An identification problem related to mud filtrate invasion phenomenon during drilling operations. Issue 12 (2nd December 2021)

• Record Type: Journal Article
• Authors: Boaca, Tudor
• Is Part Of: Inverse problems in science and engineering. Volume 29:Issue 12(2021)
• Page Start: 2401
• Page End: 2428
• Publication Date: 2021-12-02
• Subjects: Inverse problem -- optimal control -- parabolic equation -- diffusion through porous media; 35Q86 -- 35Q93 -- 35R30; Engineering mathematics -- Periodicals; Inverse problems (Differential equations) -- Periodicals; 620.001515357
• DOI: 10.1080/17415977.2021.1914605
• Languages: English
• ISSNs: 1741-5977

Abstract

Abstract : In this paper, we study two identification problems related to the mud filtrate invasion phenomenon. We want to determine a parameter (the invasion rate) in the coefficients of the parabolic equation that describes the mud filtrate invasion phenomenon. In the first problem, we determine this parameter starting from the observed values of the mud filtrate dispersion. We reduce the problem to an optimal control problem and prove the existence of the optimal control. In the second problem, we determine the invasion rate imposing the minimum condition of the quantity of mud filtrate that diffuses into the oil reservoir. We also reduce the identification problem to an optimal control problem. We prove the existence of the optimal control and we obtain a simple explicit form of this optimal control. A numerical example is presented for the second problem.