in the Ithaca siltstone, Appalachian Basin, New York, in B. Evans & T-F. Wong, (eds.), Fault me-chanics and transport properties of rocks. 297-324, Lon-don: Academic Press Ltd.McConaughy, D.T. & Engelder, T. 2000. The nature of stress concentrations associated with joint initiation in bedded clastic rocks. Journal of Structural Geology (in press). Pollard, D.D. & Aydin, A. 1988. Progress in understanding jointing over the past century. Geological Society of Amer-ica Bulletin, 100:1181-1204.Pollard, D.D., P. Segall & P.T. Delaney 1982. Formation and interpretation of dilatant echelon cracks. Geol. Soc. Bull.93:1291-1303.Warpinski, N.R. 1989. Determining the minimum in situ stress from hydraulic fracturing through perforations. Int. J. Rock Mech & Min. Sci. 26:523-532.。
流体力学英语词汇翻译(2)
流体力学英语词汇翻译(2)流体力学英语词汇翻译(2)流体力学英语词汇翻译(2)动量厚度momentum thickness能量厚度energy thickness焓厚度enthalpy thickness注入injection吸出suction泰勒涡taylor vortex速度亏损律velocity defect law形状因子shape factor测速法anemometry粘度测定法visco[si] metry流动显示flow visualization油烟显示oil smoke visualization孔板流量计orifice meter频率响应frequency response油膜显示oil film visualization阴影法shadow method纹影法schlieren method烟丝法smoke wire method丝线法tuft method氢泡法nydrogen bubble method相似理论similarity theory相似律similarity law部分相似partial similarity定理pi theorem, buckingham theorem 静[态]校准static calibration动态校准dynamic calibration风洞wind tunnel激波管shock tube激波管风洞shock tube wind tunnel水洞water tunnel拖曳水池towing tank旋臂水池rotating arm basin扩散段diffuser测压孔pressure tap皮托管pitot tube普雷斯顿管preston tube斯坦顿管stanton tube文丘里管venturi tubeu形管u-tube压强计manometer微压计micromanometer多管压强计multiple manometer静压管static [pressure]tube流速计anemometer风速管pitot- static tube激光多普勒测速计laser doppler anemometer, laser doppler velocimeter热线流速计hot-wire anemometer热膜流速计hot- film anemometer流量计flow meter粘度计visco[si] meter涡量计vorticity meter传感器transducer, sensor压强传感器pressure transducer热敏电阻thermistor示踪物tracer时间线time line脉线streak line尺度效应scale effect壁效应wall effect堵塞blockage堵寒效应blockage effect动态响应dynamic response响应频率response frequency底压base pressure菲克定律fick law巴塞特力basset force埃克特数eckert number格拉斯霍夫数grashof number努塞特数nusselt number普朗特数prandtl number雷诺比拟reynolds analogy施密特数schmidt number斯坦顿数stanton number对流convection自由对流natural convection, free convec-tion 强迫对流forced convection热对流heat convection质量传递mass transfer传质系数mass transfer coefficient热量传递heat transfer传热系数heat transfer coefficient对流传热convective heat transfer辐射传热radiative heat transfer动量交换momentum transfer能量传递energy transfer传导conduction热传导conductive heat transfer热交换heat exchange临界热通量critical heat flux浓度concentration扩散diffusion扩散性diffusivity扩散率diffusivity扩散速度diffusion velocity分子扩散molecular diffusion沸腾boiling蒸发evaporation气化gasification凝结condensation成核nucleation计算流体力学computational fluid mechanics 多重尺度问题multiple scale problem伯格斯方程burgers equation对流扩散方程convection diffusion equationkdu方程kdv equation修正微分方程modified differential equation拉克斯等价定理lax equivalence theorem数值模拟numerical simulation大涡模拟large eddy simulation数值粘性numerical viscosity非线性不稳定性nonlinear instability希尔特稳定性分析hirt stability analysis相容条件consistency conditioncfl条件courant- friedrichs- lewy condition ,cfl condition 狄里克雷边界条件dirichlet boundary condition熵条件entropy condition远场边界条件far field boundary condition流入边界条件inflow boundary condition无反射边界条件nonreflecting boundary condition数值边界条件numerical boundary condition流出边界条件outflow boundary condition冯.诺伊曼条件von neumann condition近似因子分解法approximate factorization method人工压缩artificial compression人工粘性artificial viscosity边界元法boundary element method配置方法collocation method能量法energy method有限体积法finite volume method流体网格法fluid in cell method, flic method通量校正传输法flux-corrected transport method 通量矢量分解法flux vector splitting method伽辽金法galerkin method积分方法integral method标记网格法marker and cell method, mac method 特征线法method of characteristics直线法method of lines矩量法moment method多重网格法multi- grid method板块法panel method质点网格法particle in cell method, pic method 质点法particle method预估校正法predictor-corrector method投影法projection method准谱法pseudo-spectral method随机选取法random choice method激波捕捉法shock-capturing method激波拟合法shock-fitting method谱方法spectral method稀疏矩阵分解法split coefficient matrix method不定常法time-dependent method时间分步法time splitting method变分法variational method涡方法vortex method隐格式implicit scheme显格式explicit scheme交替方向隐格式alternating direction implicit scheme, adi scheme反扩散差分格式anti-diffusion difference scheme紧差分格式compact difference scheme守恒差分格式conservation difference scheme克兰克-尼科尔森格式crank-nicolson scheme杜福特-弗兰克尔格式dufort-frankel scheme指数格式exponential scheme戈本诺夫格式godunov scheme高分辨率格式high resolution scheme拉克斯-温德罗夫格式lax-wendroff scheme蛙跳格式leap-frog scheme单调差分格式monotone difference scheme保单调差分格式monotonicity preserving difference scheme穆曼-科尔格式murman-cole scheme半隐格式semi-implicit scheme斜迎风格式skew-upstream scheme全变差下降格式total variation decreasing scheme tvd scheme迎风格式upstream scheme , upwind scheme计算区域computational domain物理区域physical domain影响域domain of influence依赖域domain of dependence区域分解domain decomposition维数分解dimensional split物理解physical solution弱解weak solution黎曼解算子riemann solver守恒型conservation form弱守恒型weak conservation form强守恒型strong conservation form散度型divergence form贴体曲线坐标body- fitted curvilinear coordi-nates[自]适应网格[self-] adaptive mesh适应网格生成adaptive grid generation自动网格生成automatic grid generation数值网格生成numerical grid generation交错网格staggered mesh网格雷诺数cell reynolds number数植扩散numerical diffusion数值耗散numerical dissipation数值色散numerical dispersion数值通量numerical flux放大因子amplification factor放大矩阵amplification matrix阻尼误差damping error离散涡discrete vortex熵通量entropy flux熵函数entropy function分步法fractional step method广义连续统力学generalized continuum mechanics 简单物质simple material纯力学物质purely mechanical material微分型物质material of differential type积分型物质material of integral type混合物组份constituents of a mixture非协调理论incompatibility theory微极理论micropolar theory决定性原理principle of determinism等存在原理principle of equipresence局部作用原理principle of objectivity客观性原理principle of objectivity电磁连续统理论theory of electromagnetic continuum 内时理论endochronic theory非局部理论nonlocal theory混合物理论theory of mixtures里夫林-矣里克森张量rivlin-ericksen tensor声张量acoustic tensor半向同性张量hemitropic tensor各向同性张量isotropic tensor应变张量strain tensor伸缩张量stretch tensor连续旋错continuous dislination连续位错continuous dislocation动量矩平衡angular momentum balance余本构关系complementary constitutive relations共旋导数co-rotational derivative, jaumann derivative非完整分量anholonomic component 爬升效应climbing effect协调条件compatibility condition错综度complexity当时构形current configuration能量平衡energy balance变形梯度deformation gradient有限弹性finite elasticity熵增entropy production标架无差异性frame indifference弹性势elastic potential熵不等式entropy inequality极分解polar decomposition低弹性hypoelasticity参考构形reference configuration响应泛函response functional动量平衡momentum balance奇异面singular surface贮能函数stored-energy function内部约束internal constraint物理分量physical components本原元primitive element普适变形universal deformation速度梯度velocity gradient测粘流动viscometric flow当地导数local derivative岩石力学rock mechanics原始岩体应力virgin rock stress构造应力tectonic stress三轴压缩试验three-axial compression test 三轴拉伸试验three-axial tensile test三轴试验triaxial test岩层静态应力lithostatic stress吕荣lugeon地压强geostatic pressure水力劈裂hydraulic fracture咬合[作用] interlocking内禀抗剪强度intrinsic shear strength循环抗剪强度cyclic shear strength残余抗剪强度residual shear strength土力学soil mechanics孔隙比void ratio内磨擦角angle of internal friction休止角angle of repose孔隙率porosity围压ambient pressure渗透系数coefficient of permeability [抗]剪切角angle of shear resistance 渗流力seepage force表观粘聚力apparent cohesion粘聚力cohesion稠度consistency固结consolidation主固结primary consolidation次固结secondary consolidation固结仪consolidometer浮升力uplift扩容dilatancy有效应力effective stress絮凝[作用] flocculation主动土压力active earth pressure被动土压力passive earth pressure 土动力学soil dynamics应力解除stress relief次时间效应secondary time effect贯入阻力penetration resistance 沙土液化liquefaction of sand 泥流mud flow多相流multiphase flow马格努斯效应magnus effect韦伯数weber number环状流annular flow泡状流bubble flow层状流stratified flow平衡流equilibrium flow二组份流two-component flow 冻结流frozen flow均质流homogeneous flow二相流two-phase flow气-液流gas-liquid flow气-固流gas-solid flow液-气流liquid-gas flow液-固流liquid-solid flow液体-蒸气流liquid-vapor flow 浓相dense phase稀相dilute phase连续相continuous phase离散相dispersed phase悬浮suspension气力输运pneumatic transport气泡形成bubble formation体密度bulk density壅塞choking微滴droplet挟带entrainment流型flow pattern流[态]化fluidization界面interface跃动速度saltation velocity非牛顿流体力学non-newtonian fluid mechanics 非牛顿流体non-newtonian fluid幂律流体power law fluid拟塑性流体pseudoplastic fluid触稠流体rheopectic fluid触变流体thixotropic fluid粘弹性流体viscoelastic fluid流变测量学rheometry震凝性rheopexy体[积]粘性bulk viscosity魏森贝格效应weissenberg effect流变仪rheometer稀薄气体动力学rarefied gas dynamics物理化学流体力学physico-chemical hydrodynamics 空气热化学aerothermochemistry绝对压强absolute pressure绝对反应速率absolute reaction rate绝对温度absolute temperature吸收系数absorption coefficient活化分子activated molecule活化能activation energy绝热压缩adiabatic compression绝热膨胀adiabatic expansion绝热火焰温度adiabatic flame temperature电弧风洞arc tunnel原子热atomic heat雾化atomization自燃auto-ignition自动氧化auto-oxidation可用能量available energy缓冲作用buffer action松密度bulk density燃烧率burning rate燃烧速度burning velocity接触面contact surface烧蚀ablation流体力学英语词汇翻译(2) 相关内容:。
流体力学常用名词中英文对照..
流体力学常用名词流体动力学fluid dynamics连续介质力学mechanics of continuous介质medium流体质点fluid particle无粘性流体nonviscous fluid, inviscid连续介质假设continuous medium hypothesis流体运动学fluid kinematics水静力学hydrostatics液体静力学hydrostatics支配方程governing equation伯努利方程Bernoulli equation伯努利定理Bernonlli theorem毕奥—萨伐尔定律Biot—Savart law欧拉方程Euler equation亥姆霍兹定理Helmholtz theorem开尔文定理Kelvin theorem涡片vortex sheet库塔-茹可夫斯基条件Kutta-Zhoukowski condition 布拉休斯解Blasius solution达朗贝尔佯廖d’Alembert paradox雷诺数Reynolds number施特鲁哈尔数Strouhal number随体导数material derivative不可压缩流体incompressible fluid质量守恒conservation of mass动量守恒conservation of momentum能量守恒conservation of energy动量方程momentum equation能量方程energy equation控制体积control volume液体静压hydrostatic pressure涡量拟能enstrophy压差differential pressure流[动]flow流线stream line流面stream surface流管stream tube迹线path,path line流场flow field流态flow regime流动参量flow parameter流量flow rate,flow discharge涡旋vortex涡量vorticity涡丝vortex filament涡线vortex line涡面vortex surface涡层vortex layer涡环vortex ring涡对vortex pair涡管vortex tube涡街vortex street卡门涡街Karman vortex street马蹄涡horseshoe vortex对流涡胞convective cell卷筒涡胞roll cell涡eddy涡粘性eddy viscosity环流circulation环量circulation速度环量velocity circulation偶极子doublet, dipole驻点stagnation point总压[力] total pressure总压头total head静压头static head总焓total enthalpy能量输运energy transport速度剖面velocity profile库埃特流Couette flow单相流single phase flow单组份流single-component flow均匀流uniform flow非均匀流nonuniform flow二维流two-dimensional flow三维流three-dimensional flow准定常流quasi—steady flow非定常流unsteady flow, non—steady flow 暂态流transient flow周期流periodic flow振荡流oscillatory flow分层流stratified flow无旋流irrotational flow有旋流rotational flow轴对称流axisymmetric flow不可压缩性incompressibility不可压缩流[动] incompressible flow浮体floating body定倾中心metacenter阻力drag, resistance减阻drag reduction表面力surface force表面张力surface tension毛细[管]作用capillarity来流incoming flow自由流free stream自由流线free stream line外流external flow进口entrance, inlet出口exit,outlet扰动disturbance, perturbation分布distribution传播propagation色散dispersion弥散dispersion附加质量added mass ,associated mass收缩contraction镜象法image method无量纲参数dimensionless parameter几何相似geometric similarity运动相似kinematic similarity动力相似[性]dynamic similarity平面流plane flow势potential势流potential flow速度势velocity potential复势complex potential复速度complex velocity流函数stream function源source汇sink速度[水]头velocity head拐角流corner flow空泡流cavity flow超空泡supercavity超空泡流supercavity flow空气动力学aerodynamics低速空气动力学low—speed aerodynamics 高速空气动力学high-speed aerodynamics 气动热力学aerothermodynamics亚声速流[动] subsonic flow跨声速流[动]transonic flow超声速流[动] supersonic flow锥形流conical flow楔流wedge flow叶栅流cascade flow非平衡流[动]non—equilibrium flow 细长体slender body细长度slenderness钝头体bluff body钝体blunt body翼型airfoil翼弦chord薄翼理论thin-airfoil theory构型configuration后缘trailing edge迎角angle of attack失速stall脱体激波detached shock wave波阻wave drag诱导阻力induced drag诱导速度induced velocity临界雷诺数critical Reynolds number 前缘涡leading edge vortex附着涡bound vortex约束涡confined vortex气动中心aerodynamic center气动力aerodynamic force气动噪声aerodynamic noise气动加热aerodynamic heating离解dissociation地面效应ground effect气体动力学gas dynamics稀疏波rarefaction wave热状态方程thermal equation of state 喷管Nozzle普朗特-迈耶流Prandtl—Meyer flow 瑞利流Rayleigh flow可压缩流[动]compressible flow可压缩流体compressible fluid绝热流adiabatic flow非绝热流diabatic flow未扰动流undisturbed flow等熵流isentropic flow匀熵流homoentropic flow兰金—于戈尼奥条件Rankine-Hugoniot condition 状态方程equation of state量热状态方程caloric equation of state完全气体perfect gas拉瓦尔喷管Laval nozzle马赫角Mach angle马赫锥Mach cone马赫线Mach line马赫数Mach number马赫波Mach wave当地马赫数local Mach number冲击波shock wave激波shock wave正激波normal shock wave斜激波oblique shock wave头波bow wave附体激波attached shock wave激波阵面shock front激波层shock layer压缩波compression wave反射reflection折射refraction散射scattering衍射diffraction绕射diffraction出口压力exit pressure超压[强]over pressure反压back pressure爆炸explosion爆轰detonation缓燃deflagration水动力学hydrodynamics液体动力学hydrodynamics泰勒不稳定性Taylor instability盖斯特纳波Gerstner wave斯托克斯波Stokes wave瑞利数Rayleigh number自由面free surface波速wave speed,wave velocity波高wave height波列wave train波群wave group波能wave energy表面波surface wave表面张力波capillary wave规则波regular wave不规则波irregular wave浅水波shallow water wave深水波deep water wave重力波gravity wave椭圆余弦波cnoidal wave潮波tidal wave涌波surge wave破碎波breaking wave船波ship wave非线性波nonlinear wave孤立子soliton水动[力]噪声hydrodynamic noise水击water hammer空化cavitation空化数cavitation number空蚀cavitation damage超空化流supercavitating flow水翼hydrofoil水力学hydraulics洪水波flood wave涟漪ripple消能energy dissipation海洋水动力学marine hydrodynamics 谢齐公式Chezy formula欧拉数Euler number弗劳德数Froude number水力半径hydraulic radius水力坡度hvdraulic slope高度水头elevating head水头损失head loss水位water level水跃hydraulic jump含水层aquifer排水drainage排放量discharge壅水曲线back water curve压[强水]头pressure head过水断面flow cross-section明槽流open channel flow孔流orifice flow无压流free surface flow有压流pressure flow缓流subcritical flow急流supercritical flow渐变流gradually varied flow急变流rapidly varied flow临界流critical flow异重流density current,gravity flow堰流weir flow掺气流aerated flow含沙流sediment-laden stream降水曲线dropdown curve沉积物sediment,deposit沉[降堆]积sedimentation, deposition沉降速度settling velocity流动稳定性flow stability不稳定性instability奥尔—索末菲方程Orr—Sommerfeld equation 涡量方程vorticity equation泊肃叶流Poiseuille flow奥辛流Oseen flow剪切流shear flow粘性流[动]viscous flow层流laminar flow分离流separated flow二次流secondary flow近场流near field flow远场流far field flow滞止流stagnation flow尾流wake [flow]回流back flow反流reverse flow射流jet自由射流free jet管流pipe flow,tube flow内流internal flow拟序结构coherent structure猝发过程bursting process表观粘度apparent viscosity运动粘性kinematic viscosity动力粘性dynamic viscosity泊poise厘泊centipoise厘沱centistoke剪切层shear layer次层sublayer流动分离flow separation层流分离laminar separation湍流分离turbulent separation分离点separation point附着点attachment point再附reattachment再层流化relaminarization起动涡starting vortex驻涡standing vortex涡旋破碎vortex breakdown涡旋脱落vortex shedding压[力]降pressure drop压差阻力pressure drag压力能pressure energy型阻profile drag滑移速度slip velocity无滑移条件non—slip condition壁剪应力skin friction, frictional drag壁剪切速度friction velocity磨擦损失friction loss磨擦因子friction factor耗散dissipation滞后lag相似性解similar solution局域相似local similarity气体润滑gas lubrication液体动力润滑hydrodynamic lubrication浆体slurry泰勒数Taylor number纳维-斯托克斯方程Navier—Stokes equation 牛顿流体Newtonian fluid边界层理论boundary later theory边界层方程boundary layer equation边界层boundary layer附面层boundary layer层流边界层laminar boundary layer湍流边界层turbulent boundary layer温度边界层thermal boundary layer边界层转捩boundary layer transition边界层分离boundary layer separation边界层厚度boundary layer thickness位移厚度displacement thickness动量厚度momentum thickness能量厚度energy thickness焓厚度enthalpy thickness注入injection吸出suction泰勒涡Taylor vortex速度亏损律velocity defect law形状因子shape factor测速法anemometry粘度测定法visco[si]metry流动显示flow visualization油烟显示oil smoke visualization孔板流量计orifice meter频率响应frequency response油膜显示oil film visualization阴影法shadow method纹影法schlieren method烟丝法smoke wire method丝线法tuft method 说明氢泡法nydrogen bubble method相似理论similarity theory相似律similarity law部分相似partial similarity定理pi theorem, Buckingham theorem静[态]校准static calibration动态校准dynamic calibration风洞wind tunnel激波管shock tube激波管风洞shock tube wind tunnel水洞water tunnel拖曳水池towing tank旋臂水池rotating arm basin扩散段diffuser测压孔pressure tap皮托管pitot tube普雷斯顿管preston tube斯坦顿管Stanton tube文丘里管Venturi tubeU形管U—tube压强计manometer微压计micromanometer多管压强计multiple manometer静压管static [pressure]tube流速计anemometer风速管Pitot— static tube激光多普勒测速计laser Doppler anemometer,laser Doppler velocimeter热线流速计hot—wire anemometer热膜流速计hot— film anemometer流量计flow meter粘度计visco[si]meter涡量计vorticity meter传感器transducer,sensor压强传感器pressure transducer热敏电阻thermistor示踪物tracer时间线time line脉线streak line尺度效应scale effect壁效应wall effect堵塞blockage堵寒效应blockage effect动态响应dynamic response响应频率response frequency底压base pressure菲克定律Fick law巴塞特力Basset force埃克特数Eckert number格拉斯霍夫数Grashof number努塞特数Nusselt number普朗特数prandtl number雷诺比拟Reynolds analogy施密特数schmidt number斯坦顿数Stanton number对流convection自由对流natural convection,free convec-tion 强迫对流forced convection热对流heat convection质量传递mass transfer传质系数mass transfer coefficient热量传递heat transfer传热系数heat transfer coefficient对流传热convective heat transfer辐射传热radiative heat transfer动量交换momentum transfer能量传递energy transfer传导conduction热传导conductive heat transfer热交换heat exchange临界热通量critical heat flux浓度concentration扩散diffusion扩散性diffusivity扩散率diffusivity扩散速度diffusion velocity分子扩散molecular diffusion沸腾boiling蒸发evaporation气化gasification凝结condensation成核nucleation计算流体力学computational fluid mechanics多重尺度问题multiple scale problem伯格斯方程Burgers equation对流扩散方程convection diffusion equationKDU方程KDV equation修正微分方程modified differential equation拉克斯等价定理Lax equivalence theorem数值模拟numerical simulation大涡模拟large eddy simulation数值粘性numerical viscosity非线性不稳定性nonlinear instability希尔特稳定性分析Hirt stability analysis相容条件consistency conditionCFL条件Courant- Friedrichs- Lewy condition ,CFL condition 狄里克雷边界条件Dirichlet boundary condition熵条件entropy condition远场边界条件far field boundary condition流入边界条件inflow boundary condition无反射边界条件nonreflecting boundary condition数值边界条件numerical boundary condition流出边界条件outflow boundary condition冯。
Hydraulic Fracturing Theory
3
– closure in-situ stress
Hydraulic Fracturing Theory
Governing equations: • linear elasticity describes how the rock (soil) responds to a force or pressure (p) so that we can compute crack aperture (w) between crack faces (edges in 2D slice)
fracture radius (m)
0.07
0.05
0.03 0.01 0
HYFRANC3D Loramec pumping time (sec)
100 200 8 e-5
Loramec is a fully-coupled 2D and axisymmetric FE code from Schlumberger
COD (m)
4 2 0
HYFRANC3D * Loramec
t – pumping time is known Q – fluid injection rate is known in-situ stresses – known/estimated ? - stochastic rock mass elastic properties – known ? - stochastic
0
v
= gh (density x gravity x depth)
=
