Recent models show means of estimating the petrophysical porosity exponent m of a reservoir when it is composed of different combinations of matrix, fractures and vugs. For both dual and triple porosity reservoirs, the system is modelled as a parallel resistance network (for matrix and fractures), a series resistance network (for matrix and non-connected vugs) or a combination of parallel-series resistance networks (for matrix, fractures and non-connected vugs. In the case of matrixfractures it has been assumed that the flow of current is parallel to the fractures. This paper shows the effect on m of current flow that is not parallel to the fractures. This type of anisotropy is co-relatable with fracture dip. Maxwell Garnett mixing formula for calculating effective permittivity of a system with aligned ellipsoids and depolarization factors of 0 and 1 leads to the parallel and series resistance networks used in the paper.
It is concluded that the change in fracture dip can have a significant effect on the value of m. Not taking thin into account can lead in some cases to significant errors. The effect of the change of fracture dip on water saturation calculations is illustrated with an example.
The petrophysical analysis of fractured and vuggy reservoirs has been an area of abundant interest in the oil and gas industry. In 1962, Towle1 gave consideration to some assumed pore geometries as well as tortuosity, and noticed a variation in the porosity exponent m in Archie's2 equation ranging from 2.67 to 7.3+ for vuggy reservoirs and values much smaller than 2 for fractured reservoirs. Matrix porosity in Towle's models was equal to zero.
Aguilera3 (1976) introduced a dual porosity model capable of handling matrix and fracture porosity. That research considered 3 different values of Archie's2 porosity exponent: One for the atrix (mb), one for the fractures (mf =1), and one for the composite system (m). It was found that as the amount of fracturing increased, the value of m became smaller.
Rasmus4 (1983) and Draxler and Edwards5 (1984) presented dual porosity models that included potential changes in fracture tortuosity and the porosity exponent (mf) of the fractures. The models are useful but must be used carefully as they result incorrectly in values of m > mb as the total porosity increases.
Serra et al. 6 developed a graph of the porosity exponent m vs. total porosity for both fractured reservoirs and reservoirs with non-connected vugs. The graph is useful but must be employed carefully as it can lead to significant errors for certain combinations of matrix and non-connected vug porosities (Aguilera and Aguilera7). The main problem with the graph is that Serra's matrix porosity is attached to the bulk volume of the "composite system". More appropriate equations should include matrix porosity (Øb) that is attached to the bulk volume of the "matrix system" (Aguilera, 1995).
Aguilera and Aguilera7 published rigorous equations for dual porosity systems that were shown to be valid for all combinations of matrix and fractures or matrix and nonconnected vugs.
