3 Phase Relative Permeability Options (EOR-BO)

STOMP-EOR and STOMP-EOR-BO consider three mobile phases: 1) aqueous, 2) nonaqueous-liquid, and 3 gas, each with a unique relative permeability. Relative permeability often varies by orders of magnitude with saturation and often is the most nonlinear component of the governing equations and constitutive relationships. For carbon sequestration in deep saline reservoirs the relative permeability of the supercritical CO₂-rich phase has been shown to a critical parameter for predicting formation injectivity and the fate of injected CO₂^[1,2]. A similar situation occurs for petroleum reservoirs; where, there is the potential for three or occasionally four relative permeability functions, but the situation is complicated by the potential for miscibility of the injected CO₂ with the oil under reservoir pressure and temperature conditions. The classical approach for predicting relative permeabilities for petroleum reservoirs is to combine binary (aqueous - nonaqueous liquid (i.e., oil-water); and nonaqueous liquid-gas (i.e., oil-gas) relative permeability relationships to yield three-phase relative permeabilities (aqueous, nonaqueous-liquid, and gas). Stone-I^[3], Stone-II^[4], and Baker^[5] combination models are common approaches and currently implemented in STOMP-EOR and STOMP-EOR-BO.

Combination Model Options (EOR) or (EOR-BO)

Click here to see the Stone I Combination Model Option

Stone-I

The three-phase aqueous relative permeability depends only on the water saturation and is that measured in aqueous/nonaqueous-liquid displacement experiments.

The three-phase gas relative permeability depends only on the gas saturation and is that measured in gas/nonaqueous-liquid displacement experiments at the irreducible aqueous saturation.

The three-phase nonaqueous-liquid relative permeability depends only on the gas and aqueous saturation and uses the relative permeability of the nonwetting fluid in the aqueous/nonaqueous-liquid experiment, and the wetting fluid in the nonaqueous-liquid/gas experiment.

Click here to see the Stone-II Combination Model Option

Stone-II

The three-phase aqueous relative permeability depends only on the water saturation and is that measured in aqueous/nonaqueous-liquid displacement experiments.

The three-phase gas relative permeability depends only on the gas saturation and is that measured in gas/nonaqueous-liquid displacement experiments at the irreducible aqueous saturation.

Click here to see the Baker Combination Model Option

Baker

The three-phase aqueous relative permeability depends the water, gas, and nonaqueous-liqud saturations and both aqueous/nonaqueous-liquid and aqueous/gas displacement experiments.

The three-phase gas relative permeability depends the water, gas, and nonaqueous-liqud saturations and both nonaqueous-liquid/gas and aqueous/gas displacement experiments.

The three-phase nonaqueous-liquid relative permeability depends the water, gas, and nonaqueous-liqud saturations and both nonaqueous-liquid/gas and aqueous/nonaqueous-liquid displacement experiments.

Binary Model Options (EOR) or (EOR-BO)

Click here to see the Corey Gas Relative Permeability versus Liquid Saturation (Gas-Oil Displacement)

Corey Gas Relative Permeability versus Total-Liquid Saturation

Corey function for non-wetting fluid.

Click here to see the Corey Nonaqueous-Liquid Relative Permeability versus Liquid Saturation (Gas-Oil Displacement)

Corey Nonaqueous-Liquid Relative Permeability versus Total-Liquid Saturation

Corey function for wetting fluid.

Click here to see the Corey Nonaqueous-Liquid Relative Permeability versus Aqueous Saturation (Oil-Water Displacement)

Corey Nonaqueous-Liquid Relative Permeability versus Aqueous Saturation

Corey function for non-wetting fluid.

Click here to see the Corey Aqueous Relative Permeability versus Aqueous Saturation (Oil-Water Displacement)

Corey Aqueous Relative Permeability versus Aqueous Saturation

Corey function for wetting fluid.

Click here to see the LET Gas Relative Permeability versus Liquid Saturation (Gas-Oil Displacement)

LET Gas Relative Permeability versus Total-Liquid Saturation

LET function for non-wetting fluid.

Click here to see the LET Nonaqueous-Liquid Relative Permeability versus Liquid Saturation (Gas-Oil Displacement)

LET Nonaqueous-Liquid Relative Permeability versus Total-Liquid Saturation

LET function for wetting fluid.

Click here to see the LET Nonaqueous-Liquid Relative Permeability versus Aqueous Saturation (Oil-Water Displacement)

LET Nonaqueous-Liquid Relative Permeability versus Aqueous Saturation

LET function for non-wetting fluid.

Click here to see the LET Aqueous Relative Permeability versus Aqueous Saturation (Oil-Water Displacement)

LET Aqueous Relative Permeability versus Aqueous Saturation

LET function for wetting fluid.

References

[1] Bennion, B, and S Bachu. 2005. “Relative permeability characteristics for supercritical CO₂ displacing water in a variety of potential sequestration zones in the Western Canada Sedimentary Basin. Society of Petroleum Engineers, SPE 95547, In proceedings of 2005 SPE Annual Technical Conference and Exhibition held in Dallas, Texas, USA, 9-12 October 2005.

[2] Juanes, R, EJ Spiten, FM Orr Jr, and MJ Blunt. 2006. “Impact of relative permeability hysteresis on geological CO₂ storage.” Water Resources Research, 42:W12418, doi:10.1029/2005WR004806.

[3] Stone, HL. 1970. “Probability model for estimating three-phase relative permeability.” Journal of Petroleum Technology, 22(2):214–218. SPE-2116-PA. http://dx.doi.org/10.2118/2116-PA.

[4] Stone, HL. 1973. “Estimation of three-phase relative permeability and residual oil data.” Journal of Canadian Petroleum Technology, 12(4):53-61. http://dx.doi.org/10.2118/73-04-06.

[5] Baker, LE. 1988. “Three-phase relative permeability correlations.” Presented at the SPE Enhanced Oil Recovery Symposium, Tulsa, Oklahoma, 16-21 April 1988. SPE-17369-MS. http://dx.doi.org/10.2118/17369-MS.