Correlating rock packing index, tortuosity, and effective cross-sectional area with electrical quality index

Abstract

In Archie's formula, cementation factor (m) is an important parameter that plays a key role in calculating fluid saturation and characterizing reservoir. Rock geometrical attributes, e.g. electrical tortuosity, particle's specific surface area, packing index, effective cross-sectional area, and porosity, considerably affect m. Natural heterogeneities of reservoir rocks cause enormous challenges in determining the aforementioned properties in particular cross-sectional area, electrical tortuosity, and packing index. To overcome this challenge while avoiding time-consuming experiments, categorizing rocks based on an appropriate criterion is a proper solution. In this study, rock classification was performed using an electrical criterion called Electrical Quality Index (EQI), which indicates the quality of rock for transmitting electricity. Since this capacity is controlled by rock geometry, EQI must be related to petrophysical properties. To correlate EQI with the effective cross-sectional area (ψ), packing index (PI), and electrical tortuosity (τe), 23 samples were analyzed. First, samples were categorized into four electrical rock types (ERTs) with different ranges of EQI. Then, the average ψ, PI, and τe of samples belong to each ERT was computed and plotted versus the average EQI of the corresponding ERT. It was ascertained that there are clear linear relations between ψ, PI, τe and EQI average values with determination coefficient values of over 0.96. This implies considerably low dispersion around the straight trendlines that provides linear functions for predicting ψ, PI, and τe of new ERTs. The developed method is a prediction module for purposes like assessing rock geometry, and fluid saturation in hydrocarbon reservoirs. Applying this algorithm to a big dataset including a high number of samples belong to a particular reservoir leads to the better assessment of reservoir heterogeneity and rock quality. Using an analogy between electrical and hydraulic rock typing, rock geometry is investigated without the necessity of performing costly and time-consuming experiments.