Additional tectonic component will produce a maximum (and minimum) horizontal stress:
水力压裂弱化顶板护孔技术
水力压裂弱化顶板护孔技术薛江达, 孙永康, 王军, 张庚(太原理工大学 安全与应急管理工程学院,山西 晋中 030600)摘要:煤矿工作面单翼布置顺序开采的情况下,工作面顺层钻孔容易受到邻近工作面采动支承应力影响导致钻孔失效。
现阶段的护孔研究集中在增强钻孔本身强度,未针对影响钻孔稳定性的根本性因素提出解决措施。
针对上述问题,提出了一种水力压裂弱化顶板护孔技术。
通过水力压裂弱化顶板,减小作用在邻近工作面煤体上的采动支承应力峰值,阻断高支承应力向顺层钻孔周围煤体的传递,并在顺层钻孔内全程下筛管,保证煤体逸散出的瓦斯可以进入顺层钻孔。
采用数值模拟分析了水力压裂弱化顶板前后顺层钻孔周围煤体垂直应力和塑性区变化规律,结果表明:通过水力压裂弱化顶板,顺层钻孔周围煤体的垂直应力峰值由21.2 MPa 降低为9.1 MPa ,煤体塑性区范围由19 m 减小为11 m 。
根据数值模拟结果确定的水力压裂参数进行了现场测试,结果表明:采用水力压裂弱化顶板护孔技术后,钻孔瓦斯抽采体积分数平均值由3.6%提高到14.1%,瓦斯抽采混合流量平均值由1.28 m³/min 降低为0.464 m³/min ,未出现大范围顺层钻孔内发生煤体氧化而产生CO 的情况。
因此,水力压裂弱化顶板护孔技术可有效避免钻孔失效漏气,提高钻孔抽采效果,保证钻孔抽采安全。
关键词:水力压裂;弱化顶板;采动支承应力;顺层钻孔;塑性区中图分类号:TD712.6 文献标志码:AHydraulic fracturing weakening roof borehole protection technologyXUE Jiangda, SUN Yongkang, WANG Jun, ZHANG Geng(School of Safety and Emergency Management Engineering, Taiyuan University of Technology,Jinzhong 030600, China)Abstract : In the case of sequential mining with single wing arrangement in coal mine working face, the drilling along the working face is easily affected by the support stress of adjacent working faces, leading to drilling failure. At present, research on borehole protection focuses on enhancing the strength of the borehole itself, without proposing solutions to the fundamental factors that affect borehole stability. In order to solve the above problems, a hydraulic fracturing weakening roof borehole protection technology has been proposed. By using hydraulic fracturing to weaken the roof, the peak mining support stress acting on adjacent coal working faces is reduced, and the transmission of high support stress to the surrounding coal bodies in the bedding boreholes is blocked. The entire process of screening is carried out in the bedding boreholes to ensure that the gas escaping from the coal body can enter the bedding boreholes. Numerical simulation is used to analyze the changes in vertical stress and plastic zone of the coal body around the borehole before and after hydraulic fracturing weakening the roof. The results show that by weakening the roof through hydraulic fracturing, the peak vertical stress of the coal body around the borehole decreases from 21.2 MPa to 9.1 MPa, and the plastic zone range of the coal body decreases from 19 m to 11 m. According to the numerical simulation results, hydraulic fracturing收稿日期:2023-08-29;修回日期:2024-03-26;责任编辑:盛男。
HYDRAULIC FRACTURING水力压裂解读
How Fracturing WorksEngineers design a fracturing operation based on the unique characteristics of the formation and reservoir.Basic components of the fracturing design include the injection pressure, and the types and volumes of materials (e.g., chemicals, fluids, gases, proppants) needed to achieve the desired stimulation of the formation. T he fracturing operation is intended to create fractures that extend from the wellbore into the target oil or gas for-mations. Injected fluids have been known to travel as far as 3,000 feet from the well.1Although attempts are made to design fracturing jobs to create an optimum network of fractures in an oil or gas formation, fracture growth is often extremely complex, unpredictable and uncontrol-lable.2Computer models are used to simulate fracture pathways, but the few experiments in which fractures have been exposed through coring or mining have shown that hydraulic fractures can behave much differently than pre-dicted by models.3Diagnostic techniques are available to assess individual ele-ments of the fracture geometry, but most have limitationsH Y D R AU L I C F RA C T U RI N G A TW E L L SI TEHYDRAULICFRACTURINGOIL & GASACCOUNTABILITY PROJECTA program of EARTHWORKSon their usefulness 4One of the better methods, microseis-mic imaging, provides a way to image the entire hydraulic fracture and its growth history. But it is expensive and is only used on a small percentage of wells. According to the Department of Energy, in coalbed methane wells “where costs must be minimized to maintain profitability, fracture diagnostic techniques are rarely used.”5And up until 2006approximately 7,500 in the Barnett shale wells had been drilled, but only 200 had been mapped using microseismic imaging.6What’s in fracturing fluids?A single fracturing operation in a shallow gas well (such as a coalbed methane well) may use several hundreds of thou-sands of gallons of water. Slickwater fracs, which are com-monly used in shale gas formations, have been known to use up to five million gallons of water to fracture on one horizon-tal well.7Many wells have to be fractured several times over the course of their lives, further increasing water use.A small proportion of wells are fractured using gases, such as nitrogen or compressed air, instead of water-based fluids. In all fracturing jobs, thousands or hundreds of thousands of pounds of proppants (such as sand or ceramic beads) are injected to hold open the fractures.In most cases, fresh water is used to fracture wells because it is more effective than using wastewater from other wells. If wastewater is used, the water must be heavily treated with chemicals to kill bacteria that cause corrosion, scaling and other problems.8Even freshwater fracturing operations, how-ever, contain numerous chemicals such as biocides, acids, scale inhibitors, friction reducers, surfactants and others, but the names and volumes of the chemicals used on a specific fracturing job are almost never fully disclosed. In general, it is known that many fracturing fluid chemicals are toxic to human and wildlife, and some are known to cause cancer or are endocrine disruptors.9It has been roughly estimated that chemicals used to fracture some gas shale wells can make up 0.44% (by weight) of the amount of fracturing fluids.10In an operation that uses 2 million gallons of water, that means roughly 80,000 pounds of chemicals would be used.11These chemicals flow back out of the well along with much of the injected water, and together, these wastes are usually disposed of by injection into underground formations rather than being treated so that the water can be re-used.Our Drinking Water at RiskThere are a number of ways in which hydraulic fracturing threatens our drinking water. Where drilling companies are developing fairly shallow oil or gas resources, such as some coalbed methane formations, drilling may take place direct-ly in the aquifers from which we draw our drinking water. In this case, contamination may result from the fracturing flu-ids that are stranded underground. The few available stud-ies have shown that 20-30% of fracturing fluids may remain trapped underground, but this number can be much higher for some chemicals, which are preferentially left behind (i.e., do not return to the surface with the bulk of the fracturing fluids).12Where drilling companies are developing deeper oil or gas resources there a number of issues and concerns:•Underground Contamination.Hydraulic fracturing can open up pathways for fluids or gases from other geo-logic layers to flow where they are not intended. This may impact deeper ground water resources that may be con-sidered for drinking water supplies in the future. If frac-turing wastewater disposal is conducted through under-ground injection wells, there is additional opportunity for groundwater contamination.•Surface Contamination.Fracturing fluid chemicals and wastewater can leak or spill from injection wells, flowlines, trucks, tanks, or pits. And leaks and spills can contaminate soil, air and water resources.•Depletion and degradation of shallow drinking water aquifers.Often companies will use massive quantities of drinking water resources from shallower aquifers in the area to conduct fracturing operations. This industrial draw down can lead to changes in traditional water quality or quantity. If wastewater disposal occurs in streams, the chemical make-up or temperature of the wastewater may affect aquatic organisms, and the sheer volume of water being disposed may damage sensitive aquatic ecosystems.Protect Our Drinking Water: Close the Halliburton Loophole in the Safe Drinking Water Act•Repeal the Safe Drinking Water Act exemption for hydraulic fracturing.•Require full chemical disclosure and monitoring of hydraulic fracturing products.•Require non-toxic hydraulic fracturing and drilling products.Visit for more information.HYDRAULIC FRACTURING– HOW IT WORKSDeveloped by OGAP/EARTHWORKSCITATIONS1IN THE SUPREME COURT OF TEXAS, No. 05-0466, Coastal Oil & Gas Corp. and Coastal Oil & Gas USA, L.P., Petitioners, v. Garza Energy Trust et al., Respondents, On Petition for Review from the Court of Appeals for the Thirteenth District of Texas, Argued September 28, 2006.2 Mayerhofer, M.J. and Lolon, E.P., Youngblood, J.E. and Heinze, J.R. 2006. “Integration of Microseismic Fracture Mapping Results with Numerical Fracture Network Production Modeling in the Barnett Shale.” Paper prepared for the 2006 SPE Technical Conference and Exhibition, San Antonio, TX. Sept. 24-27, 2006.). SPE 102103. /wattenbarger/public_html/Selected_papers/--Shale%20Gas/SPE102103%20Mayerhofer.pdf3 Warpinski, N., Uhl, J. and Engler, B. (Sandia National Laboratories). 1997.Review of Hydraulic Fracture Mapping Using Advanced Accelerometer-Based Receiver Systems./publications/proceedings/97/97ng/ng97_pdf/NG10-6.PDF4 Warpinski, N., Uhl, J. and Engler, B. (Sandia National Laboratories). 1997.Review of Hydraulic Fracture Mapping Using Advanced Accelerometer-Based Receiver Systems./publications/proceedings/97/97ng/ng97_pdf/NG10-6.PDF5U.S. Department of Energy. “Appendix A Hydraulic Fracturing White Paper.” p. A-20. In: Environmental Protection Agency. June 2004. Evaluation of Impacts to Underground Sources of Drinking Water by Hydraulic Fracturing of Coalbed Methane Reservoirs. EPA816-R-04-003./ogwdw000/uic/pdfs/cbmstudy_attach_uic_append_a_doe_whitepaper.pdf6 Mayerhofer, M.J. and Lolon, E.P., Youngblood, J.E. and Heinze, J.R. 20206. “Integration of Microseismic Fracture Mapping Results with Numerical Fracture Network Production Modeling in the Barnett Shale.” Paper prepared for the 2006 SPE Technical Conference and Exhibition, San Antonio, TX. Sept. 24-27, 2006.). SPE 102103. /wattenbarger/public_html/Selected_papers/--Shale%20Gas/SPE102103%20Mayerhofer.pdf7 Information for Barnett wells: Burnett, D.B. and Vavra, C.J. August, 2006. Desalination of Oil Field Brine - Texas A&M Produced Water Treatment. p. 25. /gpri-new/home/BrineDesal/MembraneWkshpAug06/Burnett8-06.pdf and Global Petroleum Research Institute (Texas A&M University) web site: “Conversion of Oil Field Produced Brine to Fresh Water.”/gpri-new/home/BrineDesal/BasicProdWaterMgmnt.htm; Information for Marcellus wells: Arthur, D. et al. September 23, 2008. “Hydraulic Fracturing Considerations for Natural Gas Wells of the Marcellus Shale.” Presented at Ground Water Protection Council 2008 Annual Forum./meetings/forum/2008/proceedings/Ground%20Water%20&%20Energy/ArthurWater Energy.pdf8 Fichter, J.K., Johnson, K., French, K. an Oden, R. 2008. “Use of Microbiocides in Barnett Shale Gas Well Fracturing Fluids to Control Bacterially-Related Problems.” NACE International Corrosion 2008 Conference and Expo. Paper 08658. I pp. 2, 3. /Store/Downloads/7B772A1BA1-6E44-DD11-889D-0017A446694E.pdf9The Endocrine Disruption Exchange web site: /10According to Arthur, D. et al. (2008) analysis of a fracturing fluid used at a Fayetteville shale well found that it was composed of 90.6% water (by weight); sand comprised 8.95%; and chemicals comprised0.44%. Arthur et al. assumed this same make-up for Marcellus shale wells. (Sources: Fayetteville infor-mation: Arthur, D., Bohm, B., Coughlin, B.J., and Layne, M. 2008. Evaluating The Environmental Implications Of Hydraulic Fracturing In Shale Gas Reservoirs. p. 16. http://www.all-/shale/ArthurHydrFracPaperFINAL.pdf; Marcellus shale information: Arthur, D., Bohm, B., Coughlin, B.J., and Layne, M. November, 2008. “Evaluating The Environmental Implications Of Hydraulic Fracturing In Shale Gas Reservoirs.” Presentation at the International Petroleum & Biofuels Environmental Conference (Albuquerque, NM,November 11?13, 2008). p. 22.htpp:///Conf2008/Manuscripts%20&%20presentations%20received/Arthur_73_presenta-tion.pdf11At 80°F, water weighs 8.3176 pounds per gallon (/water-density-spe-cific-weight-d_595.html). If 2 million gallons of water are used to fracture a Marcellus well when it's 80°F outside, the water weighs 16,690,808 lbs, i.e., 16.7 million pounds. If this water is 90.6% of the total weight of the fracturing fluid (as estimated by Arthur et al.), then the total fracturing fluid weighs18,361,148 lbs (18.4 million lbls). If chemicals make up 0.44% of the fluids by weight, then the chemicals weigh 0.44% of 18.4 million lbs, which is 80,789 lbs. If sand makes up 8.95% of the fluids by weight, then 1,648,816 or 1.6 million pounds of sand are used.12See discussion in Sumi, L. (Oil and Gas Accountability Project). 2005. Our Drinking Water At Risk. pp.12 and 13, and footnote 91. /pubs/DrinkingWaterAtRisk.pdfOffices:Bozeman:P.O. Box 7193Bozeman, MT 59771406-587-4473 (p)406-587-3385 (f)Durango:P.O. Box 1102Durango, CO 81302970-259-3353 (p)970-259-7514 (f)Washington, D.C.:1612 K St., NWSuite 808Washington, D.C. 20006202-887-1872 (p)202-887-1875 (f)Website:Developed by OGAP/EARTHWORKSHYDRAULIC FRACTURING– HOW IT WORKS。
水力学(hydraulics)
水力学(hydraulics)1. conditions for producing uniform flow:Answer: 1. water should be constant flow; flow should change along the way, no branch; 2. channels must be prismatic long straight slope channel; 3. roughness coefficient change along the way; local interference channels also anhydrous structures.2. if Q, I must be, n value is smaller, channel water cross section area A?Answer: A will be too small, can not pass the design flow, water flow overtopping, sediment deposition.3. if Q, I must be, n value is too big, channel water cross section area A?Answer: A will be too large, the maximum flow capacity exceeds the design flow, high cost, cross section is too large, waste, channel flushing.4. the selected cross-sectional shape has the largest flow through the known design flow when the area is minimum or the area of excess water is constant. The section with this condition has the smallest amount of work, which is called the best section of hydraulic power.5. practical economic section should meet the requirements:1) within a certain range, a larger ratio of depth to depth isobtained;2) according to the selected beta value, the designed cross section area is very close to the hydraulic optimum section area.6., if the results of channel hydraulic calculation, found that V allows >v not flush, or V allow < V not silt, how should adjust?Answer 1. According to Xie formula, V is related to I, R and n. The terrain conditions may, can also change the canal line, to extend or shorten or drop to change the concentration of the ground elevation, the requirements of I.Method two. Change V without flushing or V without deposition. For example in the canal desilting basin, canal built has this effect.7., the jet flow characteristics!Answer: slow flow, flow velocity is small, smooth water potential, meet interference, interference effects not only to propagate downstream and upstream propagation.The rapids and currents are large and the water potential is swift. The interference can only propagate downstream, but not upstream.What is the difference and connection between 8.Es and E?A: the definition is different the base level selection isdifferent, E and Es are different from one channel bottom elevation, and the Es is not related to the elevation at the bottom of the channelEs - Taking the horizontal plane at the intersection of the cross section and the bottom of the canal as the datum planeE - taking any horizontal surface as the base planeThe E must be gradually decreasing, while Es does not necessarily. When the Q, A, and the course remain unchanged, the Es is a function of water depth h, so it may increase, decrease, or possibly change.9. from the definition and calculation formula of the critical bottom slope, the following conclusions can be drawn:Answer: the critical bottom slope corresponds to a flow in the channel. When the flow rate changes, the magnitude of the critical bottom slope also varies. The critical bottom slope has nothing to do with the actual bottom slope of the channel. It is merely an imaginary value introduced for the convenience of computation and analysis. The critical bottom slope only exists on the Yu Zheng slope channel. According to the definition, the critical bottom slope is the bottom slope when the uniform flow is the critical flow, and the uniform flow can only produce the Yu Zheng bottom slope. The channel can not form uniform flow on the flat slope and the reverse slope channel.7.5 trial analysis:(1) what is the difference between the energy per unit section ES and the total energy E of a unit weight liquid? Why should we introduce this concept?(2) how does the uniform flow of open channels change with the course of ES and E?(3) how does the nonuniform flow of open channels change with the course of ES and E?Thinking question(1) the selection of base level (definition) is different, and the variation law is different,The specific energy of the inlet section is used to analyze the flow regime from the energy angle. (2) the uniform flow of open channel ES is unchanged along the course, while the E decreases along the path. (3) the inhomogeneous flow of open channel ES may increase or decrease, and the E decreases along the channel.7.7 test analysis: (1) in the wide rectangular section of prism with unchanged roughness n along the course, when the bottom slope I is certain, how does the critical bottom slope IK vary with the flow rate? (2) if the original uniform flow, when the flow increases or decreases, can become a uniform jet? (3) if the original uniform jet, when the flow increases or decreases, can become uniform flow?Answer: (2) if the original uniform flow, the slope is less than IK, when the flow rate increases, IK decreases, it is possiblefor uniform flow jet. When the flow rate decreases, the IK increases, so it is impossible to become a jet stream.