(555f) A New Method for Phase Equilibrium Calculations in Carbon Dioxide-Water-Hydrocarbons Mixtures

Phase equilibrium calculations in carbon-dioxide-water-hydrocarbons mixtures are important in a variety of processes, such as CO2 storage in depleted reservoirs or CO2 flooding, as well as thermal methods for enhanced recovery. In the presence of water, wide three-phase (vapor, hydrocarbon-rich and aqueous) VLW regions are formed, and the presence of carbon dioxide adds complexity to the phase behavior. Compositional simulators require robust and efficient phase equilibrium routines, since failures are not allowed and the correct phase distribution must be determined in a very large number of grid blocks of the discretization network.

In multiphase equilibrium calculations, the phase distribution at fixed equilibrium constants is calculated either by solving the nonlinear system of Rachford-Rice equations, or an equivalent constrained minimization problem. In negative flash calculations, the solution is sought in a mathematical domain (bordered by hyperplanes defined by the equilibrium constants), which is wider than the physical one; the negative flash allows a versatile treatment of phase appearance/disappearance during iterations. The initial guess, which is usually taken as the barycenter of a simplex (defining the physical or mathematical domains) is generally poor. A frequent problem arise when iterations on the Newton direction repeatedly hits boundaries, before eventually converging to the solution after an increased number of iterations, including many function and gradient evaluations in the line search procedure.

Some simplifications were proposed in the literature, in which either the aqueous phase is considered to be pure water (the free-water flash assumption, which is limited to moderate pressures and relatively small amounts of carbon dioxide), or only the solubility of certain components (carbon dioxide and lighter hydrocarbons) in water is taken into account (the augmented free-water flash). Both methods give approximate solutions and have with certain limitations. In this work, an exact method able to capture all phase behavior details and taking advantage of the particular mathematical structure of the problem is proposed. The new method is sequentially using a simplified calculation procedure starting from a high quality initial guess, followed by conventional Newton iterations. The former step efficiently brings the phase distribution virtually very close to the solution, from where one conventional iteration (only a few in extreme cases) is usually required in the later step. The main advantages of the new method are that: i) the simplified method is significantly less computational expensive than the conventional one (in terms of both number of iterations and cost of an iteration); ii) the feasible domain is narrower; iii) iterations are guaranteed to remain in the feasible domain and to decrease the objective function, thus an important number of function evaluations and tests are avoided iv) line-searches are avoided, in a monotonic convergent computational scheme and v) the quality of the initial estimate.

The proposed numerical procedure is tested for a very large number of flash points in the pressure-temperature plane, covering the entire negative flash domain, for various mixtures from the literature, with different degrees of complexity and exhibiting various phase envelope shapes. Several very difficult cases, in which a large number of iterations and/or function evaluations in the line search are required for convergence in the conventional approach, are discussed in detail, showing the superiority of the new method. The method proved to be extremely robust and it converges systematically faster than the conventional one, in many cases one order of magnitude faster. The results of extensive numerical experiments clearly recommend the proposed method to replace conventional solvers in compositional simulations for carbon dioxide-water-hydrocarbons mixtures.