Effect of Rock Stress on Gas Production From Low-Permeability Reservoirs
Authors: Vairogs Juris , Hearn C.L. , Dareing Donald W. , Rhoades V.W. 
Published: December 2007

The effect of stress on permeability has been incorporated into a mathematical model for gas flow based on a theoretical analysis of the stress state around a wellbore. Example calculations show that permeability reduction due to stress can significantly affect the permeability reduction due to stress can significantly affect the production characteristics of wells in tight gas reservoirs. production characteristics of wells in tight gas reservoirs.
Introduction
The decline in gas reserves has stimulated widespread interest in gas-bearing formations previously considered to be uneconomic because of extremely low permeability. Routine core analyses have indicated permeabilities in many such reservoirs on the order of 0.1 md and lower. Wells in such reservoirs have been proposed as candidates for nuclear or high-explosives stimulation to increase production rates. production rates. In investigating the flow behavior of wells in tight gas reservoirs, it has been observed that measured flow rates are sometimes much lower than predicted by transient gas flow equations based on Darcy's law. Several plausible explanations for this discrepancy have been offered.
Errors may be caused by deviation from the usual simplifying assumptions such as reservoir homogeneity, open-hole completions, and single-phase flow. Non-Darcy effects due to high gas velocity near the wellbore may restrict flow. Liquid from retrograde condensation or formation of gas hydrates can reduce permeability; however, the ranges of the temperature, pressure, and gas composition necessary for this to occur are usually not encountered in low-permeability gas reservoirs.
This paper discusses a mechanism that may have a significant effect on production from tight gas reservoirs - reduction of permeability due to rock stress. Lowering of pore pressure as gas is produced increases the confining stresses on the reservoir rock, causing it to compact. The compaction causes reduction of the effective pore diameters, resulting in a decreased permeability. This effect has been studied by several permeability. This effect has been studied by several authors. These studies covered both clean and shaly sandstones. Confining pressures were applied hydrostatically and with different pressure applied to the sides of the core than to the ends. Only one set of data was reported for a core of less than 0.1 md permeability. The effect of stress on this core with permeability. The effect of stress on this core with very low permeability was much greater than the effect on the others. A possible explanation for this is that very tight cores have smaller pore radii. Increasing the compressive stress applied to pores of small radius could decrease their flow capacity proportionately more than that of larger pores. proportionately more than that of larger pores. This study was conducted
to confirm the conclusions of previous work, and to demonstrate experimentally that permeability reduction is proportionately greater in low-permeability than in proportionately greater in low-permeability than in high-permeability cores; to incorporate the stress effect into a mathematical model for reservoir gas flow; and to use this model to check the extent of production decrease that might be expected because of production decrease that might be expected because of permeability's sensitivity to stress. permeability's sensitivity to stress.

Laboratory Measurements of Stress Effect on Permeability
A schematic diagram of the experimental apparatus is shown in Fig. 1. Basically it consisted of a cell for applying pressure to cylindrical cores, a nitrogen source for permeability measurement, pressure gauges, and a flow meter. The core samples were 2 in. long and 2 in. in diameter.
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