Some Problems Of Horizontal Steady Flow In Porous Media

DATA on the physical and thermodynamic properties of hydrocarbons have been made available in recent years but the formal method of applying these data to flow in porous media appears not to have been fully developed. By making usual thermodynamic assumptions and employing existing data on permeability to two-phase flow, Darcy's law may be applied to obtain the flow characteristics for representative combinations of flowing medium and geometry. The numerical examples presented herein are based on hydrocarbons for which complete physical and thermodynamic data are available under equilibrium conditions. INTRODUCTION Thermodynamic data are obtained in the laboratory under equilibrium conditions and their application requires the assumption that equilibrium also exists during flow. This assumption is at least usual in engineering analyses, though not easily justified in many instances, and will be followed here. In regard to hydrocarbons, laboratory experience in determining the pressure-volume-temperature relationships indicates that gas-liquid mixtures must often be stirred vigorously for periods of 15 to 20 min. before reaching equilibrium. On the other hand, boiling and condensation are known to occur on solid surfaces and the large surface exposed to the flowing substance by a porous medium may bring about rapid approach to equilibrium. For the purpose of providing at least a guide to experimentation and a standard for later comparison with experimental results, it will be assumed that the phases present in cross sections perpendicular to the direction of flow are in thermodynamic equilibrium. Another assumption usually made in the solution of problems of flow in porous media is that the fluid remains at a constant temperature; i.e., isothermal flow. This assumption is arrived at by considering the porous medium and surroundings to be an infinite heat source and the rate of heat flow to be infinite at a boiling front. Its validity depends in large measure upon the character of flow, the number of components, and the physical and thermodynamic properties of the fluid. However, the assumption of isothermal flow represents a limiting case. The other limit can be represented by the assumption that the fluid is thermally isolated; i.e., irreversible adiabatic. The thermodynamic process characterizing the actual flow of a given fluid system probably lies somewhere between these two limiting cases and might be thought of as a flow system in which the confining walls are maintained at a constant temperature. For isothermal flow the solid material of the porous media is considered as the infinite heat source capable, without loss in temperature, of giving up heat to the fluid as the latter tends to cool by expansion. For the thermally isolated system, the solid material is considered to give up no heat to the fluid. In the intermediate case the impervious walls confining the porous media are at constant temperature from which heat is transferred along various paths, solid and fluid, throughout the porous media. It would appear that an actual petroleum-