Prediction of Production-Induced Changes in Reservoir Stress State Using Numerical Model
Authors: Khan Mashiur , Teufel Lawrence W. 
Published: December 2007

Abstract
The uniaxial strain model commonly used to predict in situ horizontal stresses and the stress path followed by a reservoir during production and pore pressure drawdown is often significantly different than measured in situ stresses. A geomechanical model using the finite element method that incorporates geologic and geomechanical parameters is being developed to more accurately predict the reservoir stress path. Numerical results show that reservoir stress path is dependent on the size and geometry of the reservoir and elastic properties of the reservoir rock and bounding formations. In general, stress paths become lower as the aspect ratio of reservoir length to thickness increases. Lenticular sandstone reservoirs have a higher stress path than blanket sandstone reservoirs that are continuous across a basin. This effect is enhanced when the bounding formations have a lower elastic modulus than the reservoir and when the reservoir is transversely isotropic. In addition, laboratory experiments simulating reservoir depletion for different stress path conditions demonstrate that stress-induced permeability anisotropy evolves during pore pressure drawdown. The maximum permeability direction is parallel to the maximum principal stress and the magnitude of permeability anisotropy increases at lower stress paths.

Introduction
Matrix permeability and pore volume compressibility are fundamentally important characteristics of hydrocarbon reservoirs because they provide measures of reservoir volume and reservoir producibility. Laboratory studies have shown that these properties are stress-sensitive and are usually measured under hydrostatic (isotropic) loads that do not truly reflect the anisotropic stress state that exists in most reservoirs and do not adequately simulate the evolution of deviatoric stresses in a reservoir as the reservoir is produced. Recent laboratory studies have shown that permeability and compressibility are dependent on the deviatoric stress and change significantly with reservoir stress path (defined as the change in effective horizontal stress/change in effective overburden stress from initial reservoir conditions during pore pressure drawdown). In situ stress measurements in carbonate and clastic reservoirs indicate that the reservoir stress path is not isotropic loading (equal to 1.0) and can range from 0.14 to 0.76. The measured reservoir stress paths are also inconsistent with the elastic uniaxial strain model commonly used to calculate horizontal stress and changes in horizontal stress with pore pressure drawdown. The calculated, uniaxial strain stress path can be significantly less or greater than the measured stress path.
Knowledge of the stress path that reservoir rock will follow during production and how this stress path will effect reservoir properties is critical for reservoir management decisions necessary to increase reservoir producibility. However, in situ stress measurements needed to determine reservoir stress path are difficult and expensive to conduct, and may take several years to collect. Various analytical models have been proposed to calculate in situ horizontal stresses and could be applied to the prediction of reservoir stress path during pore pressure drawdown.