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Experimental Permeability Tensor for Fractured Carbonate Rocks

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Abstract

This paper presents a novel petrophysical experiment for measuring the 3D permeability tensor at reservoir conditions in fractured vuggy carbonate rock. The permeability variation with confining pressure is demonstrated through the experimental investigation; the permeability ellipse plots show the decrease of permeability, as a function of the increase in effective stress. The experiment was developed at reservoir conditions (120 °C temperature and variable confining pressure) in a native whole rock sample, from the Gulf of Mexico naturally fractured and vuggy reservoir. The analysis of the laboratory data reveals the elliptical behavior of permeability. Two ellipses were generated, one corresponding to the fracture network (secondary porosity system) and another for matrix porosity and permeability (primary porosity system). An important result is the compaction of the representative fracture network ellipse until it fuses with the matrix porosity ellipse at a high confining pressure state. The test contributes to the understanding of the mechanical and flow aspects of permeability, for naturally fractured reservoirs. The experimental results provide a basis for improving reservoir simulation studies, to obtain realistic predictions of reservoir behavior.

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Abbreviations

\(k\) :

Permeability

\(k_{x}\) :

Directional permeability in the “x” axis

\(k_{y}\) :

Directional permeability in the “y” axis

\(k_{z}\) :

Directional permeability in the “z” axis

\(p_{1}\) :

Nitrogen gas injection pressure

\(q_{1}\) :

Nitrogen gas volumetric flow rate

\(\mu\) :

Nitrogen gas viscosity

\(\overline{p}\) :

Mean pressure \(\left( {p_{1} + p_{2} } \right)/2\)

\(\Delta p\) :

Pressure drop between the inlet and the outlet \(\left( {p_{1} - p_{2} } \right)\)

\(b\) :

Klinkenberg parameter

\(L\) :

Length of the core

\(\theta\) :

Opening angle exposed to nitrogen gas flow

\(\alpha\) :

One half of the opening angle \(\left( {\theta /2} \right)\)

\(G\left( \alpha \right)\) :

Geometric correction factor

\(k_{\max t}\) :

Theoretical maximum permeability

\(k_{\max r}\) :

Real maximum permeability

\(k_{{{\text{matrix}}}}\) :

Maximum theoretical permeability of the pseudo-matrix region

\(p_{c}\) :

Confining pressure

\(p_{{{\text{frac}}}}\) :

Maximum closing pressure of the fractured vuggy region

\(p_{\max r}\) :

Real maximum closing pressure of the pseudo-matrix region

\(p_{\max t}\) :

Theoretical maximum closing pressure of the pseudo-matrix region

\(k_{{H{\text{MAX}}}}\) :

Maximum transversal permeability

\(k_{H90}\) :

Minimum permeability perpendicular to \(k_{{H{\text{MAX}}}}\)

\(k_{v}\) :

Vertical permeability

\(k_{df}\) :

Directional permeability in the flow direction

\(k_{dp}\) :

Directional permeability in the velocity potential gradient vector

\(\overline{\overline{k}}\) :

Permeability tensor in the principal axes

\(\overline{\overline{k}}_{f}\) :

Permeability tensor of the fractured region

\(\overline{\overline{k}}_{m}\) :

Permeability tensor of the pseudo-matrix region

\(\overline{\overline{k}}_{pr}\) :

Permeability tensor of the primary porosity region

\(k_{330}\) :

Directional permeability 330°

\(k_{60}\) :

Directional permeability 60°

\(\vec{v}\) :

Velocity vector flow

\({\Phi }\) :

Potential velocity flow function

\(\nabla\) :

Nabla operator

\(\beta\) :

The acute angle between the Darcy velocity vector and the velocity potential flow gradient vector

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Acknowledgements

The experiments were developed within the facilities of the Fractured Rocks Laboratory “Edgar R. Rangel German” of the National Autonomous University of Mexico in Mexico City.

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Authors and Affiliations

  1. School of Engineering, National Autonomous University of Mexico UNAM, Mexico City, Mexico

    D. Cabrera & F. Samaniego

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  1. D. Cabrera
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  2. F. Samaniego
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Correspondence to D. Cabrera.

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Cabrera, D., Samaniego, F. Experimental Permeability Tensor for Fractured Carbonate Rocks. Rock Mech Rock Eng 54, 1171–1191 (2021). https://doi.org/10.1007/s00603-020-02323-9

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  • DOI: https://doi.org/10.1007/s00603-020-02323-9

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