(496d) A Generalized Negative Flash Procedure for Phase Equilibrium Computations Related to Carbon Dioxide Sequestration
AIChE Annual Meeting
Thursday, November 12, 2009 - 9:45am to 10:10am
Prediction of subsurface CO2 sequestration in depleted oil and gas reservoirs involves solving coupled systems of transport equations. A particular challenge is resolving the complex multiphase thermodynamic equilibrium behaviors associated with CO2-oil-water mixtures at reservoir pressure and temperature conditions. Here, we propose a multiphase equilibrium method based on a generalized negative-flash strategy that is both robust and efficient. For this class of problem, the standard strategy based on two-phase equilibrium is inadequate, since complex three-phase states can easily exist.
In standard methods, a stability test is performed to determine the phase-state of a mixture for a given overall composition at fixed pressure and temperature. For multiphase states, a flash procedure is used to determine the phase amounts and compositions. Flash calculations usually include simultaneous solution of equality of chemical potentials for all components between any existing phases at equilibrium.
We describe a negative-flash method for multiphase (i.e., more than two phases) mixtures, where the maximum number of phases that can coexist in equilibrium for the composition, temperature and pressure ranges of interest is known a priori. For any target composition, the components are allowed to partition across the maximum number of phases; consequently, when a particular phase does not exist, its amount is negative. The system of equations used with the negative flash is identical to that employed in compositional flow simulation based on a conventional flash procedure. This generalized negative-flash method can replace the phase-stability tests in conventional simulation.
The overall algorithm combines a Successive Substitution (SS) methodology with Newton iterations. For faster convergence of flash iterations, a good initial guess for phase partitioning coefficients (K-values) is necessary for both SS and Newton procedures. We propose a general methodology to provide this initial guess for a system with an arbitrary number of phases. The procedure is based on tie-simplex parameterization of the compositional space and uses a negative-flash procedure.
During any iteration of the SS, the K-values are assumed to be constant, and therefore, a robust constant K-value negative-flash procedure (i.e., multiphase extension of the Rachford-Rice problem) is required to implement a stable SS iteration. A gradient-based methodology to solve the generalized Rachford-Rice problem is not guaranteed to converge. The problem is, however, amenable to a bracketing based scheme such as bisection. In this work, we first show the existence and uniqueness of the solution to the three-phase, constant K-value, negative-flash problem. Then, we provide a nested bisection solution procedure. The proposed method is recursively extendible to systems with any number of phases. We demonstrate the robustness of the algorithm using challenging problems, such as multiphase multi-component mixtures for a very wide range of K-values.
Unlike the two-phase negative flash procedure, this multiphase extension is not sufficient for phase identification. For three-phase systems, for example, tie-lines parameterize the space around the three-phase region, and based on the result of the three-phase negative flash, additional two-phase negative flashes may be required to accurately determine the phase-state of the fluid mixture. The method, therefore, provides not only the phase state of the mixture, but also the compositions of the actual phases at equilibrium.
Several examples of CO2 injection in depleted oil reservoirs with complex multiphase behaviors are used to demonstrate the effectiveness and computational efficiency of the proposed method.
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