(3) if the original uniform jet, namely the bottom slope is greater than IK, when the flow rate increases, the decrease of IK, so it is not possible to slow uniform flow. On the contrary, when the flow is reduced, the increase of IK, could become a uniform flow is slow.Whether the 7.9 jet, subcritical, critical flow can only occur in a gentle slope, steep slope, and critical slope? Why?Answer: wrong. The criterion must be established in the case of uniform flow. The change of the flow rate will change the critical bottom slope, and then the slope will not always be gentle slope, and the steep slope may not always be steep slope.Thinking questionUniform flow 7.12 prism channel when occurred only in the i<ik flow channels, occurs only in i>ik channels. Is this statement true? Why?Answer: rightWhat is the difference between the concept and the gradient 7.10 slow and jet flow, blast flow? Whether there is a gradient subcritical, gradient jet, jet flow, the blast blast flow?Answer: the former is the open channel flow pattern, the latter is the division of water flow according to the magnitude of thechange of the streamline. There is no necessary connection. There can be these flows.Flow characteristics of hydraulic jump:Answer: the upper water jump: surface rolling area water violent maneuver. The lower part of the hydraulic jump: the main flow velocity slows down and spreads rapidly.The water depth corresponding to J (H) min is critical water depth HKWhen h>hk, J (H) increases with the increase of H; when h<hk, J (H) decreases with the increase of h;When the flow Q and channel section shape and size are fixed, the smaller the water depth before jump and the greater the water depth after jump.Position and form of hydraulic jump?Answer: when HC ">ht", the jump cross section in the downstream of the C-C section is called "far away water jump";When HC "<ht", the jump cross section in the upper reaches of the C-C section is called submerged water jump;When HC "=ht", the water jump occurs just from the C-C section, which is called critical waterA C area for backwater curve;B area precipitation curve as H- H0, N-N line, HK curve; when h, K- and K line perpendicular to the trend; when h approaches infinity, with a horizontal asymptote for forward at that time, and have the trend of vertical line;Points of attention for analyzing water surface curves (1):Answer: the analysis of the principle of above water line only applies to the prism of non-uniform flow channels, while in non prismatic or non uniform flow channels for blast.No matter what the bottom slope is, each flow zone has only one definite water surface curve type,That is, there is no possibility of two water surface curves in the same class area. For example, the a zone on the gentle slope can only be a backwater curve, and there can be no other type of water surface.The analysis and calculation of the water surface must begin with the control section (i.e., the known depth of water and the corresponding depth of water known as the depth of water control). Because of the disturbance in the rapids upstream waves do not spread, so the jet control section in the upstream; interference wave energy flow in the upstream spread, so the flow control section in the downstream.Hydraulic characteristics of weir flow and gate flowAnswer: from the bottom or on both sides of the open channel flow to the contraction of the water flow deformation of thebuilding, known as the weir.A building at which the water is contracted at the top and deformed by the flow of water is called a gate.The same point: energy conversion; head lossDifference: surface line; over current capacityDiscrimination of weir flow and gate outflowWhen the sill is a flat topped weir or flat bottomFlow out e/H<=0.65 for the gate holeFor weir flow e/H>0.65When the sill is a curve weirFlow out e/H<=0.75 for the gate holeFor weir flow e/H>0.75Hd selection:A: if the maximum weir head is selected as the design head, the overflow weir will often work under the condition of low water head. At this time, although the weir surface does not appear negative pressure, it is safer, but the discharge capacity is small. At the same time, the designed section is too fat and uneconomical.If the minimum weir head as the design head, although the economic profile, and discharge, but weir is often under high water head condition, the weir surface prone to large negative pressure and endanger the safety of the weir.The design head used in general engineering design is:The conditions for submerged outflow are: first, hs>0 and hs>hc; this is the first condition for the formation of submerged outflow; secondly, hc>hk is a necessary condition for formation of submerged outflow.The characteristics of the discharge structure: high flow speed, large kinetic energy, large flow of single width.The two task discharge structures: one is how to connect two different downstream fluid flow problems; two is a big problem of how to eliminate or reduce the kinetic energy of discharged flow.Pool length design flow selection: pool length design flow refers to the maximum flow required when the pool size corresponds to the flow. The formula of stilling pool shows that the length of pool is proportional to the length of full hydraulic jump, and the jump length increases with the increase of flow rate in general. Therefore, the design flow of the pool length should select the maximum flow through the building.The flow field theory treats the moving fluid as a field (the so-called field, i.e., the space at which each pointcorresponds to the definite value of a physical quantity). In different time, there are different movement elements in different spatial positions in the field. These elements change in the three coordinate directions of X, y and Z, which is the most common form of liquid motion.。
HydraulicFractur...
Hydraulic Fracturing as a Global Cascade in Networked Systems David Cho*, University of Calgary and Sensor Geophysical, Calgary, AB, Canada******************andGary F. Margrave, University of Calgary, Calgary, AB, CanadaSummaryNetworked systems require the consideration of the interactions between component parts as well as the parts themselves in understanding the properties of the system. In the case of hydraulic fracturing, the process can be regarded as the spread of a fractured state through an initially unfractured network of rock elements. In this study, we implement a spreading model in networks to evaluate the dynamics of the hydraulic fracturing process in various rock types. The corresponding results regarding the stresses that must be overcome, the areal extent and energy release in hydraulic fracturing were in qualitative agreement with empirical observations.IntroductionMany macroscopic phenomena manifest as the result of a network of interacting agents and often exhibit dynamics that are reciprocal to its network structure, resulting in behavior that can exhibit nonlinearities. These network interactions govern phenomena ranging from collective behavior in schooling fish to the spreading of viruses in human networks. In these networked systems, the interactions between component parts are just as important as the parts themselves in defining the properties of the system (Motter and Albert, 2012). In addition, it is widely accepted that macroscopic phenomena do not depend on the microscopic details of the process, as in effective field theories that are applicable at some chosen length scale and ignores the substructure and degrees of freedom at shorter distances. Therefore, the description of seemingly complex phenomena can be greatly reduced in complexity by application of the above paradigms. In this study, we apply these concepts to hydraulic fracturing to investigate the dynamical process under which hydraulically induced fractures propagate in various rock types. These simplifications allow us to discard the complex fluid flow and fracture mechanics in modeling the dynamic response of hydraulic fracturing (i.e. Lutz, 1991). It should be noted that the simplified approach only provides qualitative descriptions and lacks the rigor in understanding the phenomenon at a fundamental level. It does however provide an alternative conceptual view of the problem.Many observations concerning fracture propagation in so called brittle or ductile rocks have been well established with the aid of empirical data, where brittleness is often associated with higher quartz content and a relative low for the Poisson’s ratio. For example, engineering data such as the instantaneous shut in pressure (ISIP), which provides an indication for the stress that must be overcome for fracture propagation, is found to correlate with Poisson’s ratio (i.e. Maxwell et al., 2011). It is also generally observed that fractures propagate further in brittle rocks while propagation is more localized in ductile rocks, as suggested by microseismic event locations. In addition, microseismic moment densities are observed to decrease with increasing brittleness.In the following, we implement a simple network spreading model in an attempt to model the dynamics of the hydraulic fracturing process and evaluate the corresponding fracture propagation response for various rock types.Fracture Spreading ModelHere, we adopt the abstraction of a network to represent a rock mass with interacting elements, where the network consists of a set of nodes connected by lines or edges. The network is a purely theoretical object but provides an extremely useful representation of complex systems with interactingcomponents. To investigate the dynamics of fracture propagation through a network of rock elements, we implement a spreading model proposed by Watts (2002) for the description of global cascades on random networks. In the model, a binary decision process with externalities is considered. For a given network, each individual in the population, represented by a node, must decide between two alternative actions, where their decisions are based solely on the actions of other members in the population. In the case of hydraulic fracturing, the process can be regarded as the spread of the fractured state in a network of initially unfractured rock elements. For the model specification, we consider a population where an individual agent observes the states (0 for unfractured or 1 for fractured) of its connected neighbors, where the range of connections is known as the degree, and if a certain threshold fraction, defined on the unit interval, is achieved, it adopts state 1, else it remains in state 0. To initiate thesystem, a set of seed nodes are placed in the network and the process is subsequently iterated through a series of time steps. A successful hydraulic fracture treatment is then defined by a cascade event, where if a cascade is triggered, state 1 spreads throughout the network and if a cascade is not triggered, the network remains in its initial state.To calculate the threshold, we implement the uniaxial strain condition for loading of an elastic solid given by 131σννσ-=, (1)where ν is the Poisson’s ratio and σ1 and σ3 are the maximum and minimum principle stress magnitudes respectively. For a given value of σ1, a lower value of σ3 can be achieved through lowering the value of ν, and according to the Mohr-Coulombe failure criterion (Coulomb, 1773), results in a larger Mohr circle and hence is more easily fractured. Since the quantity ν/(1-ν) is defined on the unit interval for all possible values of ν between 0 and 0.5, it can readily be used for the threshold condition. Therefore, a material with a lower Poisson’s ratio is more easily fractur ed and thus requires less influence to achieve failure.To calculate the degree, we consider how information is transferred in an elastic solid. Upon theapplication of a stress, particle motion is excited through strain waves and propagates throughout the medium. Therefore, we associate the transfer of information regarding the state of stress through the mechanics of wave propagation. The wave equation can then be used to evaluate how energypropagates through an elastic solid and provide an indication for the network of connected nodes. In a 3D homogeneous medium, the Green’s function for the scalar wave equation is given by cr r ct G πδ4)(-=, (2) where c is the P-wave velocity, t is time, r is the radial distance from the source location and δ represents an impulse function. According to equation 2, the rate at which the amplitude decays isinversely proportional to r and is scaled by the inverse of the P-wave velocity. Therefore, a material with a higher value of c corresponding to the effective medium, experiences more amplitude decay at a given radial distance r from the source point and results in a more localized connectivity.Rock ModelFor the evaluation of the fracture propagation response in different rock types, we take the mean of the Hashin-Shtrikman bounds (1963) for a two-phase material consisting of quartz and clay with varying mineral fractions. With this approach, we avoid the ill-defined concept of brittleness which is not afundamental property of an elastic solid. Figure 1 shows the upper and lower bounds and mean for the P- and S-wave velocities of the two phase material calculated using the values in Table 1.Figure 1: Hashin-Shtrikman upper and lower bounds and mean for the a) P- and b) S-wave velocities for a two-phase material consisting of quartz and clay.Table 1: Density (ρ) and P- (α) and S-wave (β) velocities used for mineral end members (From Greenberg andCastagna, 1992).Mineral ρ (g/cc) α (km/s) β (km/s)Quartz 2.65 6.05 4.09Clay 2.66 4.32 2.54Dynamical ModelingAs the dynamics of the hydraulic fracturing problem are not easily amendable to analytical treatment, we solve the system numerically and analysis the corresponding results. The simulations were performed in 2D for each set of mineral fractions ranging from pure clay to pure quartz. As mentioned above, we attribute a successful hydraulic fracture treatment with a cascade event triggered by a certain number of initially active nodes. The properties of interest are then the number of seed nodes required to trigger a cascade, the areal extent of the cascade and the energy output for each set of mineral fractions.Figure 2: a) Cascade boundary and b) simulated area as a function of the volume of quartz.Figure 2 shows the phase diagram illustrating the cascade boundary (a) and the stimulated area (b) as a function of the volume of quartz. The simulations demonstrate that less effort is required to achieve a cascade and a larger area is stimulated for a more brittle rock, which is consistent with empirical observations.Figure 3: a) Stimulated area and b) change in stimulated area as a function of time.Figure 3 shows the stimulated area (a) and the change in stimulated area (b) as a function of time. In Figure 3b, note the nonlinear behavior at small time steps for low values of the volume of quartz. This is attributed to the interactions between component parts that result in nonlinearities in defining theproperties of the system as a whole.Figure 4: Spatial distribution of total energy output for a) 70%, b) 40% and c) 10% quartz.Figure 4 shows the normalized spatial distribution of activated nodes for various sets of mineralfractions that provide an indication for the spatial distribution of total energy output. Since we associatethe activation of a node as a fracture creation event, the energy output corresponds to the generation of a microseism. Therefore, the distributions can be related to the microseismic moment density in different rock types. As the volume of quartz decreases, the energy becomes more localized, which is consistent with the observation that microseismic moment densities increase in more ductile rock. ConclusionsThe dynamics of the hydraulic fracturing process were evaluated through a spreading model in networked systems for rock types consisting of varying mineral fractions of quartz and clay. This was performed to provide an alternative view of the mechanisms that underlie the empirical observations documented by various authors concerning the fracture propagation response in brittle and ductile rock. The results of the numerical simulations were in qualitative agreement with the observations regarding the relationship between ISIP and Poisson’s ratio and the microseismic response in various rock types. As the hydraulic fracturing process is a dynamical system consisting of numerous interacting rock elements, the interactions between component parts as well as the parts themselves must be considered in understanding the properties of the system. For this reason, nonlinearities are anticipatedand are observed in the numerical modeling.AcknowledgementsThe authors thank Jeff Grossman for his insights and Bill Goodway and Marco Perez for discussions. The support provided by the sponsors of the CREWES project is also acknowledged.ReferencesGreenberg, M. L., and Castagna, J. P., 1992, Shear-wave velocity estimation in porous rocks: Theoretical formulation, preliminary verification and applications: Geophysical Prospecting, 40, 195-209.Hashin, Z., and Shtrikman, S., 1963, A variational approach to the elastic behavior of multiphase minerals: J. Mech. Phys. Solids, 11, 127-140.Lutz, E. E., 1991, Numerical methods for hypersingular and near-singular boundary integrals in fracture mechanics, Ph.D. Thesis, Cornell University.Maxwell, S. C., Cho, D., Pope, T., Jones, M., Cipolla, C., Mack, M., Henery, F., Norton, M., and Leonard, J., 2011, Enhanced reservoir characterization using hydraulic fracture microseismicity: SPE Hydraulic Fracturing Technology Conference, SPE 140449.Motter, A. E., and Albert, R., 2012, Networks in motion: Physics Today, vol. 65, no. 4, page 43.Watts, D. J., 2002, A simple model of global cascades on random networks: Proc Natl Acad Sci USA, Applied Mathematics,99(9), 5766-5771.。
酸化压裂基础知识
水力压裂概念
水力压裂就是利用地面压裂车组将一定粘度的液体以 足够高的压力和足够大的排量沿井筒注入井中。由于注入速 度远远大于油气层的吸收速度,所以多余的液体在井底憋起 高压,当压力超过岩石抗张强度后,油气层就会开始破裂形 成裂缝。当裂缝延伸一段时间后,继续注入携带有支撑剂的 混砂液扩展延伸裂缝,并使之充填支撑剂。施工完成后,由于 支撑剂的支撑作用,裂缝不致闭合或至少不完全闭合,因此 即可在油气层中形成一条具有足够长度、宽度和高度的填砂 裂缝。此裂缝具有很高的渗滤能力,并且扩大了油气水的渗 滤面积,故油气可畅流入井,注入水可沿裂缝顺利进入地层 ,从而达到增产增注的目的。
50
压裂液在地层中滞留产生液堵
• 在压裂施工中,压裂液沿缝壁渗滤入地 层,改变了地层中原始含油饱和度,使 水的饱度度增加,并产生两相流动,流 动阻力加大。毛管力的作用致使压裂后 返排困难和流体流动阻力增加。如果地 层压力不能克服升高的毛细管力,水被 束缚在地层中,则出现严重和持久的水 锁。
51
压裂液滞留的地层保护
7
(一 )压裂液组成
前置液 携砂液 顶替液
8
前置液
作用
造缝 降温 减少 携砂液滤失 防砂卡
要求
一定粘度 足够用量
9
携砂液
作用 将支撑剂代入裂缝 继续扩张裂缝 冷却地层
要求 粘度高 携砂能力强
10
顶替液
作用 中间顶替液 尾注顶替液
要求 用量适当,避免过量顶替
11
(二) 压裂液性能要求
滤失低 携砂能力强 摩阻低、比重大 稳定性好 配伍性好 残渣少 易于返排 货源广、价格便宜、便于配制
v
K f Pv
e L
实际滤失速度:
va
ppt 6 Hydraulic fracturing
w w max
Fractured well performance for unconventional tight sand or shale reservoirs
1. 2. 3. 4.
