Model Geometry and solution method Yield Hardening/ Coupling Phases Sanding criteria Permeability alteration in the sanded zone Other features
Morita et al. [25 ], Morita et al. [26 ], Burton et al. [27 ] 3D; finite element (FE) Kinematic model with a cap yes (flow friction) Iteratively coupled (1) Fluid Maximum plastic strain limit No change (1) Only the onset of sanding
(Vardoulakis et al. [7 ]) 1D; finite difference (FD) N/A N/A Fluid flow and erosion are coupled (1) Fluid Erosion
(1) Only hydromechanical effects; equilibrium eqn. is not solved
Skjaerstein et al. [28 ] 1D; FD N/A N/A Fluid flow and erosion are coupled. (1) Fluid Erosion
Forcheimer’s law was used instead of Darcy’s law to account for turbulence
Papamichos and Malmanger [29 ] 2D Axial symmetry and 3D; FE; Newoton-Paphson (NR) iterations MC Yes Fully coupled (1) Fluid Erosion
Tension cut-off: function of both plastic strain and porosity; by the factor
Papamichos et al. [9 ] 2D Axial symmetry; FEM; NR iterations MC Yes Fully coupled (1) fluid Erosion Carman-Kozeny Tension cut-off and Young mod changed by the factor
Yi [30 ] 2D axial symmetry; FD MC No (1) Fluid Erosion
Sand deposition in porous media is considered
Vaziri et al. [31 ] 2D axial symmetry; FE; fully-implicit Modified MC with tensile failure Yes Fully coupled (1) Fluid Tensile failure
Zero stiffness, compressibility and high k for the liquefied tensile zone
Wang and Xue [32 ] FE; Crank-Nicholson for time integration MC No Fully coupled (1) Oil Erosion Kozeny-Poiseuille law and Carman-Kozeny
Chin and Ramos [33 ] 2D and 3D; FE; explicit; NR iteration Drucker-Prager No Coupled (1) Fluid Shear dilation Power law with porosity (exponent = 5.6) Porosity is changed as a function of plastic volumetric strain Nouri et al. [34 ] 2D plane strain; FD Bilinear MC Yes Fully coupled (1) Fluid Tensile failure or shear-failed element falls in tension 0 Capillary is considered as a residual cohesion
Wang et al. [35 ] 2D; FE Drucker-Prager No Fully coupled (1) Solid
Cohesion and friction drop linearly with porosity
Servant et al. [36 ] 2D; FE MC No Iteratively coupled (1) Fluid Yielding Not mentioned Failed material is treated as a Poiseuille fluid.
Detournay et al. [11 ] 2D; FD MC Yes Iteratively coupled (1) Fluid Erosion
Bulk mod. Change by
Nouri et al. [12 ] 2D axial symmetry; FD Bilinear MC Yes Iteratively coupled (1) Fluid Tensile failure or a shear-failed element falls in tension
Nouri et al. [37 ] FE; NR iterations MC Yes Fully coupled (1) Fluid Tension 0 Adaptive mesh is used
Nouri et al. [38 ], Vaziri et al. [14 ] 2D plane strain and axial symmetry; FD Bilinear MC Yes Iteratively coupled (1) Fluid Complete degradation and tensile mean effective stress High permeability is assigned to infill materials (elements that satisfy sanding criteria) WH pulsing is included in the model, and stiffness changes with sanding (Vaziri et al. [14 ])
Detournay [15 ] 2D plane strain; FD Double-yield Yes Iteratively coupled (1) Fluid Same as (Detournay et al. [11 ]) Not mentioned Only cap yielding is considered
Nouri et al. [16 ]
All the features are the same as (Nouri et al. [38 ]) but fracture energy regularization is applied to remove mesh dependency and the calibration of hardening/softening behavior is discussed thoroughly
Kim et al. [17 ] 3D; FD MC Yes Not mentioned (1) Fluid Calculated from force balance on the element N/A (element removal) No calibration parameter to match the experiment is used and yet a good match is observed
Wang et al. [23 ] 2D; FE Soft rock model Yes Fully coupled (1) Fluid Displacement (the materials passing the wellface are removed) K changes as a function of dilation or volumetric strain:
(1) Adaptive mesh
Azadbakht et al. 39 ] 2D, FE for fluid and FD for solid Bilinear MC Yes Sequentially coupled (1) Fluid Erosion K changes linearly with porosityWater effect is considered by reducing the cohesion
