ELASTIC AND PLASTIC STRESSES IN A POROUS MEDIUM CONTAINING SPHERICAL OR CYLINDRICAL CAVITIES
AbstractThe influence of pore fluid flow on the elastic and plastic stresses in a porous material may be determined for a solid body containing a large spherical or cylindrical cavity.
A description of the stresses in porous media relies on a separation of the total stress into effective and neutral parts. In the elastic case, the effective stress is that part of the total stress that determines the deformation of the porous solid. The application of Drucker's postulate to a mixture of a solid and a fluid under homogeneous deformation results in a plastic flow rule written in terms of the total stress.
The elastic or plastic state of stress in the porous solid surrounding a spherical or cylindrical cavity is significantly affected by a nonuniform pore pressure distribution. For a plastic material obeying a quadratic yield condition, pore fluid flow into a spherical cavity reduces the mean compressive stress in the solid and may lead to cavity expansion. For an elastic material, pore fluid flow into a cylindrical cavity may initiate yielding in the porous solid at an unsupported, fully supported, or partially supported cavity boundary. Application of these analyses to the rock surrounding a perforated casing in a hydrocarbon reservoir gives an estimate for the well pressures that precipitate initial yielding and the production of solid material.
Several other problems related to the behavior of rock around a perforated casing may be investigated using elasticity, plasticity, and potential flow theory. An elastic porous cylinder under uniform overburden loading represents more closely the physical boundary conditions in a reservoir than the conventional plane strain analysis. Mechanical loads required for the extrusion of a porous solid are significantly reduced by simultaneous pore fluid flow through the extruded material. Finally conformal mapping provides a simple approximate description of the pore pressure distribution around a slotted casing