Theory of Plasticity of Porous Media With Fluid Flow (1974)

Abstract Plastic deformation of a porous medium containing moving fluid is analyzed as a motion of a solid-fluid mixture. The fluid is considered to be Newtonian, and the porous material consists of interconnected pore spaces and of solid particles that can deform pore spaces and of solid particles that can deform elastically. The effective stress principle and a general form of the yield function-including work-hardening characteristics-and general stress-strain relations are applied to describe the plastic deformation of the solid. The system of plastic deformation of the solid. The system of governing equations with the number of unknowns being equal to the number of equations is formed. A possible method of solution of a general problem is described. Some simplification such as problem is described. Some simplification such as the assumptions of quasi-static plastic deformation and incipient plastic deformation with the application of Darcy's law for the fluid flow are discussed. To illustrate an application of the theory, the problem of incipient plane plastic deformation of a Coulomb material is presented. Introduction The motion of fluid through a porous medium and the deformation of a porous medium containing fluid have been the subjects of many investigations. For problems concerning fluid flow through porous media in petroleum and civil engineering literature, the porous material is usually considered undeformable and Darcy's law is taken as the governing relation between the velocity and the pressure of the fluid. pressure of the fluid. Most of the effort concerning fluidization of porous media has been experimental; here the task porous media has been experimental; here the task is to find the critical pressure gradient or the critical velocity of the fluid that will cause fluidization. Only the one-dimensional equilibrium equation, which relates Ne pressure gradient of the fluid and densities of solid and fluid, has been analyzed in most fluidization studies. Recently, a more general theoretical approach has been taken and equations of motion of fluid and solid have been established. Some of the results of this theory are used in the present study. Previous investigations of the deformation of porous media containing fluid have been both porous media containing fluid have been both empirical and theoretical. In the domain of elastic deformation much of the published material has dealt with experimental work aimed at finding the relation between a change in fluid pressure and stresses and deformation of the solid phase. A general theory of elasticity of porous media containing moving fluid was established by Biot. However, that theory is approximate since Darcy's law is considered as a governing relation for the fluid, and the change of permeability with the deformation of the solid is neglected. A simplification of this theory was presented by Lubinski. Experimental work has been carried out in the domain of plastic deformation of porous media containing fluid. The effective stress principle has been established as a result of experiments using saturated sand and porous rocks with various pore pressures (fluid is static in these experiments. pressures (fluid is static in these experiments. This principle, which is considered as a fundamental principle in soil mechanics, states that the pore principle in soil mechanics, states that the pore pressure does not affect the yield criterion of the pressure does not affect the yield criterion of the solid. In other words, the yield condition of the solid depends only on stresses transmitted among the solid particles. The influence of fluid flow on plasticity of porous media was indicated by Lambe and Whitman porous media was indicated by Lambe and Whitman in the analysis of stability of an infinite slope of a soil. In the equilibrium equation of a so-called "free body" a term equal to the negative pressure gradient is added. There is no general theory for plasticity of porous media containing moving fluid. plasticity of porous media containing moving fluid. GENERAL THEORY Consider the motion of a solid-fluid mixture and suppose that the motion of the solid is a plastic deformation. Then the problem reduces to the following: define the motion of a solid-fluid mixture so that the yield criterion of the solid is satisfied. The mechanical model can be described as follows. 1. The system comprises one fluid and one should constituent. SPEJ P. 263