Journal
ADVANCES IN WATER RESOURCES
Volume 112, Issue -, Pages 170-188Publisher
ELSEVIER SCI LTD
DOI: 10.1016/j.advwatres.2017.12.016
Keywords
Multiphase flow in porous media; Viscous coupling; Mixture theory; Dynamic relative permeability; Mathematical modeling; Co- and counter-current flow
Categories
Funding
- Research Council of Norway
- ConocoPhillips Skandinavia AS
- Aker BP
- Eni Norge AS
- Maersk Oil Norway AS
- DONG Energy A/S, Denmark
- Statoil Petroleum AS
- ENGIE EP NORGE AS
- Lundin Norway AS
- Halliburton AS
- Schlumberger Norge AS
- Wintershall Norge AS of The National IOR Centre of Norway
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It is well known that relative permeabilities can depend on the flow configuration and they are commonly lower during counter-current flow as compared to co-current flow. Conventional models must deal with this by manually changing the relative permeability curves depending on the observed flow regime. In this paper we use a novel two-phase momentum-equation-approach based on general mixture theory to generate effective relative permeabilities where this dependence (and others) is automatically captured. In particular, this formulation includes two viscous coupling effects: (i) Viscous drag between the flowing phases and the stagnant porous rock; (ii) viscous drag caused by momentum transfer between the flowing phases. The resulting generalized model will predict that during co-current flow the faster moving fluid accelerates the slow fluid, but is itself decelerated, while for counter-current flow they are both decelerated. The implications of these mechanisms are demonstrated by investigating recovery of oil from a matrix block surrounded by water due to a combination of gravity drainage and spontaneous imbibition, a situation highly relevant for naturally fractured reservoirs. We implement relative permeability data obtained experimentally through co-current flooding experiments and then explore the model behavior for different flow cases ranging from counter-current dominated to co-current dominated. In particular, it is demonstrated how the proposed model seems to offer some possible interesting improvements over conventional modeling by providing generalized mobility functions that automatically are able to capture more correctly different flow regimes for one and the same parameter set.
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