Introduction

One of the most important job functions of the reservoir engineer is the prediction of future production rates from a given reservoir or specific well. Over the years, engineers have developed several methods to accomplish this task. The methods range from simple decline-curve analysis techniques to sophisticated multidimensional, multiflow reservoir simulators.^1–7 Whether a simple or complex method is used, the general approach taken to predict production rates is to calculate producing rates for a period for which the engineer already has production information. If the calculated rates match the actual rates, the calculation is assumed to be correct and can then be used to make future predictions. If the calculated rates do not match the existing production data, some of the process parameters are modified and the calculation repeated. The process of modifying these parameters to match the calculated rates with the actual observed rates is referred to as history matching.

The calculational method, along with the necessary data used to conduct the history match, is often referred to as a mathematical model or simulator. When decline-curve analysis is used as the calculational method, the engineer is doing little more than curve fitting, and the only data that are necessary are the existing production data. However, when the calculational technique involves multidimensional mass and energy balance equations and multiflow equations, a large amount of data is required, along with a computer to conduct the calculations. With this complex model, the reservoir is usually divided into a grid. This allows the engineer to use varying input data, such as porosity, permeability, and saturation, in different grid blocks. This often requires estimating much of the data, since the engineer usually knows data only at specific coring sites that occur much less frequently than the grid blocks used in the calculational procedure.

History matching covers a wide variety of methods, ranging in complexity from a simple decline-curve analysis to a complex multidimensional, multiflow simulator. We will begin with a discussion of the least complex model—that of simple decline-curve analysis. This will provide a starting point for a more advanced model that uses the zero-dimensional Schilthuis material balance equation.