Application of Homotopy Perturbation Method to One-dimensional Transient Single-phase EM Heating Model

Abstract

Thermal recovery involves well-known processes such as steam injection (cyclic steam stimulation, steam drive, and steam-assisted gravity drainage), in situ combustion, and a more recent technique that consists of heating the reservoir with electrical energy. When high frequency is used for heating, it is called electromagnetic (EM) heating. The applications of EM heating for heavy-oil reservoirs can be especially beneficial where conventional methods cannot be used because of large depth, reservoir heterogeneity, or excessive heat losses. This process can be modeled to determine temperature distribution in the porous reservoir rock during EM heating. In this paper, the homotopy perturbation method (HPM), a powerful series-based analytical tool, is used to approximate the temperature distribution, which has been modeled using a partial differential equation and special assumptions when high frequency currents are used. This method decomposes a complex partial differential equation to a series of simple ordinary differential equations which are easy to solve. According to the comparison of the solutions obtained by HPM with those of a numerical method (NM), good agreement is achieved. Moreover, a sensitivity study is done to determine the effect of initial temperature, oil rate, frequency and input power on the accuracy of HPM.