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Non-Destructive Techniques to Determine the Effective Stress Coefficient of Sandstone Formations

The concept of effective stress coefficient, "n," is critical for the study of stress and pressure-dependent behaviour of rocks. This parameter is used to scale the pore fluid pressure for the computation of effective stress and impacts on the accuracy of pore pressure and saturation predictions in reservoirs. However, "n" is relatively unknown and difficult to estimate and, in many cases, is often incorrectly assumed to be equal to one. We present a general review of "n" and give a theoretical proof that "n" is less than one for porous rocks. We also introduce a laboratory methodology to measure the value of "n" employing ultrasonic P-wave velocity (V p ) and attenuation quality factor (Q p ). We then confirm the value of "n" experimentally by using this laboratory method to estimate "n" of quartz sandstone. We compare our experimental value of "n" to both theoretical and practical results obtained from other literature that used different estimation methodology. We argue from our experimental results that: i) "n" is not one but varies from zero to one; ii) there is no single value of "n" for a particular reservoir rock; iii) "n" depends on internal factors (porosity and pore geometry) and external factors (pore pressure and confining pressure) of the rock; iv) velocity derived "n" and quality factor derived "n" are slightly different for the same rock; and, v) for the quartz sandstone used in this experiment, the velocity derived "n" is smaller and also less sensitive to changes in pressure than quality factor derived "n."