Velocity models, material balance and solution convergence in streamline-based simulation

Abstract

This thesis addresses two important issues related to streamline-based flow simulation. The first issue deals with velocity models, specifically, how to determine the velocity models in various geometries in 2D and 3D space, and how to draw streamlines and calculate time of flight in various gridblock systems. The present research builds on the previous work of Cordes and Kinzelbach, 1992. Transformations from the real space of {x,y,z} to the unit cube space of {α, β, γ} have been extensively utilized to draw the streamlines in 2D and 3D corner point cell geometry and also to calculate the time of flight. The use of cell-averaged jacobian of the transformation, as is typically done in streamline simulators to determine the time of flight is investigated for its accuracy. The impact of cell skewness in time of flight calculations is also investigated. Our results indicate that the cell-averaged jacobian leads to incorrect time of flight. The second issue that is addressed is related to material balance error during streamline simulation. The material balance error is generated during the discretization of gridblock into streamtubes ([]-discretizations) and also during the saturation assignment to a streamline from the gridblock and vice versa ([]-discretizations). The behavior of the material balance error associated with []-discretizations is studied with respect to parameters like the selection of the gridblock and the number of streamlines in the gridblock. Furthermore, we also examine the behavior of the error associated with []-discretizations with respect to the size of the discretizations along a streamline. Our results show that the material balance error associated with []-discretizations converges slowly (with a slope of -1.0) in a gridblock, if it has a stagnation point. However, if the gridblock does not have any stagnation point in it, then the error converges faster (with a slope of -2.0). For the []-discretizations along a streamline, the L₁ and L[] Norm errors are shown to be inversely proportional to the number of []-discretizations. The L₂ Norm error is shown to be inversely proportional to the square root of the number of []-discretizations.