The Physical Basis Of Darcy's Law And Its Importance In The Exploration And Production Of Petroleum

The systematic application of fluid mechanics to the problem of extracting petroleum from underground reservoirs was begun during the decade of the 1920's, and soon thereafter the equation (1) which purported to describe the flow of any homogeneous fluid in a porous solid medium, and was attributed to the French engineer Henry Darcy, came into general use as the fundamental flow equation of the petroleum industry for underground fluids. This equation asserts unequivocally:that all fluids flow in a direction perpendicular to the surfaces of constant pressure and in the direction of pressure decrease,that in the same pressure field all homogeneous fluids would flow at each point in the same direction, andthat if the fluid is at rest—a special case of a fluid in motion— the fluid pressure in three-dimensional space must be constant. However, the third of these propositions violates the known facts of hydrostatics; the second the known fact that diverse reservoir fluids, such as water, oil and gas, migrate in divergent directions and tend to become segregated; and the first can easily be violated experimentally in any desired manner. Hence, the use of this equation in reservoir engineering can hardly have produced any but inhibitory effects in the attempts to understand what really occurs during the exploitation of a petroleum reservoir. Returning to first principles, and incidentally to the original Darcy experiment, one finds that the flow of a homogeneous fluid through an isotropicporous solid can be described by the equation (2) in which is the volume of the fluid crossing unit area normal to the flow-lines in unit time, E is the force per unit mass exerted by the environment on an element of the fluid at a given point, and sigma is a fluid conductivity parameter. Further examination shows that (3) and hence is the vector sum of two separate forces per unit mass, one due to gravity and the other to the gradient of the pressure. In general, these have independent directions. Also, (4)