The Effect of Stress-Dependent Permeability on Gas Production and Well Testing

Abstract

Summary The effect of stress-dependent permeability on gas production and well testing in tight gas sands was studied by use of a modified pseudopressure that included stress dependence. This work assumes that pseudopressure that included stress dependence. This work assumes that information on cores is applicable to reservoir behavior. Because microcracks are the primary path for flow through tight-gas-sand cores, average stress-dependent permeabilities were found as an average over all crack orientations in a nonuniform stress field, with a horizontal stress only 0.6 times the vertical one. Initial in-situ permeabilities are found to be two to five times the values obtained from uniformly restressed cores. Stress dependence decreases initial gas production by at most 30%, with the loss increasing with reservoir depletion. Buildup tests yield reliable results for the properties at average reservoir pressure. Drawdown tests are more sensitive to stress effects and are much less reliable. Introduction It has been known for over 30 years that the permeability of sandstone cores is reduced by an applied, external stress. The effect is greater for lower-permeability cores; tight-gas-sand cores can lose 90% or more of their permeability when restressed to the net reservoir permeability when restressed to the net reservoir overburden stress. The net confining stress on the rock increases as the gas pressure in the reservoir decreases, so the reservoir flow capacity is reduced by gas production. This will also cause anomalous behavior during well tests. The well-test and gas-production behaviors of a stress-sensitive gas reservoir were first studied by Vairogs et al. They developed a reservoir simulator that also calculated the approximate effect of the reactive rock stresses in the reservoir resulting from changes in gas pressure. They showed that a reduction of production rate of as much as 50% was possible. Vairogs and Rhodes found that a permeability obtained from a semilog analysis of a drawdown test was unreliable, while that obtained from a buildup test yielded the permeability at the average reservoir pressure. Their calculated skin was increased by stress dependence. The present work assumes that the stress dependence of cores is characteristic of the reservoir and extends the work of Vairogs et al. and Vairogs and Rhodes by deriving general results for the effect of stress dependence on well test analysis and gas production. production. Stress-Dependent Permeability The stress dependence of permeability in tight-gas-sand cores is controlled by flow through microcracks. Also, the permeability can be well correlated by a Jones-and-Owens-type correlation using the square root of permeability, instead of the cube root, varying linearly with the permeability, instead of the cube root, varying linearly with the log of confining stress. Fig. 1 is an example of a plot of permeability data using such an approach. The stress-dependent permeability of any rock can be characterized by the permeability at initial reservoir stress and by the intercept stress, sigma *, the point at which the fit-line intercepts the pressure axis. The intercept stress is a physical property of the rock that depends on the smoothness of the crack faces. 6 Smoother cracks lead to a lower intercept stress, which causes a larger stress sensitivity. An average value of the intercept stress for the cores examined by Thomas and Wards was 29,600 psi [204 MPa], while the data of Sampath and Keighin yielded an average of 12,800 psi [88 MPa]. Typical values of 15,000 and 30,000 psi [103 and 207 MPa] were used for this study. These values would lead to permeability reductions of 77% and 57%, respectively, if the net stress were raised from 4,000 to 8,000 psi [28 to 55 MPa]. psi [28 to 55 MPa].