Abstract
Introduction
Reservoir simulation is based on well known reservoir engineering equations and techniques - the same equations and techniques the reservoir engineer has been using for years. In general, simulation refers to the representation of some process by either a theoretical or a physical model. Here, we limit ourselves to the simulation of petroleum reservoirs. Our concern is the development petroleum reservoirs. Our concern is the development and use of models that describe the reservoir performance under various operating conditions. performance under various operating conditions. Reservoir simulation itself is not really new. Engineers have long used mathematical models in performing reservoir engineering calculations. Before the performing reservoir engineering calculations. Before the development of modem digital computers, however, the models were relatively simple. For example, when calculating the oil in place volumetrically, the engineer simulated the reservoir by a simple model in which average values for the porosity, saturation, and thickness were used. Although simulation in the petroleum industry is not new, the new aspects are that more detailed reservoir features, and thus more accurate simulations, have become practical because of the capability afforded by the computers now available. The more detailed description, however, requires complex mathematical expressions that are difficult to understand, and this difficulty has caused some engineers to shy away from using simulators, and others to misuse them. We in the petroleum industry are in the reservoir simulation revolution. As time goes on, simulators will be used more and more, so a basic understanding of reservoir modeling is essential. The engineer, especially, must become competent in setting up simulation problems, in deciding on appropriate input data, and in evaluating the results.
Basic Analysis
If a reservoir is fairly homogeneous, average values of the reservoir properties, such as porosity, are adequate to describe it. The average pressure, time, and production behavior of such a reservoir under a production behavior of such a reservoir under a solution gas drive, for example, are normally calculated by the familiar methods of Tamer, Muskat, or Tracy. All of these methods use the material balance equation normally referred to as the MBE. A simple expression for the oil MBE is the following:
(cumulative net withdrawal in STB) = (original oil in place in STB) - (oil remaining in place in STB)
The cumulative net withdrawal is the difference between the oil that leaves the reservoir and the oil that enters it. In this basic analysis, there is no oil entering the reservoir since the boundaries are considered impermeable to flow. Thus, the MBE reduces to its simplest form. Such a reservoir model is called the tank model (Fig. 1). It is zero dimensional because rock, fluid properties, and pressure values do not vary from point to point. Instead, they are calculated as average values for the whole reservoir. This tank model is the basic building block of reservoir simulators. Now let us consider a reservoir represented by a sandbar. Let the two halves of the sandbar vary in lithology. The sandbar as a whole cannot be represented by average properties, but each half can. Thus, the sandbar consists of two tank units, or cells, as they are normally called. The MBE describes the fluid behavior in each cell as in the previous tank model.
SPEJ
P. 1383