Compositional space parameterization: Theory and application for immiscible displacements

Thermodynamic equilibrium calculations in compositional flow simulators are used to find the partitioning of components among fluid phases, and they can be a time consuming kernel in a compo-sitional flow simulation. We describe a tie-line-based compositional space parameterization (CSP) approach for dealing with immiscible gas-injection processes with large numbers of components. The multicomponent multiphase equilibrium problem is recast in terms of this parameterized compositional space, in which the solution path can be represented in a concise manner. This tie-line-based parameterization approach is used to speed up the phase behavior calculations of standard compositional simulation. Two schemes are employed. In the first method, the parameterization of the phase behavior is computed in a preprocessing step, and the results are stored in a table. During the course of a simulation, the flash calcu-lation procedure is replaced by the solution of a multidimensional optimization problem in terms of the parameterized space. For processes where significant changes in pressure and temperature take place, this optimization procedure is combined with linear interpolation in tie-line space. In the second method, compositional space adaptive tabulation (CSAT) is used to accelerate the equation of state (EOS) computations associated with standard compositional reservoir simulation. The CSAT strategy takes advantage of the fact that, in gas injection processes, the solution path involves a limited number of tie-lines. The adaptively collected tie-lines are used to avoid redundant phase-stability checks in the course of a flow simu-lation. Specifically, we check if a given composition belongs to one of the tie-lines (or its extension) already in the table. If not, a new tie-line is computed and added to the table. The CSAT technique was implemented in a general-purpose research simulator (GPRS), which is designed for compositional flow simulation on unstruc-tured grids. Using a variety of challenging models, we show that, for immiscible compositional processes, CSAT leads to significant speed up (at least a several-fold improvement) of the EOS calcula-tions compared with standard techniques.