Determination of Matrix Flow Units in Naturally Fractured Reservoirs
Authors: Aguilera R. 
Published: March 2010

Abstract
The integration of capillary pressures and Pickett plots has been shown recently to be a useful approach for determining flow units. The present study extends the method to the case of naturally fractured reservoirs by preparing Pickett plots for only the matrix. This requires calculation of matrix porosities and true resistivities for the matrix. By placing pore throat apertures, capillary pressures and heights above the free water table on Pickett plots, it is possible to generate matrix flow units and to estimate if the matrix will contribute to production. Pattern recognition is the key to success with this approach. Two examples are presented.
If total porosities and resistivities of the composite system are used on a Pickett plot when the partitioning coefficient (v) is constant, then the usual straight lines for fixed values of water saturation are not obtained. In this case, the Pickett plot results in downward concave lines. Not recognizing this effect might lead to significant errors in the calculation of water saturation.

Introduction
Pickett plots(1, 2) have long been recognized as very useful in log interpretation. In Pickett's method, a resistivity index, I, and water saturation, Sw, are calculated from log-log crossplots of porosity vs. true resistivity (in some cases apparent resistivity, or resistivity as affected by a shale group, Ash).
The Pickett plot has been extended throughout the years to include many situations of practical importance. For example, Aguilera(3, 4) demonstrated that Pickett plots could be used for evaluating naturally fractured reservoirs. In these formations, the value of the porosity exponent was shown to be smaller than usual. Sanyal and Ellithorpe(5) and Greengold(6) have shown that a Pickett plot should result in a straight line with a slope equal to (n - m) for intervals at irreducible water saturation. Aguilera(7) extended the Pickett plot to the analysis of laminar, dispersed, and total shale models. In this approach, the resistivity included in the plot is affected by a shale group, Ash, whose value depends on the type of shaly model being used. Aguilera showed that all equations for evaluation of shaly formations published in the literature, no matter how long they are, become Sw = Ish−1/n. He further showed that a Pickett plot for shaly formations should result in a straight line with a slope equal to (n - m) for intervals at irreducible water saturation. Aguilera(8) demonstrated that a log-log crossplot of Rt vs. effective porosity, as determined from neutron and density logs, minus free fluid porosity, as determined from a nuclear magnetic log, should result in a straight line with a negative slope equal to the water saturation exponent, n, for intervals that are at irreducible water saturation. Extrapolation of the straight line to 100% porosity yields the product aRw. Gas intervals plot above the straight line. Intervals with movable water plot below the straight line. In the same paper, Aguilera(8) showed that a Pickett plot should result in a straight line for intervals of constant permeability at irreducible water saturation.