Pipe network modeling for analysis of flow in porous media

Abstract

In this paper, a new matrix framework has been developed for the simulation of flow and pressure in porous media. In this framework, the pressure gradient formulation in Darcy’s law is considered as the head-loss equation in pipe network modeling. Then, an artificial pipe network has been constructed to find the pressure head profile in porous media. Two explicit and implicit formulations have been advanced for linear and nonlinear analysis, which the latter is an implementation of the Newton–Raphson algorithm. Both formulations iteratively solve a linear system of equations for calculating the nodal heads and apply a matrix multiplication for updating the flow vector. While the explicit method needs few iterations, the implicit method requires at least 20 iterations to converge with acceptable accuracy. For testing these formulations, four different types of network configurations were tested. The analysis of three laboratory tests showed that the application of the implicit method provides reliable and accurate results.