A Method To Improve the Mass Balance in Streamline Methods
- Vegard Kippe | Haakon Haegland | Knut-Andreas Lie (SINTEF ICT)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Simulation Symposium, 26-28 February, Houston, Texas, U.S.A.
- Publication Date
- Document Type
- Conference Paper
- 2007. Society of Petroleum Engineers
- 5.4.2 Gas Injection Methods, 4.3.4 Scale, 1.6.9 Coring, Fishing, 5.2.2 Fluid Modeling, Equations of State, 3.3.6 Integrated Modeling, 5.5.8 History Matching, 5.1.5 Geologic Modeling, 7.1.5 Portfolio Analysis, Management and Optimization, 5.5.7 Streamline Simulation, 5.5 Reservoir Simulation
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During the last decades, streamline methods have emerged as highly efficient simulation tools that are well-suited for e.g., history matching and simulation of large and complex reservoir models. Streamline methods are based on a sequential solution procedure in which pressure and fluid velocities are computed by solving a pressure equation on a grid in physical space and the fluid transport is computed by solving 1-D transport problems along streamlines. The sequential Eulerian-Lagrangian procedure is the key to the
high computational efficiency of streamline methods. On the other hand, it necessitates mapping of saturations (or fluid compositions) back and forth between the Eulerian pressure grid and the Lagrangian streamlines. Unfortunately, this introduces mass-balance errors that may accumulate in time and in turn yield significant errors in production curves.
Mass-balance errors might be reduced by considering higher-order mapping algorithms, or by increasing the number of streamlines. Since the computational speed scales linearly with the number of streamlines, it is clearly desirable to use as few streamlines as possible. Here we propose a modification of the standard mapping algorithm that: (i) improves the mass-conservation properties of the
method and (ii) provides high-accuracy production curves using few streamlines.
Mass conservation is improved by changing quantities in the transport equation locally, and we show that these modifications do not significantly affect the global saturation errors as long as a sufficient number of streamlines is used. Moreover, we propose an adaptive strategy for ensuring adequate streamline coverage. The efficiency and accuracy of the modified streamline method is demonstrated
for Model 2 from the Tenth SPE Comparative Solution Project. Highly accurate production curves (compared to reference solutions) are obtained in less than ten minutes using one processor on a standard (Intel Core 2 Duo) desktop computer.
Streamline simulation has experienced increasing industry interest and rapid technology development in recent years and is now a very efficient alternative to traditional flow modelling by numerical methods such as finite differences or finite volumes. Modern streamline methods can be used to compute complex flow physics such as compressible three-phase models with full PVT, multicomponent
models or dual-porosity models (Thiele et al., 1997; Crane et al., 2000; Di Donato and Blunt, 2004). Still, streamline simulation is most efficient for simplified physical models and engineering queries based on the 80-20 principle: 80% of the answer in 20% of the time available (Thiele, 2005). In particular, due to its low memory requirements and high computational efficiency, streamline simulation
today offers the opportunity to solve outstanding engineering queries that might otherwise be difficult or impossible to address using other approaches.
|File Size||300 KB||Number of Pages||12|