A mathematical model of fluid and gas flow in nanoporous media

Paulo J. M. Monteiro, Chris H. Rycroft, Grigory Isaakovich Barenblatt

Research output: Contribution to journalArticlepeer-review

99 Scopus citations


The mathematical modeling of the flow in nanoporous rocks (e.g., shales) becomes an important new branch of subterranean fluid mechanics. The classic approach that was successfully used in the construction of the technology to develop oil and gas deposits in the United States, Canada, and the Union of Soviet Socialist Republics becomes insufficient for deposits in shales. In the present article a mathematical model of the flow in nanoporous rocks is proposed. The model assumes the rock consists of two components: (i) a matrix, which is more or less an ordinary porous or fissurized-porous medium, and (ii) specific organic inclusions composed of kerogen. These inclusions may have substantial porosity but, due to the nanoscale of pores, tubes, and channels, have extremely low permeability on the order of a nanodarcy (∼10 -21 m2) or less. These inclusions contain the majority of fluid: oil and gas. Our model is based on the hypothesis that the permeability of the inclusions substantially depends on the pressure gradient. At the beginning of the development of the deposit, boundary layers are formed at the boundaries of the low-permeable inclusions, where the permeability is strongly increased and intensive flow from inclusions to the matrix occurs. The resulting formulae for the production rate of the deposit are presented in explicit form. The formulae demonstrate that the production rate of deposits decays with time following a power law whose exponent lies between -1/2 and -1. Processing of experimental data obtained from various oil and gas deposits in shales demonstrated an instructive agreement with the prediction of the model.
Original languageEnglish (US)
Pages (from-to)20309-20313
Number of pages5
Issue number50
StatePublished - 2012
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2021-09-21
Acknowledged KAUST grant number(s): KUS-I1-004021
Acknowledgements: We thank Dmitriy B. Silin and Simon Strazhgorodskiy for their invaluable help. This publication was based on the work supported, in part, by Award KUS-I1-004021, made by King Abdullah University of Science and Technology. G.I.B. and C.H.R. were partially supported by the Director, Office of Science, Computational and Technology Research, US Department of Energy under Contract DE-AC02-05CH11231.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

ASJC Scopus subject areas

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