Analytical model of the production from each fracture Multiple sink solutions Decline curve analysis Reservoir simulators including fracture networks
Economidies & Valko
N p I x C fD
2
4x f k f w
kx e
2
2k fV f
kV r
J D _ Max
1 if N p 0.1 0.99 0.5 lnN p 0.423 0.311N p 0.089(N p )2 6 exp if N p 0.1 2 (N p ) 1 0.667N p 0.015 6 if N p ~ 100
Role of hydraulic fracturing
Low k reservoir
Fracture geometry
Fracture geometry
Fracture geometry
Tight sand or shale formations, stimulated reservoir volume
1 ln(0.472re ) ln(x f ) f (C fD ) 1 Vf kf xf C hk fD
1 2
1 Vf kf 2 ln(0.472re ) ln C hk f (C fD ) fD 1 1 Vf kf ln(0.472re ) ln f (C fD ) 2 C fD hk
SPEARS 中国版《塑料管手册》说明书
Table of Contents
General Information .........................................................................................................1 Purpose of this Manual..................................................................................................1 Spears® PVC & CPVC Materials ..................................................................................1
Physical Properties of PVC & CPVC Pipe......................................................................2 Dimensions & Pressure Ratings.....................................................................................3
SPEARS® PLASTIC PIPE HANDBOOK
Plastic Pipe
Hydraulic_Fracturing_Simulation
Development and Validation of Fully-CoupledHydraulic Fracturing Simulation CapabilitiesMatias G. Zielonka, Kevin H. Searles, Jing Ning and Scott R. BuechlerExxonMobil Upstream Research Company3120 Buffalo Speedway, Houston, TX 77098Abstract: The problem of the propagation of a hydraulically driven fracture in a fully saturated, permeable, and porous medium is investigated. Fluid driven fracture propagation in porous media is a coupled problem with four unknown fields: the flow of the fracturing fluid within the fracture, the flow of the pore fluid within the pores, the porous medium deformation, and the fracture configuration. The corresponding governing equations are the mass balance of the fracturing fluid, mass balance of the pore fluid, equilibrium of the porous medium, and fracture initiation and propagation criteria. In this work, the recently co-developed Abaqus fully-coupled hydraulic fracturing modeling capabilities are evaluated by assessing their consistency, convergence, and accuracy qualities. The Abaqus “coupled pressure/deformation cohesive elements” and “coupled pressure/deformation extended finite elements (XFEM)” are used to model the propagation of the fracture and the flow of the fracturing fluid, while the porous medium deformation and pore-fluid flow are modeled with coupled “pore-pressure/deformation” continuum finite elements. The propagation of a vertical planar fluid-driven fracture with constant height and vertically uniform width within a prismatic-shaped reservoir (KGD model), and the propagation of a horizontal, circle-shaped, planar, fluid-driven fracture within a cylindrical reservoir (“Penny-Shaped” model) are simulated in both two and three dimensions. The Abaqus numerical solution obtained with each modeling technique (cohesive and XFEM) is compared with asymptotic analytical solutions for both the KGD and Penny-shaped models in the toughness/storage dominated and viscosity/storage dominated propagation regimes. Both methods are found to accurately reproduce the analytical solutions, and converge monotonically as the mesh is refined. This validation of the newly developed hydraulic fracturing capabilities within Abaqus provides confidence in its ability and readiness to simulate fluid driven fracturing applications for the oil and gas industry including injection, stimulation, and drilling operations.Keywords: geomechanics, soil mechanics, fracture mechanics, hydraulic fracturing, fluid-driven fracturing, geostatic, soils, pore pressure, cohesive elements, extended finite elements, XFEM, reservoir, drilling, injection.1. IntroductionHydraulic fracturing is a fundamental problem in Petroleum Engineering and plays a critical role in many applications within the oil and natural gas industry. The process can be generally defined as the intentional (or unintentional) initiation and propagation of a fracture due to the2014 SIMULIA Community Conference 1 /simuliapressurization of fluid that flows within the fracture. Examples of applications include (a) the stimulation of rock formations with poor or damaged permeability to increase conductivity between the reservoir and the producing wells, (b) improvement of produced water re-injection (PWRI) where water is injected to replace produced fluids and maintain reservoir pressure or provide enhanced oil recovery, (c) cuttings reinjection (CRI) where a slurry of drill cuttings is injected into a formation to mitigate the cost and risk of surface disposal, (d) in-situ stress measurement by balancing the fracturing fluid pressure in a hydraulically opened fracture with the geostatic stresses, and (e) wellbore integrity analysis of drilling operations to avoid propagating near-wellbore fractures that could result in drilling fluid losses to the formation and an inability to effectively clean the wellbore.Knowledge of the fracture dimensions (length/width/height), fracture geometry, and wellbore pressure is crucial for both the design and integrity of hydraulic fracturing field operations. For stimulation, PWRI and CRI, one of the fundamental questions is whether or not fracture containment is achieved. This means that the injection fluid and fracture are confined to a target interval or “pay” zone for PWRI and stimulation, or a dedicated disposal domain for CRI. Other important considerations include predictions of the injection rate, pressure, or injected volume required to initiate fractures, inject under matrix conditions, or minimize the potential for inducing fractures while drilling.Currently, there are no reliable techniques to measure fracture geometries during or after the hydraulic fracturing process. Furthermore, direct solutions of the underlying differential equations representing the different physical processes occurring during fracturing are difficult to construct, even in their most simplified forms. Therefore, the development of a numerical simulator with accurate predictive capability is of paramount importance.The computational modelling of hydraulic fracturing of porous media is a challenging endeavor. The difficulty originates primarily from the strong non-linear coupling between the governing equations, as the process involves at least the interaction between four different phenomena: (i) the flow of the fracturing fluid within the fracture, (ii) the flow of the pore fluid and seepage of fracturing fluid within the pores, (iii) the deformation of a porous medium induced by both the hydraulic pressurization of the fracture and the compression/expansion and transport of pore fluid within the pores, and (iv) the fracture propagation which is an inherently an irreversible and singular process. Additionally, fracture propagation typically occurs in heterogeneous formations consisting of multiple layers of different rock types, subjected to in-situ confining stresses with non-uniform magnitudes and orientations. Furthermore, fracturing fluids typically exhibit nonlinear rheologies and the leakoff of these fluids from the fracture into the surrounding rock is often history dependent.There are a number of commercial hydraulic fracture simulators used in the oil and natural gas industry for rapid design, analysis and prediction of fracture size, treating pressures, and flows (Clearly 1980, Meyer 1989, Warpinski 1994). These simulators rely in strong simplifying assumptions to render the problem solvable in realistic times:∙Fractures are assumed to be planar and symmetric with respect to the wellbore∙Fracture geometries are represented with few geometric parameters2 2014 SIMULIA Community Conference/simulia∙The formation is assumed to be unbounded and modeled using linear elasticity theory resulting in an integral equation relating fracture opening and fluid pressure ∙The fracture propagation is modeled within the framework of linear elastic fracture mechanics without any consideration of pore fluid pressure effects∙Leakage of fracturing fluid from the fracture into the rock is modeled as one dimensional and decoupled from the porous medium deformation.Although these simulators are useful in predicting broad trends and upper/lower bounds in operational parameters, their reliability and accuracy are restricted to unrealistic scenarios intrinsic simplistic assumptions apply, i.e., situations where some of the coupling between the many different processes involved can be neglected, and with strong symmetry in confinement stresses and geology.The accurate modelling of the hydraulic fracturing process under realistic geologies, wellbore configurations, confining stress states, and operational conditions calls for a more advanced, multi-physics numerical simulator that incorporates the complex coupling between the injected fluid, the pore fluid, the rock deformation, and the fracture configuration, thus overcoming the limitations of currently available commercial simulation tools.To this end, fully-coupled hydraulic fracturing simulation capabilities that leverage (i) the existing Abaqus non-linear soil consolidation analysis solver, (ii) Abaqus cohesive elements for modelling interface decohesion, and (iii) Abaqus extended finite element method (XFEM) for modelling propagating discontinuities, are being co-developed between ExxonMobil Upstream Research Company and Dassault Systemes Simulia Corporation.Specifically, two new element classes have been integrated into the existing Abaqus/Standard coupled pore fluid diffusion and solid stress porous media analysis solver:i. A coupled pressure/deformation cohesive element that models the progressive damage ofnormal mechanical strength and normal hydraulic conductivity as well as the flow offracturing fluid within the opening fracture.ii.An enriched version of the continuum coupled pore fluid diffusion/stress elements capable of activating arbitrarily oriented discontinuities in both displacements and porepressures while simultaneously modelling the fracturing fluid flow along the fracture. This work describes and validates these two new formulations for hydraulic fracturing modeling by assessing consistency, accuracy and convergence qualities. The propagation of a fluid-driven vertical planar fracture of uniform width and constant height within a prismatic-shaped rock formation (Khristianovich-Geertsma-de Klerk, or KGD model) and the propagation of a horizontal, circle-shaped, planar, fluid-driven fracture within a cylindrical reservoir (radial or “Penny-Shaped” model) are simulated for both two and three dimensions (Clearly 1980, Geertsma 1969, Yew 1997). The numerical solution obtained with each new modeling technique (cohesive and XFEM) are then compared with available asymptotic analytical solutions for both the KGD and Penny-shaped models in the toughness/storage dominated and viscosity/storage dominated propagation regimes. Finally, the consistency, accuracy and convergence attributes are assessed for both methods.2014 SIMULIA Community Conference 3 /simulia42014 SIMULIA Community Conference /simuliaSection 2 describes the governing equations for each of the coupled processes as well as theconstitutive and kinetic relations assumed for the porous medium, pore fluid and fracturing fluid, including:i.Equilibrium equation for the porous medium ii.Constitutive equation for the porous medium (Biot’s theory of poroelasticity) iii.Continuity equation for the pore fluid iv.Continuity equation for the fracturing fluid v.Momentum equation for the pore fluid (Darcy’s Law) vi. Momentum equation for the fracturing (Lubrication Equation)Section 3 details the procedures employed by both formulations (cohesive and extended finite element methods) and the fracture initiation and propagation criteria. Section 4 defines the test models (KGD plane-strain and the Penny-Shaped models) and the model set-up and assumptions used within Abaqus, while Section 5 presents numerical results and assesses accuracy and convergence by comparing the main solution variables obtained with meshes of differentresolutions with available asymptotic analytical solutions. Finally, some concluding remarks are summarized in Section 6.2. Governing EquationsAs stated in the introduction, hydraulic fracturing involves the interaction between four different phenomena:i.Porous medium deformation ii.Pore fluid flow iii.Fracturing fluid flow iv. Fracture propagationThe equations and constitutive relation governing these coupled processes, i.e., Biot’s theory of poroelasticity for porous media, Darcy’s Law for pore fluid flow, Reynold’s lubrication theory for fracturing fluid flow and the cohesive zone model to characterize fracturing (Abaqus 2013, Charlez 1997)) are summarized in what follows.2.1 Porous Media DeformationPorous media can be modelled as an isotropic, poroelastic material undergoing quasistaticdeformation. The equilibrium equation enforced by Abaqus, when body forces are neglected is,, 0(1) while the poroelastic constitutive relation, assuming small strains, is given by, 2 (2) 2 13in which is Biot’s coefficient, and are the dry elastic shear and bulk moduli, is the dry Young’s modulus, and is the dry Poisson’s ratio. Abaqus is formulated in terms of Terzaghi effective stresses ′, defined for fully saturated media as (Abaqus 2013, Charlez 1997)In terms of the latter, the constitutive relation takes the form2 1Defining effective strains as1the constitutive relation simplifies to2This identity is identical to the constitutive relation for linear elastic materials, but expressed in terms of Terzaghi effective stresses ′ and effective strains ′. Abaqus internally translates total stresses and strains into Terzaghi effective stresses and strains to leverage this equivalence (Abaqus 2013).2.2 Pore Fluid FlowThe continuity equation for the pore fluid is, assuming small volumetric strains, given by1, 0where is the pore fluid seepage velocity, and and are Biot’s modulus and Biot’s coefficient, respectively. These two poroelastic constants are defined by the identities111where is the pore fluid bulk modulus, is the porous medium solid grain bulk modulus, and is the initial porosity. In Abaqus, the two compressibilities and are specified using the *POROUS BULK MODULI keyword. Pore fluid is assumed to flow through an interconnected pore network according to Darcy’s law,,in which is the permeability, is the pore fluid viscosity, is the hydraulic conductivity and is the pore fluid specific weight. Combining with the continuity equation, the pore fluid diffusion equation is obtained2014 SIMULIA Community Conference 5 /simulia62014 SIMULIA Community Conference /simulia1 , (3) Within Abaqus, the hydraulic conductivity and specific weight are specified through the *PERMEABILITY keyword.2.3 Fracturing Fluid FlowLongitudinal fluid flow within the fracture is governed by Reynold’s lubrication theory defined by the continuity equation0 and the momentum equation for incompressible flow and Newtonian fluids through narrow parallel plates (i.e., Poiseuille flow)where is the fracture gap (Figure 1), ∙ is the fracturing fluid flow (per unit width) across the fracture, and are the normal flow velocities of fracturing fluid leaking through the top and bottom faces of the fracture into the porous medium, is the fracturing fluid viscosity, and is the fracturing fluid pressure along the fracture surface parameterized with the curvilinear coordinate, .Figure 1: Fracture aperture, width and fracturing fluid flowAbaqus computes the normal fracturing fluid velocities as(4where and are the pore fluid pressures on the top and bottom surface of the fracture and and are the so-called “leakoff coefficients”. This simple leakoff model simulates a layer of filtrate that might accumulate and reduce the effective normal permeability of the fracture surfaces.Inserting the Poiseuille flow equation and the simplified leakoff model into the continuity equation for the fracturing fluid yields the final form: ∙2014 SIMULIA Community Conference 7 /simulia(5) Abaqus specifies the fracturing flow viscosity and leakoff coefficients with the *GAPFLOW and the *LEAKOFF keywords, respectively.2.4 Fracture Initiation and PropagationFracturing can be conceptualized as the transition between two limiting states: the undamaged state with continuous displacements and non-zero tractions in all directions and the fully damaged state characterized by the presence of a displacement discontinuity along a material interface with zero tractions in the direction normal to the interface. In Abaqus, this transition process is modeled as a progressive degradation of cohesive strength along a zero-thickness interface whoseorientation and extent is either predefined (cohesive element method) or calculated during the simulation (extended finite element method). The gradual loss of strength in the interface with increasing separation is defined with an interface traction/interface separation relation or cohesive law (Abaqus 2013, Ortiz 1999).For the purpose of this study, a traction-separation cohesive law with linear softening (Figure 2) is assumed, defined by the cohesive energy (area under the softening part of the traction separation curve) and the cohesive strength . For the cohesive element procedure, it is also required to define the traction-separation behavior prior to damage initiation, which is assumed to be linear with initial stiffness . The cohesive traction of the interface thus evolves from a maximum tensile strength at damage initiation, down to zero when the interface is fully damaged and free to open beyond the total separation . If the interface is unloaded prior to complete damage, the traction is assumed to ramp down linearly with a damaged stiffness . The interface effective tractions are therefore given byFigure 2: Cohesive law for Cohesive and XFEM proceduresUpon damage initiation, the fracture is pressurized by instantaneously applying the fracturing fluid pressure, , calculated from the fracturing fluid equations in Equation 5. The total tractions resisted by (and acting on) the interface elements are therefore given by T r a c t i o nSeparationCOHESIVEXFEM82014 SIMULIA Community Conference /simuliaAs stated in Section 2.1, the Abaqus porous media analysis solver is formulated in terms of Terzaghi effective stresses. Therefore, the cohesive strength defining the onset of interface decohesion must be understood in terms of an effective strength (and not total strength).3. Cohesive Element and Extended Finite Element MethodsThe evolution of a fracture is modelled in Abaqus through zero-thickness interface elements with separation resisted by gradually decreasing tensile tractions. For the cohesive element procedure, these interface elements