Modeling of Non-Darcy Flow Through Porous Media

Abstract

Abstract Darcy's law is inadequate for describing high-velocity gas flow in porous media, which occurs in the near wellbore region of high capacity gas and condensate reservoirs. This study is directed at understanding the non-Darcy flow behavior. The Forchheimer equation, (1) describes the relation between pressure gradient and velocity where × represents the distance, p the pressure, v the velocity, the fluid density and the fluid viscosity, K the permeability and the non-Darcy coefficient of the porous medium. A pore-level model has been developed to describe high velocity flow and test the validity of Forchheimer equation. The inputs to the model are pore size distributions and network coordination numbers. The base case input parameters are listed in Table 1. The outputs are permeability (K), non-Darcy coefficient (), tortuousity () and porosity (). The size of the cubic network used in our computations does not influence the results if larger than 15x15x15. Typical calculations are done on 20×20×20 networks. The non-Darcy term has been found to be proportional to the square of the velocity as presented in the Forchheimer equation. This term arises due to inertial effects in pore contractions, expansions and bends. The typical contributions of these terms are listed in Table 2. Turbulent effects contribute at very high velocity, not typical of near-wellbore flow Permeability, non-Darcy coefficient, tortuousity and porosity depend on the morphological characteristics of the system, as shown in Table 3. As the average throat radius increases the non-Darcy coefficient decreases sharply, the permeability increases, the porosity increases slightly and the tortuousity decreases slightly. Any change in the average body radius has no significant impact on the permeability and the tortuousity. The porosity increases with the increase in body radii and the non-Darcy coefficient increases slightly. As the average coordination number decreases, the non-Darcy coefficient increases sharply, the permeability decreases, the porosity decreases slightly and the tortuousity increases. Finally, as pores shrink, (either due to increase in compaction factor, a or deposition thickness, b), the non-Darcy coefficient increases, the permeability decreases, the porosity decreases and the tortuousity does not change significantly. For each morphological change, a correlation between the non-Darcy coefficient and the other flow parameters has been established. The approximate correlations between the non-Darcy coefficient and the other flow parameters have been established which fit data from different morphological variations, as shown in Table 4. These correlations perform better than the correlations from the literature. They need to be tested against experimental data. P. 313^