FP-CH356

InterdisciplinaryHarmonising Rock Engineering and the Environment–Qian&Zhou(eds)©2012Taylor&Francis Group,London,ISBN978-0-415-80444-8A comprehensive approach in predicting excessive sand productionM.Bai,C.Santana&X.ShenHalliburton,Houston,TX,USABSTRACT:In contrast to the conventional approach of sanding prediction where only one particular method is selected(e.g., either empirical,analytical,numerical,or experimental),a comprehensive geomechanical approach is presented in this paper to predict excessive sand production,which includes:a)employing an analytical method with the combination of experience-based empirical rules and analytical expressions to assess the sand production risk under simplified conditions,b)performing a numerical study using the desired constitutive relationships in a three-dimensional field environment to examine wellbore and perforation device stability under the complex configurations and to validate the initial calculations,and c)conducting an experimental approach using laboratory-rock mechanical testing techniques to calibrate the sanding prediction under simulated downhole conditions.The presented approach uses the self-calibrated predictions on sand production via multiple methods, which can lead to a sensible decision for selecting effective and economical sand-control measures.The unified approach was illustrated in a case study where the critical drawdown pressure was sensibly determined by multiple methods.Subject:Petroleum geomechanicsKeywords:rock failure,stability analysis,weak rock1INTRODUCTIONA limited amount of sand production during hydrocarbon production in a form of fine migration is considered nor-mal.However,if the sand production exceeds certain level, a number of serious consequences may occur,varying from wellbore instability[Figure1(a)],sand cavity collapse[Fig-ure1(b)],and weak formation breakdown[Figure1(c)],to sand-prevention device failure[Figure1(d)].Without taking immediate remedial measures to prevent excessive sand pro-duction,normal hydrocarbon production would be severely hindered,or even terminated.Excessive sand production can directly affect well pro-duction and casing stability.Rock mechanical failure around the wellbore and near the perforation tunnels in poorly-consolidated sandstone formations subjected to aggressive hydrocarbon production appears to be the major cause of excessive sand production.Classical sand-control techniques are primarily based on the installation of sand exclusion devices,such as gravel packing,expandable screens,etc., which dramatically increase the completion cost and detrimen-tally reduce hydrocarbon production.As a result,it is desirable to predict excessive sanding potential and assess comple-tion device stability near perforation tunnels before a sensible decision can be made on whether or not to perform the costly sand-control procedures.Numerous sand prediction methods have currently been employed to assist in designing sand-prevention devices for completion and in determining the maximum depletion rate for a sand-free production.For predicting the critical draw-down pressure at the maximum bottomhole flowing pressure under the simple configurations,analytical and experience-based empirical methods are popular[Fjær et al.,(1992); Hettema et al.(2006);Willson et al.(2002);andYi(2003)].For predicting the stability of sand-prevention devices and perfo-ration tunnels with complex structural geometries,numerical methods,such as the finite element method,are generally preferred[Garolera et al.(2003);Wan and Wang(2003);and Figure1.Formation instability and sand exclusion device damage from excessive sand production.Zhang et al.(2007)].For calibrating the sanding prediction, experimental methods involving laboratory-rock mechanical testing are employed if the sample cores in the sand-prone formation are available[Nouri et al.(2004);and Core Lab (2003)].Using one particular method(e.g.,either analytical,empir-ical,numerical,or experimental)may be convenient,but it can lead to an incomplete or a biased analysis of sanding pre-diction.To avoid this shortcoming,the presented technique provides a unified approach that employs multiple methods with complementary objectives:a)analytical and empirical methods assess the sand-production risk under the simpli-fied conditions;b)numerical methods examine stability of sand prevention devices under realistic configurations;and c)experimental methods calibrate the sand predictions under simulated downhole conditions.In the present study,attentionFigure2.Critical bottomhole flowing pressure(CBHFP)versus reservoir pressure where the critical drawdown pressure(CDP)is constrained(CDP0is CDP at the initial reservoir pressure P RES,0). is focused on predicting the critical drawdown pressure(CDP) under tolerable sand production.2ANAL YTICAL&EMPIRICAL METHODSThe primary purpose of the analytical and empirical methods in this paper focuses on determining the critical drawdown pressure(CDP)constrained by the sand-free envelope.This envelope is generally shown in Figure2(i.e.,filled blue tri-angle area).The sand-free envelope is defined by the border lines of:a)an equal line between the critical bottomhole flow-ing pressure(CBHFP or P cwf)and reservoir pressure(RP or P RES),b)the critical drawdown pressure(CDP)at the current reservoir condition[e.g.,initial condition(P RES,0)or depleted condition(P RES)],and c)the minimum CBHFP,which can be expressedas:where,P cwf is the critical bottomhole flowing pressure(i.e., CBHFP),P RES is the reservoir pressure(i.e.,RP),a is the line slope between the minimum CBHFP and RP,and b is the magnitude of the line intersect.Equation1is the general form of the lower border line for the sand-free envelope.Fjær et al.