水力压裂例子ppt

τ is the shear stress,
γ is the shear strain rate,
K is the fluid consistency, and α is the power law coefficient. • Tangential volume flow rate density is defined as:
•
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Hydraulic Fracture: example
– Constitutive properties: • A linear Drucker-Prager model with hardening is used for the rock. • A quadratic traction-interaction failure criterion is used for modeling damage initiation in the cohesive elements. • A mixed-mode energy-based damage evolution law is used for modeling damage propagation. • Gap flow is specified as Newtonian with a viscosity of 1 × 10–6 kPa s (1 centipoise), close to that of water. • Fluid leak-off is specified as 5.879 × 10–10 m3/(kPa s) for the early stages. In the final stage, when the polymer is dissolved, the fluid leak-off coefficient is increased to 1 × 10–3 m3/(kPa s). – This step-dependent fluid leak-off coefficient is set in user subroutine UFLUIDLEAKOFF.
• Example: – Abaqus Example Problem 9.1.5 – Model dimensions: • 400 m diameter • 50 m thickness – Target formation is sandwiched between two shale layers. – Rock is modeled by C3D8RP elements. – Fracture is modeled by COH3D8P pore pressure cohesive elements. – Bore hole casing is modeled by M3D4 elements.
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Hydraulic Fracture: principle
– Hydraulic fractures are created by pumping fluids into oil wells at very high pressures. – Surface area exposed to the hydrocarbon bearing rocks gets increased. – Conductive pathways get created for enhanced hydrocarbon flow to the well bore. – Oil-well productivity increases. – Production lifetime of reservoirs gets extended.
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Hydraulic Fracture: flow model
– Power law tangential flow: α • Constitutive relation is defined as: τ = K γ where:
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Hydraulic Fracture: flow model
– Tangential flow is absent by default. – Newtonian tangential flow: • Volume flow rate density vector is expressed as: q = −kt∇p, where kt is the tangential permeability and ∇p is the pressure gradient along the element. • Tangential permeability is given by Reynold’s equation: kt = d3/12µ, where µ is the fluid viscosity and d is the cohesive element opening. • An upper limit on the value of kt can also be specified.
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Hydraulic Fracture: abaqus data
• Usage: Keywords interface – Tangential flow: *GAP FLOW, TYPE=NEWTONIAN *GAP FLOW, TYPE=POWER LAW – Normal flow: *FLUID LEAKOFF *FLUID LEAKOFF, USER – Requires user subroutine UFLUIDLEAKOFF – Initially open elements are defined by: *INITIAL CONDITIONS, TYPE=INITIAL GAP
2α 1 α d q = − 1 + 2α K 2
1
1+ 2α
α
∇p
1−α
α
∇p
where d is the cohesive element opening.
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Hydraulic Fracture: flow model
– Normal flow across gap surfaces: • Occurs when fluid leak-off coefficient is defined for the pore fluid. • The coefficient defines a pressure-flow relationship between the cohesive element’s middle nodes and their adjacent surface nodes. • The coefficient can be interpreted as the permeability of a finite layer of material on the cohesive element surfaces. • Normal flows are defined as qt = ct (pi− pt) and qb = cb (pi− pb), where qt and qb are the flow rates into the top and bottom surfaces, pb is the bottom surface pore pressure, pi is the mid-face pore pressure, and pt is the top surface pore pressure.
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Hydraulic Fracture: flow model
– Tangential flow within the fracture gap can be specified as: • Newtonian flow • Power law model – Normal flow across the fracture gap can be specified. • It represents resistance due to caking or fouling effects.
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Hydraulic Fracture: cohesive element
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Hydraulic Fracture: cohesive element
• Linear eห้องสมุดไป่ตู้astic tractionseparation behavior
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Hydraulic Fracture
• Abaqus take process of formation stimulus as a hydraulic fracture process. • By assigning one cohesive element layer within the target formation, Abaqus can predict the pumping pressure required to crack the formation.