Influence of Reservoir Stress Path on Deformation and Permeability of Weakly Cemented Sandstone Reservoirs
Authors: Ruistuen H. , Teufel L.W. , Rhett D. 
Published: December 2007

Abstract
The influence of production-induced changes in reservoir stress state on compressibility and permeability of weakly cemented sandstones has been analyzed. Laboratory experiments simulating reservoir depletion have been conducted for the full range of stress paths that a reservoir may follow. Samples were loaded by reducing the pore pressure and controlling the confining pressure according to the desired stress path from initial reservoir conditions. The results show that compressibility of weakly cemented sandstones are stress path dependent. Compressibilities measured under uniaxial strain conditions, or a stress path with a K value lower than the one associated with uniaxial strain, are more than twice the corresponding value found under hydrostatic loading conditions. In contrast, matrix permeability measured in the maximum stress direction show no significant stress path dependence. Independently of stress path, the observed permeability reductions fall within the general trend expected for a sedimentary rock of relatively high initial permeability. A significant permeability decrease was only observed as the shear stress exceeded the yield limit of the rock, probably due to both mobilization of fine grains and an increase in tortuosity due to collapse of pore space. Results of this study suggest the stress path dependent properties of weakly cemented sandstones is a consequence of the heterogeneous nature of the sedimentary rock. Material properties are affected by grain- scale inelastic deformation processes and the pattern of these deformation processes is primarily controlled by reservoir stress path.

Introduction
Reliable data on rock compressibility and matrix permeability are essential in reservoir engineering due to their impact on reserves and productivity calculations. Laboratory measurements of rock compressibility are applied to production forecasts, reservoir pressure maintenance evaluations as well as reservoir compaction and subsidence studies, while matrix permeability heavily influences reservoir productivity and injectivity and is essential in performance forecasting.
Formation compressibility is defined as the in situ pore volume strains that follows changes in reservoir pore pressure:
By adopting this definition, formation compressibility is not related to specific stress conditions. Formation compressibility is simply defined as the bulk response of the reservoir rock to production induced changes in effective stress state. These stress changes are uniquely defined by reservoir characteristics such as boundary conditions, reservoir geometry and the mechanical properties of the reservoir rocks. A common procedure within the oil industry has been to use the so-called uniaxial correction factor (Teeuw) to correct the results obtained from the hydrostatic compressibility test to "formation compressibility":
This relationship simply redefines formation compressibility from being the volumetric response of the rock to instead equal to the coefficient of uniaxial compaction. An inherent assumption in this procedure is that the rock is elastic throughout its production-induced deformation history, which may not be the case for weakly cemented reservoir rocks. The validity of the procedure also relies on the assumption that the uniaxial strain model adequately simulates reservoir conditions during depletion.
P. 463