A Reservoir Simulator Based on Front-Tracking

A method of solving the saturation equations (first order hyperbolic conservation laws) by approximating the fractional flow function by a piecewise linear function has been developed. The method makes it possible to solve the saturation equations without stability problems. In this new front-tracking method, the pressure equation is solved by a finite element method. The grid for the pressure equation can therefore be fitted to the reservoir geometry with great flexibility. A reservoir simulator based on the new methods for the solution of saturation equations is under development. The simulator is able to simulate two-phase immiscible flow in two dimensions at present. Both gravity and compressibility are included, as well as heterogeneities in the geological data. The simulator has been used for field simulation problems. It has proved to be insensitive to grid orientation and numerical dispersion. In addition, for larger grid systems, the simulator is computationally more efficient than finite difference simulators. A simpler version of the front-tracking simulator can also be used as a streamline simulator. The streamline simulator has the same CPU-efficiency and front-tracking capabilities as traditional streamtube simulators without the need to transform the reservoir into a set of one-dimensional regions.