TITLE:
New Regularization Algorithms for Solving the Deconvolution Problem in Well Test Data Interpretation
AUTHORS:
Vladimir Vasin, Georgy Skorik, Evgeny Pimonov, Fikri Kuchuk
KEYWORDS:
Deconvolution Problem, Volterra Equations, Well Test, Regularization Algorithm, Quasi-Solutions Method, Tikhonov Regularization, A Priori Information, Discrete Approximation, Non-Quadratic Stabilizing Functional, Special Basis
JOURNAL NAME:
Applied Mathematics,
Vol.1 No.5,
November
30,
2010
ABSTRACT: Two new regularization algorithms for solving the first-kind Volterra integral equation, which describes the pressure-rate deconvolution problem in well test data interpretation, are developed in this paper. The main features of the problem are the strong nonuniform scale of the solution and large errors (up to 15%) in the input data. In both algorithms, the solution is represented as decomposition on special basic functions, which satisfy given a priori information on solution, and this idea allow us significantly to improve the quality of approximate solution and simplify solving the minimization problem. The theoretical details of the algorithms, as well as the results of numerical experiments for proving robustness of the algorithms, are presented.