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:
THE GRAPHICAL MODEL
Archie’s classic relationships usually are considered to be clean-sand relationships. In shaly sands where clay shales produce additional electrical conductivity, Archie’s relationships are said not to apply. Relative to Archie’s original concept, this pronouncement is correct. In the concept born of this model, an overall version of Archie’s relationships emerges that is shown to apply to shaly sands and other heterogeneous rocks that exhibit uniformity within the depth of investigation of the logging tools. This concept pertains to Archie’s relationships and any other relationships that make use of Archie’s parameters. This concept derives and defines each of the terms in Archie’s relationships and explains how the relationships apply to heterogeneous rocks.
Figure 1 is an illustration of the basic resistivity model used in this concept. Figure 1 is not intended to be a working graphical procedure, it is informative and explanatory. This figure illustrates the common logarithm of the resistivity of a single sample of undisturbed total rock volume (Rt ohms m2/m) versus the common logarithm of the water volume (Swtϕt × 1.0 m3) occupying the pores of that same rock volume. The diagram shows how a unit volume of water (Swtϕt ) is related to resistivity (Rt ). The model in Figure 1 is illustrative in nature and is not drawn to scale. The X - axis has been expanded so that detail can be observed. The figure is designed primarily to illustrate the electrical behavior of a volume of formation water as its environment changes with variations of insulating rock and insulating fluid.
In Figure 1, the origin of the diagram is represented by Rwe (and Ft = 1.0) when ϕt is 1.0 or 100%. Where it commonly has been believed there are only two slopes in Archie’s concept, the diagram demonstrates that there actually are three slopes, each representing exponents in Archie's concept. They are m1, m2 , and n. The first is m1 that pertains to the single parameter ϕt . This is the familiar porosity exponent m known in industry. Sometimes for the sake of clarity the term m1 will be used instead of m. The second exponent is m2 which pertains to two parameters, ϕt and Swt , and is the exponent for the product Swtϕt . The third is the exponent n that pertains only to Swt , and is the saturation exponent commonly known in industry.
From the diagram, the total fractional volume of water in the rock is represented by the projection on the X - axis under the two slopes, representing m and n, drawn from 100% water at Rwe to the intersection of the line representing slope n extrapolated to intercept resistivity level Rt . The fraction of water in total pore volume, Swt , and the fraction of water in the total rock volume, Swtϕt , are depicted on the X - axis by log10ϕt and log10Swt . The fraction of total rock volume that is water provides the conductivity to the rock resulting in resistivity Rt. As oil or gas displaces water, the water saturation, Swt , decreases to the right as the saturation of oil or gas, (1.0 - Swt ) , increases.
It is illustrated in the model that there can be conditions related to the presence of hydrocarbon, oil in particular, that cause in situ rock resistivities to increase to extraordinarily high values. In oil-wet rocks the values of n will increase greatly (Keller, 1953; Sweeney and Jennings, 1960). The presence of oil in oil-wet rocks produces a very exaggerated interference to the flow of electrical-survey current. Resistivity Rt then will be increased correspondingly with the wettability to oil and resulting interference. The figure also shows that, under these conditions, when the commonly used default values of n = m are employed, the line representing the slope of exponent n will be extended far to the right to intersect the level of the measured or derived value of Rt at an unreasonable and unacceptably low value of Swt .
This illustrates the resistivity interpretation problem in oil-wet rocks or other rocks where resistivity is exaggerated by the properties of oil. Here, when the default value of n is equal to m, the usual n intercepts Rt far to the right in the model in Figure 1, suggesting that water saturation is very low. In such cases, the derived saturations from the basic Archie equation, or from any more comprehensive equation, cannot be correct and cannot be used in any field or reservoir description when the common default value for n is employed. This illustrates a problematic but common occurrence when using the usual resistivity interpretation methods by both private and commercial organizations. The cause of this problem and others must be recognized before they can be addressed. An exploration of the graphic model will promote a better understanding of resistivity behavior in rocks. This exploration will be accompanied by parallel development of the terms and parameters in the basic Archie relationships. What each term or parameter represents is the key to understanding where to begin to solve interpretation problems.
A CLARIFYING CONCEPT OF ARCHIE'S RESISTIVITY RELATIONSHIPS AND PARAMETERS.
A MODEL AND DISCUSSION
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