Effect of Fracture Dip on Petrophysical Evaluation of Naturally Fractured Reservoirs
Authors: Aguilera C.G. , Aguilera R. 
Published: March 2010

Abstract
Recent models show the 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 matrix/fractures, it has been assumed that the flow of the 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 this into account can lead, in some cases, to significant errors. The effect of the change of fracture dip on water saturation calculations is illustrated using two examples.

Introduction
The petrophysical analysis of fractured and vuggy reservoirs has been an area of abundant interest in the oil and gas industry. For example, a key ingredient for successful completion of wells in naturally fractured tight gas formations is the ability to distinguish gas from water-bearing intervals. Proper estimates of petrophysical parameters, including the porosity or cementation exponent m, play an important role in correct estimations of watersaturation (Sw).
Towle(1) gave consideration to some assumed pore geometries, as well as tortuosity, and noticed a variation in the porosity exponent m in Archie's(2) 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.
Aguilera(3) introduced a dual porosity model capable of handling matrix and fracture porosity. That research considered three different values of the porosity exponent: one for the matrix (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.
Rasmus(4) and Draxler and Edwards(5) 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 calculate values of m &gt; mb as the total porosity increases, even when the flow of current goes parallel to the fractures.
Serra(6) developed a graph of the porosity exponent (m) versus 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 errors for certain combinations of matrix and non-connected vug porosities(7). The main problem with the graph is that Serra's matrix porosity is attached to the bulk volume of the 'composite system.'