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Experimental and theoretical study of gas/oil relative permeability

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Abstract

Gas injection is a proven economical process that significantly increases oil and condensate recovery from hydrocarbon reservoirs. Relative permeability is an important parameter in modeling, simulation, and evaluation of gas injection. In this study, new empirical-mathematical models are developed to predict the relative permeability of gas-oil systems in different rock and fluid systems. The Multi-Gene Genetic Programming (MGGP) technique is employed to develop relative permeability equations. The smart correlations presented in this work require capillary number, interfacial tension, API, gas molecular weight, and viscosity ratio as extra input variables to improve its precision and accuracy. The significance of each parameter is evaluated by statistical approach and Taguchi experimental design. The new models are evaluated by experimental data extracted from literature and validated by extensive error analysis. Additionally, laboratory tests were performed for determining gas-oil relative permeability which were used to check the accuracy of new developed correlations. In relative permeability curves for different gas flow rates, the coupling effect becomes strong and, in competition with the inertia effect, causes changes in the relative permeability with flow rate. The comparison of the experimental results of this study with the new proposed correlation resulted in a root-mean-square error (RMSE) of 0.0796 for gas relative permeability and 0.0564 for oil relative permeability. The results strongly admit the MGGP approach and high accuracy of developed mathematical correlations.

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Abbreviations

K abs :

absolute permeability

\(S_{\mathrm {g},\max }\) :

maximum gas saturation

API:

American Petroleum Institute gravity

MWg :

gas molecular weight

IFT:

interfacial tension

μ g/μ o :

ratio of gas viscosity to oil viscosity

N ca :

capillary number

k ro :

oil relative permeability

S o :

oil saturation

S g :

gas saturation

\(S_{\mathrm {o},\max }\) :

maximum oil saturation

S wc :

connate water saturation

S or :

residual oil saturation

S gc :

critical gas saturation

\(K_{\text {ro},\max }\) :

critical gas saturation

\(K_{\text {ro},\max }\) :

maximum oil relative permeability

\(K_{\text {rg},\max }\) :

maximum gas relative permeability

k rg :

gas relative permeability

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Authors and Affiliations

  1. Department of Petroleum Engineering, Faculty of Petroleum, Gas and Petrochemical Engineering, Persian Gulf University, Bushehr, 7516913897, Iran

    Zohreh Farmani & Reza Azin

  2. Gas Condensate and Carbon Management (GCCM) Research Group, Persian Gulf University, Bushehr, Iran

    Reza Azin

  3. Department of Chemical Engineering, Faculty of Petroleum, Gas and Petrochemical Engineering, Persian Gulf University, Bushehr, Iran

    Mohamad Mohamadi-Baghmolaei

  4. Department of Mechanical Engineering, Faculty of Engineering, Persian Gulf University, Bushehr, Iran

    Rouhollah Fatehi

  5. Department of Petroleum Engineering, School of Chemical and Petroleum Engineering, Shiraz University, Shiraz, Iran

    Mehdi Escrochi

  6. IOR-EOR Research Institute, Shiraz University, Shiraz, Iran

    Mehdi Escrochi

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  1. Zohreh Farmani
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  2. Reza Azin
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Correspondence to Reza Azin.

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Farmani, Z., Azin, R., Mohamadi-Baghmolaei, M. et al. Experimental and theoretical study of gas/oil relative permeability. Comput Geosci 23, 567–581 (2019). https://doi.org/10.1007/s10596-018-9806-9

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