Laboratory Investigation of Inertial Flow in High-Strength Fracture Proppants

Abstract

ABSTRACT High velocity fluid flow down hydraulic fractures will create pressure gradients that are proportional to the square of the velocity. As such, Forchheimer's equation, rather than Darcy's law must be used to correctly' estimate the pressure gradients near the wellbore and, consequently, the flow behavior of the hydraulically fractured well. To properly use the Forchheimer equation, one must know the value of β, which is the inertial flow coefficient. Cooke measured values of β for various sizes of Brady sand at several different closure pressures. Cooke's correlation has been widely used in the industry but we have found that the correlation did not span the permeability range needed for all situations. Specifically, data are needed to estimate the pressure gradients of gas flowing through high strength, high permeability, man-made proppants. We also need the inertial flow data for sand that has been severely crushed, A laboratory system has been constructed to investigate high velocity flow through fracture proppants. From test data, both proppant permeability and the inertial flow coefficient can be computed. The proppants tested included 12–20 and 20–40 mesh samples of Brady sand, Interprop Plus, and Carbolite. An improved correlation of inertial flow coefficient as a function of proppant permeability and initial mesh size has been developed using our laboratory system. The results indicate that the inertial flow coefficient depends upon the initial mesh size of the proppant, and is independent of the proppant type. Grain size distribution was found to be a factor controlling the inertial flow coefficient for a given fracture proppant. It was found that different samples with similar permeabilities and inertial flow coefficients also had similar grain size distributions. A variation in the pore pressure of the nitrogen used in the experiments was shown to have a significant effect on the inertial flow coefficient. The permeabilities calculated from the Forchheimer equation exhibited the same trend of decreasing permeability with increasing pore pressure as the Klinkenberg relationship for Darcy flow. Slip flow was found to influence the results significantly at Reynolds Numbers below 0.1.