Permeability calculations in unconsolidated homogeneous sands

Abstract

Permeability, k, is a property of a porous medium that measures the capacity and ability of the medium to transmit fluids. The permeability of a porous medium (porous rock, soil, packing) can be predicted using empirical relationships, capillary models, statistical models, and hydraulic radius theories. It generally has been recognized that grain size is the fundamental independent variable that controls permeability in unconsolidated sediments [Shepherd, R. G. 1989].Sub-pore scale modeling is used in this study to evaluate the relation between grain size distribution and permeability of the porous media. In this method the governing equations are applied directly on the porous medium images. The meshing algorithm is applied directly on the pore and grain sections of the images, and the studied mechanism is simulated at the level of pores and grains. Virtual porous media are generated using regular packings of uniforms spheres. The permeability of each packing is calculated computationally and then compared to the predictions of the Kozeny-Carman equation. An in-house developed pattern generator is used to generate spherical grains packing with pre-specified particle size distributions. A sub-pore scale modeling approach is used to calculate permeabilities of generated virtual porous media. The equivalent diameters that provide match from the Kozeny-Carman equation are then predicted.