Analytical Solutions for Transient Temperature Distribution in Heavy-Oil Reservoir due to Heating Producer Well
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Analytical Solutions for Transient Temperature Distribution in Heavy-Oil Reservoir due to Heating Producer Well P. E. Morozov* (Submitted by A. M. Elizarov) Institute of Mechanics and Engineering, Federal Research Center Kazan Scientific Center, Russian Academy of Sciences, Kazan, Tatarstan, 420111 Russia Received March 5, 2020; revised March 17, 2020; accepted March 21, 2020
Abstract—This paper presents the results of a study of transient temperature distribution in the reservoir during the heat treatment of the producer well. Analytical solutions of the problem for heating the bottomhole zone using a heater with a constant temperature or power are obtained. The analytical solutions are compared with the known approximate solutions. A nonlinear equation is obtained for evaluating well productivity during stationary heating of the bottomhole zone. DOI: 10.1134/S1995080220070306 Keywords and phrases: heavy-oil reservoir, downhole heater, heat transfer, Peclet number, temperature distribution, analytical solution, well productivity.
1. INTRODUCTION The most effective methods for heavy-oil recovery are thermal methods: continuous and cyclic steam injection, steam-assisted gravity drainage (SAGD), in-situ combustion, heating of the formation by downhole heaters, etc. [1–4]. The heating of heavy-oil producer wells is of great practical interest. As a result, the production rate can increase both due to a reduce oil viscosity, and due to dewaxing of near-wellbore zone. The effect of high temperature and low viscosity near-wellbore zone is same as if the well has negative skin factor. There are two possibilities for heating the bottom-hole zone: 1) periodic; 2) stationary, in which heating is performed without shutting down the operation of the well, i.e. with a continuous flow of oil to the well [5, 6]. The main feature of heating producer well is that the conductive heat transfer from the downhole heater is obstructed by the reverse convective heat transfer by the formation fluid moving to the well (Fig. 1). After sufficient time has elapsed, temperature distribution in the reservoir tends to steady state. Earliest analytical model for steady-state temperature distribution in reservoir by heating producer well at a constant temperature on the wellbore was proposed in [7]. To date, many theoretical and experimental studies of heating producer wells were carried out [5, 6, 8–12]. First analytical solution of the problem of unsteady-state temperature distribution in the reservoir was obtained in [8], but it was difficult for practical use. Therefore, an approximate solution for unsteady-state temperature distribution in the bottomhole zone with a heat source of constant temperature or constant power was developed [5]. The numerical solutions of the problem of heating producer wells by the finite difference method were considered in [6, 9–11]. In this paper, exact and approximate solutions for unsteady-state temperature distribution in the vicinity of a producer well with a heat source of constant temperature or constant power are obt
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