Abstract
INTRODUCTION
Well tests have been used for many years for evaluating reservoir characteristics, and numerous methods of interpretation have been proposed in the past. A number of these methods have become very popular, and are usually referred to as 'conventional'. In the last ten years, many others have been developed, that are often called 'modern', but the relationship between 'conventional' and 'modern' well test interpretation methods is not always clear to the practicing reservoir engineer.
To add to the confusion, some methods have become the subject of much controversy, and conflicting reports have been published on what they can achieve. This is especially true of the 'type-curve matching' technique, which was first introduced in the oil literature in 19701, for analyzing data from wells with wellbore storage and skin effects. This method, also called 'log-log analysis', was supposed to supplement 'conventional' techniques with useful qualitative and quantitative information. In recent years, however, it was suggested that this technique be only used in emergency or as a checking device, after more conventional methods have failed.2,3
The relationship between 'conventional' and 'modern' interpretation methods is examined in detail in this paper. It is shown that type-curve matching is a general approach to well test interpretation, but its practical efficiency depends very much on the specific type-curves that are used. This point is illustrated with a new type-curve for wells with wellbore storage and skin, which appears to be more efficient than the ones already available in the literature.
METHODOLOGY OF WELL TEST INTERPRETATION
The Concept of Model
The principles governing the analysis of well tests are more easily understood when one considers well test interpretation as a special pattern recognition problem.
In a well test, a known signal (for instance, the constant withdrawal of reservoir fluid) is applied to an unknown system (the reservoir) and the response of that system (the change in reservoir pressure) is measured during the test.
The purpose of well test interpretation is to identify the system, knowing only the input and output signals, and possibly some other reservoir characteristics, such as boundary or initial conditions, shape of drainage area, etc.
This type of problem is known in mathematics as the inverse problem. Its solution involves the search of a well-defined theoretical reservoir, whose response to the same input signal is as close as possible to that of the actual reservoir. The response of the theoretical reservoir is computed for specific initial and boundary conditions (direct problem), that must correspond to the actual ones, when they are known.
Interpretation thus relies on models, whose characteristics are assumed to represent the characteristics of the actual reservoir. If the wrong model is selected, then the parameters calculated for the actual reservoir will not be correct.
On the other hand, the solution of the inverse problem is usually not unique : i.e., it is possible to find several reservoir configurations that would yield similar responses to a given input signal. However, when the number and the range of output signal measurements increase, the number of alternative solutions is greatly reduced.
The Concept of Model
The principles governing the analysis of well tests are more easily understood when one considers well test interpretation as a special pattern recognition problem.
In a well test, a known signal (for instance, the constant withdrawal of reservoir fluid) is applied to an unknown system (the reservoir) and the response of that system (the change in reservoir pressure) is measured during the test.
The purpose of well test interpretation is to identify the system, knowing only the input and output signals, and possibly some other reservoir characteristics, such as boundary or initial conditions, shape of drainage area, etc.
This type of problem is known in mathematics as the inverse problem. Its solution involves the search of a well-defined theoretical reservoir, whose response to the same input signal is as close as possible to that of the actual reservoir. The response of the theoretical reservoir is computed for specific initial and boundary conditions (direct problem), that must correspond to the actual ones, when they are known.
Interpretation thus relies on models, whose characteristics are assumed to represent the characteristics of the actual reservoir. If the wrong model is selected, then the parameters calculated for the actual reservoir will not be correct.
On the other hand, the solution of the inverse problem is usually not unique : i.e., it is possible to find several reservoir configurations that would yield similar responses to a given input signal. However, when the number and the range of output signal measurements increase, the number of alternative solutions is greatly reduced.