Empirical equations have been developed to show the analytical relation between the fluid and rock properties and oil recovery by water flooding. Studies were made on both consolidated and unconsolidated porous media. Observations were made on cores having permeabilities ranging from 6 md to 11 darcies. The core porosities ranged from 17 to 40 per cent. The oil had viscosities ranging up to 90 cp. The actual oil recoveries varied from approximately 40 to 80 per cent depending upon the nature of the oil and the rock. The equations were successful in predicting waterflood recoveries in the laboratory experiments with an average error of three per cent.
The predicting equation utilizes an electrical rock property, formation resistivity factor, which may be obtained from conventional well logs.
Various attempts have been made to simulate natural porous media by simplified models in order to describe mathematically the nature of fluid flow in porous media. One of the earliest attempts was a study of packs of spheres. However, the range of properties of assemblages of spheres is not great enough to represent reliably the many different reservoir rocks.
A bundle of capillary tubes as a model has been suggested by Fatt and Dykstra and Burdine, et al., and they developed equations relating capillary size distribution to capillary pressure curves, permeability, and porosity for actual porous media. However, this model was not useful in describing dynamic properties such as permeability and electrical conductivity. In a later attempt, Fatt proposed the analogy of a network of interconnected capillary tubes of random sizes and overcame this difficulty. Dehn made studies of a similar network using actual fluid flow models.
Although many models have been employed to represent actual rock-fluid systems, none has been very successful in describing the natural porous media adequately enough to predict displacement efficiency of oil by other fluids. In view of this inadequacy it seems reasonable to turn to observed performance as related to measurable rock properties.
In a rather complete resume of the implications of Darcy's Law applied to homogeneous fluid flow, Muskat points out that the permeability coefficient constitutes the complete dynamical characterization of the porous material as a fluid transmitting medium. It is a property independent of the type homogeneous fluid in the rock if there is no interaction between the rock and fluid. Therefore, it is an absolute rock property and should be a single parameter useful in characterizing the rock.
Porosity is an important property since it is a measure of the fluid-containing capacity of a rock and a function of cementation and the complexity of a rock structure. Rose developed theoretical equations for evaluating relative permeability based on porosity and fluid saturation.
Pore size distribution in petroleum reservoir rocks was studied by Burdine, et al., and an equation was developed relating homogeneous fluid permeability to tortuosity, porosity, and pore size distribution expressed in terms of pore entry radii and incremental pore volumes. in subsequent work Burdine calculated relative permeabilities on the same basis and compared these with measured relative permeabilities. The two compared extremely well and gave an excellent indication that pore size distribution is a significant factor contributing to relative permeability. It was pointed out that data obtained by mercury injection was usually more reliable than that obtained by drainage through a semi-permeable porcelain plate.