Parameter Estimation for Nonlinear Diffusion Problems by the Constrained Homotopy Method

Tao Liu (), Zijian Ding, Jiayuan Yu and Wenwen Zhang
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Tao Liu: School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China
Zijian Ding: School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China
Jiayuan Yu: School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China
Wenwen Zhang: School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore

Mathematics, 2023, vol. 11, issue 12, 1-12

Abstract: This paper studies a parameter estimation problem for the non-linear diffusion equation within multiphase porous media flow, which has important applications in the field of oil reservoir simulation. First, the given problem is transformed into an optimization problem by using optimal control framework and the constraints such as well logs, which can restrain noise and improve the quality of inversion, are introduced. Then we propose the widely convergent homotopy method, which makes natural use of constraints and incorporates Tikhonov regularization. The effectiveness of the proposed approach is demonstrated on illustrative examples.

Keywords: non-linear diffusion problem; inversion; parameter estimation; constrained homotopy method; porous media flow (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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