An elastoplastic model of fluid-saturated porous media

In many engineering problems, such as those found in petroleum and geotechnical engineering, rocks have to be modeled as porous materials saturated with fluid. The solid-phase deformation and fluid-phase diffusion must be fully-coupled. In this study, the coupled rock-fluid system was modeled mathematically, numerically and experimentally. As it is observed that the stress-strain behavior of rock can be strongly nonlinear and path-dependant, the model developed has been extended into the nonlinear plastic range.; A three-dimensional explicit Lagrangian finite-difference code was developed which simulates the elastoplastic behaviors of structures built of soil, rock, or other fluid-saturated porous materials. Accurate and efficient static or quasi-static solutions are obtained using a Lagrangian differencing scheme in space and explicit integration in time with dynamic relaxation. The interaction between skeleton strains and the pore-fluid flow has been fully-coupled into the code by the application of the mixtures theory. Numerical schemes have been developed to perform gradient calculation and explicit time-integration of pore fluid pressure.; The performance of the numerical code has been validated first by some decoupled cases: elastic and plastic tests. The analytic solutions for one-dimension consolidation and Mandel's problem were then derived based on the mixtures theory to verify the numerical algorithm for coupled systems. Thorough testing of the numerical model indicates its validity and capability.; A series of drained triaxial compression tests were performed to study experimentally elastoplastic behaviors and material properties of soft sandstones. A new test, the depletion test, was designed to simulate the rock behavior along the wall of a producing borehole. The mathematical description of the tested rock sample followed either linear elasticity or a Drucker-Prager yield criterion with strain hardening. The numerical simulation of the drained triaxial compression test was successfully carried out.; The numerical tool developed can be a powerful means to solve difficult problems in petroleum engineering, such as sand production, borehole stability, and hydraulic fracturing. Finally, as a sample of application in petroleum engineering, the sand production process was numerically simulated and analyzed.