New Regularization Algorithms for Solving the Deconvolution Problem in Well Test Data Interpretation

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

A Study on Optimization of CBM Water Drainage by Well-Test Deconvolution in the Early Development Stage

“…Water 2018, 10, x FOR PEER REVIEW 3 of 14 [19][20][21]. Using pressure derivative data in deconvolution leads to a nonlinear least-squares objective function that is different from those used in the earlier deconvolution methods and eliminates the dependency of the deconvolved responses on the initial reservoir pressure.…”

“…A small error in the initial reservoir pressure could make a significant difference in the late time periods of the deconvolved responses that can lead to an incorrect interpretation model, particularly misinterpretation of the boundaries. The method presented above is based on pressure derivative data rather than pressure data that are used in all published deconvolution algorithms [19][20][21]. Using pressure derivative data in deconvolution leads to a nonlinear least-squares objective function that is different from those used in the earlier deconvolution methods and eliminates the dependency of the deconvolved responses on the initial reservoir pressure.…”