Abstract
• An analytical solution for reservoir temperature during EM heating is derived. • Power transmission through the multilayers in the wellbore is investigated. • A simple method is proposed to estimate the energy absorption number. • An effective heating zone is defined to evaluate the thermal efficiency of EM heating. Electromagnetic (EM) heating for heavy oil extraction has been recognized as an eco-friendly and economical thermal technique to enhance oil recovery (EOR). This work constructs an analytical model to identify the reservoir temperature distribution based on power transmission during EM heating. For homogenous and isotropic reservoirs, governing equations of the reservoir temperature reduce to a one-dimensional radial heat transfer model by neglecting heat convection. The heating source is derived from Maxwell’s equations, and the amount of power transmitted into the reservoir is estimated by the transfer matrix method. Analytical solutions to the reservoir temperature are in the form of Bessel’s functions, which agree well with the numerical method and are close to experimental data. Further calculations show that the Beer-Lambert power form would underestimate the temperature near the wellbore by about 59% compared to Maxwell’s equations. The transmitted power increases with the wave frequency for the air-filled annulus but decreases when the annular fluid is water or completion fluid. High frequencies (> 1 GHz) would produce a satisfactory power ratio for the air-filled annulus, while moderate frequencies (∼ MHz) are proper for the water- or completion fluid-filled annuli. Thickening the non-metallic sleeve could enhance the power transmission. The current model also proposes a simple method to estimate the energy absorption number by the asymptotic solution for a long time. The analytical solution demonstrates that the thermal penetration depth defined by the diffusion front is independent of the wave frequency. On the contrary, the effective heating zone, reflecting the influence of the frequency and heating time, is a better indicator to evaluate the thermal efficiency of EM heating. The obtained solutions would help engineers estimate the reservoir temperature fast, optimize the frequency of the heater, and assess the efficiency of EM heating.
Published Version
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