## Simultaneous phase-stability/-split computation for multiphase oil-displacement simulation

##### Abstract

Solvent injection is a widely used method for enhanced oil recovery. Phase behavior of reservoir-oil/injection-gas mixtures should be effectively used for successful implementation of solvent injection. Complex phase behavior involving three hydrocarbon phases has been observed for many solvent injection processes at temperatures typically below 120°F. Well-known examples are CO₂ injection for West Texas oils and enriched gas injection for Alaskan viscous oils, for which the multiphase behavior consisted of the oleic, solvent-rich liquid, and gaseous phases.
Such multiphase behavior makes it challenging to study details of solvent injection. Firstly, it is computationally difficult to robustly solve for multiphase behavior using an equation of state. Secondly, how the interplay between multiphase flow and multiphase behavior affects oil displacement is much more involved than the traditional gas injection problem with only two hydrocarbon phases. This research is concerned with two main technical challenges in multiphase behavior modeling for solvent injection: robust multiphase flash calculation, and quantification of the miscibility development through three-hydrocarbon-phase flow.
In the initial part of this dissertation, a novel algorithm is presented for multiphase isobaric isothermal flash. The formulation is derived from global minimization of the Gibbs free energy using the tangent plane defined at an equilibrium phase composition at a specified temperature and pressure. The new algorithm solves for two groups of stationary points of the tangent-plane-distance (TPD) function: tangent and non-tangent stationary points of the TPD function. Equilibrium phases, at which the Gibbs free energy is tangent to the TPD function, are found as a subset of the solution.
Unlike the traditional flash algorithms, the new algorithm does not require finding false solutions for robust multiphase flash. The advantage of the new algorithm in terms of robustness is shown to be more pronounced for more complex phase behavior, for which multiple local minima of the TPD function are present. It can be robustly initialized even when no K value correlation is available for the fluid of interest; e.g., multiphase behavior involving a solvent-rich liquid phase.
The final part of this dissertation presents a straightforward application of a mass conservation equation to explain and quantify the local oil displacement efficiency in three-hydrocarbon-phase flow. Mass conservation dictates how components must partition into phases upon a multiphase transition (e.g., between two and three phases) in multiphase convective flow. Detailed analysis of multiphase compositional flow equations leads to the distance parameter that quantifies the level of the miscibility developed between a displaced phase and a displacing phase in the presence of other immiscible phases. This distance parameter becomes zero when multicontact miscibility is developed, for example, between the oleic and solvent-rich liquid phases in the presence of the gaseous phase in low-temperature CO₂ flooding.
However, the application of the distance parameter is complicated when a composition path is calculated by using the equation-of-state compositional formulation that takes into account volume change on mixing. In such an application, the mapping of the distance parameter from volume space to composition space was performed, which made the calculated distance parameter less accurate near a displacement front where the solvent concentration rapidly changes.
In this research, the distance parameter is applied directly in volume space for a given composition path. This is a more direct and accurate way to validate the utility of the distance parameter to quantify the local displacement efficiency in three-phase flow. A composition path in three-phase oil displacement is obtained by numerically solving 1-D convective compositional flow equations with no volume change on mixing in this research. The new flash algorithm mentioned above is implemented in this in-house slim-tube simulator. In case studies based on experimental data, the distance parameter is shown to successfully quantify the local oil displacement efficiency in three-phase flow. It properly captures the effects of numerical dispersion and relative permeability on the development of multicontact miscibility. This is because the distance parameter is derived by a simple rearrangement of the weak form of a compositional flow equation.