Summary
Our interest lies in extending the streamline method to compositional simulation. In this paper, we develop improved mappings to and from streamlines that are necessary to obtain reliable predictions of gas injection processes. Our improved mapping to streamlines uses a piecewise linear representation of saturations on the background grid in order to minimize numerical smearing. Our strategy for mapping saturations from streamlines to the background grid is based on kriging. We test our improvements to the streamline method by use of a simple model for miscible flooding based on incompressible Darcy flow. Results indicate that our mappings offer improved resolution and reduce mass-balance errors relative to the commonly used mappings. Our mappings also require fewer streamlines to achieve a desired level of accuracy. In compositional cases where the computational cost of a streamline solve is high, we anticipate that this will lead to an improvement in the efficiency of streamline-based simulation.
Introduction
The overall goal of our research is to improve the accuracy and efficiency of the streamline method in simulating compositional problems such as those that occur in miscible or near-miscible gas injection processes. This is our second paper suggesting improvements to this end. In Mallison et al. (2005) we investigated a 1D compositional finite-difference solver based on a high-order upwind scheme and adaptive mesh refinement that is appropriate for use in a compositional streamline simulator. Here, we propose new mappings to and from streamlines that improve the accuracy of the streamline method for problems in which the flow pattern does not remain fixed for large time intervals. Such problems require that streamlines be periodically updated in order to account for changing flow directions and for the treatment of gravity terms (Thiele et al. 1996; Bratvedt et al. 1996). For each set of streamlines, fluids must be mapped from an underlying background grid, on which the pressure is solved (or, say, the flow), to the streamlines, moved forward in time, and then mapped from the streamlines back to the background grid. The mappings introduce numerical smearing and generally also mass-balance errors. When streamlines are updated frequently, the mapping errors limit the overall accuracy of the streamline method. Our improved mapping algorithms are aimed at minimizing this type of error.