Semi-analytical Approach to Modeling Forchheimer Flow in Porous Media at Meso- and Macroscales

Darcy’s law (which states that a fluid flow rate is directly proportional to the pressure gradient) is shown to be accurate in a rather narrow range of flow velocities. Numerous studies show that at low pressure gradients gas slippage effect occurs, which gives overestimated flow rates compared to Darcy’s law. At higher flow rates, Darcy’s law is usually replaced by the Forchheimer equation which accounts for inertial forces including a quadratic term in the flow rate. Darcy’s and Forchheimer’s laws and the problem of detecting transitions between their ranges of applicability are discussed in this study. Analysis of experimental data shows that deviation from Darcy’s law is governed by the Forchheimer number, which is defined by the authors as a product of tortuosity and Reynolds number. The use of the Forchheimer number and semi-analytical approaches enables us to describe non-Darcy flow as a simple universal equation valid for any flow geometry. Comparison of the experimental data with predictions based on a semi-analytical model shows excellent agreement for a wide range of reservoir properties.