are defined a priori and placed between continuum element faces, whereas in the extended finite element method (XFEM), they are inserted and oriented automatically during the course of the simulation within existing continuum elements.3.1 Cohesive Element MethodThe coupled pressure/deformation cohesive elements implemented in Abaqus (COHPE4P , COHAX4P , COH3D8P ) are standard linear isoparametric elements with displacement and pore pressure degrees of freedom associated with their corner nodes, as depicted in Figure 3 (nodes 1,2,3,4). Theseelements must be inserted a priori between the faces of adjacent pressure diffusion/stress elements (CPE4P , CAX4P , C3D8P ) in order to model the yet to open fracture. To accommodate the coupling of the fracturing fluid flow equations, the elements are equipped with additional pressure degrees of freedom (attached to the center of the element edges perpendicular to the fracture) to interpolate the fracturing fluid pressure after damage initiation (nodes 5 and 6, Figure 3).Figure 3: Coupled pressure/deformation cohesive elements for hydraulic fracturing The cohesive elements can have arbitrary undeformed geometric thickness as the instantaneous gap coupled in the fracturing fluid flow equation (Equation 5) is defined in Abaqus as thedifference between the deformed and underfed thickness, i.e., . Prior to damage, the top and bottom faces of the unopened fracture are subjected to the pore fluid pressure acting towards increasing separation and the cohesive effective tractions resisting separation,where is the stiffness of the cohesive element prior to failure (Figure 2). After damageinitiation, the pore fluid is displaced by the fracturing fluid pressurizing the interface. The total tractions acting on the top and bottom faces of the opening fracture are then substituted by5 64UndeformedConfiguration Deformed Configuration 243 12 56312014 SIMULIA Community Conference 9 /simuliawhere is the damaging stiffness (Figure 2). A coupled cohesive element method for hydraulic fracturing similar to the formulation just outlined is described by Boone, 1990 and Carrier, 2012.3.2 Extended Finite element method (XFEM)The Extended Finite Element Method (XFEM) is implemented within Abaqus using the so called “phantom node” approach (Abaqus 2013, Remmers 2008, Song 2006, Sukumar 2003). In this implementation, each enriched pressure diffusion/stress element (CPE4P , CAX4P , C3D8P ) isinternally duplicated with the addition of corner phantom nodes, as depicted in Figure 4, in which original nodes are represented with full circles and corner phantom nodes with hollow circles. Prior to damage initiation only one copy of the element is active. Upon damage initiation the displacement and pore pressure degrees of freedom associated with the corner phantom nodes are activated and both copies of the element are allowed to deform independently, pore pressures are allowed to diffuse independently, and the created interface behavior is enforced with a traction-separation cohesive law.Figure 4: Implementation of the XFEM with “corner” and “edge” phantom nodes In order to enable the solution of the fracturing fluid flow equations, the enriched elements also incorporate new “edge-phantom nodes” (depicted as red triangles in Figure 4) that interpolate the fracturing fluid pressure within the fracture. The pore fluid pressure and at the top and bottom faces of the fracture are interpolated from the pore pressure degrees of freedom at the corner real nodes and phantom nodes. The difference with the fracturing fluid pressure(interpolated at the edge-phantom node) is the driving force that controls the leakage of fracturing fluid into the porous medium (Equation 4).The fracture is extended to a new element ahead of the fracture tip when the maximum effective principal stress at this element (interpolated to the tip) in a given iteration is equal to the cohesive strength . The orientation of the fracture segment to be extended into the tip element is set to the Undeformedconfigurationafter damage Deformed configuration after damage 2,2 4,4 3,3 1,1342 13 4 1 22 43 1 Undeformed configuration before damagedirection perpendicular to the minimum principal stress of the current iteration. This fracture initiation/orientation criterion is defined in Abaqus through the keyword*DAGAMAGE INITATION, CRITERION=MAXPS, POSITION=CRACKTIPAs in the cohesive element formulation, the fracturing fluid pressure is applied to the top and bottom faces of the fracture and superposed to the cohesive tractions.4. Benchmark ModelsIn this section, the two formulations previously outlined (coupled pressure/displacement cohesive and extended finite elements) are applied to model the propagation of a hydraulically driven fracture in two different configurations:i.Horizontal, circle-shaped, planar, fracture within a cylindrical domain, (radial or “Penny-Shaped” model (Clearly 1980, Charlez 1997, Yew 1997))ii.Vertical, rectangle-shaped, planar fracture within a prismatic-shaped domain (Khristianovich-Geertsma-de Klerk, or KGD model (Charlez 1997, Geertsma 1969, Yew 1997)).These models serve as benchmark examples to assess the consistency, convergence and accuracy of the numerical solution obtained with Abaqus.4.1 Fracture Propagation RegimesDespite the simplicity of the fracture geometry and strong symmetry in the chosen benchmark problems, there are no available closed-form analytical solutions for these problems when all coupled processes are considered in the analysis, i.e., when the formation is assumed to be porous and permeable with pore fluid flow and fracturing fluid is leaking into the pore space displacing the pore fluid. However, using the more restrictive theoretical framework resulting from assuming (i) an infinite domain, (ii) material fully impermeable, (iii), material linear elastic, (iv) linear-elastic fracture mechanics, and (v) Carter’s leakoff model (Howard 1957, Charlez 1997), approximate analytical solutions exist in the form of regular asymptotic expansions (Bunger 2005, Detournay 2006, Garagash 2006, Hu 2010, Garagash 2011, Peirce 2008, Savitski 2002). The governing equations then simplify to (i) the equilibrium equation for the linear elastic material, that for an infinite domain can be represented as an singular integral equation relating fracture opening and fluid pressure, (ii) the local and global mass balance equations for the fracturing fluid, and (iii) the fracture propagation criterion, also expressible as a singular integral equation relating fracturing pressure and fracture toughness. A non-dimensional analysis of this reduced system of equations uncovers the presence of two pairs of competing physical processes. The first pair consists of competing dissipative mechanisms: (a) energy dissipated due to fluid viscosity and (b) energy dissipated due to fracture propagation; the second pair consists of competing components of fluid balance: (a) fluid storage within the fracture and (b) fluid leakage from the fracture into the surrounding material. Depending on which of the two dissipative mechanisms and which of the two storage mechanisms dominate, four primary limiting regimes of propagation emerge: ∙Viscosity dominated and storage dominated propagation regime ( ).∙Toughness dominated and storage dominated propagation regime ( ).10 2014 SIMULIA Community Conference/simulia2014 SIMULIA Community Conference 11 /simulia∙Viscosity dominated and leak-off dominated ( ). ∙ Toughness dominated and leak-off dominated regime (). These four fracture propagation regimes can be conceptualized in a rectangular parametric space where each limiting regime corresponds to each of the vertices of the rectangle with one dissipation mechanism dominating and the other being neglected, and one component of fluid global balance dominating with the other also neglected (Figure 5).Figure 5: Parametric diagram representing the four limiting propagation regimes ofhydraulically driven fracturesThis work analyzes each benchmark problem in both the toughness/storage-dominated (near- ) and the viscosity/storage-dominated (near- ) propagation regimes. The near- and the near- asymptotic solutions (small time solutions in the toughness and viscosity regimes) are used to compare to Abaqus numerical solutions for each formulation (cohesive element method and XFEM) with material parameters, loads, and boundary conditions that reproduce each of these propagation regimes.In order to render the Abaqus solution comparable with the asymptotic solutions, the modeldimensions and material properties are selected such that the more restrictive conditions for which these solutions apply are adequately recreated. Specifically, the dimensions of the domain of analysis are much bigger than the fracture aperture and length, the permeability is defined tominimize the influence of poroelastic effects ahead of the fracture tip, and cohesive properties are selected to ensure a small cohesive zone relative to the size of the fracture.4.2 Radial (Penny-Shaped) ModelThe first benchmark problem consists of an axisymmetric, penny-shaped, hydraulically-driven fracture propagating in a cylindrically shaped poroelastic formation as illustrated in Figure 6.∞∞0 ∞∞12 2014 SIMULIA Community Conference/simuliaFigure 6: Cylindrical domain with a horizontal, circular-shaped, hydraulically drivenfractureThe domain of analysis is characterized by the inner radius , outer radius , and height . The porous medium is characterized by Young’s modulus , Poisson ratio , fracture toughness , porosity , Biot’s coefficient , Biot’s modulus , and hydraulic conductivity. An incompressible Newtonian fluid with viscosity is injected at a constant rate at the center of the fracture from a vertical wellbore. The fracture aperture , , the net pressure , (defined as the difference between the fracturing fluid pressure , and the confining stress ), and the fracture radius are the sought quantities.4.3 Plane Strain (KGD) ModelThe second benchmark problem considers a hydraulically-driven vertical fracture propagating in a poroelastic prismatic-shaped formation of length L, depth R and height H as illustrated in Figure 7. 01,,。
Hydraulic fracturing
专利名称:Hydraulic fracturing发明人:Jeffrey, Robert Graham,Coleman, Anthony Charles申请号:AU2011257894申请日:20110526公开号:AU2011257894A1公开日:20121206专利内容由知识产权出版社提供摘要:A tool for use in initiating a hydraulic fracture in a bore hole comprises an elongate cylindrical bore hole packer structure (11) having an inner longitudinal passage 5 (12), a mid-portion (13) provided with ports (14) extending outwardly from passage (12) to the exterior periphery of the packer structure (11) and expandable circumferential wall portions (15A) surrounding the inner longitudinal passage (12) to each side of the mid-portion 10 (13). In use of the tool the circumferential wall portions (15A) can be expanded by injection of hydraulic fracturing fluid into passage 12) and exit of the injected fluid through the ports (14) to produce a pressure difference between the inside of the packer structure and 15 the outside of the packer structure as the fluid passes through the ports (14) such that the hydraulic fluid exiting the packer structure can initiate a fracture. The packer structure (11) is disposed between a pair of tool end pieces (16) one of which provides a fluid inlet for 20 injection of hydraulic fluid into one end of passage (12) and the other of which closes the other end of passage (12) against outflow of hydraulic fluid therefrom.申请人:COMMONWEALTH SCIENTIFIC AND INDUSTRIAL RESEARCH ORGANISATION 代理人:Griffith Hack更多信息请下载全文后查看。
水力压裂第一部分
Fundamentals of Hydraulic Fracturing水力压裂基础知识
Fracturing fluids 压裂液– Section 5 Fracturing Fluid additives压裂液添加剂 –
Section 6 Propping agents 支撑剂– Section 7 On-Site Data gathering 现场数据采集– Section 8 Basic treatment sizing 基础压裂设计– Section 9 Equipment & operations overview 设备和操作 概述– Sectio Effects地 层伤害的影响
Additional pressure loss reduces
maximum possible production rate In the absence of an active drive it may also reduce ultimate recovery Costly!
Formation Damage Effects储 层伤害的影响
An induced reduction in permeability
near the wellbore 近井眼渗透率下降 In the pores or in natural fractures 发生 在孔隙或天然裂缝中 Results in an area of high pressure drop 产生高压降区域
Hydraulic Fracturing and other Stimulation 2014水力压裂和其他增 产措施
For Sage Energy Development by Denis R. Gaudet, P.Eng. DRG Resources Ltd. Beijing, China
reservoir stimulation英文书籍
reservoir stimulation英文书籍Reservoir Stimulation: Enhancing Productivity of Oil and Gas WellsIntroduction:Reservoir stimulation plays a crucial role in enhancing the productivity of oil and gas wells. It involves a set of techniques aimed at increasing the flow of hydrocarbons from the reservoir to the wellbore. This article explores the various methods utilized in reservoir stimulation and their significance in improving well productivity.1. Hydraulic Fracturing:Hydraulic fracturing, also known as fracking, is one of the most widely used reservoir stimulation techniques. It involves injecting fluid at high pressure into the reservoir, creating fractures in the rock formations. These fractures serve as pathways for the hydrocarbons to flow more easily into the wellbore. The success of hydraulic fracturing lies in optimizing fluid composition, injection rate, and proppant selection, leading to increased reservoir contact and enhanced productivity.2. Acid Stimulation:Acid stimulation involves injecting acids, such as hydrochloric acid, into the reservoir to dissolve or etch the rock formations. This technique is particularly beneficial for carbonate reservoirs, where acid reacts with the rock mineralogy, enlarging existing pores and fractures. Acid stimulation helps to increase permeability and porosity, enabling better fluid flow and consequently enhancing the productivity of the well.3. Matrix Acidizing:Matrix acidizing is a form of acid stimulation that targets the well matrix rather than creating fractures. It aims at dissolving or removing damaging materials, such as scale and formation damage, from the reservoir rock. Matrix acidizing improves the reservoir's permeability by removing the obstructing substances, thus allowing efficient flow of hydrocarbons to the wellbore.4. Proppant Placement:Proppant placement is a technique associated with hydraulic fracturing. It involves choosing and positioning proppants, such as sand or ceramic particles, within the created fractures. Proppants keep the fractures open, preventing them from closing under pressure, and ensuring the flow of hydrocarbons. Optimizing proppant size and concentration is crucial for achieving efficient proppant placement and maximizing the effectiveness of hydraulic fracturing.5. Chemical EOR (Enhanced Oil Recovery):Chemical enhanced oil recovery (EOR) techniques represent an important aspect of reservoir stimulation. These techniques include polymer flooding, surfactant flooding, and alkaline flooding. Polymer flooding involves injecting polymers into the reservoir to increase the viscosity of injected water, enabling better sweep efficiency. Surfactant flooding focuses on reducing interfacial tension between oil and water, enhancing oil recovery. Alkaline flooding adjusts the pH of injected water, altering the wettability of the reservoir rock and improving oil displacement. Thesechemical EOR methods significantly contribute to reservoir stimulation and maximize oil recovery.6. Thermal Stimulation:Thermal stimulation methods, such as steam injection and in-situ combustion, are widely employed in reservoir stimulation, particularly for heavy oil reservoirs. Steam injection heats the reservoir, reducing the oil's viscosity and improving its mobility. In-situ combustion involves burning a portion of the reservoir's oil, which generates heat, expands gas, and creates pressure, enhancing oil displacement and flow. Thermal stimulation techniques enable the extraction of heavy oil resources, thereby enhancing reservoir productivity.Conclusion:Reservoir stimulation is an essential aspect of the oil and gas industry. Techniques such as hydraulic fracturing, acid stimulation, proppant placement, chemical EOR, and thermal stimulation significantly contribute to increasing well productivity. Understanding and optimizing these methods play a crucial role in maximizing hydrocarbon recovery and ensuring the efficient utilization of reservoir resources. Continual advancements in reservoir stimulation techniques continue to shape the industry, enabling the extraction of valuable oil and gas resources.。
水力压裂专业英语
水力压裂专业英语Hydraulic fracturing, commonly known as "fracking," is a technique used to extract natural gas and oil from deep underground rock formations. It involves injecting a high-pressure fluid into the rock, which creates fractures that allow the trapped hydrocarbons to flow more freely to the surface.This process has been a subject of debate due to its environmental impact. Critics argue that fracking can contaminate groundwater, while proponents highlight its potential to boost domestic energy production and reduce reliance on foreign oil.The fluid used in hydraulic fracturing is a mixture of water, sand, and chemicals. The sand acts as a proppant, keeping the fractures open after the pressure is released, facilitating the flow of oil and gas.Advancements in fracking technology have made it possible to access previously untapped reserves, leading to a surge in domestic energy production. However, the industry must also address concerns about the potential environmental consequences.Regulations and best practices are crucial to ensure that hydraulic fracturing is conducted safely and sustainably. This includes proper well construction, waste management, andmonitoring of air and water quality.As the demand for energy continues to grow, the role of hydraulic fracturing in meeting this demand is significant. Balancing the benefits with the environmental considerations is a key challenge for the industry moving forward.Education and public awareness are essential components in the ongoing conversation about fracking. Understanding the science and technology behind the process can help inform discussions and decisions regarding its use and regulation.。
美国水力压裂基础培训-支撑剂与压裂液 Fracture Fluids and Materials
8
The Proppant Breakthrough
• One of the big lessons learned during the scramble for proppant was that marginal wells did amazingly better when better proppants were used.
• Supply for the traditional markets began to dry up and even resin coated manufacturers could not get proppant substrate.
• Companies such as Santrol had already established a plant in China and imported proppants revealed the emergence of a worldwide market.
• The demand from the unconventional sector during that year led to an acute shortage of sand and unparalleled competition for the proppants consumed in the conventional market such that service companies had to cancel treatments and turn down jobs at the peak of the activity.
