Black Oil Streamline Simulator With Capillary Effects

Abstract

Abstract A streamline simulation with capillary and gravity is presented. The black oil streamline simulator [3DSL 0.25 by R.P. Batycky, SUPRI-C group, Department of Petroleum Engineering, Stanford University, 1997] was modified to incorporate capillary effects. The new simulator has been applied to several simulation cases. We discuss the influence of different factors that may impact performance prediction of water floods. The capillary forces are demonstrated to stabilize the displacement front and increase oil production even in rather viscous-dominated cases. The new approach can provide a fast and a reliable tool for the simulation of water flooding in low permeable and heterogeneous oil reservoirs as well as for reservoir screening and upscaling studies. Introduction Reservoir simulators based on the streamline principle have been developed as an alternative to conventional finite difference simulators. The main advantages of the streamline simulators are the high speed and the smaller impact of the numerical dispersion, making them useful tools for fast evaluation of multiple methods of reservoir development prior to computationally expensive full-scale simulations. A limitation of the currently available black-oil streamline simulators is the absence of a representation of the effect of capillary forces. Streamline methods work well for flows that are dominated by convection. They are less well suited to describe physical phenomena that transport fluid across the streamlines. In the streamline method the flow along each streamline is treated as independent, and the effects of flow transverse to the streamlines are not represented. Capillary pressure differences between phases, for example, can lead to flow transverse to streamlines. In some flow settings, capillary forces can alter significantly the character of the flow, as crossflow drives imbibition of wetting phase into low permeability zones adjacent to high permeability flow paths. In this paper we present the results, obtained with the streamline simulator, modified to incorporate capillary effects. Modification of the pressure equation changes the locations of the streamlines. Modification of the saturation equation allows description of crossflow effects by means of an operator splitting technique [1]. In this paper we briefly discuss the modification of governing equations to account for the gravity and the capillary forces. We focus on the prediction of water flooding performance in cases when capillary and gravity effects cannot be neglected. We discuss the potential, advantages and possible further improvements of the existing streamline simulator. Solution Procedure Streamline simulators are based on the IMplicit Pressure Explicit Saturation (IMPES) approach to solve the governing conservation equation. The general conservation equation is represented by the pressure and the saturation equations. The numerical solution incorporates the following routine for each time step:The pressure equation is solved implicitly on the finite difference gridThe Darcy velocity is computed based on a cell centered pressure valuesStreamlines are traced from injection wellsThe saturation equation is solved explicitly along the streamlinesSaturation values are mapped back from the irregular grid (streamlined nodes) to the regular (finite difference) grid Streamline methods are not restricted by the global CFL (Courant-Freidrichs-Lewy [2]) condition, but rather local CFL along each streamline. As a result they have an advantage over conventional finite difference IMPES simulators, allowing less frequent pressure updates. They also suffer less numerical dispersion. Details of the streamline methods can be found in [3–6].