A quantitative model of fault reactivation due to depletion of hydrocarbon reservoirs has been developed based on accurate mechanical modeling. We represent the reservoir by a thin poroelastic inclusion in a poroelastic matrix and analyze the effect of depletion on fault stability for the general case of non-uniform pressure distributions and reservoir shape. Expressions for stresses inside and near a depleting reservoir have been developed in closed form based on asymptotic analysis and using complex potentials. We consider the case of heterogeneous formations and demonstrate the importance of taking into consideration the difference between material properties of the reservoir and the surrounding rock while considering the poroelastic effect on fault stability. We have identified dimensionless combinations of rock properties that control the fault response to reservoir depletion.
1. INTRODUCTION
Geological discontinuities such as faults are inherent in most petroleum formations [1]. There are a number of human activities, such as hydrocarbon production, that can sufficiently alter the in-situ stresses within a period of a few years or even a few months resulting in reactivation and slip of the nearby faults. Fault reactivation due to reservoir depletion may have various consequences ranging from shearing boreholes drilled through the fault zone [2] to inducing seismicity [3] to drastically affecting the formation permeability [4, 5]. Stress state perturbation resulting from subsurface fluid extraction clearly and robustly demonstrates the importance of the poroelastic effect (in this context first suggested probably in [6]).
The increasing number of induced seismicity and well damages initiated great interest in studying the mechanics of fault reactivation, ground subsidence, reservoir deformation, and in-situ stress changes caused by fluid withdrawal [3-6]. In most cases, the reservoir has been treated as a (partially) drained poroelastic inclusion surrounded by an elastic host material. Usually two approaches are implemented: (1) the reservoir is modeled by an inclusion with a rather arbitrary pore pressure distribution but with the same material properties as the surrounding rock matrix [3, 6]; (2) the reservoir is modeled as a uniformly pressurized homogeneous ellipsoidal inclusion with material properties different compared to the surrounding rock [4, 5]. The first approach is based on a homogeneous formation and accounts for the principle reason for stress redistribution around depleted reservoirs, i.e., a change in the reservoir pore pressure. The second approach, utilizing an ellipsoidal inclusion, accounts for another important factor of material inhomogeneity, but considers uniform pressure distribution inside the reservoir.
In the previous papers by the authors [7, 8], both non-uniform reservoir pressure and material inhomogeneity were taken into account in the model. However in those papers, the emphasis was on the fault stability outside a depleting reservoir. In this paper, fault stability inside and near the boundaries and edges of a depleting reservoir has been analyzed. In the previous papers, stresses were evaluated numerically outside the reservoir. In this paper, expressions for stresses have been developed in closed form based on asymptotic analysis [9] and complex potentials [10]. This allowed us to consider a full range of fault positions, inclinations, and strength parameters as well as poroelastic properties of the depleting reservoir and surrounding rock.
