Abstract
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 form 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) desk-top computer.
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 form 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) desk-top computer.