Filtration Theory for Oil-Well Drilling Fluids

Abstract

In the oil industry it has been customary to describe water loss or filtration from benton-ite drilling fluids by adaptation of Darcy’s law to the filtration process. Thus, the rate of filtration varies directly with the differential pressure and permeability and inversely with the filtrate viscosity and the thickness of the deposited filter cake. Since the thickness of the filter cake is variable, however, it is necessary that the rate of deposition of the filter cake be related to the volume of filtrate. In establishing this relation certain workers have made questionable allowance for the water adsorbed on the bentonite particles with the result that the filtration equation is not valid in certain instances (Larsen, 1938; Rogers, 1953, p. 268).

Other workers have indicated the significance of the adsorbed phase in their presentation of experimental techniques for relating the filter cake and the filtrate (Williams and Cannon, 1938; von Englehardt, 1954).

The filtration relationship may be derived analytically by the simultaneous use of Darcy’s law and mass and volumetric balances on the filtration process. Such a derivation is here presented. The validity of the filtration relationship presented is experimentally confirmed using three groups of unlike systems—Wyoming bentonite suspensions, low-yield clay suspensions, and sodium carboxymethylcellulose suspensions—as well as four sets of clay filtration data from the literature.