Darcy's law from water to the petroleum industry: When and who?

Henry Darcy, in an appendix of his work "Les Fontaines Publiques de la Ville de Dijon", described the law governing the flow of water through a saturated sand filter. In this law, flow velocity is correlated to hydraulic gradient by means of a linear proportionality constant K, defined as "permeability" (perméabilite). In using this terminology, Darcy apparently followed the practice of hydraulic engineers of his time. Indeed, the permeability concept formulated by Darcy is known today as hydraulic conductivity, a flow parameter describing both the physical properties of the porous medium and the characteristics of the fluid. Only in the 1950s did M. K. Hubbert provide a complete theoretical foundation to Darcy's empirical expression, deriving it from the general Navier-Stokes equations. It is important to remember that Darcy's law was already utilized in many technical fields, and especially in the petroleum industry. In the petroleum industry Darcy's law is formulated in terms of pressure gradient and generalized for oil and gas flow, which led to the concept of multiphase flow. This was accomplished by separating the properties of the rock from that of the fluid by manipulating the proportionality constant K, thereby obtaining a "generalized" law. By doing so, permeability becomes a property of the porous media, dictated by pore geometry alone. The origin of the generalization of Darcy's law can be traced back to the work of American geoscientists at the end of the 1920s. The present paper proposes to establish when and by whom Darcy's law was first generalized and made suitable for petroleum reservoir engineering. In particular, the paper retraces some historical developments of the permeability concept by reviewing the earliest studies that contributed to the popularization of the generalized form of Darcy's law for fluid flow other than water. © 2004 ASCE.