(1992)proposed the following equation for calculating the critical drawdown pressure(CDP): where,UCS is the unconfined compressive strength,Cs is the cohesion,φis the internal friction angle,and n is an empirical coefficient that is related to the well flow geometry,as shown in Figure3.The empirical coefficient,n,ranges from1to2depending on whether it is an open hole(i.e.,n=1)or a cased hole(i.e., n=2).Sometimes,n is chosen as a variable between1and 2depending on the uncertainty level of the sanding analysis. For this method,the general relationship between CBHFP and RP is the same as shown that in Equation1,with the definition of coefficients,a and b,as:Figure3.Wellbore flow geometries with respect to the empirical constant,n.Figure4.Critical bottomhole flowing pressure versus reservoir pressure using the method in Equation2.The relationship between CBHFP and RP can be graphically depicted in Figure4.Without relating the critical drawdown pressure(CDP)to the stress state,Hettema et al.(2006)]proposed the followingformulation:where,m is the field parameter,and CDP0is the CDP at the initial reservoir condition.Equation4can be arrangedas: Observations from Equation5are:Equation4can be re-arranged into the general form as shown in Equation1with the followingparameters:If the initial critical drawdown pressure(CDP0)is related to the rock strength as shown in Equation2,Equation8can be rewrittenas:For m>1,this method is graphically shown in Figure5.It is clear that the case shown in Fig.4is the case for m=0in Figure5.Figure 5.CBHFP versus RP subject to variations of the field parameter,m ,by Equation4.Figure 6.Assessment of perforation tunnel stability with various shot densities by the finite-element method.3NUMERICAL METHODSIt has been shown in the last section that relatively simple perforation geometry is implied in the sanding prediction by analytical and empirical methods.For complex perfora-tion geometry,numerical methods,such as the finite-element method,are more ing critical plastic strain to assess the sanding-induced perforation tunnel stability via the finite-element method,Figure 6indicates that perforations with denser shots lead to a greater risk of perforation structural failure [Garolera et al.(2003);and Zhang et al.(2007)].It is a fact that excessive sand production is prone to occur in weak rocks,such as in unconsolidated sandstones.Under elevated stress,rock status can be subjected to the brittle-ductile transition,and consequently,the associated large plastic deformation can lead to eventual drastic structural failure,as demonstrated by the numerical modeling shown in Figure 7(Zhang et al.,2007).Numerical methods can also evaluate the critical drawdown pressure (CDP)under the specific production scenario.The process parallel to the analytical and empirical methods can provide a sensible validation for the determined CDP .The basic numerical method is to select a block-reservoir section with predefined boundary loading conditions (i.e.,stress and pore pressure conditions)and with the designated flow rate (or fluid pressure)at the wellbore.With defined initial and boundary conditions,the simulation run is performed until wellbore failure occurs when the plastic deformationexceedsFigure 7.Plastic deformation zone owing to perforations by finite elementcalculation.Figure 8.3-D finite-element mesh and boundary constraints for the simulation of production-induced sanding around the wellbore.the critical value,which may lead to excessive sand production near the wellbore.For complex perforation configurations,three-dimensional,finite-element simulation is necessary to improve the quality of the simulation.When proper initial and boundary condi-tions are established,the 3-D simulated domain of a reservoir section can be reduced to a slice of formation layer.As an example,the associated finite-element mesh layout and boundary constraints are shown in Figure 8.The numerical results will be illustrated in the Case Study section.4NUMERICAL METHODSNumerous experimental methods involving laboratory-rock mechanical testing are available for the sanding analysis [Nouri et al.,2004,and Core Lab (2003)].When the core samples from the field are secured,experimental testing is an effective way to simulate the sanding scenarios under realis-tic,simulated downhole conditions.The results can be used to validate the studies obtained from analytical and empirical methods.When cores are available,the triaxial compression test (TXC)can be considered a required test to determine rock strength under downhole conditions (e.g.,at various confine-ment pressures).In addition,the relationships between critical plastic strain and rock failure stress under the designated confinements can be used for determining the possibility of excessive sand production,as shown in Figure 9.For the test involving fluid flow or simulated hydrocarbon production,the pore-volume compressibility test (PVC)can be used to determine the sample rock strength under the max-imum depletion and the designated stress path (i.e.,ratio of horizontal