Robust Nonlinear Regression for Parameter Estimation in Pressure Transient Analysis


Parag Bandyopadhyay







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Parameter estimation in pressure transient analysis is used to match analytical transient flow models to measured field data. This matching of nonlinear models to observed data is also referred to as regression. Ordinary least squares (OLS) is the most commonly used regression method. However, the assumptions inherent to OLS that; a) errors are present only in the dependent variable (pressure) and b) these errors follow a Gaussian distribution, may make it unsuitable for certain data sets.

In this research report, the development of methods that address the possibility of errors in both pressure and time variables is discussed first. These methods were tested and compared to OLS and found to provide more accurate estimates in cases where random time errors are present in the data. These methods were then modified to consider errors in breakpoint flow rate measurement.

OLS parameter estimates for datasets with non-Gaussian error distributions are shown to be biased. A general method was developed based on maximum likelihood estimation theory that estimates the error distribution iteratively and uses this information to estimate parameters. This method was compared to OLS and found to be more accurate for cases with non-Gaussian error distributions.

In the final chapter, we discuss issues relating to computational performance such as hybrid methods for efficient and robust parameter estimation and scaling of methods with increasing problem size. Stochastic iteration methods, which are used commonly in machine learning problems, were adapted for use with the methods developed in the report. These methods were shown to be computationally efficient for larger problems while maintaining accuracy.

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Copyright 2014, Parag Bandyopadhyay: Please note that the reports and theses are copyright to their original authors. Authors have given written permission for their work to be made available here. Readers who download reports from this site should honor the copyright of the original authors and may not copy or distribute the work further without the permission of the author, Parag Bandyopadhyay.

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