The Eshelby like approach has been used to successfully model the stress, strain and displacement fields associated with a depleting reservoir. A modified Cam-Clay material model was implemented for the constitutive equations for the reservoir material. The exterior of the reservoir is modeled as an infinite homogeneous linear elastic material. Body forces are not considered. These assumptions allow an semi-analytical approach to be applied. Applications of this approach include “quick look” solutions for well failure estimates, evaluating time-lapse seismic candidates, effects of reservoir tilting, CO2 sequestration, estimates of fault activation etc. Here we discuss the use of the model to investigate how the external stress field of a depleting reservoir effects fault activation exterior to the reservoir. This is accomplished by running the model to determine the stress and strain fields induced in the elastic host by the depleting reservoir. The fault is then represented as an elastic-plastic (modified Cam-Clay) ellipsoidal inclusion imbedded in the host stress field calculated in the first step. Two initial conditions are considered for the fault material model. First where no constraints are applied and the initial material model is an input from the user. Second where the fault is assumed to be in the vicinity of the critical state line. The implications of these two assumptions are disused. Three mechanisms are discussed as criteria for fault activation. Runaway instability and negative rate of plastic work are criteria for determining when the material significantly weakens. Runaway instability is equivalent to the scenario when uncontrollably growing strains develop inside the fault. Negative rate of plastic work represents the case when the model predicts that the fault delaminates from the host material. Strain localization is beyond the scope of this paper and will be addressed in a later paper. The criteria for fault reactivation is sensitive to fault, reservoir, and host material properties and their contrast. The orientation and spacing of the reservoir and fault and their impact on fault reactivation are explored and found to be critical. However, the aspect ratio of the fault is not a critical parameter.
For both the reservoir and the fault, an ellipsoidal geometry is assumed. They are embedded in a host matrix and the Eshelby theorem [1] is employed. This theorem relates the inelastic strain rates (eigenstrain rates) in the reservoir to the total strain rates via the “Eshelby tensor” which depends only on the ellipsoidal geometry of the reservoir and host matrix Poisson's ratio. This approach leads to a system of differential equations for the evolution of the internal stress and strain fields due to pressure depletion which is to be explicitly derived. The independent variable (the loading parameter) is the depletion pressure in the reservoir. A similar relation has been derived for the exterior stress and strain field [2]. Continuous traction and displacements are assumed at the interface between the reservoir and the host rock. The reservoir and the fault are assumed to be noninteracting in the calculations.
