Published by the DTI Oil & Gas Directorate for the reservoir engineering and IOR community in the UK.
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Fazed by Three-Phase Relperms?

Eugene Balbinski, AEA Technology examines the use and misuse of three-phase relperm correlations (co author Stephen Goodyear) - (eugene.balbinski@aeat.co.uk)

Three-phase flow may occur in practice when injected gas is not fully miscible, or when gas is released from solution as oil pressures fall below the bubble point. There is increasing interest in modelling such flows reliably, due to existing and potential gas injection and depressurisation projects in the North Sea and elsewhere. In modelling such flows reservoir engineers might be forgiven for regarding three-phase relperm models as 'black-boxes' and trusting in simulator defaults, as laboratory measured data are rare, sparse and prone to error. However, choice and application of model can significantly affect predictions of oil rates and recovery, which can be critical in decisions regarding the future of a development.

Three-phase oil relperm models - The most popular models generally use conventional two-phase oil/water and oil/gas relperms to predict three-phase oil relperms. Although such models may look impressive, all that is really being done is some form of mathematical interpolation, with little physical input. It might be hoped that the range of estimates from different models is not too large. To test this, the immiscible WAG process was simulated for a number of three-phase models on a fine grid assuming a typical North Sea geology and realistic well constraints. The range of predictions was large, from a significant incremental recovery to less than nothing! This could be the difference between a viable economic project and one not even technically viable. However, by understanding the main reasons for the different predictions, some models can be discarded and the range of predictions narrowed.

Recommendations for best practice

• Use transparent and readily understandable three-phase relperm models without unwarranted physical assumptions or mathematical problems. In particular, don't use either of Stone's models. They both assume the oil relperm increases linearly at low oil saturations and, furthermore, Stone II tends to predict high residual oil saturations.
• Calculate a range of estimates, not only from different models, but also from alternative physical assumptions, for example, three-phase residual oil saturation.
• It is best to choose models which allow the three-phase residual oil saturation to be specified, or can be modified to do so.

References available through websites

• Fazed by three-phase relperms?, Eugene Balbinski and Stephen Goodyear, SPE Review, March 1999.

• Key characteristics of three-phase oil relative permeability formulations for improved oil recovery predictions, Balbinski, E F, Fishlock, T P, Goodyear, S G and Jones, P I R, Petroleum Geoscience, Vol 5, 1999, pp339-346.

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