A model is developed for petrophysical evaluation of naturally fractured reservoirs where dip of fractures ranges between zero and 90 degrees, and where fracture tortuosity is greater than 1.0. This results in an intrinsic porosity exponent of the fractures (mf) that is larger than 1.0.
The finding has direct application in the evaluation of fractured reservoirs and tight gas sands, where fracture dip can be determined, for example, from image logs. In the past, a fracture-matrix system has been represented by a dual porosity model which can be simulated as a series-resistance network or with the use of effective medium theory. For many cases both approaches provide similar results.
The model developed in this study leads to the observation that including fracture dip and tortuosity in the petrophysical analysis can generate significant changes in the dual porosity exponent (m) of the composite system of matrix and fractures. It is concluded that not taking fracture dip and tortuosity into consideration can lead to significant errors in the calculation of water saturation. The use of the model is illustrated with an example.
The petrophysical analysis of fractured and vuggy reservoirs has been an area of interest in the oil and gas industry. In 1962, Towle1 considered 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 matrix (mb), one for the fractures (mf =1), and one for the composite system of matrix and fractures (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 of the fractures (mf). 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. The non-connected vugs and matrix equations were validated using core data published by Lucia.8
