Fast, Approximate Solutions for 1D Multicomponent Gas-Injection Problems

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Abstract
Summary: This paper presents a new approach for constructing approximate analytical solutions for 1D, multicomponent gas displacement problems. The solution to mass conservation equations governing 1D dispersion-free flow in which components partition between two equilibrium phases is controlled by the geometry of key tie lines. It has previously been proven that for systems with an arbitrary number of components, the key tie lines can be approximated quite accurately by a sequence of intersecting tie lines. As a result, analytical solutions can be constructed efficiently for problems with constant initial and injection compositions (Riemann problems). For fully self-sharpening systems, in which all key tie lines are connected by shocks, the analytical solutions obtained are rigorously accurate, while for systems in which some key tie lines are connected by spreading waves, the analytical solutions are approximations, but accurate ones. Detailed comparison between analytical solutions with both coarse- and fine-grid compositional simulations indicates that even for systems with nontie-line rarefactions, approximate analytical solutions predict composition profiles far more accurately than coarse-grid numerical simulations. Because of the generality of the new approach, approximate analytical solutions can be obtained for any system having a phase behavior that can be modeled by an equation of state. The construction of approximate analytical solutions is shown to be orders of magnitude faster than the comparable finite difference compositional simulation. Therefore, the new approach is valuable in situations requiring fast compositional solutions to Riemann problems are required.