A New Look at Nonlinear Regression in Well-Test Interpretation

2010 ◽  
Author(s):  
Aysegul Dastan ◽  
Roland N. Horne
Keyword(s):  
Nonlinear Regression ◽  
Test Interpretation ◽  
Well Test ◽  
New Look

Robust Well-Test Interpretation by Using Nonlinear Regression With Parameter and Data Transformations

SPE Journal ◽  
2011 ◽  
Vol 16 (03) ◽  
pp. 698-712 ◽  
Author(s):  
Aysegul Dastan ◽  
Roland N. Horne
Keyword(s):  
Parameter Space ◽  
Nonlinear Regression ◽  
Wavelet Transformation ◽  
Data Sets ◽  
Wavelet Basis ◽  
Test Interpretation ◽  
Well Test ◽  
Reduced Basis ◽  
Data Set ◽  
Improved Performance

Summary Nonlinear regression is a well-established technique in well-test interpretation. However, this widely used technique is vulnerable to issues commonly observed in real data sets—specifically, sensitivity to noise, parameter uncertainty, and dependence on starting guess. In this paper, we show significant improvements in nonlinear regression by using transformations on the parameter space and the data space. Our techniques improve the accuracy of parameter estimation substantially. The techniques also provide faster convergence, reduced sensitivity to starting guesses, automatic noise reduction, and data compression. In the first part of the paper, we show, for the first time, that Cartesian parameter transformations are necessary for correct statistical representation of physical systems (e.g., the reservoir). Using true Cartesian parameters enables nonlinear regression to search for the optimal solution homogeneously on the entire parameter space, which results in faster convergence and increases the probability of convergence for a random starting guess. Nonlinear regression using Cartesian parameters also reveals inherent ambiguities in a data set, which may be left concealed when using existing techniques, leading to incorrect conclusions. We proposed suitable Cartesian transform pairs for common reservoir parameters and used a Monte Carlo technique to verify that the transform pairs generate Cartesian parameters. The second part of the paper discusses nonlinear regression using the wavelet transformation of the data set. The wavelet transformation is a process that can compress and denoise data automatically. We showed that only a few wavelet coefficients are sufficient for an improved performance and direct control of nonlinear regression. By using regression on a reduced wavelet basis rather than the original pressure data points, we achieved improved performance in terms of likelihood of convergence and narrower confidence intervals. The wavelet components in the reduced basis isolate the key contributors to the response and, hence, use only the relevant elements in the pressure-transient signal. We investigated four different wavelet strategies, which differ in the method of choosing a reduced wavelet basis. Combinations of the techniques discussed in this paper were used to analyze 20 data sets to find the technique or combination of techniques that works best with a particular data set. Using the appropriate combination of our techniques provides very robust and novel interpretation techniques, which will allow for reliable estimation of reservoir parameters using nonlinear regression.

scholarly journals An approximation of behind-casing hydraulic conductivity between layers from transient pressure analysis

DYNA ◽  
2019 ◽  
Vol 86 (210) ◽  
pp. 108-114
Author(s):  
Freddy Humberto Escobar ◽  
Angela María Palomino ◽  
Alfredo Ghisays Ruiz
Keyword(s):  
Hydraulic Conductivity ◽  
Transient Analysis ◽  
Test Interpretation ◽  
Well Test ◽  
Transient Pressure ◽  
Pressure Transient Analysis ◽  
Pressure Transient ◽  
Transient Pressure Analysis ◽  
Pressure Analysis

Flow behind the casing has normally been identified and quantified using production logging tools. Very few applications of pressure transient analysis, which is much cheaper, have been devoted to determining compromised cemented zones. In this work, a methodology for a well test interpretation for determining conductivity behind the casing is developed. It provided good results with synthetic examples.

Well Test Interpretation Method of Horizontal Well in Stress-Sensitive Gas Reservoir

2013 ◽  
Vol 295-298 ◽  
pp. 3183-3191
Author(s):  
Xiang Yi Yi ◽  
Zhi Zhang ◽  
Cheng Yong Li ◽  
De Cai Li ◽  
Sheng Bo Wang
Keyword(s):  
Horizontal Well ◽  
Test Interpretation ◽  
Fractured Reservoir ◽  
Well Test ◽  
Gas Reservoir ◽  
Type Curve ◽  
Flow Through ◽  
Function Integration ◽  
Lord Kelvin ◽  
Interpretation Method

Stress-sensitive widely exists in fractured reservoir. In this paper, a mathematical model of flow in stress-sensitive reservoir with horizontal well is established based on experimental data and with process of linearization. By using of Lord Kelvin point-source solution, Bessel function integration and Poisson superimpose formula, the dimensionless pressure response function of horizontal well in infinite stress-sensitive reservoir is obtained. And then the derivative type curve is calculated. Based on the type curve, the characteristics and influencing factors of the fluid flow through porous medium of horizontal well in stress-sensitive gas reservoir are analyzed.

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