Formation-Resistivity Theory: How Archie Equations, Shaly-Reservoir Models, Conductive Rock-Matrix Model, and Dual-Triple-Porosity Models Are Related
- Philip C. Iheanacho (Smart Drilling Services Limited)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- May 2014
- Document Type
- Journal Paper
- 141 - 151
- 2014.Society of Petroleum Engineers
- 2.4.3 Sand/Solids Control, 4.1.2 Separation and Treating, 5.8.2 Shale Gas, 4.1.5 Processing Equipment, 5.6.1 Open hole/cased hole log analysis
- well log analysis interpretation
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- 736 since 2007
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The 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 reservoirs give unreliable results for others. No single model works for all types of reservoir 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 the series-resistivity model. When applied for clean sand, the theory derives Archie equations from the 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 the 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 types 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 the 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 the reliable HCPV of different reservoir scenarios and types. Moreover, the strength of this theory is its ability to generate models that closely resemble 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 tightsand, shale-gas, and other unconventional reservoirs because of the unavailability of such data, the author is of the opinion that the theory can easily be extended for such reservoirs if the necessary data are available.
|File Size||379 KB||Number of Pages||11|
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