Practical Considerations for Pressure-Rate Deconvolution of Well Test Data

Abstract

Pressure-rate deconvolution provides equivalent representation of variable-rate well test data in the form of characteristic constant rate drawdown system response. Deconvolution allows one to develop additional insights into pressure transient behavior and extract more information from well test data than is possible by using conventional analysis methods. In some cases it is possible to interpret the same test data in terms of larger radius of investigation. There are a number of specific issues one has to be aware when using pressure-rate deconvolution. In this paper, we identify and discuss these issues, and provide practical considerations and recommendations on how to produce correct deconvolution results. We also demonstrate reliable use of deconvolution on a number of real test examples. Introduction Evaluation and assessment of pressure transient behavior in well test data normally begins with examination of test data on different analysis plots: e.g. a Bourdet1,2 derivative plot, a superposition (semi-log) plot, a Cartesian plot, etc. Each of these plots provides a different view of the pressure transient behavior hidden in the test data by well rate variation during a test. Integration of these several views into one consistent picture allows one to recognize, understand, and explain the main features of the test transient pressure behavior. Recently, a new method of analyzing test data in the form of constant rate drawdown system response has emerged with development of robust pressure-rate deconvolution algorithm.3–5 Deconvolved drawdown system response is another way of presenting well test data. Pressure-rate deconvolution removes the effects of rate variation from the pressure data measured during a well test sequence and reveals underlying characteristic system behavior that is controlled by reservoir and well properties and is not masked by the specific rate history during the test. In contrast to a Bourdet derivative plot or to a superposition plot, which display the pressure behavior for a specific flow period of a test sequence, deconvolved drawdown response is a representation of transient pressure behavior for a group of flow periods included in deconvolution. As a result, deconvolved system response is defined on a longer time interval and reveals the features of transient behavior that otherwise would not be observed with conventional analysis approach. The deconvolution discussed in this paper is based on the algorithm first described by von Schroeter, Hollaender, and Gringarten.3,4 An independent evaluation of the von Schroeter et al. algorithm by Levitan5 confirmed that with some enhancements and safeguards it can be used successfully for analysis of real well test data. There are several enhancements that distinguish our form of the deconvolution algorithm. The original von Schroeter algorithm reconstructs only the logarithm of log-derivative of the pressure response to constant rate production. Also, it requires the initial reservoir pressure to be provided by user. Our form of deconvolution algorithm reconstructs the pressure response to constant rate production along with its log-derivative. Depending on the test sequence, in some cases we can recover the initial reservoir pressure. We have applied deconvolution analysis to a large number of well tests that included both conventional test sequences and permanent downhole gauge data from producing wells. The deconvolution algorithm in the form described by Levitan5 has been implemented in the well test analysis software and is routinely used in our work. There are several important features/capabilities that distinguish this form of the algorithm and simplify its use for analysis of real well test data. We have found that pressure-rate deconvolution is not a replacement of conventional techniques but a useful addition to the suite of tools used in well test analysis. It allows us to develop additional insights into pressure transient behavior and extract more information from well test data than is possible by using conventional analysis methods. In some well test analysis literature6 the term deconvolution is used in the context of removing effects of afterflow associated with wellbore storage. In contrast, the pressure-rate deconvolution discussed here deals with removing effects of the step-wise constant rate variation observed (measured) during a multi-rate test sequence. In fact, the constant rate system response function reconstructed in this process incorporates wellbore storage and skin effects.

Production-Data Analysis—Challenges, Pitfalls, Diagnostics

“…In general, deconvolution techniques are applied to well test data [see recent work by von Schroeter et al and Levitan, (refs [16][17][18][19]]. On the other hand, although there are no "theoretical" limitations for the application of deconvolution methods to production dataand there are few recent attempts (refs.…”

Deconvolution of Variable-Rate Reservoir Performance Data Using B-Splines

“…In the work by Levitan 26 , some modifications were suggested such as applying deconvolution to each individual flow period for handling inconsistencies present in real well test data. Furthermore, Levitan et al 28 also proposed critical considerations and recommendation on producing accurate deconvolution results.…”

Interpreting Pressure and Flow-Rate Data From Permanent Downhole Gauges by Use of Data-Mining Approaches

“…von Schroeter et al (2001Schroeter et al ( , 2002 made important breakthroughs by proposing a formulation that enables solving the deconvolution problem as a separable nonlinear total least square problem, and applied this algorithm to PDG data. Levitan et al (2004) described a deconvolution technique by use of an unconstrained objective function constructed by matching pressure and pressure derivative generated by the response functions derived from different pressure-buildup (PBU) periods. This method proved effective when the flow-rate history is simple and the flow-rate data are accurate, especially when the breakpoints of the flow rate are identified accurately.…”