hydraulic_fracturing_101
SPE 152596Hydraulic Fracturing 101: What Every Representative, Environmentalist, Regulator, Reporter, Investor, University Researcher, Neighbor and Engineer Should Know About Estimating Frac Risk and Improving Frac Performance in Unconventional Gas and Oil Wells.George E. King, Apache CorporationCopyright 2012, Society of Petroleum EngineersThis paper was prepared for presentation at the SPE Hydraulic Fracturing Technology Conference held in The Woodlands, Texas, USA, 6–8 February 2012.This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright. AbstractIdentification of risk, the potential for occurrence of an event and impact of that event, is the first step in improving a process by ranking risk elements and controlling potential harm from occurrence of a detrimental event. Hydraulic Fracturing has become a hot environmental discussion topic and a target of media articles and University studies during development of gas shales near populated areas. The furor over fracturing and frac waste disposal was largely driven by lack of chemical disclosure and the pre-2008 laws of some states.The spectacular increase in North American natural gas reserves created by shale gas development makes shale gas a disruptive technology, threatening profitability and continued development of other energy sources. Introduction of such a disruptive force as shale gas will invariably draw resistance, both monetary and political, to attack the disruptive source, or its enabler; hydraulic fracturing.Some “anti-frack” charges in media articles and university studies are based in fact and require a state-by-state focused improvement of well design specific for geology of the area and oversight of overall well development. Other articles have demonstrated either a severe misunderstanding or an intentional misstatement of well development processes, apparently to attack the disruptive source.Transparency requires cooperation from all sides in the debate. To enable more transparency on the oil and gas side, both to assist in the understanding of oil and gas activities and to set a foundation for rational discussion of fracturing risks, a detailed explanation of well development activities is offered in this paper, from well construction to production, written at a level of general public understanding, along with an initial estimation of frac risk and alternatives to reduce the risk, documented by literature and case histories. This discussion is a starting point for the well development descriptions and risk evaluation discussions, not an ending point.Introduction to RiskThere are no human endeavors without risk. “Risk management is the identification, assessment and prioritization of risks followed by coordinated and economical application of resources to minimize, monitor and control probability and/or impact of unfortunate effects” (Wikipedia). At a minimum, basic risk concerns are: People, Economic Loss (to all concerned), Environmental Damage and Reputation Loss. Figure 1, a standard loss matrix used by Apache Canada in the Horn River development (DeMong, 2010), is a good starting place for the discussion. Consequences run from slight and practically unavoidable to severe and avoidable at all costs. This paper, for purposes of brevity, will focus solely on risk to the environment from hydraulic fracturing operations,152596 2 SPEstarting with transport of materials and ending when the well is routed to the production facilities and gas salesbegin. The form of Figure 1 will be expanded and comments and descriptions of problems that begin with drilling,well construction and production will be discussed, but their risk assessment is in a separate category.Many well development problems are blamed on fracturing, but have nothing to do with the fracturing process.Some of these excluded problems are real and are definitely worthy of inclusion in the discussion, to help definethe boundaries of the fracturing risk and as a starting point for further understanding and work.The initial assumption for the risk matrix is that the well is new and was constructed correctly (to designrequirements) so that all producible formations are securely isolated behind the barriers of casing (pipe) andcompetent cement. No assessment of fracturing risk is made here for wells outside of the design requirements.The justification for this assumption is that the vast majority of fracturing is the first major stimulation in a well andoccurs immediately after completing a new well. If an older well is re-fractured, then an assessment of wellintegrity and a separate risk analysis would be required.Introduction to FracturingHydraulic fracturing and horizontal wells are not new tools for the oil and gas industry. The first fracturingexperiment was in 1947 and the process was accepted as commercial by 1950. The first horizontal well was inthe 1930’s and horizontal wells were common by the late 1970’s. Millions of fracs have been pumped (Society ofPetroleum Engineers estimate 2.5 million fracs world-wide and over 1 million in the US) and tens of thousands ofhorizontal wells have been drilled over the past 60 years. Even shale gas, especially from the Devonian shales(including Marcellus), are not new producing intervals. Devonian shales are the source rocks for the shallow oilwells of eastern Pennsylvania, where Mr. Drake drilled the first US oil well after noticing a number of naturalseeps of oil and gas in the area. Concentrated shale fracturing research was kicked off by a Department ofEnergy (DOE) grant in the 1970’s. Earlier forays include the first shale gas well in 1821 in Fredonia, New York,and archeological data on gathering of oil and tar from natural seeps by North American native inhabitants goingback over 1500 years.SPE 152596 3 The technical literature around the “adaptation” of horizontal wells and hydraulic fracturing to shale developments is extensive, addressing nearly every aspect of shale gas and oil development with over 550 papers in shale fracturing and 3,000 on all aspects of horizontal wells. These publically presented and peer reviewed technical papers are from contributors covering 30+ years of shale technology development. The shale papers in the past three years alone are from over 70 universities, 4 US national labs, over a dozen state, federal and international agencies and more than a hundred energy and service companies. The references presented here are a very small part of the 60,000 industry and academia papers and studies available on oil and gas operations. A historical review of shale gas fracturing “Thirty Years of Gas Shale Fracturing: What Have We Learned” was presented in 2010, that reviewed 270 literature sources, focusing on the critical papers of shale development (King, 2010). Many other technical resources are available from universities, government, industry and study groups (Arthur, 2009; Engelder, 2008; Cramer, 2008; Lash; Modern, 2009; Zammerilli, 1989; Yost, 1989; Sumi, 2008; Soeder, 2008; Suarez-Riveria, 2009; Milici, 2005; Perkins, 2008).For purposes of this paper, the components of well development, i.e., from seismic evaluation to production, are explained with intent to educate using basic descriptions and information on each step. Problem areas are purposely identified, not to vilify or glorify, but to help the public understand the risks and the steps that can be taken to reduce those risks.In any risk matrix, local conditions will influence the conclusions. For regional or area studies, the impact and the occurrence information, from traffic accidents to well incidents should be from the area, but wider studies of other factors may be necessary for purposes of well population and incident review. There are over 840,000 oil and gas wells in the US (EIA, 2009) and a world-wide well count of approaching 1.2 million, but in a given field or even a small basin, the well population may not be sufficient for reasonably accuracy in risk estimates. Estimating risk at both regional and area levels allows identification of risk areas and refinement of that risk through knowledge of local conditions. Different companies operating in different areas of the country may use the same risk estimation approach but reach different values due to differences in roads, well construction requirements, infrastructure, engineering experience, local geology, regulations and other factors.The gas and oil containing “shales” featured in this paper are classified as shales on the basis of the size of the very fine particles or grains that make up the rock. They are actually very fine grained sandstones, often with similar mechanical properties to the sandstones that comprise conventional gas and oil producing reservoirs. The difference is that conventional sandstones may have permeabilities in the range of 0.5 to 20 millidarcies (abbreviated as “md”), while these gas shales may have permeabilities of 0.000001 to over 0.0001 md (or 1 to over 100 nanodarcies). Permeability is a measurement of the ease of flow of fluids through the rock and a typical shale gas reservoir with a permeability of 100 nanodarcies has a permeability of 1/1000 of 1% of the permeability of a conventional reservoir with 10 millidarcy permeability. Fluid flow is much easier in materials with higher permeability. For reference, beach sand is roughly 2000 md, construction-grade cement averages about 0.005 md and shales vary from about 0.000001 to 0.0001 (Table 1). Not every shale has sufficient permeability to produce gas, even with the assistance of hydraulic fracturing.Permeabilities are measured in the matrix or porous part of the rock. Gas and oil productive shales have natural fractures and micro-fissures, a characteristic missing from high-clay content shales that serve as natural seals4 SPE152596and barriers (with permeabilities so low they approach the permeability of steel pipe). Natural barriers are therock seals that have held the gas, oil, and salt water in the reservoir for millions of years.Bridging the Language BarrierEnvironmentalist critics insist that some “fracks” have contaminated ground and surface waters while engineersinsist that not one frac has ever contaminated ground waters; thus, there seems to be a wide disparity in accuracyof the statements. Surprisingly, both sides have valid arguments – just a mismatch of definitions. Much of theturmoil concerns how each group defines fracturing. In engineering terms, fracturing concerns a precisestimulation activity, limited to the fluid action in initiating and extending cracks in the rock; while, for manyconcerned citizens, bloggers and environmentalists, fracturing has come to represent nearly every phase of thewell development cycle from drilling to production.Accuracy in any argument rests on defining the subject; in this case it is activities in gas or oil resourcedevelopment. The science behind well development activities, including fracturing, resides in about sixtythousand presented papers and peer-reviewed papers in the literature from a dozen or more engineering andgeoscience societies, representing a hundred thousand engineers and scientists in the oil and gas industry,world-wide. The following are general descriptions of the steps in the well development process. More detail onspecific areas related to improving regulations, pollution control and general understanding of disputed processeswill be developed later.First, scale drawings of the distance from the surface and near-surface fresh water supplies (nearly all fresh waterformations are within the first 1000 feet or 305 meters from the surface) are needed to show the physical distancebetween the surface and the completion interval of interest (called the pay zone). Figure 2 illustrates theseparation of the pay zone from the surface for a typical shale depth of 7000 ft (2130 m).Fracture height predicted by computer models and confirmed by micro-seismic monitoring during fracturing, post-frac tracer flows, temperature logs and even mine-back experiments (Warpinski, 1985), show most verticaleffective fracture growth at 300 ft (90 m) or less. Frac height growth in most formations is known to be effectivelylimited by barriers and leak off (loss of fluid to the rock). Frac heights limited by these physical and active barrierswill simply not reach into fresh water sands.If the fracturing process is thousands of feet away from the water table, then why is methane showing up inresidential water wells? Methane is a common contaminant in water wells, caused by both natural and man-made causes. Part of the reason is natural occurrence with biogenic methane forming from shallow decay oforganic materials and natural seeps of thermogenic methane (gas formed deep in the earth) that have beencoming to the surface for millions of years, particularly in regions with shale and coal outcrops or shallowformations that share the water table with fresh water wells.However, part of the increasing methane content in a water well may be coming from near-by improperlyconstructed gas or oil wells. This is a common cause of contamination in northwestern Pennsylvania, when 100year old oil wells at about the same depth as the water wells, have either leaked from the old well or beennaturally connected by faults. Although not in the risk matrix, this paper looks at both natural and man-madepossibilities and suggests methods to identify the culprit and how to control those sources that do come fromwells. The reader must remember that these older wells predate the invention of hydraulic fracturing and mostpredate any significant well construction regulations.SPE 152596 5Testing of water wells in West Virginia showed 11% contained measurable methane content before gas drilling started (1312 well study – Daily Journal, 2011) and a small well population gas presence study inPennsylvania/New York study showed up to 85% of water wells contained methane in a limited geographical area (no pre-drill trend line), whether or not gas drilling exists in the area (60 well study - Howarth, 2011). From the variance in these two studies, clearly the local geology makes a large difference in presence and migration of shallow methane. Since methane is odorless and nontoxic, it often escapes detection until it reaches a concentration in air where it can burn. This happens in undrilled areas as well as drilled areas, and is very common in areas of natural gas seeps such as shallow shale and coal containing areas of Pennsylvania, New York, Colorado and California. Methane concentration can increase in water wells that penetrate shallow coal seams in search of the fresh water in some coals. Coals may have as much as 90+ Percent organic content and gas that is naturally adsorbed on the organic materials in the coal desorbs as fresh water is removed, even where water drawdown is for home use. If a gas well drilled to the deeper shales is constructed improperly and the shallow gas zones are not isolated, the methane content in adjacent water wells may increase due to the gas pressure build-up in the annulus (open area between the outside of the casing and the drilled hole wall). The gas that may accumulate in this area comes from coals and shales that are not the target of drilling but can still produce small amounts of gas. Deeper formations are at higher pressures, and exposure of these zones without sufficient cementing isolation will allow gas seepage that will build up a higher pressure than was customary at shallower depths. This type of methane leak is usually low volume and is made possible by poor or incomplete cementing practices. The incidence may be noticed soon after drilling and can start before the well is fractured. This problem and its causes will be explained in the section on well construction.Methane in the near-surface area is continually produced as a by-product from decay of organic materials by microorganisms) (Heintz, 2010). Methane generated from these real-time decay reactions in wet lands, sewage, landfills, agriculture, etc., is called biogenic methane. Thermogenic methane is formed deep within the earth from high temperature degradation of organic materials laid down millions of years ago with the sediments that eventually made up the rock. The common stable (non-radioactive) carbon isotopes are carbon 12 (C12 has 6 neutrons) and carbon 13 (C13 has 7 neutrons). Biogenic and thermogenic methane differ in the carbon isotopes they contain, with biogenic methane containing more C12 carbon while thermogenic methane contains more of the C13 carbon isotope. Recently generated methane is biogenic. Biogenic methane is nearly 100% methane while thermogenic methane may also contain some propane and butane from thermal decomposition.152596 6 SPEAlthough some sources have tried to use the difference between biogenic and thermogenic gas to determinewhether the gas in a water well is from natural shallow generation (biogenic) or a gas well leak (thermogenic), thisapproach is not accurate. Thermogenic methane may migrate completely to surface or to water wells throughnatural seeps (with no drilling in the area). Also, shale reservoirs such as the Antrim and New Albany shalesproduce significant amounts of water (as much as 30 bbls/day) with predominantly biogenic methane (EMDAAPG).Absence of frac chemicals, such as a polymer (non-toxic), is usually the telling point of difference between wellconstruction problems that fail to seal gas, and accusations of a frac treatment that somehow “communicates”with a fresh water sand.The following are brief descriptions of well development activities that are expanded for the topics of chemicalsand fracturing.1. Exploration - Location of a potential hydrocarbon resource – geologic studies, seismic interpretation,petrophysical assessment; followed by leasing of mineral rights and negotiation of surface access. Theseare generally behind-the-scene activities but the laboratory methods and general products are welldescribed in several industry and academic papers. The output from this work is the best scientificproposal on where to drill and where not to drill. Information on geological pre-drilling work ranges fromwide area geological investigation to petrophysical evaluation of rocks and cores (Britt, 2009; Bustin;Jacobi, 2009; Kundert, 2009; Rickman, 2008; Wrightstone, 2009; Kubik, 1993)2. Permitting with federal, state, provincial and/or local governments and meetings with groups fromconcerned citizens to wildlife experts may take a few months to several years. Every phase of oil and gasdevelopment is regulated in states with extensive hydrocarbon development infrastructure.3. Initial or exploratory drilling activities, which take from a few weeks to a few months, drill into the reservoirand assess the composition of fluids in the rock and the productive capacity of the formation. As drillingprogresses from exploratory to development, drilling time and expense usually drops sharply as drillingequipment and technology is matched to local geology. The pay zones and development areas are alsoremapped with information gathered in this step, causing many development areas to be shifted to thebest areas to develop and away from areas with poor reserves, shallow hazards or other problems (Mroz,1990).4. The interlinked completions phase includes formation logging (data gathering), with intermediary and finalwell completion (or well construction) activities that focus on running various strings of casing in phases ofthe drilling operation, along with sufficient cement to effectively isolate sections of the wellbore as drillingprogresses. Many exploratory wells are vertical wells, with horizontal wells drilled later during the fullscale development phase. Each casing and cementing operation forms an individual but interconnectedsystem of pressure barriers, all designed to keep hydrocarbons inside the tubulars and fresh or salt watersources outside the tubulars. Poor well construction that leads to barrier failure, as will be seen later, is apotential pathway for pollution of ground water. As a failure source, it can be eliminated by proven designand proper application. Testing of every upper cemented string is required and for the majority of upperwell barriers (pipe plus cement), a cement bond log or other in-depth investigation is just good businesspractice, and may be required in some cases.5. Final well completion and facilities and pipelines – When the final casing strings of the well are set andcemented, the blow out preventer (BOP) is replaced with a wellhead complete with control valves andconnections to the production facilities. Facilities are specially designed surface vessels that aid inseparation of gas, oil and water phases with no loss of any fluid, including gas. Methane may be ventedor temporarily from the first few wells in an area to determine well production rates and the correct sizeneeded for a connecting pipeline. If the well is in development stage, the pipeline will already have beenconnected and methane emissions during post-frac well preparation or flow back can be minimized withSPE 152596 7 saleable gas recovered, even as the frac water flows back and is separated in the facilities for re-processing.6. Fracturing Design and Chemicalsa. Fracturing design is usually by computer or local experience and specify frac volume, rate andother factors to achieve goals of frac height, frac width and frac length or frac complexity.Monitoring using fluid tracers, micro-seismic analysis or tilt meters is useful to check the first fewfracs in an area and to tune the results of the frac models (Woodroof, 2003; King, 2011;Warpinski, 2007; Fix, 1991; Fischer, 2004). The goal is to design a frac that will stay in the payzone, develop the maximum pay or producing formation contact and achieve maximum flow ofhydrocarbons and minimum flow of produced water.b. Transport and storage of fresh or salty frac water, chemicals and equipment fall under the generalheading of transport, and along with well construction, have been identified as a potential sourceof pollution. Chemical spill risk can be reduced by using double wall containers, collision-prooftotes and/or use of dry additives. Surface storage vessel leaks and spills