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Journal of Porous Media
IF: 1.752 5-Year IF: 1.487 SJR: 0.43 SNIP: 0.762 CiteScore™: 2.3

ISSN Print: 1091-028X
ISSN Online: 1934-0508

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Journal of Porous Media

DOI: 10.1615/JPorMedia.v14.i8.50
pages 709-720

THE GAS-OIL GRAVITY DRAINAGE MODEL IN A SINGLE MATRIX BLOCK: A NEW RELATIONSHIP BETWEEN RELATIVE PERMEABILITY AND CAPILLARY PRESSURE FUNCTIONS

Morteza Dejam
Department of Petroleum Engineering, College of Engineering and Applied Science, University of Wyoming, 1000 E. University Avenue, Laramie, Wyoming 82071-2000, USA
Mohammad Hossein Ghazanfari
Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, Iran
Mohammadreza Kamyab
Department of Petroleum Engineering, Curtin University, Bentley, WA, Australia
Mohsen Masihi
Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, Iran

ABSTRACT

This work concerns modeling of gas-oil gravity drainage for a single block of naturally fractured reservoirs. The non-linearity induced from saturation-dependant capillary pressure and relative permeability functions makes a gravity drainage model difficult to analytically and numerically solve. Relating the capillary pressure and relative permeability functions is a potential method to overcome this problem. However, no attempt has been made in this regard. In this study a generalized one-dimensional form of gas-oil gravity drainage model in a single matrix block, presented in the literature, is considered. In contrast with commonly used forms of capillary pressure and relative permeability functions, more realistic models, which are in power law, are used in the model. It has been found that the nonlinearity of the generalized model is canceled only if the powers of capillary pressure and relative permeability functions are related as n = m + 1. The Fourier Laplace inversion method is applied to numerically solve the developed model and generate the drainage flow rate and the oil saturation profiles at different values of m and n powers. The results of this work might help to obtain a new transfer function for a dual-porosity model, which might improve the reliability of simulators for evaluation of naturally fractured reservoirs.


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