A Fully Compositional Streamline Simulator

Abstract

A new 3-D three phase compositional reservoir simulator based on extension of the streamline method has been developed. This paper will focus on the new methods developed for compositional streamline simulation as well as the advantages and disadvantages of this strategy compared with more traditional approaches. Comparisons with a commercially available finite difference simulator will both validate the method and illustrate the cases in which this method is useful to the reservoir engineer. Introduction Streamline methods have been used as a tool for numerical approximation of the mathematical model for fluid flow since the 1800's (Helmholtz28 and later Muskat45) and have been applied in reservoir engineering since the 1950's and 1960's19,29–31,21,57. The reason behind using the approach has been both the needs for solving the governing equations accurately and achieving reasonable computational efficiency. Streamline methods continued to be explored through the 1970's by LeBlanc and Caudle37, Martin et al40,41 and Pitts et al50 and 1980's by Lake et al36,70, Cox11, Bratvedt et al8 and Wingard et al71, but the focus of reservoir simulation was on developing finite difference simulators. In the 1990's streamline methods have emerged as an alternative to finite difference simulation for large, heterogeneous models that are difficult for traditional simulators to model adequately. These efforts are described in numerous papers notably by Renard56, Batycky et al1–4, Peddibhotla et al48,49, Thiele et al64–66, Ingebrigtsen33, Ponting52 and in an overview paper by King and Datta-Gupta35. The application of the method has been described by numerous other authors10,12–17,26,34,53–55,69. Use of the streamline simulator used for the work in this paper has also been extensively described24,39,42,47,58,61,62,68. Several similar approaches such as the method of characteristics18,27,38,43,44, particle tracking20,63 and front-tracking25,7 have also been used in reservoir simulation. Conventional finite difference methods suffer from two drawbacks, numerical smearing and loss of computational efficiency for models with a large numbers of grid cells. Large models (105 –106 cells) are routinely generated in order to accurately represent geologically heterogeneous, multi-well problems.. Finite difference methods based on an IMPES approach suffer from the time step length limiting CFL condition, so as the number of cells increases the maximum time step length get shorter for a given model. For a large number of cells the shortness of the time step can render the total CPU time for a simulation impractical. Fully implicit finite difference simulators can take longer time steps but require the inversion of a much larger matrix than the IMPES approach. This is an even larger issue with compositional simulation where a large number of components will make the matrix very large. Also the non-linearity of the governing equations might require a limitation on the time step length again making very large models impractical to run. This can be improved by using an adaptive implicit aproach73. Conventional streamline methods are based on an IMPES method. In these methods the pressure is solved implicitly and then streamlines are computed based on this pressure solution. In this way the 3D domain is decomposed into many one-dimensional streamlines along which fluid flow calculations are done. This method assumes that the pressure is constant throughout the movement of fluids. One weakness with this concept is the lack of connection between the changing pressure field and the movement of fluids. This can cause instabilities and limitations on the time step length.

Parallel implementations of streamline simulators

“…The streamline method is similar to an implicit pressure, explicit saturations approach for oil-water or black-oil systems, or an implicit pressure, explicit compositions approach for compositional problems [8,29], with the difference that the transport equations are solved on the specialized transport grid formed by the streamlines. The two distinct time step sizes in this process are the time step between pressure updates (the global time step) and the time step used in the numerical transport solve along streamlines to move saturations or compositions between pressure updates (the local time step).…”

“…The computational efficiency of streamline methods for many-reservoir settings make them especially suitable for history matching and optimization problems, and commercial streamline simulators are applied for such purposes. Streamline simulation has recently been extended to handle (near-) miscible gas injection processes [8,29], as well as flow in fractured reservoirs [11].…”

Industrial Compositional Streamline Simulation for Efficient and Accurate Prediction of Gas Injection and WAG Processes

“…Second, the improved mappings discussed in the previous section reduce smoothing and mass balance errors so that more frequent pressure updates are acceptable if needed. Ingebrigtsen et al (1999) and Crane et al (2000) suggested updating the pressure along streamlines during a global time step to better honor the strong coupling between the pressure and transport equations. For gas injection problems, a similar approach may help to account for volume change at gas fronts.…”

Application of Streamline Simulation for Gas Displacement Processes

“…Gas displacement processes are one of the critical areas in SL simulation, as the compressibility remains a significant issue. Crane et al [26] used 1D fully implicit solutions of FD simulation to solve for pressure and fluid compositions together along each streamline, and account for the changes of the phase behavior that depend on the changes in pressure. It was tested and compared against FD compositional simulator using the SPE 9 Model.…”