Negative Flash for Calculating the Intersecting Key Tie-lines in Multicomponent Gas Injection

Gas injection is a widely used enhanced oil recovery method and its application is expected to increase due to the high oil price and the need for sequestering carbon dioxide. In order to build a method of characteristics (MOC) solution to a two-phase gas injection system, we need to construct the composition path from the injection gas to the initial oil where all the intersecting key tie-lines must be identified. Calculation of these intersecting tie-lines requires a series of special negative flashes, which allow not only phase fractions outside the physical interval [0, 1] but also negative feed compositions. The phase compositions from one negative flash are used to recombine the feed for the next negative flash. Despite the apparent complexity due to multicomponent equilibrium and transport, for pure component gas injection, negative flash and elimination of components can be performed in an alternating manner. In particular, if the K-values are constant, there exists a simple feature that the vapor fraction roots (β-roots) for the Rachford-Rice equation for the initial oil are the roots to be found in all the negative flashes involved. This leads to a simple and well-structured algorithm for the solution at constant K-values. A unique problem with pure component gas injection is that there could be two possible roots in the β-interval of interest. But if the component to be eliminated is left with an infinitesimal amount, only one of them can still give non-negative phase compositions and thus should be selected. For multicomponent gas injection at constant K-values, we further prove that in addition to the invariant β-roots in the solution procedure, the λ-values for constructing the feeds are simply the vapor phase fraction roots for the injection gas. By solving two negative flashes for the initial oil and the injection gas, we can readily determine all the intersecting tie-lines at constant K-values.