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# Difference between revisions of "Electromagnetic heating process"

Electromagnetic heating has a different effect on heavy oil reservoirs than other enhanced oil recovery processes that use heat. This article describes the ways in which electromagnetic heating can be applied to a reservoir.

## Describing the heat effect

As shown in Fig. 1, Q(t), the time-dependent rate of production of a given reservoir with either horizontal or vertical wells, depends on the flow of oil through the reservoir and through the producing wells. In the reservoir, the flow is conditioned by a temperature-dependent viscosity, μ(T), porosity, permeability, and compressibility (Φ , k, and c). To a first approximation, the last three parameters are unchanged by the heating. In the wells, the flow is conditioned by the geometry of the wells (radius, depth, and length, in the case of horizontal wells) and again by the oil viscosity.

The heating effect in the porous media of the reservoirs is simply represented by Darcy’s law with a temperature-dependent viscosity, μ(T).

....................(1)

where

V →= fluid velocity, k = effective permeability, and P(r → , t) = the space- and time-dependent pressure.

The effect of the heating in a well (along the z direction), is represented by a temperature dependent viscosity used in the Hagen-Poiseville law.

....................(2)

where

Rwell = the radius of the well.

The viscosity, μ, is related to the kinematic viscosity, ν, by the relation

....................(3)

where ρ is the density of the hydrocarbon. The strong temperature dependence of the viscosity ν for values of kinematic viscosities ν above 2 mm2/s) is given by the law shown in Eq. 4.[1]

....................(4)

where A1 and A2 are characteristic constants for each liquid hydrocarbon (with no dissolved gases), and T is the absolute temperature. As shown schematically in Fig. 2, in the range of reservoir temperatures (40 to 60°C), a temperature increase of a few degrees can reduce the viscosity significantly with the corresponding increase in production. For 9.9°API oil, a temperature increase from 30 to 40°C reduces the viscosity by 67%, an increase from 40 to 50°C causes a 62% reduction, and an increase from 50 to 60°C reduces the viscosity by 57%. The corresponding production increases depend on the temperature spatial distribution throughout the reservoir and in the well system.

As in many other applications of electrical heating and in the case of well and reservoir heating, there is a wide range of available frequencies in the electrical spectrum, which can be used in diverse heating schemes. At the low-frequency (LF) end, energy is supplied directly from the 60 Hz distribution grid.[2] Induction heating requires higher frequencies in the radio frequency (RF) range of 103 to 105 Hz, while heating is also possible at frequencies in the microwave (MW) range (MW 109 to 3 × 1010 Hz).[3] So far, most of the enhanced oil recovery (EOR) heating schemes used successfully in the oil industry have been in the low-frequency range. Microwave heating has been widely used industrially in the past, but its application to reservoir heating is not widespread, although it has been receiving more attention lately.[4][5][6]

The analysis of low-frequency heating up to radio frequencies can be carried out through a circuital approach based on the application of Kirchhoff’s laws: the voltage law (KVL) for voltages around a loop, and the current law (KCL) for currents into a node. In this range of frequencies, the process is commonly defined as electrical heating and the parameters used are voltage, current, resistance, capacitance, and inductance. The analysis of microwave heating processes requires the full description provided by electromagnetic theory, as described by Maxwell’s field equations in terms of electric and magnetic field vectors, E →,H →, vector current density, J →, with material properties represented by permittivity, ε, permeability, μM, and conductivity, σ. In this range, the process is correctly defined as electromagnetic heating. The case of induction heating can be described through a mixed approach.

## Concentrated heating scheme: resistive LF and inductive RF

In the case of vertical wells, Figs. 3(a) and 3(b) illustrate the possible concentrated heating schemes that have been proposed and used in practice. In this concentrated case, a heating unit is located in the well at the depth of the producing zone. The heating is generated locally over the heater volume and then transferred to the system. Heat flow is conductive and convective in the reservoir and well volumes, and conductive in the rest of the system. Radiative heat transfer is generally not considered, in view of the low range of temperatures obtained.

In the case of resistive concentrated heating, the heating unit consists of one or more resistances (in Fig. 3(a), we show a Wye-connected three-phase arrangement) connected by a set of metallic conductors to a surface power supply (which in the simplest of cases is a 60 Hz source connected to the power grid). As shown in Fig. 3(b), in the case of inductive concentrated heating, the heating unit consists of a coil wound around a core of metal. The coil is connected by a set of metallic conductors to a surface power unit, which can operate at frequencies up to several kHz, deriving its primary power from the 60-Hz power grid.

## Distributed heating scheme: resistive LF

The case of distributed resistive heating is shown in Fig. 4. In this case, an external power supply (generally fed from the 60-Hz power grid) generating low-frequency currents and voltages is connected by cable to a pressure device in contact with the perforated section of the production casing, while the other terminal is either connected to ground at the surface (a) or at some lower level (b).

In either case, electrical current flows through the overburden, reservoir and underburden, and in each volume element of material, it dissipates electrical power in accordance with the value of the resistance and capacitance per unit volume of the different media. Sections of insulated tubing are required to direct most of the current flow into the reservoir, thus, keeping the generated power within the reservoir volume. This scheme has been described in the literature as electromagnetic heating, although this term should be strictly applied to those cases in which the frequencies used are much higher than 60 Hz.

## Distributed microwave heating scheme

High frequency electromagnetic energy can be transferred from power supplies situated at the surface to the reservoir region by the structures shown on Fig. 5. In the first arrangement (a), energy is transmitted in the annular space between the casing and the production tubing in the form of transverse electromagnetic (TEM) waves. In the second case (b), energy is transmitted along the production tubing in the form of transverse electric (TE) or transverse magnetic (TM) modes. The schemes shown do not require cables to be connected to the source at the surface, which implies a great reduction in installation complexities. Coaxial cables can of course also be used for the transmission of TEM waves from the surface to the reservoir. In all cases some sort of radiating element must be situated in the well at reservoir depth, in order to transfer electromagnetic energy to the reservoir.

## References

1. Burger, J., Souriau, P., and Combarnous, M. 1985. Thermal Methods of Oil Recovery, Ch. 12, 37-41. Paris, France: Technip Editions.
2. Orfeil, M. 1987. Electric Process Heating, 391-621. Paris, France: Bordan Dunod.
3. Davies, E.J. 1990. Conduction and Induction Heating, 93-102. London, England: Peter Peregrinus Ltd.
4. Metaxas, A.C. and Meredith, R.J. 1990. Industrial Microwave Heating, 1-102. London, England: Peter Peregrinus Ltd.
5. Okress, E.C. ed. 1968. Microwave Power Engineering, Vols. 1 and 2, 1-27. New York City: Academic Press.
6. Saad, T.S. ed. 1984. Historical Perspectives of Microwave Technology. IEEE Transactions on Microwave Theoryand Techniques, MTT-32, 9, 955-1271. New York City: IEEE Press.