Drained pore modulus and Biot coefficient from pore-scale digital rock simulations

Abstract

We present a digital rock workflow to determine poroelastic parameters which are difficult to extract from well-log or laboratory measurements. The drained pore modulus is determinant in the compaction problem. This modulus represents the ratio of pore volume change to confining pressure when the fluid pressure is constant. In laboratory experiments, bulk volume changes are accurately measured by sensors attached to the outer surface of the rock sample. In contrast, pore volume changes are notoriously difficult to measure because these changes need to quantify the pore boundary deformation. Hence, accurate measures of the drained pore modulus are challenging. We simulate static deformation experiments at the pore-scale utilizing a digital rock image. We model an Ottawa F-42 sand pack obtained from an X-ray micro-tomographic image. This image is segmented into a network of grains and pore space. The network of grains is taken as an elastic, isotropic and homogeneous continuum. We then compute the linear momentum balance for the network of grains. We calculate the change in pore volume using a post-processing algorithm, which allows us to compute the local changes in pore volume due to the applied load. This process yields an accurate drained pore modulus. We then use an alternative estimate of the drained pore modulus. We exploit its relation to the drained bulk modulus and the solid phase bulk modulus (i.e., Biot coefficient) using the digital rock work- flow. Finally, we compare the drained pore modulus values obtained from these two independent analyses and find reasonable agreement.