Compositional Streamline Simulation of CO2 Injection Accounting for Gravity and Capillary Effects Using Orthogonal Projection
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The effective use of streamline simulators for flow simulation of high resolution 3D models relies on the ability to take large simulation time-steps with few pressure solutions. For processes that are convective, the streamline approach works quite well, but for flow simulation with strong capillarity or gravity terms, the maximum time step size is reduced, limiting the utility of streamline simulation. This is the case with the conventional operator-splitting approach, where the nonlinear terms associated with capillarity and gravity limit the time step size. The impact is particularly pronounced for compositional simulations that require numerous flash calculations. This paper presents the development of a 3D 3-phase compositional streamline simulator and its application to field-scale CO2 injection. The novel aspect of our approach is the ability to incorporate gravity and capillary effects into compositional streamline simulation without adversely impacting its computational efficiency. In our approach, we use an orthogonal projection method to reformulate the streamline transport equations so that the fluxes of capillary and gravity are separated into components parallel and orthogonal to the total velocity defining the streamline trajectories. Fluxes parallel to total velocity are included within the solution of the convective flow equations on streamlines. The remaining terms are calculated on the underlying three dimensional grid. Our proposed formulation still uses an operator splitting approach, but the size of the remaining transverse flux correction terms is significantly reduced, allowing for large time steps. The ability to effectively incorporate transverse fluxes in streamline transport calculations will be a step change in streamline simulation in general. We demonstrate that our proposed treatment of transverse fluxes allows us to efficiently study high resolution migration of CO2 in the subsurface with potential applications to both improved oil recovery as well as carbon sequestration. First, we establish the validity and computational efficiency of our approach using a series of numerical experiments and compare the results with a commercial finite difference simulator. Next, we apply the method to a field-scale CO2 WAG injection. The streamline model is shown to be particularly effective to examine and visualize the interactions between natural heterogeneity, capillary and buoyancy forces, and CO2 transport and the resulting impact on the vertical and areal sweep efficiencies.
author list (cited authors)
Tanaka, S., Datta-Gupta, A., & King, M. J.