Use of Pressure Derivative in Well Test Interpretation

Abstract

Abstract In this paper, a well test interpretation method based on the analysis of the time rate of change of pressure, together with the actual pressure response, is discussed. A differentiation algorithm is proposed and several field examples are provided to illustrate how the method simplifies the analysis process. Interpretation of well tests is therefore easier and more accurate. Introduction The interpretation of pressure data recorded, during a well test has been used for many years to evaluate oil and gas reservoir characteristics. Static reservoir pressure, measured in shut-in wells, is used to predict reserves in place through material balance calculations. Transient pressure analysis provides a description of the reservoir flowing behavior. Many methods have been proposed for interpretation of transient tests (ref. 1), but the best known and most widely utilized by petroleum engineers is that published by Horner (ref.2) in 1951. More recently, type curves were introduced which indicate the pressure response of flowing wells under a variety of reservoir descriptions (ref. 3 to 6). Comparison of transient pressure measurements with type curves provide,; the only reliable means for identifying that portion of provide,; the only reliable means for identifying that portion of the pressure data which can be analyzed by conventional straight line analysis methods. In recent years, the quality of well test interpretations has considerably improved due to the availability of accurate pressure data (from electronic pressure gauges) and to the development of new software for computer-aided analysis. An increasing number of theoretical interpretation models are now in current use which allow one to reach a detailed definition of the flow behavior in the producing formation. Surprisingly, the commonly used analysis techniques have not followed the general progress evident in hardware and in interpretation models, thus making the interpretation procedure complicated and time consuming. Type curves are seen by various analysts as overly simplistic, or overly complex, difficult to distinguish, and/or cumbersome to use. Yet mere identification of straight lines on pressure versus time graph is a "ruler approach", convenient for hand analysis, but ignoring powerful computing facilities that are currently available. Furthermore, powerful computing facilities that are currently available. Furthermore, the conventional straight line analysis methods fail to make use of all the data available and can result in significant errors. In this work, an interpretation method is proposed, based on the analysis of the derivative of the pressure with respect to the appropriate time function: natural logarithm of time or Horner/ superposition times. This method considers the response as a whole, from very early time data to the last recorded point and uses the type curve matching technique. It provides a thorough description of the flow behavior in the reservoir but, with the logarithmic derivative, it also emphasizes the infinite acting radial flow regime, of prime interest in well test interpretation. The new approach is a natural extension of the Horner method to analyse the global response with an improved definition. Use of the derivative of pressure versus time is mathematically satisfying because the derivative is directly represented in one term of the diffusivity equation, which is the governing equation for all the models of transient pressure behavior currently in use in well test analysis. Consequently, the derivative response is more sensitive to small phenomena of interest which are integrated and, hence, diminished, by the pressure versus time solutions presently used in well test pressure versus time solutions presently used in well test interpretation. One practical limitation of the use of the pressure derivative in analysis is the ability to collect pressure derivative in analysis is the ability to collect differentiable pressure transient data. Accurate and frequent pressure measurements are required. However, as will be shown in pressure measurements are required. However, as will be shown in this paper, current pressure measurement and computer processing technologies allow use of pressure derivative in analysis.