Statistical Model for Dispersion in a 2D Glass Micromodel

Summary Microscopic visualization of a porous medium can provide valuable information to enhance understanding of pore-scale transport phenomena. In this work, a novel and unique approach is provided to combine experimentally measured pore-size distribution with theoretical statistical analysis to predict longitudinal and transverse dispersion coefficients. The approach presented can be easily extended to predict other fluid-flow parameters through porous media, such as permeability, and capillary pressure. Here, a micromodel is considered as a porous medium. The grains and pores of the micromodel are nonuniform in size, shape, and distribution. The pore-size distribution, as well as pore-length distribution, was extracted by applying an image analysis technique. A 2D random network model of the micromodel has been constructed for which the nonuniformity is considered by assigning measured distribution functions. The random particle method was applied for correlating and predicting dispersion coefficients on the basis of probabilistic approaches. Statistical derivations result in a new functional dependence for the longitudinal and transverse dispersion coefficients in terms of pore velocity and ensemble averages. Prediction from the derived model, for both longitudinal and transverse dispersion, is in agreement with the experimental data. Despite the simplicity of the proposed network model, its reasonable prediction provides some confidence that it can be considered as a reasonable approximation of the complex nature of porous media.