Utilizing a modified Cam clay cap model, we have transformed laboratory measurements of the stress-dependency of unconsolidated deformation to reservoir space (i.e., in terms of in-situ stress and pore pressure) such that changes in both stress and strain can be assessed as a function of depletion. In previous studies, this transformation, which we term Deformation Analysis in Reservoir Space (DARS), has been performed based on static laboratory experiments. Although this static approach yields a reasonable first order approximation of total deformation, it fails to capture the effects of the change in production rate and the time-dependency of inelastic deformation associated with depletion in unconsolidated reservoirs. To address time-dependent deformation (e.g., creep strain), we have incorporated Perzyna viscoplasticity theory to the modified Cam clay cap model. Following the procedure described by Hagin and Zoback in the accompanying paper, the threshold compaction pressure as a function of strain rate is determined from basic hydrostatic compression tests. As strain rate can also be expressed as a function of production rate, the static DARS can now be extended into a dynamic formalism that predicts the change in physical properties such as porosity reduction, permeability reduction and changes in rock properties associated with production.
In a depleting reservoir, the reduction in pore pressure can induce marked reductions in porosity leading to compaction (and possibly subsidence), and potentially significant reductions in permeability. Thus, understanding the relationship between production, compaction and permeability loss is an important factor in reservoir management. For most weak sand reservoirs, both elastic and inelastic deformations occur during production. While most reservoir deformation models are based on poroelasticity theory, the impact of viscoplasticity on reservoir deformation cannot be ignored [e.g., 1,2]. In this paper, we will first review standard formalism we termed as Deformation Analysis in Reservoir Space (DARS) in previous studies . Incorporating the viscoplastic theory, we will then extend the standard DARS from a static analysis to a dynamic analysis that characterizes both instantaneous and time-delayed deformations in terms of reservoir compaction and the associated permeability changes. We will also present a plausible relationship between porosity reduction and permeability change during reservoir depletion based on laboratory experiments. This relationship will then be applied to our case studies to demonstrate how permeability can be estimated in a producing reservoir.
A number of laboratory studies of the dependency of permeability on porosity, stress and deformation mechanism have been published. Zhu and Wong  suggested that permeability and porosity changes for most low-porosity sandstones closely track one another in the cataclastic flow regime. However, a drastic change in permeability was triggered by the onset of shear-enhanced compaction once the sample is loaded beyond the elastic domain into the plastic deformation domain in the reservoir stress space. The effects of plastic deformation and permeability alteration can be extremely significance in reservoir simulations of a highly compressible reservoir . another in the cataclastic flow regime. However, a drastic change in permeability was triggered by the onset of shear-enhanced compaction once the sample is loaded beyond the elastic domain into the plastic deformation domain in the reservoir stress space.