Determining the Parameters of the Forchheimer Equation From Pressure-Squared vs. Pseudopressure Formulations

Abstract

Summary This paper presents a comparison of the accuracy of the pressure-squared and pseudopressure formulations of the Forchheimer equation for simultaneous determination of the permeability and non-Darcy flow coefficient from high-velocity flow tests using core plugs. We show that the pressure-squared formulation must satisfy two contradictory conditions. The core length should be sufficiently small so that the average viscosity and real gas deviation factor, which are dependent on the pressure drop, approach the actual values. The core length, however, should be long enough to be representative of the characteristic length of the porous media. Because these two conditions cannot be met simultaneously, the pressure-squared formulation is less accurate. We show that these effects are more pronounced for tight formations because of higher pressure drop across the core. The pseudopressure formulation requires only that the core length should approach the representative core length, and, therefore, it provides more accurate interpretation of the high-velocity core flow tests and generates accurate values of the permeability and non-Darcy flow coefficient and the representative core length.