Thermohydrodynamic Studies of Vertical Wells in Non-Linear Filtration
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Thermohydrodynamic Studies of Vertical Wells in Non-Linear Filtration E. R. Badertdinova1* , R. M. Khairullin1** , V. R. Gadil’shina2*** , and M. Kh. Khairullin2**** (Submitted by A. M. Elizarov) 1 2
Kazan National Research Technological University, Kazan, Tatarstan, 420015 Russia
Institute of Mechanics and Engineering, Federal Research Center Kazan Scientific Center, Russian Academy of Sciences, Kazan, Tatarstan, 420111 Russia Received March 8, 2020; revised March 16, 2019; accepted March 21, 2020
Abstract—In this paper the computational algorithm for interpreting the results of hydrodynamic and thermohydrodynamic studies in non-linear filtration is proposed. The algorithm allows to determine the conductivity of the reservoir, the limiting pressure gradient, reservoir pressure and the regularization parameter. Temperature and pressure changes data, measured on a vertical well, are taken as the initial information. DOI: 10.1134/S1995080220070082 Keywords and phrases: limiting pressure gradient, vertical well, thermohydrodynamic studies, numerical simulation.
1. INTRODUCTION The field and laboratory studies shown that the oil of some reservoirs have structural and mechanical properties because of the high content of high molecular weight components—resins, asphaltenes, paraffin. The experimental results show that deviations from the linear Darcy law appear in filtration process such oils at low pressure gradients [1, 2]. In recent years, the methods to determine the non-Newtonian nature of oils not only based on viscometric studies, but also according to hydrodynamic researches of wells have been developed. The determination of the limiting gradient and reservoir pressure in the case of viscoplastic fluid filtration was considered in [3]. This approach had been applied to highly permeable reservoirs. In the case of low permeability reservoirs, it’s usage requires long research. Hydrodynamic methods of the determination the reservoir parameters in non-linear filtration were considered in [4, 5]. In this paper the computational algorithm for interpreting the results of thermohydrodynamic and hydrodynamic studies in non-linear filtration is proposed. *
E-mail: [email protected] E-mail: [email protected] *** E-mail: [email protected] **** E-mail: [email protected] **
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THERMOHYDRODYNAMIC STUDIES OF VERTICAL WELLS
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2. PROBLEM STATEMENT In case of the filtration with a limiting gradient, it is assumed that fluid movement occurs only in domains of the reservoir, where the pressure gradient exceeds a certain critical value. Usually in the numerical simulation of such problems, regularization of the problem is made [6–8]. In this case, the process of nonisothermal non-Newtonian fluid filtration in a circular reservoir to a vertical well is described by the following system of equations 1 ∂ ∂p 1 ∂ ∂p ∂p ∂p β∗ = sr −G + εsr , > G, ∂t r ∂r ∂r r ∂r ∂r ∂r 1 ∂ ∂p ∂p ∗ ∂p = εsr , ≤ G, 0 < t ≤ texp , (1) β ∂t r ∂r ∂r ∂r 1 ∂ ∂T = CR ∂t r ∂r
∂T rλR ∂r
k ∂p + ρCp μ ∂r
∂T ∂p + εD ∂r
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