Affiliations: Institute for Biocomplexity and Informatics,
University of Calgary, Calgary, Canada | Intelligent Systems Technology Inc., California,
USA
Abstract: The deconvolution method, which has received considerable attention
recently, is rapidly becoming one of the major tools for well test and
production data analysis in the oil and gas industry. The clear justification
for this approach is the fact that in well-test and production data analysis we
are interested in the transient response which, for a stable linear system, is
a linear combination of exponential functions. In this paper, we present a new
deconvolution approach, which is potentially an important contribution to the
existing body of knowledge in this field. We show that the solution of the
deconvolution problem can be successfully represented as a linear combination
of non-orthogonal exponential functions. In addition, we present three
deconvolution algorithms. The first two algorithms are based on regularization
concepts borrowed from the wellknown Tikhonov and Krylov methods. The third
algorithm is based on the stochastic Monte Carlo method. Our analysis results
show that the Tikhonov regularization method is stable, and feasible for a
modest number of data points. Based on the results, the Krylov conjugate
gradient method requires minimal storage and achieves fast convergence. This
method is recommended for small to large data sets. The Monte Carlo method
achieved the best results. It was able to handle large amounts of data, had
minimal storage requirements, was robust to noise and avoided local minima.
However, the Monte Carlo method was noticeably slower than the others. The
computational results show that the exponential basis functions decomposition
method provides a robust, solution in the presence of moderate levels of
noise.
Keywords: Exponential Functions, Deconvolution, Tikhonov Regularization, Krylov Method, Monte Carlo Method, Conjugate Gradient
