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Quantifying the Directional Connectivity of Rock Constituents and its Impact on Electrical Resistivity of Organic-Rich Mudrocks

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Quantifying the hydrocarbon transport mechanism in organic-rich mudrocks is still a challenge. Scientific consensus holds that directional connectivity of organic matter within organic-rich mudrocks significantly affects production in such unconventional reservoirs. Furthermore, directional connectivity of matrix constituents has a significant impact on the physical properties of organic-rich mudrocks such as electrical resistivity. The latter causes a significant uncertainty in assessment of petrophysical properties such as hydrocarbon saturation. A quantitative approach is, however, required to improve formation evaluation of organic-rich mudrocks. This paper first introduces a method to quantify directional connectivity of the matrix constituents. Electrical resistivity of three-dimensional pore-scale rock images is then numerically estimated using the finite difference method. The results of numerical simulations for synthetic organic-rich mudrocks with different levels of directional connectivity of kerogen network confirmed that (a) the presence of conductive mature kerogen can significantly impact the electrical resistivity of the rock in different directions and the corresponding estimates of fluid saturations and (b) the directional connectivity of the kerogen network has a measurable impact on the electrical resistivity of the rock. The synthetic examples, including pyrite, confirm that pyrite’s presence and its directional connectivity affects the electrical resistivity of the rock even in low concentrations. Neglecting the presence of conductive kerogen and pyrite can result in up to a 17.9 and 23 % overestimate in water saturation, respectively. The results show up to 31 and 37 % variation in electrical resistivity caused by variation in directional connectivity (i.e., ranging from dispersed to layered distribution) of kerogen and pyrite networks, respectively. Furthermore, a measurable difference was observed in effective electrical resistivity of organic-rich mudrocks between the horizontal and vertical directions. Finally, the results confirm the importance of taking into account anisotropy and directional connectivity of conductive rock components for enhanced assessment of hydrocarbon saturation in organic-rich mudrocks.

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The work reported in this paper was funded by the Texas A&M University Joint Industry Research Program on Multi-Scale Formation Evaluation, jointly sponsored by Aramco Services Company, BHP Billiton, BP, Chevron, ConocoPhillips, and Devon Energy. Our sincere gratitude goes to Society of Petroleum Engineers (SPE) for supporting this project via Junior Faculty Research Initiation Award and American Chemical Society (ACS) through ACS PRF Doctoral New Investigator (DNI) Research Grant. Finally, we thank the Texas A&M Supercomputing Facility for providing computing resources used for the numerical simulations in this paper.

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Correspondence to Zoya Heidari.



List of symbols

\(a\) :

Archie’s factor ()

\(C_\mathrm{w}\) :

Formation water salt concentration (kppm)

\(h\) :

Dimension of a cubic voxel (m)

\(i_{\alpha }(t)\) :

Position in \(i\) direction at time t for the \(\alpha \)th random walker

\(i_{\alpha }(0)\) :

Initial position in \(i\) direction for the \(\alpha \)th random walker

\(M\) :

Total number of the connected conductive clusters

\(m\) :

Archie’s porosity exponent ()

\(N\) :

Total number of random walkers

\(n\) :

Archie’s water saturation exponent ()

\(R_\mathrm{h}\) :

Electrical resistivity in horizontal direction (ohm m)

\(R_\mathrm{v}\) :

Electrical resistivity in vertical direction (ohm m)

\(S_\mathrm{w}\) :

Water saturation (%)

\(t\) :

Simulation time (s)

\(U\) :

Electric potential (V)

\(V_\mathrm{HC,k}\) :

Volume of hydrocarbon in kerogen pore space (m\(^{3})\)

\(V_\mathrm{HC,nk}\) :

Volume of hydrocarbon outside kerogen pore space (m\(^{3})\)

\(V_\mathrm{k}\) :

Volume of mature kerogen (m\(^{3})\)

\(V_\mathrm{R}\) :

Volume of rock (m\(^{3})\)

\(V_\mathrm{w}\) :

Volume of formation water (m\(^{3})\)

\(Z_{j}\) :

Volumetric concentration of the \(j\)th connected conductive cluster (%)

\(Z_\mathrm{k}\) :

Volumetric concentration of kerogen (%)

\(Z_\mathrm{w}\) :

Volumetric concentration of water (%)

\(\beta \) :

Connectivity parameter

\(\gamma \) :

Connectivity parameter

\(\sigma \) :

Electrical conductivity (S/m)

\(\tau \) :


\(\tau _i\) :

Directional tortuosity in i direction

\(\tau _\mathrm{h}\) :

Directional tortuosity in horizontal direction

\(\tau _\mathrm{k,h} \) :

Directional tortuosity of kerogen network in horizontal direction

\(\tau _\mathrm{v} \) :

Directional tortuosity in vertical direction

\(\tau _\mathrm{k,v} \) :

Directional tortuosity of kerogen network in vertical direction

\(\phi \) :

Total porosity (%)

\(\phi _\mathrm{w} \) :

Water-filled porosity (%)

\(\Psi _i \) :

Directional connectivity in i direction

\(\Psi _\mathrm{h} \) :

Directional connectivity in horizontal direction

\(\Psi _\mathrm{k,h} \) :

Directional connectivity of kerogen network in horizontal direction

\(\Psi _\mathrm{p,h} \) :

Directional connectivity of pyrite network in horizontal direction

\(\Psi _\mathrm{v} \) :

Directional connectivity in vertical direction

\(\Psi _\mathrm{k,v} \) :

Directional connectivity of kerogen network in vertical direction

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Chen, H., Heidari, Z. Quantifying the Directional Connectivity of Rock Constituents and its Impact on Electrical Resistivity of Organic-Rich Mudrocks. Math Geosci 48, 285–303 (2016).

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