Effect of Overburden Pressure and the Nature and Microscopic Distribution of Fluids on Electrical Properties of Rock Samples

Abstract

Summary Laboratory equipment aimed at determining the exact correlation between resistivity and water saturation under stress, pressure, and temperature conditions is described in the first part of this paper. The porous-plate method adapted to reservoir conditions is used to obtain porous-plate method adapted to reservoir conditions is used to obtain different saturation values during both drainage and imbibition. With this equipment, the influence of the effective stress on the porosity and formation resistivity factor can be studied before the test. In the second part of this paper, the values of the formation resistivity factor and part of this paper, the values of the formation resistivity factor and resistivity index are compared for water-wet samples from sandstone and carbonate reservoirs. These measurements indicate that the influence of the effective stress depends on the nature of the rock sample. In addition, the resistivity/water-saturation law depends on the direction of the saturation change (drainage or imbibition) and on the nature of the fluids (water/oil or water/gas). Introduction Electric well logs are commonly used for evaluating porosity and water saturation in oil reservoirs. The interpretation of such electric logs is based on research by Archie, who worked out relations (1) between the formation resistivity factor, FR, and porosity, (P: .......................(1) in which a and Fc are constants for a given rock, and (2) between the electrical resistivity index, IR =Rt/Ro, and water saturation, Sw, ..............................(2) in which n is a constant, commonly equal to 2. These equations of empirical origin have the following assumptions. 1. There is a one-to-one relationship between the formation resistivity factor and porosity as well as between the resistivity index and water saturation. Yet, in a brine-saturated porous medium, the electric streamlines are affected by the irregularity of the solid surface, so throat radii and pore radii should be involved in Eq. 1. Likewise, the distribution of fluids in the porous medium, and not just the brine saturation, should appear in Eq. 2. 2. The value of n is constant for a given porous medium and a given system of fluids. 3. The porous medium is perfectly insulating, as is the oil in place. Also, until recently, the a, Fc, and n parameters were determined place. Also, until recently, the a, Fc, and n parameters were determined under laboratory conditions and it was assumed that their values would be the same under reservoir conditions. The limits of these fundamental assumptions for interpreting electric logs have been only partially investigated. The importance of clay (the third hypothesis above) on Eqs. 1 and 2 has been described by modifying these equations according to the clay content without taking into account the geometrical continuity or discontinuity of the clay. Partially oil-wet porous media do not lead to the same fluid distributions as water-wet media (first hypothesis). The values of n are generally higher in oil-wet porous media than in water-wet ones. The restoration of the overburden pressure decreases the porosity and increases the formation resistivity factor. Its effect porosity and increases the formation resistivity factor. Its effect on the value of n is less clear. both increases and decreases have been reported. These hypotheses deserve to be systematically tested to determine the limits of validity of Eqs. 1 and 2. In particular, the representativeness of the n values obtained in the laboratory by standard drainage experiments with the water/air system can be questioned when the effective reservoir conditions (fluids, pressure, temperature, stress, etc.) are not restored. The research described here concerns the influence of the effective stress, the nature of the fluids, and the microscopic distribution of fluids on the electrical properties of sandstone and carbonate samples. Laboratory equipment was built for this purpose, and a procedure was defined for accurately determining purpose, and a procedure was defined for accurately determining the formation resistivity factor as a function of the effective stress and the resistivity-index/water-saturation relation under pore pressure, effected stress, and temperature during drainage and pore pressure, effected stress, and temperature during drainage and imbibition with the water/oil system. Experimental Apparatus Fig. 1 is a diagram of the equipment, which was based on that used by Waxman and Thomas and Swanson. The apparatus can continuously measure the electrical conductivity of a sample saturated with oil and water and the pressure difference between both fluids. Drainage (decreasing water saturation) and imbibition (increasing water saturation) can be performed. The method used to obtain different values of the saturations is the porous-plate method, which uses a highly hydrophilic capillary diaphragm placed at the bottom of the sample. The apparatus can restore conditions as close as possible to reservoir conditions-i.e., pore pressure up to 34.47 MPa possible to reservoir conditions-i.e., pore pressure up to 34.47 MPa [5,000 psi], effective stress up to 48.26 MPa [7,000 psi], and temperature up to 121 degrees C [250 degrees F]. At the start of the test when the sample is entirely water saturated, the apparatus can be used to determine variations in the formation resistivity factor and porosity as a function of the effective stress. A full description of the apparatus is given in Appendix A. On some samples, measurements were made of only the formation resistivity factor and porosity under stress. For this, we used a simplified apparatus without any capillary diaphragm similar to that used by Abgrall. Operating Procedure The procedure used to prepare the samples is summarized in Appendix B. Measurements With the Water/Refined-Oil System. The study of the influence of stress on the resistivity/water-saturation law was conducted in five stages. 1. After the core was evacuated, it was saturated by brine and the initial properties were determined (initial PV, and F Ro) under low effective stress (= 3 MPa [435 psi], pore pressure MPa [145 psi], and temperature = 40 degrees C [104 degrees F]). 2. The first series of measurements was made at various saturations. During drainage, pressure in the oil was increased by steps while pressure in the water was held constant until saturation equilibrium was reached. During imbibition. pressure in the oil was decreased by steps. Maximum capillary pressure applied was 0.2 MPa [29 psi]. This limit was imposed by the capillary diaphragm. Ten to 20 equilibrium points were achieved, depending on the saturation range covered. In this way, the electrical resistivity and capillary pressure relationships were determined as a function of water saturation.