An Analysis of High-Velocity Gas Flow Through Porous Media

Abstract

Darcy's law is inadequate for representing high-velocity gas flow in porous media, such as near the wellbore. An analysis of pressure lost during flow through conduits of alternating cross sections suggests more appropriate words for describing the mechanism for energy loss and terms in the flow equation. Updated correlations are presented for the coefficient of the velocity-squared term. Introduction Much research has been conducted to understand flow through porous media. Regarding high velocity, suitable correlations and nomenclature are the subject of controversy because of different views on the mechanism causing pressure drop. This study tries to improve the understanding of high-velocity flow through porous media. Using available data and this research, the best correlation is sought to permit the calculation of high-velocity flow based on permeability, porosity, and character of the rock. permeability, porosity, and character of the rock. We hope that a nomenclature can be suggested that is acceptable to both reservoir engineers and fluid mechanics research scientists. The results should be useful for improving correlations of gas-well flow data and for predicting well flow from core data, fluid properties, and specified conditions. properties, and specified conditions. Early Work on High-Velocity Flow Fancher et al. measured pressure drop during flow through a large number of unconsolidated and consolidated porous media. They correlated the data by using the porous media. They correlated the data by using the friction factor and Reynolds number, with grain diameter as a characteristic length. They showed that for flow through porous media, an increased pressure drop at high velocity is beyond that proportional to velocity. Data taken at the USBM were correlated using a quadratic equation of pressure drop with the second term of velocity to the nth power. Green and Duwez increased the understanding of high-velocity gas flow data when studying sintered metals. They adapted the equation with a velocity term squared that Forchheimer had developed: dp v- ---- = ----- + pv 2......................(1)dL k Comell and Katz measured the porosity, permeability, and B factors for cores, resulting in a correlation of B with permeability. The term B was called a "turbulence factor," but the expression was unacceptable to several researchers. Language Used in Literature Space limitations prohibit quoting completely the language used when describing the mechanism that consumes energy at more than a linear rate with velocity. The term used in flow equations (generally the in a quadratic flow equation) also has been given various names according to the author's view of the flow mechanism. Table 1 assembles selected typical titles and statements quoted from published works. After the flow mechanism has been reviewed, a more appropriate language will be submitted to agree with the concepts developed here. JPT P. 211