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Numerical and Experimental Study to Determine the Permeability Anisotropy in Porous Rocks from Probe Permeameter Measurements

  • Research Article-Petroleum Engineering
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Abstract

Probe permeameter has been widely used to obtain measurements and spatial distributions of permeability in both the laboratory and field outcrop applications. It provides cheap, fast, intensive, and nondestructive permeability measurements. In the literature, the difference between steady-state and unsteady-state measurements and the effects of heterogeneity and anisotropy on probe permeameter measurements have been investigated both numerically and experimentally. However, the available work provides a method for the determination of the permeability in two principal directions only. This study fills such a gap by providing a novel solution for the steady-state single-phase flow problem for the determination of permeability anisotropy in the three principal directions using probe permeameter measurements. The solution was obtained by solving the diffusivity equation describing the steady-state flow of a single-phase fluid in a three-dimensional (3D) rectangular system. Different permeability anisotropy ratios were tested for different anisotropy cases starting from a fully isotropic sample to a fully anisotropic sample. The obtained results are presented graphically in a dimensionless space. The dimensionless parameters include the dimensionless pressure and anisotropy ratios in different flow directions. A practical procedure based on the solution is then described to evaluate the permeability in a 3D rectangular rock sample. This method requires a few measurements of steady-state flow rate and pressure drop conducted using the probe permeameter at different directions on a rectangular rock sample. The applicability of the proposed solution and developed technique is demonstrated by conducting probe permeameter measurements on three different directions of one cubical cement sample and two outcrop carbonate samples. The results obtained from the proposed method show good match (an average root-mean-square error of 0.653 mD) when compared to the reference permeability values measured on directional plugs by conventional nitrogen permeameter. The procedure described in this work can be used to have a quick and robust evaluation of permeability anisotropy from rock samples in either outcrop or laboratory studies.

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Abbreviations

\(A_{s}\) :

Cross-sectional area in s-direction, ft2

\(B\) :

Formation volume factor, bbl/STB

b :

Klinkenberg slip factor, psi

C i :

Arbitrary constants

cc:

Cubic centimeter (cm3)

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

Gas permeability, mD

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

Liquid permeability, mD

\(k_{s}\) :

Permeability in s-direction, mD

\(L\) :

Length of the sample, ft

\({\text{min}}\) :

Minute

\(P\) :

Pressure, psi

\(P_{{{\text{atm}}}}\) :

Atmospheric pressure = 14.7 psi

\(P_{{{\text{D}}_{s} }}\) :

Dimensionless pressure in s-direction

\(P_{{\text{m}}}\) :

Mean pressure, psi

\(P_{{\text{p}}}\) :

Probe pressure, psi

\(p\) :

Pressure drop across the sample, psi

\(q\) :

Fluid flow rate, cc/min

\(q_{{\text{m}}}\) :

Fluid flow rate at \(P_{{\text{m}}}\), cc/min

\(r_{{\text{p}}}\) :

Probe size, cm

\(R_{{{\text{D}}_{Pij} }}\) :

Ratio of dimensionless pressure in i-direction to that in j-direction

\(R_{ij}\) :

Permeability ratio between i-direction and j-direction (anisotropy ratio)

RMSE:

Root-mean-square error

\(s\) :

Subscript to denote the direction

\(x\) :

x-Direction

\(y\) :

y-Direction

\(z\) :

z-Direction

\(\beta_{{\text{c}}}\) :

Conversion factor to field units = \(1.127 \times 10^{ - 3}\)

\(\mu\) :

Fluid viscosity, cP

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Authors and Affiliations

  1. College of Petroleum Engineering and Geosciences, King Fahd University of Petroleum and Minerals, Dhahran, 34464, Saudi Arabia

    Khaled Al-Azani, Ammar El-Husseiny, Mohamed Mahmoud, Hasan Al-Yousef & Mahmoud Elsayed

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  1. Khaled Al-Azani
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  2. Ammar El-Husseiny
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  3. Mohamed Mahmoud
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  4. Hasan Al-Yousef
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  5. Mahmoud Elsayed
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Correspondence to Mohamed Mahmoud.

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Al-Azani, K., El-Husseiny, A., Mahmoud, M. et al. Numerical and Experimental Study to Determine the Permeability Anisotropy in Porous Rocks from Probe Permeameter Measurements. Arab J Sci Eng 46, 7019–7030 (2021). https://doi.org/10.1007/s13369-021-05433-w

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