Pore-Scale Investigation of Porosity-Resistivity-Permeability Relationships: Implications for Petrophysical Rock Typing
- Zhonghao Sun (University of Texas at Austin) | Ayaz Mehmani (University of Texas at Austin) | Carlos Torres-Verdín (University of Texas at Austin)
- Document ID
- Society of Petrophysicists and Well-Log Analysts
- SPWLA 61st Annual Logging Symposium - Online, 24 June - 29 July, Virtual Online Webinar
- Publication Date
- Document Type
- Conference Paper
- 2020. held jointly by the Society of Petrophysicists and Well Log Analysts (SPWLA) and the submitting authors
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Porosity-resistivity-permeability relationships are critical for reliable formation evaluation. Archie’s equation, for instance, has been widely used for quantification of petrophysical properties. However, several fundamental questions remain concerning the reliability and accuracy of such relationships and their range of validity. First point of concern is the physical meaning of the associated parameters and their controlling physical properties, such as the porosity exponent, m. Second, the selection of parameter values can be ambiguous. Third, the reliability of the relationships becomes questionable when extrapolating them to spatially complex rocks, or to a wider porosity range. Underlying these questions is the fundamental notion of petrophysical rock classes, wherein a rock class is defined as exhibiting common petrophysical equations and constant associated parameters, regardless of porosity.
In this study, we use microfluidics (micromodels) augmented with pore-network modeling to shed physical intuition and quantify the range of practical validity of fundamental porosity-resistivity-permeability relationships. We develop an experimental system that provides precise electrical measurements of microfluidic chips with controlled pore-space patterns. A combination of experimental and numerical methods is used to investigate the effects of different pore geometries, pore-space evolution processes, and bimodal pore-size distributions on electrical resistivity and permeability. Further analyses of flow patterns and interstitial flow velocity distributions from pore-network modeling provide valuable information about flow phenomena in porous media.
Results indicate that both pore-size distribution and its evolution during diagenesis considerably impact the porosity-resistivity-permeability relationships. Either a large pore-size variation or a significant porosity decrease for small pores gives rise to an increase of m. In such cases, flow of electrical current is spatially localized and the fraction of porosity responsible for total conductivity decreases; m is not constant for all porosity values due to changes in interstitial flow patterns. In the case of bimodal pore-size distributions, the formation factor-porosity relationship is not linear in log-log scale because the associated flow is primarily dependent on the fraction of macropores. These results suggest that using porosity alone as pore-space property is inadequate when describing electrical flow behavior in complex rocks. We identify several flow-pattern parameters to describe effective flow underlying electrical conductivity, as well as to define and assign electrical rock classes based on available core measurements.
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