Direct Prediction of the Absolute Permeability of Unconsolidated and Consolidated Reservoir Rock

Abstract

Abstract A procedure of estimating the absolute rock permeability directly from a microscopic 3D rock image has been developed. Both computer-tomography and computer- generated images of reconstructed reservoir rock samples can be used as input. A physics-based depositional model serves to reconstruct natural sedimentary rock, and generate 3D images of the pore space at an arbitrary resolution. This model provides a detailed microstructure of the rock, and makes it possible to calculate the steady state velocity field in the single-phase fluid flow. In particular, using our model, one can analyze unconsolidated rocks whose micro-tomographic images cannot be obtained. The lattice-Boltzmann method is used to simulate viscous fluid flow in the pore space of natural and computer-generated sandstone samples. Therefore, the permeability is calculated directly from the sample images without converting them into a pore network or solving Stokes' equation of creeping flow. We have studied the effect of compaction and various styles of cementation on the microstructure and permeability of reservoir rock. The calculated permeability is compared with the Kozeny-Carman formula and experimental data. Introduction The quantitative prediction of the continuum flow descriptors of porous media, such as the absolute permeability, the relative permeabilities, the capillary pressures, the formation resistivity, etc., is essential in earth sciences and - in particular - in petroleum engineering. Usually, the theoretical prediction of the absolute rock permeability is performed in two steps:A model of the rock microstructure is formulated, anda discretized field equation, such as Poisson's or Stokes' equation, is numerically solved on this model.1 Rock flow properties cannot be predicted without an accurate 3D representation of the rock microstructure. Several approaches have been proposed to reconstruct the 3D microstructures of natural rock:Experimental;2–6Statistical;7–12 andProcess- or physics-based.13–18 The experimental approach is necessary, but it is time- consuming, expensive, and not applicable to damaged core material or drill cuttings. As an alternative, computer- based rock models have become increasingly attractive, because of their low cost and high speed, as well as the ability to overcome the present resolution constraints of experiment. Quantitative comparisons between computer- generated and microtomographic rock images have shown that the process-based models reproduce the 3D geometry of natural sedimentary rock much better than the stochas- tic models. The process-based models are also superior in their predictions of the pore space connectivity1,19–21 and, thus, the rock permeability.22,23