Abstract:
Knowledge of Biot poroelastic coefficient is crucial to geoscientists for a number of applications, including oil and gas exploration and production, and hydrogeology. This in turn requires estimation of bulk and grain modulus or compressibility. Although bulk modulus estimation is a standard laboratory method for shale, no effort was made till date to directly measure grain compressibility in the laboratory. This paper presents a laboratory study to fill this gap. The experimental program described here starts with validation of the technique using aluminum sample. Following this, one Berea sandstone and one shale sample was tested. Finally, using the measured data, Biot coefficient was estimated for shale. General agreement with published literature was observed. However, since none of the reported data was obtained through laboratory measurement, further measurements need be performed for shale and other reservoir rocks.
Introduction
During deposition and diagenesis, cracks and pores are created in subsurface strata. These void spaces or porosity are in turn occupied with one or more fluid phases ranging from water to liquid or gaseous hydrocarbon depending on depositional/post-depositional environment. Intuitively, the mechanical behavior of subsurface strata filled with fully or partially saturated pore spaces differs from that of a rigid or non-porous rock. The extraction of hydrocarbon results into change in pore fluid pressure in subsurface strata. The processes of drilling and completion impact the existing in situ stress field. This is further complicated when intentional/unintentional production of hydrocarbon occurs as the resulting change in pore pressure once again affects the stress field. The effects of pore pressure change on the deformation around a borehole (Detournay and Cheng, 1988), hydraulic fracturing (Detournay et al., 1989) and slip along active faults (Rudnicki and Hsu, 1988) have been reported earlier. To fully understand this, the theory of effective stress was first proposed by Carl Terzaghi on one-dimensional consolidation of soil which was later extended to three-dimension by Biot (1941). Following this, Geertsma (1957) and Skempton (1961) separately defined the expression for effective stress for a fully saturated material, which was later mathematically derived by Nur and Byerlee (1971). In their work, effective stress is expressed as:
(equation)
(equation)
where Pe, Pt and Pp are effective, total and pore pressure, respectively, a is Biot coefficient and K and Ks are bulk and grain modulus. Biot coefficient was subsequently utilized in estimating insitu stress (Thiercelin and Plumb, 1994) as well as in wellbore stability analysis and hydraulic fracture design (Cheng et al, 1993). As revealed in Eq. (2), it requires estimation of both bulk and grain modulus. This in turn involves saturating the rock material with pore fluid which presents a challenge for fine-grained rock like shale. The complex pore structure and nanometer range pore diameter of shale makes the saturation a shale sample in the laboratory significantly longer, making the test protocol impractical. This paper explores an alternative laboratory technique which is simply a variant of the unjacketed compressibility test. The paper begins with a description of the experimental technique in detail. This is followed by presenting the results conducted using an aluminum cylinder, the purpose of which is entirely validation of the experimental technique. The presentation is concluded by reporting results on Berea sandstone and shale and estimating Biot's coefficient for those samples. The results presented here indicates usability of the technique in estimation of grain modulus and hence, Biot coefficient, for shale. The readers should note that as shown in Eq. (2), Biot coefficient is estimated using modulus instead of compressibility, it's reciprocal. Similarly, all laboratory measurements presented in this paper report a modulus value and one can estimate compressibility from them.
