Fully Coupled Fluid-Flow/Geomechanics Simulation of Stress-Sensitive Reservoirs
Authors: Osorio Jose G. , Chen Her-Yuan , Teufel Lawrence W. 
Published: December 2007

Abstract
Production of oil and gas reservoirs changes the reservoir pore pressure and stress state. These changes in the pore pressure and in-situ stress cause changes in the volume of both reservoir fluids and the reservoir rock. The prediction of the variation of the fluid volume and rock volumetric deformation, and their interaction and influence on the flow conditions, is essential when examining different operating strategies for stress-sensitive reservoirs.
The simultaneous interaction between changes in the pore pressure and variation in the in-situ stress lead to the coupling of two different, yet fully connected, processes: (1) motion of the pore fluid and (2) deformation of the rock solid skeleton. Any attempt to model the interaction of the rock-fluid system should not separate these two processes.
In this study, a 3D finite-difference model for the simulation of stress-sensitive reservoirs has been developed. The reservoir is treated as a multiphase poroelastic system consisting of a deforming solid skeleton and a moving compressible pore fluid. The governing equations describing the deformation of the solid and the motion of the pore fluid are fully coupled. Solid displacement and fluid pressure are chosen as the primary variables. Discretization is accomplished by using a 15-point and 7-point operators for the solid-displacement and fluid-flow equations, respectively. The resulting system of equations is solved fully implicitly.
Numerical results obtained from the application of this model to a centered-well producing at a constant flow rate from a poroelastic medium have been analyzed. The model parameters used are presented in Table 1. The discretization grid consists of 15 blocks in each x- and y-direction, and 5 blocks in the z-direction, each block having a length of 10 ft.
At the boundaries, the pore pressure is constant and equal to the initial pore pressure, and the displacements are zero.
Fig. 1 shows the pore pressure distribution at 5 and 200 days. After 5 days of production, the radius of investigation has already arrived to the outer boundaries and, consequently, the pressure maintenance at the boundaries has become active. As production time increases, a conventional fluid-flow model will predict, for this particular example, a constant pore pressure distribution with time. In the case of our fluid-flow/geomechanical model a stress-transfer effect is observed. As the solid part of the rock expands, the pore fluid receives the load change caused by the rock expansion. Accordingly, after the radius of investigation reaches the outer boundaries the pore pressure distribution does not remain constant with time, but rises until equilibrium conditions are attained, as observed in Fig.1b after 200 days of production.
Fig. 1a also shows that after 5 days of production, the pore pressure in the region close to the outer boundaries reaches values slightly greater than the initial pore pressure. This behavior is possible because the load caused by the initial expansion of the solid skeleton is higher than the decrease in the pore pressure which results in pressure rises above the initial pressure. After equilibrium conditions are reached, this excess in pore pressure is dissipated as observed after 200 days of production (Fig. 1b).
Besides the pore pressure, the stress state also alters the physical properties (e.g., permeability and porosity) which are important to the performance of stress-sensitive reservoirs. A convenient way of expressing the stress state of the rock is through the effective stress, which is a measure of the "actual" stress acting on the solid part of the porous system. Fig. 2 shows the distribution of the change in the effective stress in the x-direction (compressive stress is taken negative). Note that after 5 days of production (Fig. 2a), the change in effective stress (with respect to the initial effective stress) switches from compression to extension. The region under compressive stress is due to production and, therefore, is located around the wellbore where the pore pressure is always minimum. The region in extension is close to the outer boundaries where zero-displacement is specified. After 200 days of production, the increment in pore pressure (caused by the pressure maintenance and the load received from the rock expansion) reduces the magnitude of the change in the effective stress in the tensile region (Fig. 2b).