A Streamline-Based 3D Field-Scale Compositional Reservoir Simulator
Authors: Thiele Marco R. , Batycky Rod P. , Blunt Martin J. 
Published: December 2007

Abstract
This paper presents the extension of the streamline approach to full-field, three-dimensional (3D) compositional simulation. The streamline technique decomposes a heterogeneous 3D domain into a number of one-dimensional (1D) streamlines along which all fluid flow calculations are done. Streamlines represent a natural, dynamically changing grid for modeling fluid flow. We use a 1D compositional finite-difference simulator to move components numerically along streamlines, and then map the 1D solutions back onto an underlying Cartesian grid to obtain a full 3D compositional solution at a new time level.
Because of the natural decomposition of the 3D domain into a number of 1D problems, the streamline approach offers substantial computational efficiency and minimizes numerical diffusion compared to traditional finite-difference methods. We compare our three and four component solutions with solutions from two finite difference codes, UTCOMP and Eclipse 300 (E300). These examples show that our streamline solutions are in agreement with the finite-difference solutions, are able to minimize the impact of numerical diffusion, are faster by orders of magnitude. Numerical diffusion in finite-difference formulations can interact with reservoir heterogeneity to substantially mitigate mobility differences and lead to optimistic recovery predictions.
We demonstrate the efficiency and usefulness of the streamline-based simulator on a 518,400 gridblock, 3D, heterogeneous, 36-well problem for a condensing-vaporizing gas drive with four components. We can simulate this problem on an average-size workstation in three CPU days. It takes approximately the same amount of time to simulate the upscaled 28,800 gridblock version of the problem using finite-differences.
We conclude with a qualitative discussion explaining the near-linear scaling of the streamline approach with the number of gridblocks and the cubic and higher scaling exhibited by one of the finite-difference codes.

Introduction
The use of streamlines and streamtubes to model convective displacements in heterogeneous media has been presented repeatedly since the early work by Muskat, Fay and Prats, and Higgins and Leighton. Important subsequent contributions are due to Parsons, Martin and Wegner, Bommer and Schechter, Lake et al., Mathews et al., Emanuel et al., Renard, and Hewett and Behrens.
Recently, streamline methods have received renewed attention by several groups as a viable alternative to traditional finite-difference (FD) methods for large, heterogeneous, multiwell, multiphase simulations, which are particularly difficult for FD simulators to model adequately. Large speed-up factors compared to traditional FD solutions, minimization of numerical diffusion and grid orientation effects, and the inherent simplicity of the approach offer unique opportunities for integration with modern reservoir characterization methods. Examples include ranking of equiprobable earth models, estimation of the uncertainty in production forecasts due to the uncertainty in the geological description, rapid assessment of production strategies such as infill drilling patterns and miscible gas injection. In addition, streamlines may offer an attractive alternative to well-known problems with upscaling of absolute and pseudorelative permeabilities by allowing larger geological models and requiring upscaling across a smaller range of scales.
Our streamline approach for reservoir simulation hinges on two important extensions to past streamline/streamtube methods:the use of true 3D streamlines andand numerical solutions of the transport equations along periodically changing streamlines.
With these extensions we have been able to simulate realistic fluid flow in detailed, heterogeneous, 3D reservoir models much more efficiently than FD methods. We emphasize that reservoir simulation using streamlines is not a minor modification of current FD approaches, but instead represents a significant shift in methodology.
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