Coupled wellbore erosion and stability analysis

This paper extends earlier work(1) on sand erosion and presents an attempt to couple sand erosion to mechanical damage of rock around a wellbore. Porosity which evolves in time and space as surface erosion progresses, is chosen as the coupling parameter. Both rock elasticity and strength (cohesion) are assumed to depend on porosity in such a way that the material becomes weaker with increasing porosity. The mathematical model, consists of erosion equations, mixture flow equations and stress equilibrium equations, is solved numerically by Galerkin finite element method. Numerical results suggest that erosion, resulting in sand production, is high close to the free surface. Erosion is accompained by changes in porosity and a significant permeability increase. Erosion in the vicinity of the wellbore induces alterations in the mechanical behaviour of the medium. Weakening of rock stiffness leads to severe alteration of both effective stresses and pore pressure near the cavity. Since cohesion decreases with increasing porosity, one can also identify the time instant at which rock mechanical failure starts. (C) 1998 John Wiley & Sons, Ltd.