Dual-Porosity Equations From Effective Medium Theory

Abstract

Abstract Aguilera's1 dual porosity model for fractures and matrix porosity was developed because fractures tend to lower the porosity or cementation exponent (m) of rocks. An assumption in the derivation of the dual porosity model was that fracture systems are parallel with the current direction, i.e. that fracture m (mf) is equal to 1.0. A new equation derived from effective medium theory allows mf higher than 1.0. The new relationship agrees closely with two models by Aguilera which allow mf greater than 1.0. In addition to the dual porosity equation, a new relationship is derived for calculating mf based on fracture orientation relative to current flow. In the past, dual porosity models for vuggy porosity have mainly used the physical model of resistors in series with the inherent assumption that the vugs were non-touching. A new equation to calculate the effect of vugs on m is derived from effective medium theory. At low total porosity, calculations are very similar to those of the series model, but at higher porosities the results differ, eliminating the need to distinguish between connecting and non-connecting vugs. In addition, vug m (mv) can be varied on the basis of the shape and orientation of the vugs. When mv is raised to high values, the results are equivalent to the dual porosity series vug model. A triple-porosity method is developed that utilizes adjustable mf and mv from new dual porosity relationships. The model works by first calculating a new, composite m for the bulk porosity and vugs and then it uses that composite value along with mf to calculate a triple-porosity m. When mf is equal to 1.0, the results resemble those of the triple porosity model of Aguilera and Aguilera2, but with increasing values of mf, the effects of fractures on triple-porosity m is dampened. Introduction Fractures and vugs can have profound effects on the porosity exponent (m) and calculated water saturation (Sw) of carbonate rocks. Proper prediction of m in reservoirs avoids overestimation of Sw commonly caused by the presence of fractures and also avoids the underestimation of Sw commonly caused by vuggy or oomoldic porosity.