A new semi-analytical streamline simulator and its applications to modelling waterflooding experiments

Reservoir simulation is a tool to model the fluid flow in a reservoir over time. Streamline simulation has been proven to be an efficient approach for fine-scale geology models. With the development of engineering applications of streamline methods, researchers are now facing more challenges, for example, 1) tracing streamlines in structurally complex reservoirs; 2) improving the computational accuracy and efficiency for modeling transport problems. This research offers significant potential to meet these challenges. More specifically, this research is mainly focused on the development of a new three-dimensional, two-phase streamline simulator (using Matlab) that can model real physical displacement processes in a fast and accurate manner. This streamline simulator solves the pressure and saturation equations sequentially. First, streamlines are traced by pressure distribution approximations; and then transport problems are solved along streamlines. This new streamline simulator applies new semi-analytical methods to trace streamlines, including the Bilinear, Trilinear and Cubic methods. These methods generate streamlines based on pressure distribution approximations using piece-wise polynomials. Then the velocity field, streamline trajectory functions, and time-of-flight (the time a particle takes to travel along a streamline) are derived accordingly. The new streamline method and Pollcok’s method are systemically compared via pressure and velocity approximations, plus streamline determinations. Through these comparisons, the new methods are proven to be more accurate than Pollock’s method, especially in heterogeneous problems and/or when grid resolution is low. When certain initial conditions are imposed, this new streamline simulator applies a Riemann approach to solving transport problems along streamlines. Standard streamline simulators apply the classical Riemann solution under constant total flow rate conditions. However, the boundary conditions can also be specified by constant injection and production pressures. In this case, the flow rate varies with time, and a new semi-analytical Riemann solver presented in this thesis can be applied to map the Riemann solution along streamlines in terms of time-of-flight. Through a series of case studies using different reservoir properties, the abilities of the new streamline simulator to give sufficiently accurate solutions for homogeneous, heterogeneous, and anisotropic problems are demonstrated. Moreover, a large mobility ratio range (0.5 to 50) is tested to evaluate the performance of this streamline simulator. Through comparisons with a standard reservoir simulator (Eclipse100, Schlumberger) in these cases studies, it is demonstrated that this new streamline simulator significantly enhances the calculation speed and improves the accuracy of simulations when the underlying assumptions are valid. Finally, the ability of the new simulator is validated and demonstrated by modeling physical waterflooding displacements. This is the first time that waterflooding experiments are performed under constant differential pressure boundaries in a two-dimensional heterogeneous macro-model. Two experiments with the same reservoir and fluid properties are performed under different boundary conditions. The new simulator is applied to history match and simulate these two experiments. The predicted and observed results show excellent agreement. The flow behavior of the fluid under a constant pressure boundary is also well understood by using the visual power of the simulator. We conclude that the new streamline simulator is very efficient and accurate in physical waterflooding processes simulations when the viscous force dominates the flow