A Streamline Reservoir Simulator With Dynamic Gridding
Authors: Bundy B.C. , Hales H.B. 
Published: March 2010

Abstract
A prototype reservoir simulator is described which combines three new simulation technologies to create a simulator of increased speed, accuracy and versatility. These new technologies are:New finite difference equations for the determination of reservoir pressures that incorporate the sharp pressure gradients that occur around the wells.Streamline simulation. The reservoir pressures are used to determine the location of the streamlines. Saturations are then determined by 1D solutions along each streamline.Dynamic gridding. The saturations on each streamline are determined by solving 1D finite difference approximations to the saturation equation. However, the locations of specific saturation values are determined rather than the usual determination of saturations at specific locations. The re-sulting dynamic spatial grid is finely spaced in areas where saturations are changing most rapidly.The resulting method rigorously accounts for gravity, capillary pressures and all other phenomena that can be incorporated into traditional, non-streamline, finite difference equations.
The results of a 2D, 2-well waterflood simulation illustrate the substantial detail and understanding that can be gained from a relatively coarsely gridded simulation.

Introduction
Since the beginning of the Petroleum Industry, reservoir simulation has played an important part in the optimization of oil and gas production(1–4). With the advent of computers, physical and analog models were replaced with faster digital computational simulations. However, despite the enormous increases in computer speeds and memories that have occurred over the years, computers have never been fast enough or big enough to meet the ever-escalating needs of reservoir simulation. Several emerging technologies which employ reservoir simulators make the need for faster simulators and faster computers as acute as ever:

Automatic History Matching
Simulated reservoir histories seldom exactly match actual histories. Differences usually result from inaccurate data, but sometimes they occur as the result of mathematical shortcuts. Whatever the reason, simulation engineers, even in the early years of simulation, have tried to improve their match by adjusting their data(5). It has been proposed that this time-intensive process be automated. The process is relatively simple when the data values to be adjusted are less than fifty and when simulations can be accomplished in a few minutes. However, the problem of matching by adjusting thousands of data values, using simulators that take hours to run, remains a very difficult task(6).

Geostatistics
It is never possible to have enough data to accurately describe the reservoir. Even for relatively shallow reservoirs, it is impractical to have wells drilled sufficiently close to one another that well logs can accurately determine all the variations in properties throughout the reservoir. Hence, the science of geostatistics has emerged in recent years. Geostatistics involves gathering large quantities of data on out-crops, where such mea-surements can be made. The same statistical variations in properties are then applied to subterranean reservoirs. This approach results in not one, but many possible models of the reservoir, each with some probability of being correct(7).