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Technische Universität München St. Petersburg Polytechnical University Joint Advanced Student School (JASS) FEM study of the faults activation Author: Ulanov Alexander
Problem significance Geomechanics application: - Subsidenceof rocks - Sliding of bed near oil well
Аrea of study • Faults activation in deforming saturated porous medium.
Particularity Parameters of the media may discontinue Nonlinear problem Interface (contact) element concept Examples of the elastic bodies (3D case and 2D case) with the possible surfaces of slipping.
Goals and objectives • Simulation of joint transient process of diffusion porous pressure and stress state calculation in saturated porous medium.
Our estimates Saturation porous medium - combinationof pore space, deformableskeleton and moving fluid. Examples:sandstone,clay. Еstimates: - Darcy's law for fluid. - Fluidis compressible. • Porous mediumis isotropic • and linear. -Small deflection.
Coupled solution for saturated one-phase flow in a deforming porous medium Continuity equation: Biot 1955 p -pore pressure u - displacement vector Equilibrium equation: G- shear modulus k -coefficientof permeability μ - viscosity of the pore fluid
Variational formulation (part 1) Variational formulation of equilibrium equation Ω – domain in 2D(3D) space; S - boundary; n – external normal
Variational formulation (part 2) Variational formulation of continuity equation
Interface model Sc – surface of contact
Interface element concept Characteristics of interface layer elements: -infinitesimal thickness - permeabilityD -stiffness C Goodman 1968
Slip computation Slipping condition(Mohr-Coulomb) : σn - normal stress σs - shear stress K -friction coefficient StiffnessС: СH- cohesion stress Iterative process: 1 Calculation of strain state. If contact element is sliding Cs =0 2 Slip conditional test. 3Calculation of strain with new stiffnesses form.
Program structure Geometry and Grid generation • Ansys ICEM • Gambit Solution of problem • FEM solver • Optimization of data ( sparce-matrix ) • Iteration lib (ITL MTL) Processing and result аnalysis • GID • Tecplot10
Domain example (1) Mesh generationinGambit (format .CDB ) GID output
Domain example (2) Mesh quality adaptation
Results No interface (slip) zone Modelling of sliding - Diffusioneffect • Influence of cohesionCoh • Influence of permeabilityk • Influence of nonuniform permeabilityD
No interface (slip) zone. Diffusioneffect • - Pressure on lateral side is fixed • - Zero-initial condition for pressure • -No fluid flux in normal direction Establishment of linear pressure distribution
Influence of cohesion (Coh) • Fixed pressure • Fixed permeabilityk • External load • Slipping condition Relative displacement of interface layer
Influence of permeabilityk - Fixed valueof cohesion - Different value of permeability k - External load - Diffusioneffect ( P = constant )
Effect of nonuniform permeability Destruction of rock in contact layer – Slip zone in contact layer kis–isotropicpermeability ( no slip case ) kslip– additional component ( appear in slip case )
Influence of nonuniform permeability ( part 1 ) • - Different valueofDs • - Establishment of linear pressure distribution • - Zero-initial condition for pressure • - Zerodisplacement • - Sliding on all contact layer
Influence of nonuniform permeability ( part 1 ) Ds=1 Ds=10 Ds=100
Influence of nonuniform permeability ( part 2 ) • - Establishment of linear pressure distribution • - Zero-initial condition for pressure • - External load • - Ds=100
Conclusions The model of coupled solution for saturated one-phase flow in a deforming porous medium is considered. Goodman interface element concept is used. Influence of various parameters on sliding is investigated .