Deconvolution of Well Test Data as a Nonlinear Total Least Squares Problem

Schroeter, Thomas von; Hollaender, Florian; Gringarten, Alain C.

doi:10.2118/71574-ms

Cited by 71 publications

(48 citation statements)

References 11 publications

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“…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.…”

Section: Deconvolution As a Diagnostic Tool For Production Data Analysismentioning

confidence: 99%

Production-Data Analysis—Challenges, Pitfalls, Diagnostics

Ilk

Anderson²,

Stotts³

et al. 2010

SPE Reservoir Evaluation &Amp; Engineering

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TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractAlthough production analysis (PA) for reservoir characterization is approaching the popularity of pressure transient analysis (PTA), there are few consistent diagnostic methods in practice for the analysis of production data. Many of the "diagnostic" methods for production data analysis are little more than observation-based approachesand some are essentially "rules of thumb."

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Section: Deconvolution As a Diagnostic Tool For Production Data Analysismentioning

confidence: 99%

Production-Data Analysis—Challenges, Pitfalls, Diagnostics

Ilk

Anderson²,

Stotts³

et al. 2010

SPE Reservoir Evaluation &Amp; Engineering

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“…In the presence of random noise and/or other inconsistencies, a positive α is selected based on an informal interpretation of the discrepancy principle -i.e., we increase the value of the regularization parameter until the calculated (model) pressure difference begins to deviate from the observed pressure difference in a specific manner. The mean and standard deviation of the arithmetic difference of the computed and input pressure functions are also computed, but algorithmic rules (e.g., L-curve method) for selecting α are not recommended -for reasons discussed by von Schroeter et al 25 ).…”

Section: Regularizationmentioning

confidence: 99%

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

Ilk

2006

SPE Reservoir Evaluation &Amp; Engineering

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This work presents the development, validation and application of a novel deconvolution method based on B-splines for analyzing variable-rate reservoir performance data. Variable-rate deconvolution is a mathematically unstable problem which has been under investigation by many researchers over the last 35 years. While many deconvolution methods have been developed, few of these methods perform well in practice -and the importance of variable-rate deconvolution is increasing due to applications of permanent downhole gauges and large-scale processing/analysis of production data. Under these circumstances, our objective is to create a robust and practical tool which can tolerate reasonable variability and relatively large errors in rate and pressure data without generating instability in the deconvolution process.We propose representing the derivative of unknown unit rate drawdown pressure as a weighted sum of Bsplines (with logarithmically distributed knots). We then apply the convolution theorem in the Laplace domain with the input rate and obtain the sensitivities of the pressure response with respect to individual B-splines after numerical inversion of the Laplace transform. The sensitivity matrix is then used in a regularized least-squares procedure to obtain the unknown coefficients of the B-spline representation of the unit rate response or the well testing pressure derivative function. We have also implemented a physically sound regularization scheme into our deconvolution procedure for handling higher levels of noise and systematic errors.We validate our method with synthetic examples generated with and without errors. The new method can recover the unit rate drawdown pressure response and its derivative to a considerable extent, even when high levels of noise are present in both the rate and pressure observations. We also demonstrate the use of regularization and provide examples of under and over-regularization, and we discuss procedures for ensuring proper regularization.iv Upon validation, we then demonstrate our deconvolution method using a variety of field cases.Ultimately, the results of our new variable-rate deconvolution technique suggest that this technique has a broad applicability in pressure transient/production data analysis. The goal of this thesis is to demonstrate that the combined approach of B-splines, Laplace domain convolution, least-squares error reduction, and regularization are innovative and robust; therefore, the proposed technique has potential utility in the analysis and interpretation of reservoir performance data. v Dr. Ali Beskok, for his advice and suggestions; and for his service as a member of my graduate advisory committee;Fekete Associates and Louis Mattar for their enthusiasm; and providing me the opportunities to improve this research;My friends in 611:

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“…In the analysis of PDG data, deconvolution may also be used. 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.…”

Section: Introductionmentioning

confidence: 99%

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

Liu

Horne

2012

SPE Journal

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The permanent downhole gauge (PDG) is a promising tool for reservoir testing but has yet to reach its full potential. Generally, conventional well-testing methods are most able to use small sections of constant-flow-rate data. However, data mining, a newly developed technique in computer science, is a tool that can reveal the relationship among variables from large volumes of data. The application of data-mining algorithms to synthetic and field data has been successful in extracting the reservoir model from variable-flow-rate and pressure-transient data. In fact, because of uncertainty in flow-rate measurements, this technique is one of the few ways to make use of the flow-rate data that are now available with some modern PDG tools.The application is conducted in two steps. First, the pressure and flow-rate data from the PDG are used to train a nonparametric data-mining algorithm. The reservoir model is obtained implicitly in the form of polynomials in a high-dimensional Hilbert space defined by kernel functions when the algorithm converges after being trained to the data. Next, a specific flow-rate input (for example, constant rate) is fed into the data-mining algorithm. The datamining algorithm will make a pressure prediction subject to the input flow rate. Because the data-mining algorithm has already obtained the reservoir model, the pressure prediction is expected to be the reservoir response given the constant flow rate. Therefore, the proposed constant flow rate and the predicted pressure reveal the reservoir model underlying the variable PDG data, without needing to specify in advance which reservoir model is to be used. Three methods (Methods A, B, and C), differing by input vectors, kernel functions, and presence of breakpoints detection, are proposed in the paper.Synthetic noisy data and real field data were used to test this approach. Methods B and C were able to satisfactorily recover the wellbore/reservoir model in most considered cases. Even in extreme cases when the flow-rate data are noisy and changing frequently, and in the absence of any shut-ins, the method was still able to extract the reservoir models.

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Deconvolution of Well Test Data as a Nonlinear Total Least Squares Problem

Cited by 71 publications

References 11 publications

Production-Data Analysis—Challenges, Pitfalls, Diagnostics

Production-Data Analysis—Challenges, Pitfalls, Diagnostics

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

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

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