FLUID POTENTIAL

Every branch of science and engineering has its own particular heroes, one only has to think, for example, of the hallowed names of Newton and Einstein in physics or Darwin in the natural sciences. In reservoir engineering, our equivalent is the nineteenth century French engineer Henry Darcy who, although he didn't realise it, has earned himself a special place in history as the first experimental reservoir engineer. In 1856 Darcy published a detailed account of his work2 in improving the waterworks in Dijon and, in particular, on the design of a filter large enough to process the town's daily water requirements.

Although fluid dynamics was a fairly advanced subject in those days, there were no published accounts of the phenomenon of fluid flow through a porous medium and so, being a practical man, Darcy designed a filter, shown schematically in fig. 4.1, in an attempt to investigate the matter. The equipment consisted of an iron cylinder containing an unconsolidated sand pack, about one metre in length, which was held between two permeable gauze screens. Manometers were connected into the cylinder immediately above and below the sand pack. By flowing water through the pack Darcy established that, for any flow rate, the velocity of flow was directly proportional to the difference in manometric heights, the relationship being

Darcy's only variation in this experiment was to change the type of sand pack, which had the effect of altering the value of the constant K; otherwise, all the experiments were carried out with water and therefore, the effects of fluid density and viscosity on the flow law were not investigated. In addition the iron cylinder was always maintained in the vertical position.

Subsequently, others repeated Darcy's experiment under less restrictive conditions, and one of the first things they did was to orientate the sand pack at different angles with respect to the vertical, as shown in fig. 4.2. It was found, however, that irrespective of the orientation of the sand pack, the difference in height, ∆h, was always the same for a given flow rate. Thus Darcy's experimental law proved to be independent of the direction of flow in the earth's gravitational field.