can range from lessthan a gallon during connections in frac fluid lines to the very rare leak of a truck load (130 bbls or5460 gallons) or the highly unlikely leak of a full frac tank (500 barrels or 21,000 gallons) of water.Leak impact can be reduced by container mats underneath pipe connections, portable tankcontainment berms and tank monitoring to immediately spot leaks. Impact of frac base fluid leaksis usually minor if the leaking fluid is fresh water, since most frac chemicals are mixed into thefluid only as it is pumped into the well. Safe transport, storage and handling of chemicalconcentrates are major concerns. These risks are sharply reduced when non-toxic or even food-grade additives replace traditional chemicals.c. Mixing and pumping of the frac increases risk of leaks and spills as stored frac fluid is pumped,first to the chemical addition trailer and then the blender where sand is added, before going to thehigh pressure pumps and down the well.d. Chemicals, or more precisely, the lack of disclosure of chemical identities, have probablyreceived and deserved the most vitriolic attacks in the “anti-frack” literature. There are very fewchemicals used in fracturing and definitely not the “hundreds of toxic chemicals” claimed in “GasLand”. Independent laboratory analysis of surface water sources used for fracs do show a varietyof chemicals at trace concentrations below EPA limits, that are not added as part of the fracturingprocess, but instead come from agricultural sources (herbicides, pesticides, fungicides, etc.), thatcarry over into ground water runoff. These same chemicals are found in the raw water feed intodrinking waters in nearly all areas of the country, whether or not oil and gas operations arepresent. BTEX, diesel, fluorocarbons, etc., have been removed from fracs in the past severalyears as a caution or by regulations based on fear of somehow contaminating fresh watersupplies with frac fluids. Most of the fracture treatments used in shales are water with a frictionreducer and no significant gelling agents – called a slick water frac. The shales respond very wellto these inexpensive fracture treatments. The chemicals used in the slick water fracs are coveredin detail later in the paper where chemical abstract society (CAS) identifying numbers aresupplied. Further information on chemical usage in specific fracturing jobs in most of the US isavailable directly from . Basic slick water formulation (Fontaine, 2008) forshales may include:i. Water – About 98% to 99% of total volume - commonly fresh water (<500 ppm TDS), butincreasingly containing treated produced water.ii. Proppant – about 1% to 1.9% of total volume – usually sand or ceramic particles carried by the frac fluid into the fracture to keep the fracture open when hydraulic pressure isreleased.152596 8 SPEiii. Friction reducer – about 0.025% of total volume – the non-acid form of polyacrylamide(NOTE – this is not acrylamide) used as adsorbent in baby diapers and as a flocculent indrinking water preparation (Entry), and reduces friction pressure of water flowing throughthe pipe during high rate pumping, thereby reducing required pump horsepower outputand air emissions from the pumps. Polyacrylamide is stable to over 390o F (200o C) anddoes not appear to decompose into toxic monomers at the 150o F to 250o F (conditions ina shale well (Carman, 2007).iv. Disinfectant (biocide) – about 0.005% to 0.05% of total volume – common biocides ofglutaraldehyde (a common antimicrobial used in hospitals and even municipal watertreating systems) or quaternary amine (drinking water disinfectant and common over-the-counter skin antiseptics). Disinfectants are used to control the growth of certain kinds ofmicrobes that would destroy gelled fracture fluids, or, in unusual cases, may create asour gas generation (H2S or hydrogen sulfide) problem in the reservoir. Safer andbiodegradable glutaraldehyde blends are being produced (Enzien, 2011). Thesechemical based materials are also giving way to UV light, ozone, and low concentrationchlorine dioxide. These non-bromine and even non-chemical methods of biologicalcontrol are already in commercial use in shale fracs.v. Surfactants that modify surface or interfacial tension, break or prevent emulsions, andperform other specific actions are used at 0.5 to 2 gallons per thousand gallons in all orpart of the fracture fluid volume in some cases.vi. Gelation chemicals (thickeners) such as guar gum and cellulose polymers are notfrequent additions to slick water frac formulations, but may be used in hybrid fracs (thatuse a ungelled water to initiate the frac and a gelled water to carry some of the proppantor sand. These gelling materials are common food additives, do not break down intotoxin and are not considered of concern (Hoeman, 2011).vii. Scale inhibitors – rarely to commonly used depending on the specific shale, preventmineral scale precipitates, eliminating the potential for concentrating problem ions inscale and blockage of tubing and equipment. The common scale inhibitors are polymer,phosphate esters or phosphonates (similar compositions to detergents) and are non-toxicat the very low concentrations used in frac jobs (Houston, 2009; Blauch, 2009), however;lower toxicity anti-scalants have been advanced for the North Sea (Dickinsin, 2011; Holt,2009).viii. Hydrochloric acid (same material used in swimming pools and to clean brick and othermasonry projects) may be used in some cases to reduce fracture initiation pressure (thedownhole pressure needed to create the first small crack in the rock). When acid is used,the average volume is about 500 to 2000 gallons (1.9 to 7.6 m3). The HCl acid is spent(used up) within inches of the frac entry point and yields calcium chloride, water and asmall amount of CO2. No live acid is returned to the surface. Acid is not used in everyjob, is borderline beneficial in most jobs and has been eliminated in many areas for lackof benefit. The amount of spent hydrochloric acid (by products of calcium chloride, waterand CO2) in returned well flow that is re-injected is just slightly higher than that containedin swimming pool water that is drained into the public sewer system.ix. Corrosion inhibitor, one of several organic compounds that may be toxic, is used at 0.2%to 0.5% in only the acid (total inhibitor volume per frac is 5 to 10 gallons (29 to 38 liters)and only used if acid is used. The inhibitor is adsorbed on steel and then in the formationand only about 5 to 10% total (about a gallon in a million gallons of water) returns tosurface in the backflow.。
流体力学英语词汇翻译(1)
流体力学英语词汇翻译(1)流体动力学 fluid dynamics连续介质力学 mechanics of continuous media介质 medium流体质点 fluid particle无粘性流体 nonviscous fluid, inviscid fluid连续介质假设 continuous medium hypothesis流体运动学 fluid kinematics水静力学 hydrostatics液体静力学 hydrostatics支配方程 governing equation伯努利方程 bernoulli equation伯努利定理 bernonlli theorem毕奥-萨伐尔定律 biot-savart law欧拉方程 euler equation亥姆霍兹定理 helmholtz theorem开尔文定理 kelvin theorem涡片 vortex sheet库塔-茹可夫斯基条件 kutta-zhoukowski condition 布拉休斯解 blasius solution达朗贝尔佯廖 d'alembert paradox雷诺数 reynolds number施特鲁哈尔数 strouhal number随体导数 material derivative不可压缩流体 incompressible fluid质量守恒 conservation of mass动量守恒 conservation of momentum能量守恒 conservation of energy动量方程 momentum equation能量方程 energy equation控制体积 control volume液体静压 hydrostatic pressure 涡量拟能 enstrophy压差 differential pressure流[动] flow流线 stream line流面 stream surface流管 stream tube迹线 path, path line流场 flow field流态 flow regime流动参量 flow parameter流量 flow rate, flow discharge 涡旋 vortex涡量 vorticity涡丝 vortex filament涡线 vortex line涡面 vortex surface涡层 vortex layer涡环 vortex ring涡对 vortex pair涡管 vortex tube涡街 vortex street卡门涡街 karman vortex street 马蹄涡 horseshoe vortex对流涡胞 convective cell卷筒涡胞 roll cell涡 eddy涡粘性 eddy viscosity环流 circulation环量 circulation速度环量 velocity circulation偶极子 doublet, dipole驻点 stagnation point总压[力] total pressure总压头 total head静压头 static head总焓 total enthalpy能量输运 energy transport速度剖面 velocity profile库埃特流 couette flow单相流 single phase flow单组份流 single-component flow均匀流 uniform flow非均匀流 nonuniform flow二维流 two-dimensional flow三维流 three-dimensional flow准定常流 quasi-steady flow非定常流 unsteady flow, non-steady flow 暂态流 transient flow周期流 periodic flow振荡流 oscillatory flow分层流 stratified flow无旋流 irrotational flow有旋流 rotational flow轴对称流 axisymmetric flow不可压缩性 incompressibility不可压缩流[动] incompressible flow浮体 floating body定倾中心 metacenter阻力 drag, resistance减阻 drag reduction表面力 surface force表面张力 surface tension毛细[管]作用 capillarity来流 incoming flow自由流 free stream自由流线 free stream line外流 external flow进口 entrance, inlet出口 exit, outlet扰动 disturbance, perturbation分布 distribution传播 propagation色散 dispersion弥散 dispersion附加质量 added mass ,associated mass 收缩 contraction镜象法 image method无量纲参数 dimensionless parameter 几何相似 geometric similarity运动相似 kinematic similarity动力相似[性] dynamic similarity平面流 plane flow势 potential势流 potential flow速度势 velocity potential复势 complex potential复速度 complex velocity流函数 stream function源 source汇 sink速度[水]头 velocity head拐角流 corner flow空泡流 cavity flow超空泡 supercavity超空泡流 supercavity flow空气动力学 aerodynamics低速空气动力学 low-speed aerodynamics 高速空气动力学 high-speed aerodynamics 气动热力学 aerothermodynamics亚声速流[动] subsonic flow跨声速流[动] transonic flow超声速流[动] supersonic flow锥形流 conical flow楔流 wedge flow叶栅流 cascade flow非平衡流[动] non-equilibrium flow细长体 slender body细长度 slenderness钝头体 bluff body钝体 blunt body翼型 airfoil翼弦 chord薄翼理论 thin-airfoil theory构型 configuration后缘 trailing edge迎角 angle of attack失速 stall脱体激波 detached shock wave波阻 wave drag诱导阻力 induced drag诱导速度 induced velocity临界雷诺数 critical reynolds number前缘涡 leading edge vortex附着涡 bound vortex约束涡 confined vortex气动中心 aerodynamic center气动力 aerodynamic force气动噪声 aerodynamic noise气动加热 aerodynamic heating离解 dissociation地面效应 ground effect气体动力学 gas dynamics稀疏波 rarefaction wave热状态方程 thermal equation of state喷管 nozzle普朗特-迈耶流 prandtl-meyer flow瑞利流 rayleigh flow可压缩流[动] compressible flow可压缩流体 compressible fluid绝热流 adiabatic flow非绝热流 diabatic flow未扰动流 undisturbed flow等熵流 isentropic flow匀熵流 homoentropic flow兰金-于戈尼奥条件 rankine-hugoniot condition 状态方程 equation of state量热状态方程 caloric equation of state完全气体 perfect gas拉瓦尔喷管 laval nozzle马赫角 mach angle马赫锥 mach cone马赫线 mach line马赫数 mach number马赫波 mach wave当地马赫数 local mach number 冲击波 shock wave激波 shock wave正激波 normal shock wave斜激波 oblique shock wave头波 bow wave附体激波 attached shock wave 激波阵面 shock front激波层 shock layer压缩波 compression wave反射 reflection折射 refraction散射 scattering衍射 diffraction绕射 diffraction出口压力 exit pressure超压[强] over pressure反压 back pressure爆炸 explosion爆轰 detonation缓燃 deflagration水动力学 hydrodynamics液体动力学 hydrodynamics泰勒不稳定性 taylor instability盖斯特纳波 gerstner wave斯托克斯波 stokes wave瑞利数 rayleigh number自由面 free surface波速 wave speed, wave velocity 波高 wave height波列 wave train波群 wave group波能 wave energy表面波 surface wave表面张力波 capillary wave规则波 regular wave不规则波 irregular wave浅水波 shallow water wave深水波 deep water wave重力波 gravity wave椭圆余弦波 cnoidal wave潮波 tidal wave涌波 surge wave破碎波 breaking wave船波 ship wave非线性波 nonlinear wave孤立子 soliton水动[力]噪声 hydrodynamic noise 水击 water hammer空化 cavitation空化数 cavitation number空蚀 cavitation damage超空化流 supercavitating flow水翼 hydrofoil水力学 hydraulics洪水波 flood wave涟漪 ripple消能 energy dissipation海洋水动力学 marine hydrodynamics 谢齐公式 chezy formula欧拉数 euler number弗劳德数 froude number水力半径 hydraulic radius水力坡度 hvdraulic slope高度水头 elevating head水头损失 head loss水位 water level水跃 hydraulic jump含水层 aquifer排水 drainage排放量 discharge壅水曲线 back water curve压[强水]头 pressure head过水断面 flow cross-section明槽流 open channel flow孔流 orifice flow无压流 free surface flow有压流 pressure flow缓流 subcritical flow急流 supercritical flow渐变流 gradually varied flow急变流 rapidly varied flow临界流 critical flow异重流 density current, gravity flow堰流 weir flow掺气流 aerated flow含沙流 sediment-laden stream降水曲线 dropdown curve沉积物 sediment, deposit沉[降堆]积 sedimentation, deposition沉降速度 settling velocity流动稳定性 flow stability不稳定性 instability奥尔-索末菲方程 orr-sommerfeld equation 涡量方程 vorticity equation泊肃叶流 poiseuille flow奥辛流 oseen flow剪切流 shear flow粘性流[动] viscous flow层流 laminar flow分离流 separated flow二次流 secondary flow近场流 near field flow远场流 far field flow滞止流 stagnation flow尾流 wake [flow]回流 back flow反流 reverse flow射流 jet自由射流 free jet管流 pipe flow, tube flow内流 internal flow拟序结构 coherent structure猝发过程 bursting process表观粘度 apparent viscosity运动粘性 kinematic viscosity动力粘性 dynamic viscosity泊 poise厘泊 centipoise厘沱 centistoke剪切层 shear layer次层 sublayer流动分离 flow separation层流分离 laminar separation湍流分离 turbulent separation分离点 separation point附着点 attachment point再附 reattachment再层流化 relaminarization起动涡 starting vortex驻涡 standing vortex涡旋破碎 vortex breakdown涡旋脱落 vortex shedding压[力]降 pressure drop压差阻力 pressure drag压力能 pressure energy型阻 profile drag滑移速度 slip velocity无滑移条件 non-slip condition壁剪应力 skin friction, frictional drag 壁剪切速度 friction velocity磨擦损失 friction loss磨擦因子 friction factor耗散 dissipation滞后 lag相似性解 similar solution局域相似 local similarity气体润滑 gas lubrication液体动力润滑 hydrodynamic lubrication 浆体 slurry泰勒数 taylor number纳维-斯托克斯方程 navier-stokes equation 牛顿流体 newtonian fluid边界层理论 boundary later theory边界层方程 boundary layer equation边界层 boundary layer附面层 boundary layer层流边界层 laminar boundary layer湍流边界层 turbulent boundary layer温度边界层 thermal boundary layer边界层转捩 boundary layer transition边界层分离 boundary layer separation边界层厚度 boundary layer thickness位移厚度 displacement thickness。
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Review articleHydraulic fractures:How far can they go?Richard J.Davies a ,*,Simon A.Mathias a ,Jennifer Moss b ,Steinar Hustoft c ,Leo Newport aaDurham Energy Institute,Department of Earth Sciences,Durham University,Science Labs,Durham DH13LE,UK b3DLab,School of Earth and Ocean Sciences,Main Building,Park Place,Cardiff University,Cardiff CF103YE,UK cUniversity of Tromsø,Department of Geology,Dramsveien 201,N-9037Tromsø,Norwaya r t i c l e i n f oArticle history:Received 14February 2012Received in revised form 5April 2012Accepted 7April 2012Available online 24April 2012Keywords:Fracture Pressure Shale Natural Stimulateda b s t r a c tThe maximum reported height of an upward propagating hydraulic fracture from several thousand fracturing operations in the Marcellus,Barnett,Woodford,Eagle Ford and Niobrara shale (USA)is w 588m.Of the 1170natural hydraulic fracture pipes imaged with three-dimensional seismic data offshore of West Africa and mid-Norway it is w 1106m.Based on these empirical data,the probability of a stimulated and natural hydraulic fracture extending vertically >350m is w 1%and w 33%respectively.Constraining the probability of stimulating unusually tall hydraulic fractures in sedimentary rocks is extremely important as an evidence base for decisions on the safe vertical separation between the depth of stimulation and rock strata not intended for penetration.Ó2012Published by Elsevier Ltd.1.IntroductionHydraulic fractures propagate when fluid pressure exceeds the least principal stress and the tensile strength of the host sediment (Hubbert and Willis,1957).They continue to propagate until the stress-intensity at the fracture tip is lower than the critical stress-intensity of the rock being fractured (e.g.Savalli and Engelder,2005).These conditions can occur naturally (e.g.Cosgrove,1995)but they can also be stimulated to recover oil and gas (Simonson et al.,1978),or during injection of water into geothermal bore-holes (e.g.Legarth et al.,2005;Julian et al.,2010)and unintentionally as the result of subsurface blowouts (e.g.Tingay et al.,2005).Hydraulic fractures are commonly described in outcrops at centimetre to metre scale (e.g.Cosgrove,1995e Fig.1ab).They can be up to w 50m in height in the Devonian Marcellus shale (e.g.Engelder and Lash,2008)and sand filled fractures (injectites)have been documented to extend hundreds of metres (Hurst et al.,2011).But three-dimensional (3D)seismic data now show that natural hydraulic fractures probably cluster,forming pipe-like features that often extend vertically for even greater distances than this (see Løseth et al.,2001;Zuhlsdorff and Spieß,2004;Cartwright et al.,2007;Davies and Clarke,2010).Stimulation of hydraulic fractures as a technique for improved hydrocarbon production from low permeability reservoirs datesback to the late 1940s (Montgomery and Smith,2010).Measure-ments of the microseismicity they cause (e.g.Maxwell et al.,2002)have shown that they can extend for several hundred metres upwards and downwards from the wellbore (Fisher and Warpinski,2011).Multiple stages of hydraulic fracture stimulation on multiple wells are routine for the recovery of oil and gas from low perme-ability sedimentary reservoirs in shale gas provinces in the USA (e.g.King,2010).Shale gas exploration is starting in many other countries with sediments from Neogene to Cambrian age being potential future targets.Therefore constraining the probability of stimulating unusually tall hydraulic fractures in sedimentary rocks is critically important,as it will help avoid the unintentional penetration of shallower rock strata (Fig.2)that might be impor-tant aquifers or subsurface geological storage sites.Mathematical methods for estimating hydraulic fracturing height are simplistic (Fisher and Warpinski,2011)and it is generally accepted that we cannot yet accurately predict fracture propagation behaviour in detail,so to date much of what we know of how fractures will behave in situ conditions comes from operational experience (King et al.,2008).Future shale gas targets could be in a variety of different stress regimes and in rocks with varied mechanical properties and ages.Therefore at this stage our approach is to include a wide range of the tallest examples of hydraulic frac-tures that have different geometries,geological settings and trigger mechanisms.Although hydraulic fractures are 3D,here we compile new and existing data on the extents of only the vertical component of both*Corresponding author.E-mail address:richard.davies@ (R.J.Davies).Contents lists available at SciVerse ScienceDirectMarine and Petroleum Geologyjournal h omepage:ww w.elsevi /locate/marpetgeo0264-8172/$e see front matter Ó2012Published by Elsevier Ltd.doi:10.1016/j.marpetgeo.2012.04.001Marine and Petroleum Geology 37(2012)1e 6natural and stimulated hydraulic fracture systems hosted in sediment from Neogene to Devonian in age from eight different locations (Fig.3a).We brie fly report on key statistics,compare them and consider which factors control the extent of upward fracture propagation.1.1.Hydraulic fracturingThere are several types of natural hydraulic fracture:injectites (e.g.Hurst et al.,2011),igneous dikes (e.g.Polteau et al.,2008),veins (e.g.Cosgrove,1995),coal cleats (ubach et al.,1998),and joints (e.g.McConaughy and Engelder,1999).They have been extensively studied.In the case of joints in the Devonian Marcellus Formation,USA,it is even possible to study how they grow on the basis of plume lines that occur at centimetre to metre scale (Savalli and Engelder,2005).Marcellus shale fractures are thought to form due to gas diffusion and expansion within shale through multiple propagation events.In contrast the tallest examples of hydraulic fractures tend to cluster,are commonly termed chimneys,pipes or blowout pipes (herein we use the term ‘pipe ’)and can extend vertically for hundreds of metres (e.g.Cartwright et al.,2007;Huuse et al.,2010).The origin of pipes is not certain,but they probably form due to critical pressurisation of aquifers and oil and gas accumulations (Zuhlsdorff and Spieß,2004;Cartwright et al.,2007;Davies and Clarke,2010).Pipe development may be followed by stoping,fluid-driven erosion and collapse of surrounding strata (Cartwright et al.,2007).Gases that have come out of solution andexpandFigure 1.(a)Examples of natural hydraulic fractures in shale (b)close-up of a natural hydraulic fracture filled with shale clasts (both examples from onshoreAzerbaijan).Figure 2.Schematic diagram showing stimulated hydraulic fractures within a shale gas reservoir,natural hydraulic fractures initiated at a naturally overpressured reser-voir,the vertical extent (VE)of hydraulic fractures reported here and the safe sepa-ration between shale gas reservoir and shalloweraquifer.Figure 3.(a)Map of the globe showing location of the eight datasets.Red font e datasets for stimulated hydraulic fractures,blue font e datasets for natural hydraulic fractures (pipes).(b)Seismic line from offshore Mauritania showing a representative vertical pipe imaged on 3D seismic re flection data and its vertical extent (from Davies and Clarke,2010).(c)Graph of stimulated hydraulic fractures in the Marcellus,Barnett,Woodford and Eagle Ford shales (after Fisher and Warpinski,2011)and including unpublished data provided by Halliburton for the Niobrara shale.Inset e extract of the graph showing how the vertical extents of fractures were measured.All depths are in true vertical depth (TVD).Coloured spikes e separate hydraulic fractures propagating upwards and down-wards from the fracture initiation depth.R.J.Davies et al./Marine and Petroleum Geology 37(2012)1e 62duringfluid advection may also contribute to their development (Brown,1990;Cartwright et al.,2007).They are recognised on seismic reflection data on the basis of vertically aligned disconti-nuities in otherwise continuous reflections(Fig.3b and Cartwright et al.,2007;Løseth et al.,2011).Stimulated hydraulic fractures are created to significantly increase the rate of production of oil and gas fromfine-grained,low permeability sedimentary rocks such as monly a vertical well is deviated so that it is drilled strata-parallel through the shale reservoir(Fig.2).The production casing is perforated and hydraulic fractures stimulated by injecting saline water with chemical additives.