The Ergun Equation is a key tool for studying fluid flow through porous media, incorporating Darcy’s law for laminar flow and the Forchheimer equation for turbulent flow. It predicts pressure drop across porous media by considering viscous and inertial effects. It is essential for filtration, petroleum recovery, and chemical reactors. Research involving this equation uses experimental and computational approaches to validate its parameters and broaden its applicability. Although using a numerical approach to validate the Ergun equation is difficult, this study concentrates on it.

Figure 1: A porous media

Simulation Process

The porous media is modeled by means of spherical solids inside a tube using Gambit. A journal has been written to locate spheres. Based on the ergun equation, phi equals 1 for spherical porosity. In our study, ε=0.71 and Dp=0.005m. Integration of these values and ergun equation gives a pressure drop of 5.62pa.

Figure 2- Pressure drop in a porous media based on Ergun equation

Post-processing

In contrast to the theoretically predicted pressure drop of 5.62, the simulation findings to validate the Ergun Equation revealed a pressure decrease 6.8. This disparity implies that although the Ergun Equation has a strong theoretical basis, other factors influencing the pressure drop might be introduced by the particular circumstances or features of the simulated porous media. However, it is inevitable that modeling the spherical domain as a porous medium can be one of the major reasons.