3 Phase Relative Permeability Syntax (EOR-BO)

STOMP-EOR and STOMP-EOR-BO 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. The 3-phase relative permeability model and its parameters are considered to be intrinsic properties of the rock/soil and are associated with grid cells via the rock/soil zonation.  The syntax for the 3 Phase Relative Permeability Card requires that a combination model be specified, followed by a series of binary models and parameters, for each rock/soil type.

Card Title

~3 Phase Relative Permeability Card,

 Combination Model, Binary Models and Parameters

Repeat

Repeat for each rock/soil type 

 

Info

IJK, JKI, or KIJ Indexing

Expand for Syntax

If Rock/Soil Name is IJK Indexing, JKI Indexing, or KIJ Indexing then a parameter value can replaced with an external file using the following formatting for ASCII files:

...,file:file name,...

or binary files:

...,binary file:file name,...

The external file will contain parameter values for every grid-cell ordered according to the indexing scheme (i.e., IJK, JKI, or KIJ). Units shown in the input line will be applied to all parameters in the external file.

Choose One

Chose one Combination Model

Stone I Combination Model

Rock/Soil Name,Stone I,...

 

Click here to see binary models...

Choose One

Choose one Gas Relative Permeability versus Liquid Saturation Model

Corey Gas Relative Permeability versus Liquid Saturation (Gas-Oil Displacement)

...,End-Point Relative Permeability,Exponent,Residual Total-Liquid Saturation,Residual Gas Saturation,...

LET Gas Relative Permeability versus Liquid Saturation (Gas-Oil Displacement)

...,End-Point Relative Permeability,L Parameter,E Parameter,T Parameter,Residual Total-Liquid Saturation,Residual Gas Saturation,...

Choose One

Choose one Nonaqueous-Liquid Relative Permeability versus Liquid Saturation Model

Corey Nonaqueous-Liquid Relative Permeability versus Liquid Saturation (Gas-Oil Displacement)

...,End-Point Relative Permeability,Exponent,Residual Total-Liquid Saturation,Residual Gas Saturation,...

LET Nonaqueous-Liquid Relative Permeability versus Liquid Saturation (Gas-Oil Displacement)

...,End-Point Relative Permeability,L Parameter,E Parameter,T Parameter,Residual Total-Liquid Saturation,Residual Gas Saturation,...

Choose One

Choose one Aqueous Relative Permeability versus Aqueous Saturation Model

Corey Aqueous Relative Permeability versus Aqueous Saturation (Oil-Water Displacement)

...,End-Point Relative Permeability,Exponent,Residual Aqueous Saturation,Residual Nonaqueous-Liquid Saturation,...

LET Aqueous Relative Permeability versus Liquid Saturation (Oil-Water Displacement)

...,End-Point Relative Permeability,L Parameter,E Parameter,T Parameter,Residual Aqueous Saturation,Residual Nonaqueous-Liquid Saturation,...

Choose One

Choose one Nonaqueous-Liquid Relative Permeability versus Aqueous Saturation Model

Corey Nonaqueous-Liquid Relative Permeability versus Aqueous Saturation (Oil-Water Displacement)

...,End-Point Relative Permeability,Exponent,Residual Aqueous Saturation,Residual Nonaqueous-Liquid Saturation,...

LET Nonaqueous-Liquid Relative Permeability versus Liquid Saturation (Oil-Water Displacement)

...,End-Point Relative Permeability,L Parameter,E Parameter,T Parameter,Residual Aqueous Saturation,Residual Nonaqueous-Liquid Saturation,...

Stone II Combination Model

Rock/Soil Name,Stone II,...

Click here to see binary models...

Choose One

Choose one Gas Relative Permeability versus Liquid Saturation Model

Corey Gas Relative Permeability versus Liquid Saturation (Gas-Oil Displacement)

...,End-Point Relative Permeability,Exponent,Residual Total-Liquid Saturation,Residual Gas Saturation,...

LET Gas Relative Permeability versus Liquid Saturation (Gas-Oil Displacement)

...,End-Point Relative Permeability,L Parameter,E Parameter,T Parameter,Residual Total-Liquid Saturation,Residual Gas Saturation,...

Choose One

Choose one Nonaqueous-Liquid Relative Permeability versus Liquid Saturation Model

Corey Nonaqueous-Liquid Relative Permeability versus Liquid Saturation (Gas-Oil Displacement)

...,End-Point Relative Permeability,Exponent,Residual Total-Liquid Saturation,Residual Gas Saturation,...

LET Nonaqueous-Liquid Relative Permeability versus Liquid Saturation (Gas-Oil Displacement)

...,End-Point Relative Permeability,L Parameter,E Parameter,T Parameter,Residual Total-Liquid Saturation,Residual Gas Saturation,...

