Application of the theory of mixtures, two phase non-Darcian flow through a porous media

Two phase flow through a porous media has many practical applications which covers a wide range of engineering disciplines. Most previous studies have relied mainly on Darcy's law. While Darcy's law provides a simple model for studying fluid flow through a porous media, several investigators have shown that the use of Darcy's law in certain applications may lead to inaccurate results.; A mathematical model for two phase flow in a non-deformable porous media is developed with the context of the Theory of Mixtures, Interacting Continua. The governing equations for a three phase mixture is developed. The generalized governing equations are then reduced to a set of nonlinear equations with the boundary conditions for steady pressure driven two phase flow in a pipe packed with spherical particles. The spherical particles are uniform in size. The investigation studies both uniformly and randomly distributed particles. The resulting boundary value problem is solved using finite differences.; The results based on the Theory of Mixtures are compared with the predictions from Darcy's law and experimental results. The effect of particle size, flow rate, and pipe diameter on the pressure gradient and the velocity profiles is analyzed for the constant porosity case. A discussion of the importance of the interaction forces that exists between each of the constituents is provided. Additionally, the Darcian versus non-Darcian flow regimes are discussed.; The variable porosity case was also studied. The porosity distribution was assumed to vary exponentially from the center of the cylinder to the solid boundary. For this part of the investigation, an optimization method was used to analyze this problem.; In the optimization method, the flow was assumed to be one dimensional and that the pressure gradient was minimized in all regions. The results showed that a ten percent increase in porosity at the wall lowered the overall pressure gradient of the system.