Matrix computations (3rd ed.)
Linear Systems
Numerical Mathematics and Computing
Numerical Mathematics and Computing
Numerical Recipes in C: The Art of Scientific Computing
Numerical Recipes in C: The Art of Scientific Computing
| Hi-index | 0.00 |
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.