Summary
Reservoir stress path is defined as the ratio of change in effective horizontal stress to the change in effective vertical stress from initial reservoir conditions during pore-pressure drawdown. Measured stress paths of carbonate and sandstone reservoirs are always less than the total stress boundary condition (isotropic loading) and are either greater or less than the stress path predicted by the uniaxial strain boundary condition. Clearly, these two boundary-condition models that are commonly used by the petroleum industry to calculate changes in effective stresses in a reservoir and to measure reservoir properties in the laboratory are inaccurate and can be misleading if applied to reservoir management problems. A geomechanical model that incorporates geologic and geomechanical parameters was 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 on 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 studies1–3 have shown that permeability and compressibility are dependent on the deviatoric stress and change significantly with reservoir stress path. 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. 4 The measured reservoir stress paths are also inconsistent with the elastic uniaxial strain model5 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.4
Knowledge of the stress path that reservoir rock will follow during production and how this stress path will affect 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 they could be applied to the prediction of reservoir stress path during pore-pressure drawdown.5–9 However, none of these models addresses all of the essential geological and geomechanical factors that influence reservoir stress path, such as reservoir size and geometry or the coupled mechanical interaction between the reservoir and the bounding formations. Accordingly, a geomechanical model was developed to more accurately predict reservoir stress path. The model incorporates essential geological and geomechanical factors that may control reservoir stress path during production.
In addition, laboratory results showing the effect of reservoir stress path on permeability and permeability anisotropy in a low-permeability sandstone are also presented. These experiments clearly demonstrate that during pore-pressure drawdown permeability decreases and that permeability parallel and perpendicular to the maximum stress direction decreases at different rates. The smallest reduction in permeability is parallel to the maximum principal stress. Consequently, stress-induced permeability anisotropy evolves with pore-pressure drawdown and the magnitude of permeability anisotropy increases at lower stress paths.
Field Measurements of Stress Path in Lenticular Sandstone Reservoirs
Salz10 presented hydraulic fracture stress data and pore-pressure measurements from reservoir pressure build-up tests in low-permeability, lenticular, gas sandstones of the Vicksburg formation in the McAllen Ranch field, Texas (Table 1). This work was one of the first studies to clearly show that the total minimum horizontal stress is dependent on the pore pressure. Hydraulic fractures were completed in underpressured and overpressured sandstone intervals from approximately 3100 to 3800 m. Some of the sandstones (9A, 10A, 11A, 12A, 13A, and 14A) were later hydraulically fractured a second time to improve oil productivity after several years of production.
For initial reservoir conditions before production, the total minimum horizontal stress shows a decrease with decreasing pore pressure for different sandstone reservoirs. The effective stress can also be determined from these data. Following Rice and Cleary11 effective stress is defined by
σ = S − α P , ( 1 )
where ? is the effective stress, S is the total stress, ? is a poroelastic parameter, and P is the pore pressure. For this study ? is assumed to equal unity. A linear regression analysis of the minimum horizontal and vertical effective stress data shows that at initial reservoir conditions the ratio of change in minimum effective horizontal stress to the change in effective vertical stress with increasing depth and pore pressure is 0.50.
Experimental Study of Silty Clay Plane Strain Tri-axial Test under RTC Path and Modified Cam-clay Model
