In 1949, William E. Stiles presented an article entitled, "Use of Permeability Distribution in Water Flood Calculations" in which he outlined a method for prediction of water flood performance. In the method Stiles derived equations which were based upon the assumption that the direction of fluid flow from an injection well was in a linear direction. These equations were mathematically derived by a statistical presentation of permeability data.
This paper introduces to the method the fact that initially the direction of fluid flow from an injection well is radial and then continues to treat the direction of flow in three distinct periods. The first is radial flow; the second is a period of transistion from radial to linear flow; and the third is after reservoir fill-up when it is assumed that linear flow conditions do predominate. Equations are then derived for the radial flow period which express water cut and the commensurate fraction of water flood oil recovered in terms of dimensionless permeability. Additional modifications are also suggested in application to field performance.
