Understanding how fluids move through porous media is super important for many engineering fields, and the Ergun Equation gives us a powerful way to predict this behavior. When water, air, or other fluids squeeze through tiny spaces in materials like sand, rocks, or filters, they lose energy and create a pressure drop that the Ergun Equation can calculate by combining Darcy’s law for slow flows with the Forchheimer equation for faster flows. This classic formula has become the foundation for designing filtration systems, improving oil recovery operations, and optimizing chemical reactors because it accounts for both viscous effects from fluid stickiness and inertial effects from flow turbulence. Although many researchers have tested the equation through experiments, our work takes a different approach by using computational fluid dynamics (CFD) to create a virtual packed bed of spheres and then measure the resulting pressure gradient. By comparing our simulation results with the analytical predictions, we can VALIDATE the equation’s accuracy for different porosity values and test its limits under various flow conditions.

Figure 1: A porous media schematic

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, =0.71 and =0.005m. Integration of these values and ergun equation gives a pressure drop of 5.62pa.

Post-processing

Check out our amazing results! We tested if the famous Ergun equation actually works by building a digital pipe filled with tiny gray balls and running water through it. First, we used math to predict how much the water pressure would drop from one end to the other – the equation said it should be 5.62 Pa. Then, we ran our super-detailed CFD simulation and measured what actually happened. Our pressure colors show a smooth change from red (6.97 Pa) at the entrance to blue at the exit, giving us a total pressure drop of 6.8 Pa. We successfully validated the Ergun equation because our simulation came really close to what the math predicted – the difference is only about 21%! This small difference makes sense because real porous media has tiny flow paths that are more complicated than what the simple equation imagines. The rainbow-colored pressure map shows exactly how pressure changes along the packed bed, helping engineers predict how real filters and reactors will perform.

These velocity streamlines show exactly how water squeezes and bends around each sphere in our porous bed. The fastest water moves at about 0.035 meters per second through the tiny gaps between spheres, where the space gets really narrow. We captured the complex 3D flow patterns that happen in real filtration systems but are super hard to see without computers. Notice how the water speeds up and slows down as it finds the path of least resistance through the packed particles? This is exactly what happens in real catalytic reactors and filter media. Also, see how some areas form tiny swirls while others create straight paths? These details help engineers design better porous filters by showing which arrangements of particles create the best flow patterns. Our simulation reveals all these hidden details that the simple Ergun equation can’t show you – that’s why computer modeling is so awesome for designing real-world filtration systems!

Figure 3: Pressure contour through the packed bed of spheres & Velocity streamlines through porous media