Numerical simulation of electromagnetic heating of heavy oil reservoir based on multi-physical fields coupling model

ABSTRACT

Electromagnetic (EM) heating is an advanced technology that can improve the oil recovery rate. Previous studies usually focus on the coupling of EM and thermal reservoir models, with little attention to multi-phase flow in EM heating. In order to accurately analyze the heat and mass transfer in the reservoir under EM heating, this work developed an advanced model coupling the EM-temperature-seepage fields, in which the variation of the physical properties of heavy oil reservoirs has been considered. In addition, the influence of the EM heating factors is also analyzed. The results show a significant saturation partitioning in the heat and mass transfer in heavy oil reservoirs under EM heating, and heavy oil flows more rapidly in areas of high oil saturation. Increasing the EM frequency and power can extend the heating range of the reservoir, but it can cause a dramatic rise in the temperature of the antenna. When the temperature of the production well induces heavy oil flow, increasing the production pressure can significantly improve output. The average flow rate of heavy oil at the producing well increased by 17.61% when the bottom flow pressure decreased from 19 MPa to 17 MPa. The study of the distance between the production well and the antenna finds that the average temperature of the production well is only 463.06 K when the antenna spacing is 15 m. Compared with other situations, 10 m is the most suitable for efficient and continuous exploitation of heavy oil.

KEYWORDS:

• Electromagnetic heating
• heavy oil
• oil recovery rate
• multi-physical fields coupling model
• heat and mass transfer

Disclosure statement

No potential conflict of interest was reported by the author(s).

Nomenclature

$\mathbf{B}$magnetic flux density, Wb/m2	=
$c$	=	speed of light, 299,792.458 km/s
$C_P$heat capacity of the reservoir at constant pressure, J/(kg·K)	=
$C_{p,f}$reservoir fluid heat capacity, J/(kg·K)	=
$C_{p,s}$reservoir solid heat capacity, J/(kg·K)	=
$\mathbf{D}$electric flux density, C/m2	=
E	=	electric field intensity, V/m2
$f$	=	frequency of EM waves, Hz
$g$	=	acceleration of gravity, m/s2
H	=	magnetic field intensity, A/m
$\mathbf{J}$current density, A/m2	=
$k_0$free space wave number	=
$k_{eff}$thermal conductivity of the reservoir,W/(m·K)	=
kf	=	fluid thermal conductivity, W/(m·K)
ks	=	solid thermal conductivity of reservoir,W/(m·K)
p	=	pressure, Pa
$\mathbf{q}$heat flux, W/m2	=
$Q_e$EM source power, W/m3	=
$Q_{rh}$resistance loss, W/m3	=
$Q_{ml}$magnetic loss, W/m3	=
$s_i$heavy oil and water saturation	=
$s_1$heavy oil saturation	=
$s_2$water saturation	=
t	=	EM heating time, d
T	=	temperature, K
u	=	seepage velocity of heavy oil, m/s

Greek symbols

${\epsilon }_0$free space permittivity, 8.85×10−12 F/m	=
${\epsilon }_r$reservoir relative dielectric constants	=
$\epsilon { }^{\mathrm{\prime }}$	=	dielectric constant
$\epsilon { }^{\mathrm{\prime }\mathrm{\prime }}$	=	loss coefficient
${\text{isin}}_{\mathrm{p}}$porosity of the reservoir	=
$\kappa$	=	reservoir permeability, mD
${\kappa }_{rsi}$oil and water relative permeability	=
${\kappa }_{rs1}$oil relative permeability	=
${\kappa }_{rs2}$water relative permeability	=
$\lambda$	=	in-situ wavelength, m
$\mu$	=	fluid viscosity, mPa·s
${\mu }_0$permeability of vacuum $4\pi$×10−7 H/m	=
${\mu }_1$oil phase viscosity, mPas	=
${\mu }_2$water phase viscosity, mPas	=
${\mu }_r$relative magnetic permeability	=
$\rho$	=	density of reservoir, kg/m3
${\rho }_f$fluid density, kg/m3	=
${\rho }_s$solid density, kg/m3	=
${\sigma }_r$electrical conductivity of the reservoir, S/m	=
$\omega$	=	angular frequency, rad/s
Superscript	=
*	=	conjugate
Subscript	=
1	=	heavy oil in fluids
2	=	water in fluids
s	=	reservoir solid phase
f:	=	reservoir fluid phase

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (No.52006094), Educational Commission of Liaoning Province of China (No. L2020045, L2020046), Doctoral Research Start-up Foundation of Liaoning Province of China (No.2021-BS-248, 2022-BS-289). It was also supported by Fushun Revitalization Talents Program (No.FSYC202107007)