oa Permeability in the thin section

Numerical simulations of fluid flow through 3D pore space can provide accurate estimations for permeability. A digital volume required for these numerical experiments may be obtained directly by microtomography or statistically reconstructed from 2D thin sections. Such a digital pore volume has to be statistically representative of the original rock. However, only small rock fragments, such as drill cuttings, and only 2D images of those may be available in the field. To address this practical constraint, we investigate how permeability can be estimated from small 2D images. We select a number of natural and artificial medium-to-high porosity well-sorted sandstones.            3D microtomography volumes are obtained from each of these physical samples. Then, analogous to making thin sections of drill cuttings, we select a large number of small 2D slices from a 3D scan. As a result, a single physical sample is used to produce hundreds of virtual-drill-cutting 2D images. Corresponding 3D pore space realizations are statistically generated from these 2D images, fluid flow is simulated in 3D, and the absolute permeability is computed. As expected, this permeability does not match the measured permeability of a physical sample, which is due to inherent variations of pore-space geometry among the small images. However, for all the physical samples, a single and clear trend is formed by cross-plotting the simulated permeability versus porosity. This trend is typical for clean sandstone. The simulated permeability of under-representative sandstone fragments does not match the physically measured data. Instead it provides a valid permeability-porosity transform which can be used to estimate permeability if porosity is independently known from well log or seismic measurement.