Analytical solution of heat equation taking into account convection with isothermal boundary conditions

About the author:

Rodion M. Ganopolskij, Cand. Sci. (Phys.-Math.), Head of the Department of Modeling of Physical Processes and Systems, Institute of Physics and Technology, University of Tyumen, Tyumen, Russia, r.m.ganopolskij@utmn.ru

Abstract:

The problem of determining the distribution of heat through the reservoir constantly arises in the production of hydrocarbons. Changes of temperature affect the viscosity of oil and consequently the rate of its production. Taking into account the filtration process, additional terms appear in the classical heat conduction equation, including nonlinear ones. Various numerical schemes are used to solve the modified equations. The question of the convergence of such methods often arises. The task of this work is to obtain an analytical solution of the heat equation in cases where it is possible, in order to further compare numerical solutions with them.

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