Estimation of hydrocarbon pore volume, HCPV, from resistivity logs can be quite troublesome in some complex heterogeneous reservoirs. Most water saturation-formation resistivity models that work well for some reservoir give unreliable results for others. No single model works for all types of reservoirs scenarios.
This paper presents the theory of formation resistivity in porous media. The paper develops the theory from the parallel resistivity model and then extends it for series resistivity model.
When applied for clean sand, the theory derives Archie equations from first principle. The derivations show that both porosity exponent and saturation exponent are of the same origin and should have the same name. A better name for both parameters should be tortuosity exponent of a component with respect to its fraction in a control volume. It is also advantageous to treat as a single parameter rather than two separate parameters.
In addition, this theory derives new shaly sand models for estimating HCPV. These new shaly sand models can be used for different type of shale distribution by adjusting the value of a single parameter in the models. The formation resistivity theory is also used to derive formation resistivity models for conductive rock matrix reservoirs and dual/triple porosity reservoirs. A new equation for calculating composite porosity exponent is also developed.
Field data are used to validate this work. The theory, when applied for each scenario, derives formation resistivity models for estimating reliable HCPV of different reservoir scenarios and types. Moreover, the strength of this theory is its ability to generate models that closely resembles models that have proved to work well for the reservoir cases for which they were developed. Although this work does not test the theory for the cases of tight sand, shale gas and other unconventional reservoirs due to unavailability of such data, there is a strong possibility that it would work for such reservoirs if the necessary data were available.