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Study of empirical correlation between permeability and porosity with application for permeability upscaling

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Abstract

The determination of porosity and permeability distribution along the reservoir is very important and can be determined by different field and laboratory experiments, i.e., core flooding experiments, seismic and well log data, well testing. At the field level, however, information regarding spatial distribution of porosity and permeability is very sparse, and additional techniques such as geostatistics and correlations may be used. The literature presents a variety of correlations between permeability and porosity, considering different parameters, such as probability distribution functions and tortuosity of porous media. General behavior of porous media, however, can be described with a normal distribution for porosities and log-normal distribution for permeabilities. This paper proposes the use of a simplified empirical equation to represent the correlation between porosity and permeability. Methodologies to derive the empirical parameters from experimental data, or desired ranges of porosities and permeability are proposed and applied. Considerations regarding range of validity of this correlation are made by the use of a steady-state single-phase reservoir simulation. Results show that the procedures for the creation of maps of permeability, obtained from the empirical correlation, provide a reasonable distribution of values and represent well the observed data from the laboratory. The procedure for the creation of synthetic fields, obtained by fixing values of maximum and minimum permeabilities, also shows good results and can be a faster way to create synthetic field cases. Regarding the application of these correlations for upscaling, results show that the correlation remains valid when the scale is increased. Numerical dispersion can, however, be observed. The errors obtained, however, increase significantly when permeability ranges increase, meaning that the correlation can only be used with confidence when no significant variations in porosity and permeability are present. Although the literature shows other methodologies for estimating upscaling values of permeability, the approach proposed here is easier and faster to be implemented and may be used in a complementary way for field-level upscaling.

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Abbreviations

\(A, \,B\) :

Coefficient for empirical correlation

\(a,\, b, \,c, \,d,\, e, \,f, \,h,\,m,\, Z\) :

Parameters for generation of 2D 5-spot porosity map

\(g\) :

Acceleration of gravity (m/s2)

\(H\) :

Height of grid block (m)

\(k\) :

Absolute permeability

\(L\) :

Length of core sample

\(p\) :

Pressure (kPa)

\(x, y\) :

Spatial coordinates in the 2D porosity map

\(\mu\) :

Viscosity (cp)

\(\rho\) :

Specific mass (kg/m3)

\(\phi\) :

Porosity (fraction

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Acknowledgements

The authors are grateful to the University of Campinas (UNICAMP), the Center of Petroleum Studies (CEPETRO), and the National Brazilian Petroleum, Gas and Biofuels Agency, ANP for their support to accomplish this work. The authors thank CMG for the software support.

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Authors and Affiliations

  1. Center for Superior Education Foz Do Itajaí / Santa Catarina State University – CESFI/UDESC, Balneário Camboriú, Brazil

    L. F. Lamas

  2. Center for Petroleum Studies / University of Campinas – CEPETRO/UNICAMP, Campinas, Brazil

    E. M. Ruidiaz & A. C. Vidal

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  1. L. F. Lamas
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  2. E. M. Ruidiaz
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  3. A. C. Vidal
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Correspondence to L. F. Lamas.

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Technical Editor: Celso Kazuyuki Morooka.

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Lamas, L.F., Ruidiaz, E.M. & Vidal, A.C. Study of empirical correlation between permeability and porosity with application for permeability upscaling. J Braz. Soc. Mech. Sci. Eng. 43, 530 (2021). https://doi.org/10.1007/s40430-021-03227-7

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