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Four-Component Gas/Water/Oil Displacements in One Dimension: Part III, Development of Miscibility

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Abstract

The structure of the system of conservation laws in fully compositional three-phase, four-component flow is examined for the first time. Two of the eigenvalues can be found analytically for this flow regime, regardless of the equation of state used to model the phase behavior. A cubic equation of state is used to calculate the gas/oil phase behavior and Henry’s law is used to represent the partitioning of hydrocarbons between the hydrocarbon and water phases. Sample analytical solutions are found for Riemann problems modeling the injection of carbon-dioxide and water into an oil reservoir. Finally, the structure of the solutions at the minimum miscibility pressure (MMP) for the hydrocarbon system is studied. We show that when water is injected simultaneously with gas at the MMP, multicontact miscible displacement of the oil by the injected gas develops only if the fraction of water in the injected fluid is below a critical value. For water fractions above the critical value, water flowing at a high velocity forces the composition path of the solution to remain in the three-phase region in which two hydrocarbon phases are present. We study both condensing and vaporizing gas drives to demonstrate that this result is general.

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Abbreviations

a 1 :

Defined in 10

a 2 :

Defined in 10

b 1f :

Defined in 10

b 2f :

Defined in 10

b 1S :

Defined in 10

b 2S :

Defined in 10

C i :

Overall volume fraction of component i

c ij :

Volume fraction of component i in phase j

F ij :

\({{{\partial F_i}\big{/} \partial}C_j}\)

f j :

Fractional flow of phase j

f ij :

\({{{\partial f_i}\big{/} \partial}S_j}\)

i :

Component

j :

Phase

\({K_i^1}\) :

Variable K-value for partitioning of i between the gas and oleic phase

\({K_i^2}\) :

Variable K-value for partitioning of i between the aqueous and oleic phase

\({K_i^3}\) :

variable K-value for partitioning of i between the aqueous and gas phase

k rj :

Relative permeability of phase j

\({k^o_{rj}}\) :

Endpoint relative permeability of phase j

n j :

Corey exponent of phase j

n p :

Number of phases present

S j :

Saturation of phase j

\({S_j^*}\) :

Normalized saturation of phase j

S jr :

Residual saturation of phase j

x i :

Volume fraction of component i in the oleic phase

y i :

Volume fraction of component i in the gas phase

w i :

Volume fraction of component i in the aqueous phase

α :

Defined in 4

β :

Defined in 4

γ :

Defined in 5

δ :

Defined in 5

η :

Defined in 5

μ j :

Viscosity of phase j

λ:

Eigenvalue (characteristic velocity)

Λ:

Shock velocity

χ :

Nontie-triangle eigenvalue

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Authors and Affiliations

  1. Department of Earth Sciences and Engineering, Imperial College London, London, SW7 2AZ, UK

    Tara LaForce

  2. Department of Energy Resources Engineering, Stanford University, Stanford, CA, 94305, USA

    Franklin M. Orr Jr.

Authors
  1. Tara LaForce
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  2. Franklin M. Orr Jr.
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Correspondence to Tara LaForce.

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LaForce, T., Orr, F.M. Four-Component Gas/Water/Oil Displacements in One Dimension: Part III, Development of Miscibility. Transp Porous Med 79, 225–247 (2009). https://doi.org/10.1007/s11242-008-9311-z

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  • DOI: https://doi.org/10.1007/s11242-008-9311-z

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