Analysis of Variable-Rate Well-Test Pressure Data Using Duhamel's Principle

1986 ◽  
Vol 1 (05) ◽  
pp. 453-469 ◽  
Author(s):  
L.G. Thompson ◽  
A.C. Reynolds
Keyword(s):  
Variable Rate ◽  
Well Test ◽  
Pressure Data ◽  
Test Pressure

Practical Application of Pressure-Rate Deconvolution to Analysis of Real Well Tests

2005 ◽  
Vol 8 (02) ◽  
pp. 113-121 ◽  
Author(s):  
Michael M. Levitan
Keyword(s):  
Test Data ◽  
Rate Data ◽  
Well Test ◽  
Pressure Data ◽  
Well Test Analysis ◽  
Test Analysis ◽  
Deconvolution Algorithm ◽  
Constant Rate ◽  
Test Pressure ◽  
Real Test

Summary Pressure/rate deconvolution is a long-standing problem of well-test analysis that has been the subject of research by a number of authors. A variety of different deconvolution algorithms have been proposed in the literature. However, none of them is robust enough to be implemented in the commercial well-test-analysis software used most widely in the industry. Recently, vonSchroeter et al.1,2 published a deconvolution algorithm that has been shown to work even when a reasonable level of noise is present in the test pressure and rate data. In our independent evaluation of the algorithm, we have found that it works well on consistent sets of pressure and rate data. It fails, however, when used with inconsistent data. Some degree of inconsistency is normally present in real test data. In this paper, we describe the enhancements of the deconvolution algorithm that allow it to be used reliably with real test data. We demonstrate the application of pressure/rate deconvolution analysis to several real test examples. Introduction The well bottomhole-pressure behavior in response to a constant-rate flow test is a characteristic response function of the reservoir/well system. The constant-rate pressure-transient response depends on such reservoir and well properties as permeability, large-scale reservoir heterogeneities, and well damage (skin factor). It also depends on the reservoir flow geometry defined by the geometry of well completion and by reservoir boundaries. Hence, these reservoir and well characteristics are reflected in the system's constant-rate drawdown pressure-transient response, and some of these reservoir and well characteristics may potentially be recovered from the response function by conventional methods of well-test analysis. Direct measurement of constant-rate transient-pressure response does not normally yield good-quality data because of our inability to accurately control rates and because the well pressure is very sensitive to rate variations. For this reason, typical well tests are not single-rate, but variable-rate, tests. A well-test sequence normally includes several flow periods. During one or more of these flow periods, the well is shut in. Often, only the pressure data acquired during shut-in periods have the quality required for pressure-transient analysis. The pressure behavior during the individual flow period of a multirate test sequence depends on the flow history before this flow period. Hence, it is not the same as a constant-rate system-response function. The well-test-analysis theory that evolved over the past 50 years has been built around the idea of applying a special time transform to the test pressure data so that the pressure behavior during individual flow periods would be similar in some way to constant-rate drawdown-pressure behavior. The superposition-time transform commonly used for this purpose does not completely remove all effects of previous rate variation. There are sometimes residual superposition effects left, and this often complicates test analysis. An alternative approach is to convert the pressure data acquired during a variable-rate test to equivalent pressure data that would have been obtained if the well flowed at constant rate for the duration of the whole test. This is the pressure/rate deconvolution problem. Pressure/rate deconvolution has been a subject of research by a number of authors over the past 40 years. Pressure/rate deconvolution reduces to the solution of an integral equation. The kernel and the right side of the equation are given by the rate and the pressure data acquired during a test. This problem is ill conditioned, meaning that small changes in input (test pressure and rates) lead to large changes in output result—a deconvolved constant-rate pressure response. The ill-conditioned nature of the pressure/rate deconvolution problem, combined with errors always present in the test rate and pressure data, makes the problem highly unstable. A variety of different deconvolution algorithms have been proposed in the literature.3–8 However, none of them is robust enough to be implemented in the commercial well-test-analysis software used most widely in the industry. Recently, von Schroeter et al.1,2 published a deconvolution algorithm that has been shown to work when a reasonable level of noise is present in test pressure and rate data. In our independent implementation and evaluation of the algorithm, we have found that it works well on consistent sets of pressure and rate data. It fails, however, when used with inconsistent data. Examples of such inconsistencies include wellbore storage or skin factor changing during a well-test sequence. Some degree of inconsistency is almost always present in real test data. Therefore, the deconvolution algorithm in the form described in the references cited cannot work reliably with real test data. In this paper, we describe the enhancements of the deconvolution algorithm that allow it to be used reliably with real test data. We demonstrate application of the pressure/rate deconvolution analysis to several real test examples.

Reparameterization Techniques for Generating Reservoir Descriptions Conditioned to Variograms and Well-Test Pressure Data

SPE Journal ◽  
1996 ◽  
Vol 1 (04) ◽  
pp. 413-426 ◽  
Author(s):  
A.C. Reynolds ◽  
Nanqun He ◽  
Lifu Chu ◽  
D.S. Oliver
Keyword(s):  
Well Test ◽  
Pressure Data ◽  
Test Pressure

Determination of Permeability Distribution From Well-Test Pressure Data

1994 ◽  
Vol 46 (07) ◽  
pp. 607-615 ◽  
Author(s):  
G.S. Feitosa ◽  
Lifu Chu ◽  
L.G. Thompson ◽  
A.C. Reynolds
Keyword(s):  
Well Test ◽  
Pressure Data ◽  
Test Pressure ◽  
Permeability Distribution

Smoothing Tidal Effects in Well Test Pressure Data

2020 ◽  
Vol 17 (5) ◽  
pp. 899-902
Author(s):  
Felipe de Oliveira ◽  
Andrea Lins ◽  
Abelardo Barreto ◽  
Marcos Craizer ◽  
Helio Lopes ◽  
...  
Keyword(s):  
Well Test ◽  
Pressure Data ◽  
Tidal Effects ◽  
Test Pressure

scholarly journals A New Method for De-Noising of Well Test Pressure Data Base on Legendre Approximation

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 989
Author(s):  
Fengbo Zhang ◽  
Yuandan Zheng ◽  
Zhenyu Zhao ◽  
Zhi Li
Keyword(s):  
Test Data ◽  
Numerical Approximation ◽  
Convergence Result ◽  
New Method ◽  
Well Test ◽  
Pressure Data ◽  
Numerical Tests ◽  
Test Pressure ◽  
Legendre Expansion ◽  
Derivatives Of

In this paper, noise removing of the well test data is considered. We use the Legendre expansion to approximate well test data and a truncated strategy has been employed to reduce noise. The parameter of the truncation will be chosen by a discrepancy principle and a corresponding convergence result has been obtained. The theoretical analysis shows that a well numerical approximation can be obtained by the new method. Moreover, we can directly obtain the stable numerical derivatives of the pressure data in this method. Finally, we give some numerical tests to show the effectiveness of the method.

scholarly journals A comparison of methods for denoising of well test pressure data

2018 ◽  
Vol 8 (4) ◽  
pp. 1519-1534 ◽  
Author(s):  
Seyedeh Robab Moosavi ◽  
Jafar Qajar ◽  
Masoud Riazi
Keyword(s):  
Comparison Of Methods ◽  
Well Test ◽  
Pressure Data ◽  
Test Pressure
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