Solver for a new theory for revisiting hydraulic conductivity and pore size distribution of porous media -

Abstract

Methods to characterize the structure of porous media are needed for a broad range of applications, from prediction of the dynamics of water flow to understanding petroleum reservoir performance. Classic porous media experiments focused on water as the fluid of choice, thus limiting theoretical development by modelers into a single average hydraulic conductivity. Abou Najm and Atallah (2015) overcame this challenge by experimentally estimating the pore structure of porous media using a combination of Newtonian and non-Newtonian fluids. Results of N infiltration experiments using water and N-1 non-Newtonian solutions are transformed into a system of equations that yields N representative radii (R¡) and their corresponding percent contribution to flow (w¡), thus mimicking the functional behavior of real porous media in terms of flow and porosity. However, estimating the radii and-or their corresponding weights involved solving a complex system of equations (linear or nonlinear) composed of non-analytical functions under different constraints. This complexity can hinder adopting the proposed theory; thus the need arises for developing a user-friendly solver that seamlessly solves the system of equations. This dissertation focuses on formulating and developing the numerical and optimization techniques required to solve for the radii and weights, and presents a tool with a user friendly interface that solves for any problem-type or number of fluids. As a numerical application, published pore size distributions (PSD) were discretized into different pore-classes (Rm), where m refers to the class number out of the M classes (where M is the entire set of radii describing a soil). Given the total porosity, the number of pores in every class was calculated and thus the corresponding theoretical flow. Having gathered all the input, three guar gum concentrations following the Cross (1965) model were adopted to determine the representative radii of each soil sample. As a real life validation to the theory, multi