Fast 3-D Reservoir Simulation and Applications Using Streamlines
Authors: Portella R.C.M. , Hewett T.A. 
Published: December 2007

Abstract
Nowadays there is a great need for flow simulation methods that are at the same time fast and accurate. In this paper we present a streamtube based flow simulation method that is very fast and that can handle large three dimensional reservoir models. The speed of the method relies on the fact that the streamtube geometry is just calculated once. The flow rate of each streamtube is updated based on the total resistance in each streamtube at a given moment. The difficulties of defining streamtubes in three dimensions are overcome by the use of streamlines and time-of-flight (TOF) techniques. Although the implementation presented here is limited to two-phase, incompressible flow and negligible gravity, it has many direct applications in ranking geostatistical images and history matching techniques. The paper shows several applications using this streamtube simulator. Perhaps the most consequential application of this fast 3-D simulation method is its application in grid generation and upscaling techniques.

Introduction
The flow simulation of large reservoir models using conventional finite difference simulators is very difficult, and in the majority of the cases not practical without the use of a supercomputer. This situation leads to the use of smaller, coarser grids that usually give poor results in terms of the accuracy of oil production forecasting. So, nowadays many research projects are being conducted to investigate faster methods of flow simulation.
The streamtube method is an old technique that recently has received much attention because it provides a fast way to simulate large and complex reservoir models. Streamtube methods basically determine the fluid paths either by solving the stream function equation or by solving the single-phase flow pressure field. Then in each streamtube a one dimensional solution, in the majority of cases the Buckley-Leverett equation solution, is applied to give the final results of the simulation. There are two main approaches in streamtube methods. The first approach considers the streamtubes fixed in time and the flow rate in each streamtube is updated as the flow proceeds. The second approach considers the flow rate in each streamtube fixed but the position of the streamtubes is updated as the flow proceeds. A problem that prevented the use of streamtubes on a larger scale in the past was the extension of the method for three dimensions. The definition of streamtubes in three dimensions using stream functions is very difficult but the development of particle tracking techniques and the time-of-flight method eliminates this difficulty.
In this paper we present a three-dimensional implementation of a streamtube method for oil recovery calculations. This is a fixed streamtube method in which the flow rates are updated according to the total resistance in each streamtube. As we just calculate the streamtube geometries once, the method is very fast and at the same time accurate. Although the method is limited to problems with two-phase, incompressible flow and negligible gravity, it still has many direct applications. Some applications in the ranking of geostatistical images and history matching are shown here. Perhaps the best application of this streamtube method is in the upscaling and grid generation areas. A brief description of the research being conducted in this area is also included in this paper.