stress to vertical stress).Figure 10schematicallyFigure 9.Critical plastic strains versus rock failure stresses deter-mined from the triaxial compression test(TXC).Figure 10.Schematics of simulated depletion under the pore-volume compressibility test (PVC).shows the PVC test where the testing plug is positioned within the triaxial testing cell and effective stress is imposed to the plug.With the increase of the effective mean stress,which equivalently simulates the depletion of reservoir pore pres-sure,the maximum depletion pressure is obtained when the compactant cap is determined.If the rock sample is the unconsolidated sandstone,the thick-wall cylinder test (TWC)can be employed to deter-mine the critical-rock pore strength under the internal load as well as the cylinder sample strength under the external load.The amount of sand production can be also measured from the TWC test with the internal load.Figure 11schematically depicts the loading configurations in a testing cell from the TWC test (Core Lab,2003).5CASE STUDYA study was conducted to determine the maximum drawdown pressure under controlled sand production for a sandstone reservoir with an average reservoir pressure of 3,000psi in the perforated section.The weak spots of the reservoir sec-tion were picked by evaluating the wireline logs (i.e.,Gamma Ray –GR and sonic travel time –DT)and the assessed rock strength (i.e.,unconfined compressive strength –UCS)from the correlation using McNally criterion (McNally,1987).The weakest spot was the sandstone interval at 2,032m withtheFigure 11.Schematic test configuration of the thick-wall cylinder test to determine rock sample strength under simulatedconditions.Figure 12.Identified weak spots in the reservoir section from log analysis and rock strengthcorrelations.Figure 13.Critical drawdown pressure (CDP)of 606psi predicted by Equation 2assuming n =1.derived UCS of 606psi (Figure 12).This spot will be used for the sanding assessment of a present case study.The prediction of critical drawdown pressure (CDP)by the analytical/empirical method shown in Equation 2is illustrated in Figure 13(i.e.,CDP =606psi),where the reservoir pressure of 3,000psi is maintained (i.e.,reservoir is not depleted)and the open-hole condition (i.e.,n =1)is assumed.Figure 14.Prediction of CDP by using the method from Willson et al.(2002).Figure 15.Pore pressure in the reservoir section and equivalent plastic strain around the wellbore under the critical drawdown pressure of 400psi by the finite-element method.Applying the analytical/empirical method proposed by Willson et al.(2002),the critical drawdown pressure (CDP)of 436psi and sand free envelope is shown in Figure 14.The comparison of CDPs between the one shown in Figure 13and the one shown in Figure 14indicates the noticeable difference.It should be noted that the former result was obtained from the empirical method (i.e.,Equation 2),while the latter result was achieved from the analytical method that examines wellbore stability using the conservative tensile-failure criterion (Willson et al.,2002),in contrast to the radical compression-failure criterion (Yi,2003).In fact,the match between the two approaches can be obtained if parameter,n ,in Equation 2is increased.Using the numerical finite-element method with the assess-ment of critical plastic strain to determine the onset of sand production under the condition of open-hole completion and boundary constraints shown in Figure 8,Figure 15indi-cates the local pore-pressure distribution and near-field plastic strain contour.Applying the critical plastic strain of about 1%(Van den Hoek et al.,1996),the critical drawdown pressure (CDP)is 400psi,which is close to the value determined from the analytical method described in Figure14.Figure 16.A unified approach for predicting excessive sand production.In the present case study,experimental methods were also proposed but were not performed owing to a lack of cores in the reservoir section.6CONCLUSIONSThe comprehensive approach in predicting excessive sand pro-duction presented in this paper can be best summarized as a unified approach for sanding prediction,as illustrated in Figure 16.The functions of four methods in the unified approach for evaluating critical drawdown pressure (CDP)during hydro-carbon production can be expounded as follows:•The analytical method can be used to calculate the CDPunder simple field conditions and simplified completion configurations for initial sanding assessment.•The empirical method can be used to adjust the CDP calculations with the field data and past experience.•The numerical method can be used to validate the CDP cal-culations under the realistic field conditions and complex perforation configurations for detailed sanding assessment.•The experimental method can be used to calibrate the CDP calculations using the laboratory testing result with real core samples and under simulated downhole scenarios.The benefits of adopting the unified approach are partially explained in the case study of this paper.The ultimate purposes of employing the unified approach can be given as follows:•To avoid applying one particular method that can be biasedand can lead to an insensible decision for sand control.•To generate the self-calibrated results of sanding predic-tion that can result in making an effective and economical decision for sand 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