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Scale dependent dynamic capillary pressure effect for two-phase flow in porous media

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posted on 04.11.2014 by Luqman K. Abidoye, Diganta Das
Causes and effects of non-uniqueness in capillary pressure and saturation (Pc–S) relationship in porous media are of considerable concern to researchers of two-phase flow. In particular, a significant amounts of discussion have been generated regarding a parameter termed as dynamic coefficient (τ) which has been proposed for inclusion in the functional dependence of Pc–S relationship to quantify dynamic Pc and its relation with time derivative of saturation. While the dependence of the coefficient on fluid and porous media properties is less controversial, its relation to domain scale appears to be dependent on artefacts of experiments, mathematical models and the intra-domain averaging techniques. In an attempt to establish the reality of the scale dependency of the τ–S relationships, we carry out a series of well-defined laboratory experiments to determine τ–S relationships using three different sizes of cylindrical porous domains of silica sand. In this paper, we present our findings on the scale dependence of τ and its relation to high viscosity ratio (μr) silicone oil–water system, where μr is defined as the viscosity of non-wetting phase over that of the wetting phase. An order of magnitude increase in the value of τ was observed across various μr and domain scales. Also, an order of magnitude increase in τ is observed when τ at the top and the bottom sections in a domain are compared. Viscosity ratio and domain scales are found to have similar effects on the trend in τ–S relationship. We carry out a dimensional analysis of τ which shows how different variables, e.g., dimensionless τ and dimensionless domain volume (scale), may be correlated and provides a means to determine the influences of relevant variables on τ. A scaling relationship for τ was derived from the dimensionless analysis which was then validated against independent literature data. This showed that the τ–S relationships obtained from the literature and the scaling relationship match reasonably well.

Funding

This study has been funded by the EPSRC [grant no. GR/S94315/01]. A PhD studentship awarded to Mr. Luqman Abidoye under the Petroleum Technology Development Fund (PTDF), Nigeria, to carry out the work in this paper is much appreciated.

History

School

  • Aeronautical, Automotive, Chemical and Materials Engineering

Department

  • Chemical Engineering

Published in

Advances in Water Resources

Volume

0

Issue

0

Pages

0 - ?

Citation

ABIDOYE, L.K. and DAS, D.B., 2014. Scale dependent dynamic capillary pressure effect for two-phase flow in porous media. Advances in Water Resources, 74, pp.212-230.

Publisher

Elsevier © The authors

Version

VoR (Version of Record)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution 3.0 Unported (CC BY 3.0) licence. Full details of this licence are available at: http://creativecommons.org/licenses/by/3.0/

Publication date

2014

Notes

This is an Open Access Article. It is published by Elsevier under the Creative Commons Attribution 3.0 Unported Licence (CC BY). Full details of this licence are available at: http://creativecommons.org/licenses/by/3.0/

ISSN

0309-1708

Language

en

Licence

Exports