Robert C. Ransom
What are Archie’s Basic Relationships
What is Meant by the Plot of Rt versus Swtϕt
Parallel Resistivity Equations Used in Resistivity Interpretation
What is the Formation Resistivity Factor
Table of Retrievable Contents:
HOW IS EXPONENT n RELATED TO EXPONENT m
The saturation exponent n is related to both pore geometry and the interference to electrical current flow within the complex water-filled paths remaining in the pores after displacement by hydrocarbon has taken place. In Figure 1 and Eq. (3b) it is shown that n is a geometrical element similar to m. In Figure 1, it can be seen that slope n is what slope m becomes after hydrocarbon has migrated into the pores and has displaced a fraction of the water.
Historically, and in the absence of better information, the usual default value for n in water-wet rocks has been the same as for m, i.e. exponent m1. Also see discussion in APPENDIX (B)(4). However, the presence of oil at any saturation displaces some water volume and produces some electrical interference and, therefore, must increase the minimum value of n to some value higher than the value of m, all other things remaining the same. Because n is what m1 has become after hydrocarbon has occupied a fraction of the pore space, exponent n cannot have a lower value than the actual value of m1. A detailed explanation appears in APPENDIX (D), based on Figure 6, why the actual value of n cannot be lower than the actual value of m1 in the same sample, in situ or in the laboratory. Exponent n can and will increase over m1 in the presence of oil or gas as the presence of hydrocarbon decreases the volume of electrically conductive water and changes the dimensions of electrical paths, or otherwise impedes the flow of the electrical-survey current. Additionally, there can be multiple values for both m and n as oil saturation changes and/or wettability to oil changes. For oil-wet and partially-oil-wet rocks this effect can be quite significant. When oil is present, in partially oil-wet and oil-wet rocks, for any given water saturation the saturation exponent n can vary from as low as 3.0, or lower, to as high as 9.0 or more depending on the degree of wettability to oil, physical distributions of oil and water, oil properties, and rock-framework surface properties and characteristics. In Figure 1, it can be seen that at any constant value of Swt , if the redistribution of a constant fraction of oil causes the electrical interference to change, then Rt will change, and this will result in a corresponding change in the value of n.
The maximum value for n in any specific rock is that value where the presence of oil or gas produces the greatest interference. The theoretical maximum should occur where water saturation is at its irreducible value. The minimum value for n occurs where the presence of hydrocarbon produces the least interference. This minimum should occur at the water saturation where the hydrocarbon saturation is irreducible. These statements suggest that there might be a causative relationship with n in a crossplot of the relative permeabilities (kro , krw ) or of the mobilities (kro /µo, krw / µw) for oil and water vs Swt .
The exaggerated influence due to the presence of oil will increase both the combination exponent m2 for the product Swtϕt and the usual exponent n for Swt . For any given porosity and any given oil saturation, the exponents m2 and n will increase with those properties of the rock and pore walls that when covered with adhesive oil films increase the interference to the flow of electrical current through the conductive paths. These factors increase in severity with the increase in wettability to oil, finer grained sandstone (increased surface area), increased efficiency of packing, increased number of grain-to-grain contacts, finer pores and pore throats, properties of oil, interfacial tension between oilfield brine and crude oil, isolation of pores, and the physical saturation distributions of both the wetting- and nonwetting- phases whether oil or water. All these influences act in concert at their respective levels of severity to cause or alter interference to electrical current flow. These features relative to the presence of oil, and sometimes gas, must be recognized. Is there any exception? Theoretically, it is possible to hypothecate a condition whereby the value of n could have a value lower than m. But, could this condition exist where oil exists as a continuous phase and is producible? This condition will be discussed in APPENDIX (E).
Gas usually does not have the same exaggerated effect on n unless the reservoir has been filled with oil at some former time in geologic history and an adhesive film of remnant oil precedes the occupation by gas. The resistivity of a gas-bearing zone can increase, however, due to the decrease in irreducible water saturation. This, too, can be demonstrated in Figure 1. The primary exaggeration in n is with partially oil-wet and oil-wet rocks that are filled with oil or have been filled with oil at a former time whether as a reservoir or as a migration path.
A CLARIFYING CONCEPT OF ARCHIE'S RESISTIVITY RELATIONSHIPS AND PARAMETERS.
A MODEL AND DISCUSSION
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