Choose One

Choose one Aqueous Relative Permeability versus Aqueous Saturation Model

Corey Aqueous Relative Permeability versus Aqueous Saturation (Oil-Water Displacement)

...,End-Point Relative Permeability,Exponent,Residual Aqueous Saturation,Residual Nonaqueous-Liquid Saturation,...

LET Aqueous Relative Permeability versus Liquid Saturation (Oil-Water Displacement)

...,End-Point Relative Permeability,L Parameter,E Parameter,T Parameter,Residual Aqueous Saturation,Residual Nonaqueous-Liquid Saturation,...

Choose One

Choose one Nonaqueous-Liquid Relative Permeability versus Aqueous Saturation Model

Corey Nonaqueous-Liquid Relative Permeability versus Aqueous Saturation (Oil-Water Displacement)

...,End-Point Relative Permeability,Exponent,Residual Aqueous Saturation,Residual Nonaqueous-Liquid Saturation,...

LET Nonaqueous-Liquid Relative Permeability versus Liquid Saturation (Oil-Water Displacement)

...,End-Point Relative Permeability,L Parameter,E Parameter,T Parameter,Residual Aqueous Saturation,Residual Nonaqueous-Liquid Saturation,...

Baker Combination Model

Rock/Soil Name,Baker,...

Click here to see binary models...

Choose One

Choose one Gas Relative Permeability versus Liquid Saturation Model

Corey Gas Relative Permeability versus Liquid Saturation (Gas-Oil Displacement)

...,End-Point Relative Permeability,Exponent,Residual Total-Liquid Saturation,Residual Gas Saturation,...

LET Gas Relative Permeability versus Liquid Saturation (Gas-Oil Displacement)

...,End-Point Relative Permeability,L Parameter,E Parameter,T Parameter,Residual Total-Liquid Saturation,Residual Gas Saturation,...

Choose One

Choose one Nonaqueous-Liquid Relative Permeability versus Liquid Saturation Model

Corey Nonaqueous-Liquid Relative Permeability versus Liquid Saturation (Gas-Oil Displacement)

...,End-Point Relative Permeability,Exponent,Residual Total-Liquid Saturation,Residual Gas Saturation,...

LET Nonaqueous-Liquid Relative Permeability versus Liquid Saturation (Gas-Oil Displacement)

...,End-Point Relative Permeability,L Parameter,E Parameter,T Parameter,Residual Total-Liquid Saturation,Residual Gas Saturation,...

Choose One

Choose one Aqueous Relative Permeability versus Aqueous Saturation Model

Corey Aqueous Relative Permeability versus Aqueous Saturation (Oil-Water Displacement)

...,End-Point Relative Permeability,Exponent,Residual Aqueous Saturation,Residual Nonaqueous-Liquid Saturation,...

LET Aqueous Relative Permeability versus Liquid Saturation (Oil-Water Displacement)

...,End-Point Relative Permeability,L Parameter,E Parameter,T Parameter,Residual Aqueous Saturation,Residual Nonaqueous-Liquid Saturation,...

Choose One

Choose one Nonaqueous-Liquid Relative Permeability versus Aqueous Saturation Model

Corey Nonaqueous-Liquid Relative Permeability versus Aqueous Saturation (Oil-Water Displacement)

...,End-Point Relative Permeability,Exponent,Residual Aqueous Saturation,Residual Nonaqueous-Liquid Saturation,...

LET Nonaqueous-Liquid Relative Permeability versus Liquid Saturation (Oil-Water Displacement)

...,End-Point Relative Permeability,L Parameter,E Parameter,T Parameter,Residual Aqueous Saturation,Residual Nonaqueous-Liquid Saturation,...

Choose One

Choose one Gas Relative Permeability versus Aqueous Saturation Model

Corey Gas Relative Permeability versus Aqueous Saturation (Gas-Water Displacement)

...,End-Point Relative Permeability,Exponent,Residual Aqueous Saturation,Residual Gas Saturation,...

LET Gas Relative Permeability versus Liquid Saturation (Gas-Oil Displacement)

...,End-Point Relative Permeability,L Parameter,E Parameter,T Parameter,Residual Aqueous Saturation,Residual Gas Saturation,...

Choose One

Choose one Gas Relative Permeability versus Aqueous Saturation Model

Corey Aqueous Relative Permeability versus Aqueous Saturation (Gas-Water Displacement)

...,End-Point Relative Permeability,Exponent,Residual Aqueous Saturation,Residual Nonaqueous-Liquid Saturation,...

LET Aqueous Relative Permeability versus Liquid Saturation (Oil-Water Displacement)

...,End-Point Relative Permeability,L Parameter,E Parameter,T Parameter,Residual Aqueous Saturation,Residual Nonaqueous-Liquid Saturation,...

 

 

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.