MAXWELL, HUBBERT, AND FLUID FLOW IN RESISTIVE MEDIA

The first publication that established M. King Hubbert as a major figure in geology was his 1940 paper, The Theory of Ground-Water Motion. As Hubbert would later explain, this paper came about because of his almost total ignorance of the subject of groundwater flow. During the 1930s, he found that many earth scientists were routinely using Darcy’s Law to describe groundwater flow by analogy with Ohm’s Law of electricity. Yet, he also found that none of them clearly understood the analogy between electricity potential and the corresponding water potential. To remedy the situation, Hubbert started from first principles, defined an energy potential, gave physical meaning to permeability of a porous medium, derived an expression for the refraction of flow lines, and assembled a self-consistent potential theory for steady-state groundwater flow in three dimensions. It is commonly believed that Hubbert placed Darcy’s Law on firm hydrodynamic foundations. But, it turns out that in a well-known paper, Faraday’s Lines Force, published in 1856, James Clerk Maxwell assembled a theory for the flow of an incompressible fluid in a resistive medium as an artifact to explain electricity and magnetism. This theory has all the essential elements of Hubbert’s theory, although Hubbert’s application of the theory to porous materials is entirely original. Judging from his publications, Hubbert was quite meticulous in referencing previous work, and it is therefore reasonable to assume that he was not aware of Maxwell’s theory for the flow of an incompressible fluid in a resistive medium. It is intriguing to think as to how Hubbert’s work might have evolved had he been aware of Maxwell’s work during the 1930s.