‘Proppant’(for example sand)is used to keep the fractures open(see King,2010).Hydraulic fracture stimulation from a hori-zontal borehole is usually carried out in multiple stages with known volumes and compositions offluid(e.g.Bell and Brannon,2011). Rather than pipes forming,clustering of fractures commonly occurs along planes,which are theoretically orthogonal to the least principle stress direction.So there are fundamental differences in the geometry of these fracture systems compared to those that cluster to form pipes,the reasons for which are not yet understood.Hydraulic fractures can be also be stimulated unintentionally for example as an underground blowout(e.g.Tingay,2003)and they can unintentionally be caused by the injection of waste water at high enough rates to generate pore pressures which exceed the pressure required for hydraulic fracturing(e.g.Løseth et al.,2011).2.DatasetsHundreds of pipes have recently been identified on3D seismic reflection surveys in continental margin settings(Davies and Clarke,2010;Hustoft et al.,2010;Moss and Cartwright,2010; Løseth et al.,2011).We compile new data based upon these surveys on the vertical extents of1170pipes(e.g.Fig.3ab).Pipe heights were measured by recording their bases and tops in two-way-travel time and converting these to heights using estimated seismic velocities for the host successions(Davies and Clarke,2010;Moss and Cartwright,2010;Hustoft et al.,2010).Errors are related to the seismic resolution and the estimation of the velocity of the sediment and are probably<20%.Because of the limits of vertical seismic resolution the numbers of hydraulic fractures that have vertical extents of less than100m are probably underestimated. We have not included in this study the heights of vertically extensive injectites or igneous intrusions because their likely modes of formation are quite different to stimulated hydraulic fractures and pipe structures.The vertical and horizontal extents of stimulated hydraulic fractures used to recover hydrocarbons can be estimated using the energy released by the hydraulic fracturing which is recorded as microseismicity in a nearby borehole(e.g.Maxwell et al.,2002).Both tension and shear fractures are detected.We used a compilation of microseismic events(Fisher and Warpinski,2011).They presented measurements of the fracture tops and bottoms for‘thousands’of mapped fracture treatments performed in the Barnett,Woodford, Marcellus and Eagle Ford shale gas formations recorded from early 2001to the end of2010(their Figs.2e6respectively).Afifth unpublished dataset from the Niobrara shale(Colorado,USA)was compiled in the same way and released by Halliburton for publica-tion here.These operations varied in terms of the depth of fracturing operations,the execution of the fracturing process and the geolog-ical setting.It represents the majority of the data released into the public domain at the time of writing.Because we did not have access to the primary database our measurements of fracture height were made by digitising their published and unpublished graphs(Fisher and Warpinski, 2011e Fig.3c).This will have introduced errors but again this will be mainly with the shorter hydraulic fractures(with vertical extents<100m)therefore the numbers of these are also under-estimated.Because it is the taller fractures we focus on,this bias does not change our main conclusions.There are also errors asso-ciated with the microseismic method,mainly due to estimating the velocity of the rock between the hydraulic fracture and the moni-toring well(e.g.Maxwell et al.,2002).There is significant uncertainty in the depth of the initiation of fracture systems caused by underground well blowouts,hence we do not draw on this source of data in this paper.But the depth of the fracture initiation is well constrained where waste water is being injected,so here we use a recently reported example from the Tordis Field,offshore Norway where the fractures eventually intersected the seabed(Løseth et al.,2011).This example provides some addi-tional context for the natural and stimulated datasets described.3.Results3.1.Natural hydraulic fracturesOffshore of Mauritania368vertical pipes were identified over an area of1880km2(Davies and Clarke,2010e Fig.3ab)and it was possible to measure the vertical extent of360of these.They are hosted on a passive continental margin,probably withinfine-grained turbidites and foram-nannofossil hemipelagites of Neogene age (Henrich et al.,2010).A graph of frequency against vertical extent shows the most common vertical extent is between w200m and w300m.The tallest conduit is w507m(Fig.4a).The average vertical extent is247m.Offshore of Namibia,we measured366vertical chimneys in a succession composed offine-grained claystones of Miocene to Recent age(Moss and Cartwright,2010).The average vertical extent is360m.The maximum vertical extent is w1106m(Fig.4a).Vertical chimneys also form offshore mid-Norway within the OligocenetoFigure4.(a)Graph of frequency against vertical extent for natural hydraulic fractures(pipes)identified on3D seismic data from offshore Mauritania,Namibe Basin and mid-Norway.(b)Probability of non-exceedance against fracture height for offshore Mauritania,offshore mid-Norway and Namibe Basin.R.J.Davies et al./Marine and Petroleum Geology37(2012)1e63Recentfine-grained mudstone and siliceous mudstones of the Brygge,Kai and Naust Formations(Hustoft et al.,2010).66%of these terminate at the seabed.Of the446pipes the average vertical extent is338m.The maximum vertical extent is w882m(Fig.4a).Graphs of hydraulic fracture height against the probability of non-exceedance of this height for each dataset show the probability of pipes exceeding a range of vertical extents(Fig.4b).Based upon these data the probability of a pipe extending vertically>350m is w33% (Fig.6ab).3.2.Stimulated hydraulic fracturesOur compilation of data from the USA shales(Fisher and Warpinski,2011e Fig.3c)shows that generally the Marcellus is the shallowest reservoir,then the Niobrara,Barnett,Woodford and Eagle Ford.The maximum upward propagation of fractures initiated in these reservoirs is w588in the Barnett shale but in each case the vast majority of hydraulic fractures propagate much shorter distances(Fig.5ab).The maximum upward propagation recorded to date in the Marcellus shale is w536m.The graphs show that the probability of an upward propagating fracture exceeding a height of 200m,for example,is highest for those initiated in the Marcellus then the Barnett,Woodford,Niobrara and Eagle Ford shale reser-voirs.Based upon these data the probability that an upward propagating hydraulic fracture extends vertically>350m is w1% (Fig.6ab),but the probability is probably lower than this because we cannot measure all of the shorter fractures.We cannot accurately estimate the average vertical extent for the same reason.3.3.Unintentionally stimulated hydraulic fracturesAt the Tordis Field,offshore Norway,waste water produced due to oil production was injected at w900m below the surface.This caused hydraulic fractures to propagate approximately900m to the seabed.Pressure profiles from the injection well show a stepped fracturing of the overburden(Løseth et al.,2011).The injection lasted for approximately5.5months,while the leakage to seafloor may have occurred for between16and77days(Løseth et al.,2011).4.Interpretation and discussion4.1.Vertical extentOffshore mid-Norway there are controls on the locations of the bases of the pipes as many emanate from overpressured strata and 66%terminate at the present-day seabed(Hustoft et al.,2010)and these controls cause the peak in the frequency versus depth plot between300and350m(Fig.4a).Both of these factors haveanFigure6.(a)Graph of frequency against fracture height for all stimulated and natural hydraulic fractures.(b)Graph of probability of non-exceedance against fracture height for stimulated and natural hydraulicfractures.Figure5.Graphs of frequency against hydraulic fracture height for(a)upward and(b)downward propagating fractures in the Marcellus,Barnett,Woodford,Eagle Ford and Niobrara shales.Graphs of probability of exceedance against height of(c)upward propagating fractures and(d)downward propagating fractures.R.J.Davies et al./Marine and Petroleum Geology37(2012)1e64influence on the shape of the probability of exceedance versus height curves(Fig.4b).In contrast only12of the360pipes from offshore Mauritania terminate at a palaeo-seabed and a small number of pipes in the Namibe Basin do this.Despite the limita-tions of the datasets it is clear most of the natural hydraulic fractures reported here are200e400m in height and that very few natural fracture systems reported to date propagate beyond a height of700m.The tallest is1106m,which is comparable to the tallest injectites documented(Hurst et al.,2011).Lastly hydraulic fractures that cluster to form pipe structures generally propagate upwards further than stimulated hydraulic fractures(Fig.6ab).The vast majority of stimulated hydraulic fractures have a very limited vertical extent of<100m(Figs.3c and5a)and the tallest is w588m.These taller hydraulic fractures probably form by inter-secting existing faults which has been recognised on the basis of changes in the clustering and the magnitude of microseismic events(Warpinski and Mayerhofer,2008).4.2.Controls on vertical extentStimulated hydraulic fractures probably form by a number of small fracture propagation events rather than a single one.The stimulation of the hydraulic fractures in shale gas reservoirs nor-mally takes place over time periods of only1e2h for a single fracturing stage.When this period has been increased,for example in the Barnett Shale,where pumping for an11.7h period took place with a total volume of c.5565m3,the maximum height of hydraulic fractures was only w266m(Maxwell et al., 2002).During pumping periods of up to11.3h into the Barnett Shale the relationship between height and pumping time and volume was shown not to be strong(Shelley et al.,2011)and frac-tures stopped propagating vertically after only1e3h.Therefore there is little relationship between pumping time and fracture height when measured over these timescales.In the shale gas provinces local geology such as variations in lithology,provide natural barriers to propagation because of higher confining stress or high permeability which allows thefluid to bleed off(Fisher and Warpinski,2011).For example in the Barnett shale the Viola and Ellenberger limestones located below the Barnett shale can limit the downward propagation of hydraulic fractures(King et al., 2008).We propose that natural hydraulic fractures that cluster to form pipe structures have greater vertical extents for a number of reasons.There is much morefluid and much longer timescales available for multiple stages of fracture propagation.A volume of w6Â109m3is reported for an aquifer in the North Sea(UK) (Heward et al.,2003).Although theflux of only some of thefluid from an aquifer would cause pressure to drop to hydrostatic levels and therefore only some of thisfluid would have a role in pipe development,there are orders of magnitude higher volumes of fluid available than used in fracture stages in shale gas wells.Gas that comes out of solution during ascent offluid in natural hydraulic fractures could also have a contributory role in propa-gation(Cartwright et al.,2007).The pipes recorded here are hosted withinfine-grained,relatively homogenous successions on conti-nental margins where there are fewer mechanical boundaries and generally low permeability strata that do not allowfluid to bleed off and therefore pressure to stly there are significant geometrical differences between natural and stimulated hydraulic fractures and we do not know what influence this has on height. Despite these differences there are similar trends in the datasets. The vast majority of both natural and stimulated hydraulic fractures included in this study are<500m in vertical extent (Fig.6a).This is again because of variations in-situ stress,weak interfaces,material property contrasts and high permeability layers in sedimentary successions,particularly heterogeneous ones, which provide natural barriers to fracture propagation.At the Tordisfield the average rate of injection of water was 7000m3a day for5.5months(total volume w1,115,000m3). Fractures grew from w900m depth to the surface through Ceno-zoic(Tertiary)rather than Palaeozoic strata.But this volume offluid is over w123times greater than typically used for fracture stages in the shale gas reservoirs and over a time period hundreds of times longer.Løseth et al.(2011)reported that pressure profiles from the injection well show a stepwise fracturing of the overburden and that fractures actually propagated for900m reaching the surface (the seabed).The complexity of fracture propagation,role of bed boundaries and pre-existing natural fractures was also demonstrated at centimetre to metre scale through the mine-back experiments carried out in the USA where stimulated fractures were exposed by excavating them(e.g.Cipolla et al.,2008).Prop-agation continues once the stress at the new boundary exceeds the least principal stress and the tensile strength of the host sediment and the stress-intensity at the fracture tip is lower than the critical stress-intensity of the rock being fractured.Therefore to develop the vertically most extensive fracture systems there needs to be long,probably multiple episodes of injection of high pressurefluid (probably>>1day).There would be several steps in the propa-gation of the fracture system,breaking through permeable beds and mechanical boundaries.Mechanically homogeneous succes-sions with low permeability will result in vertically more extensive fractures than heterogeneous formations with variable perme-ability and confining stress.4.3.Implications and further workFurther research should include additional datasets,particularly from new settings that have not undergone fracturing treatments to further increase confidence that exceptional propagation heights have been captured.Additional data may allow for a better understanding of several potential relationships between the height of fractures and variables such as the type of stress regime (i.e.conducive for shear failure or tensile failure),rock type,volume of pumpedfluid and pumping time.There are some geological scenarios where there could be connectivity of permeable reservoirs through a significant thick-ness of overburden.For example sand injectites can cut through w1000m of shale(e.g.Hurst et al.,2011)and this could,given long enough pumping time cause critical pressurisation of shallower strata and therefore shallower fractures.These and other geological scenarios should be considered and modelled.Lastly,stimulated hydraulic fractures have been proposed as a mechanism for methane contamination of aquifers located1e2km above the level of the fracture initiation in the Marcellus shale (Osborn et al.,2011).Because the maximum upward propagation recorded to date in the Marcellus shale is w536m this link is extremely unlikely(Davies,2011;Saba and Orzechowski,2011; Schon,2011).Other mechanisms for contamination such as the leakage of biogenic or thermogenic gas from porous and permeable strata behind well casing and natural migration of methane are more likely.5.ConclusionsNatural hydraulic fracture pipes have the potential to propagate upwards further than stimulated ones.The maximum upward propagation recorded for a stimulated hydraulic fracture to date is w588m in the Barnett shale in the USA.Based upon the dataR.J.Davies et al./Marine and Petroleum Geology37(2012)1e65presented here the probability that stimulated hydraulic fractures extend vertically beyond350m is w1%.Microseismic measurement of fracture propagation is an essential monitoring tool which allows us to provide an evidence base for the setting of the minimum vertical separation between the shale gas reservoir and shallower aquifers.This is a comprehensive compilation of data,but of course should be added to with new fracture height data from other regions,as the different geological conditions may result in unusually short or tall fractures.Building upon this dataset and deriving probabilities from it will help inform industry and academic geoscientists and engineers,regulators,non government organisations and publics on safe separation distances and help ensure environmentally safe shale gas operations. AcknowledgementsWe are very grateful to Steve Wolhart(Halliburton)for providing the unpublished data from the Niobrara shale(Fig.3). Katie Roberts is thanked for providingfield photographs(Fig.1ab), Jonny Imber,Roger Crouch,Jon Trevelyan and Joe Cartwright are thanked for discussion,although the opinions are those of the authors.Both Mads Huuse(Manchester University,UK)and Terry Engelder(The Pennsylvania State University,USA),provided very thorough,constructive and informative reviews that allowed important revisions to the manuscript.ReferencesBell,C.E.,Brannon,H.D.,2011.Redesigning Fracturing Fluids for Improving Reliability and Well Performance in Horizontal Tight Shale Applications.SPE.140107. Brown,K.M.,1990.The nature and hydrogeological significance of mud diapirs and diatremes for accretionary systems.Journal of Geophysical Research95,8969e8982. Cartwright,J.,Huuse,M.,Aplin,A.,2007.Seal bypass systems.American Association of Petroleum Geologists91,1141e1166.Cipolla,C.L.,Warpinski,N.R.,Mayerhofer,M.J.,2008.Hydraulic Fracture Complexity: Diagnosis,Remediation and Exploitation.SPE.115771.Cosgrove,J.W.,1995.The expression of hydraulic fracturing in rocks and sediments.In:Fractography:Fracture Topography as a Tool in Fracture Mechanics and Stress Analysis.Geological Society Special Publication No92,pp.187e196. Davies,R.J.,Clarke,A.L.,2010.Storage rather than venting after gas hydrate disso-ciation.Geology38,963e966.Davies,R.J.,2011.Methane contamination of drinking water caused by hydraulic fracturing remains unproven.Proceedings of the National Academy of Sciences 108(43),E871.Engelder,T.,Lash,G.G.,2008.Marcellus Shale Play’s Vast Resource Potential Causing Big Stir in Appalachia.The American Oil and Gas Reporter.Fisher,K.,Warpinski,N.,2011.Hydraulic Fracture-Height Growth:Real Data.SPE.145949.Henrich,R.,Cherubini,Y.,Meggers,H.,2010.Climate and sea level induced turbidite activity in a canyon system offshore the hyperarid Western Sahara (Mauritania):the Timiris Canyon.Marine Geology275,178e198.Heward,A.P.,Schofield,P.,Gluyas,J.G.,2003.The Rotliegend reservoir in Block30/ 24,UK Central North Sea:including the Argyll(renamed Ardmore)and Innes fields.Petroleum Geoscience9,295e307.Hubbert,M.K.,Willis,D.G.W.,1957.Mechanics of hydraulic fracturing.Transaction of the American Institute of Mining,Metallurgical,and Petroleum Engineers Incorporated210,153e168.Hurst,A.,Scott,A.,Vigorito,M.,2011.Physical characteristics of sand injectites.Earth-Science Reviews106,215e246.Hustoft,S.,Bünz,S.,Mienert,M.,2010.Three-dimensional seismic analysis of the morphology and spatial distribution of chimneys beneath the Nyegga pock-markfield,offshore mid-Norway.Basin Research22,465e480.Huuse,M.,Jackson,C.A.-J.,Van Rensbergen,P.,Davies,R.J.,Flemings,P.B.,Dixon,R.J., 2010.Subsurface sediment remobilization andfluidflow in sedimentary basins: an overview.Basin Research22,342e360.Julian,B.R.,Foulger,G.R.,Monastero,F.C.,Bjornstad,S.,2010.Imaging hydraulic fractures in a geothermal reservoir.Geophysical Research Letters37,L07305. King,G.E.,Haile,L.,Shuss,J.,Dobkins,T.A.,2008.Increasing Fracture Path Complexity and Controlling Downward Fracture Growth in the Barnett Shale.SPE.119896. King,G.E.,2010.Thirty Years of Shale Gas Fracturing:What Have We Learned?SPE.133456.Laubach,S.E.,Marrett,R.A.,Olson,J.E.,Scott,A.R.,1998.Characteristics and origins of coal cleat:a review.International Journal of Coal Geology35,175e207. Legarth,B.,Huenges,E.,Zimmermann,G.,2005.Hydraulic fracturing in a sedi-mentary geothermal reservoir:results and implications.International Journal of Rock Mechanics and Mining Sciences42,1028e1041.Løseth,H.,Wensaas,L.,Arntsen,B.,Hanken,N.,Basire,C.,Graue,K.,2001.1000m Long Gas Blow Out Chimneys.In:63rd EAGE Conference and Exhibition, Extended Abstracts,524p.Løseth,H.,Wensaas,L.,Arntsen,B.,Hanken,N.-M.,Basire,C.,Graue,K.,2011.1000m long gas blow-out chimneys.Marine and Petroleum Geology28,1047e1060. Maxwell,S.C.,Urbancic,T.J.,Steinsberger,N.,Zinno,R.,2002.Microseismic Imaging of Hydraulic Fracture Complexity in the Barnett Shale.SPE.77440. McConaughy,D.T.,Engelder,T.,1999.Joint interaction with embedded concretions: joint loading configurations inferred from propagation paths.Journal of Struc-tural Geology21,1637e1652.Montgomery,C.T.,Smith,M.B.,2010.Hydraulic fracturing:history of an enduring technology.Journal of Petroleum Technology62,26e32.Moss,J.L.,Cartwright,J.,2010.3D seismic expression of km-scalefluid escape chimneys from offshore Namibia.Basin Research22,481e501.Osborn,S.G.,Vengosh,A.,Warner,N.R.,Jackson,R.B.,2011.Methane contamination of drinking water accompanying gas-well drilling and hydraulic fracturing.Proceedings of the National Academy of Sciences108,8172e8176.Polteau,S.,Mazzini,A.,Galland,O.,Planke,S.,Malthe-Sørenssen,A.,2008.Saucer-shaped intrusions:occurrences,emplacement and implications.Earth and Planetary Science Letters266,195e204.Saba,T.,Orzechowski,M.,ck of data to support a relationship between methane contamination of drinking water wells and hydraulic fracturing.Proceedings of the National Academy of Sciences108,E663.Savalli,L.,Engelder,T.,2005.Mechanisms controlling rupture shape during subcritical growth of joints in layered rock.Geological Society of America Bulletin117,436e449.Schon,S.C.,2011.Hydraulic fracturing not responsible for methane migration.Proceedings of the National Academy of Sciences108(37).Shelley,R.F.,Lyle,P.E.,Lehman,V.,Shah,K.,2011.Survey of More than1,000Fracture Stage Database with Net Pressure in the Barnett Shell,Part2.SPE.143330. Simonson, E.R.,Abou-Sayed, A.S.,Clifton,J.J.,1978.Containment of Massive Hydraulic Fractures,SPE,J18(1),27e32pp.Tingay,M.R.P.,Hillis,R.R.,Morley,C.K.,Swarbrick,R.E.,Drake,S.J.,2005.Present day stress orientation in Brunei:a snapshot of‘prograding tectonics’in a Tertiary delta.Journal of the Geological Society,London162,39e49.Tingay,M.R.P.2003.In situ stress and overpressures of Brunei Darussalam.PhD thesis,University of Adelaide.Warpinski,N.R.,Mayerhofer,M.J.,2008.Stimulating Unconventional Reservoirs: Maximizing Network Growth while Optimizing Fracture Conductivity.SPE.114173. Zuhlsdorff,L.,Spieß,V.,2004.Three-dimensional seismic characterization ofa venting site reveals compelling indications of natural hydraulic fracturing.Geology32,101e104.R.J.Davies et al./Marine and Petroleum Geology37(2012)1e6 6。