Mathematical model for in situ oil shale retorting by electromagnetic radiation

Mathematical model for in situ oil shale retorting by electromagnetic radiation James

Baker-Jarvis

and Ramarao

Inguva”

Department of Physics, North Dakota State University, Fargo, ND 58105, USA “Department of Physics, University of Wyoming, Laramie WY 82071, USA (Received 2 1 September 7987) A mathematical model for electromagnetic heating of oil shales is developed. The model simulates the process of oil and gas evolution and transfer through consolidated blocks of oil shale. The model includes equations for temperature, pressure, saturations, chemical reactions, mass conservation and source terms. The inert gases are all assumed to form one bulk species and the oil is assumed to be either in the gaseous or liquid phase. The chemical reactions include pyrolysis of kerogen and char, release of bound water, coking and decomposition of carbonates. Porosity and permeability are dynamic functions of the shale constituents. Non-linear relationships for viscosity, thermal properties and source terms are used as inputs to the model. A detailed solution to the monopole applicator fields is presented. A finite difference approximation to the differential equations is derived and solved using Newton’s iteration technique. For the cases studied the solutions are quite stable. Numerical results are included and a preliminary study of the optimization of the heating process is presented. Reasonable agreement is obtained between the model and experimental results when a monopole antenna is used as a heat source. (Keywords: oil shale; modelling; electromagnetic

radiation)

An abundance of models for in situ oil shale retorting have been developed in recent yearslp3. These models of combustion retorts all require some sort of rubblizing to increase permeability of the shale to maintain a combustion front. The results of Bridges et ~1.~~~and Sresty’ have shown that it should be possible to perform true in situ recovery using the energy from radio frequency waves to heat the shale. They have demonstrated that permeabilities increase upon heating to values of up to one Darcy, which is a significant permeability. They have also shown that the oil is recoverable from the shale by the autogeneous gas drive developed by the steam and gases evolved in pyrolysis. That is, as the shale heats the permeability increases, which permits the evolved gases of the pyrolysis to drive the oil to recovery wells. A numerical model for electromagnetic heating of oil shales would be useful in that analytical solutions to the complicated non-linear system is not possible. The development of a model yields insight into the basic physical processes of mass transfer in oil shale blocks or particles. A realistic model for in situ recovery via electromagnetic heating requires a mathematical formulation of the problem, a reliable numerical procedure and empirical relations for such quantities as specific heats, permeabilities, thermal conductivity, dielectric constant and viscosities. In this paper the mathematical foundations describing the underlying physical processes for in situ retorting by electromagnetic heating are discussed.

RADIATION HEATING PROCESS The radiation heating process converts electrical power supplied by an a.c. oscillator into thermal energy to heat oil shale. Energy is dissipated from the electrical field as work is performed in rotating the polar molecules in the shale. The dissipated energy produces the heat necessary 0016-2361/88/070916-11$3.00 0 1988 Butterworth & Co. (Publishers) Ltd.

916

FUEL, 1988, Vol 67, July

for pyrolysis. There are many advantages in using dielectric heating as a means of recovering oil from shale. Dielectric heating techniques make it possible to heat large volumes of shale in situ, in a uniform manner and under controlled conditions. The dielectric heating process is not limited by the poor thermal diffusion of oil shales, rather the shale heats from within. Various strategies have been developed in the past for electromagnetic heating of shales and oil sands. Among the most notable are filament heating’, ohmic heating**9, microwave heating” and radio frequency (RF) heating4T5. Also Fisher’ proposed the concept of induction heating of carbonaceous deposits. The use of oscillating electric fields in the microwave or radio frequency band to heat shale internally has been studied by Abernathy”, DuBow and Rajeshwar”, Bridges4*5 and Wall et ul.‘* The advantage of the volumetric heating process over ohmic heating processes is that it does not rely on the electrical conduction of the shale to transport energy and is not limited by the arcing problem of ohmic heating. Raytheon13 has also carried out a series of studies on radiating systems in oil shales. In the volumetric heating process the ability of electromagnetic fields to heat shale depends both on the magnitude and frequency of the applied fields. The attenuation of the electric fields in the shale depends on the frequency of the fields and dielectric constant of the shale. It has been found experimentally that the magnitude of the fields that can be used to heat the shale are limited by electrical breakdown characteristics of the shale. (Electrical breakdown occurs when field strengths reach a point where arcing across a narrow path in the shale effectively shorts out the system.) At microwave frequencies the attenuation lengths are quite short (0. l2.0 m) and could be useful for heating small beds of shale. Short attenuation lengths cause uneven heating rates in the shale bed, which in turn cause some regions to be over

Mathematical

model

for in situ oil shale retorting

by electromagnetic

or under heated. Radio frequency waves, on the other hand, have large attenuation lengths (of the order of 2200m) and if they can be confined to a given region they have great potential for realistic in situ oil recovery. In the dielectric heating process there are basically two approaches to heating a given resource. Either a waveguide type of system or a radiating antenna system can be used to heat. Bridges4*S approach was an example of the waveguide approach. In this work he used a modified triplate transmission line. On the other hand an example of the radiated field approach where antennas are inserted into the resource was proposed by Raytheon’ 3. Our present work is in the area of radiating systems, in particular we have studied in depth the monopole and dipole antenna in a lossy medium. Monopole applicators (which by symmetry are the bottom half of a dipole) consist of a tubular antenna and a ground plane. Dipole applicators of electromagnetic energy are easy to insert into the shale bed (whereas monopoles are easier to test in the laboratory) and when a number of these applicators are phased together it may be possible to confine the fields and obtain a relatively uniform heating profile in the shale bed.

MODEL

DESCRIPTION

The present model is a transient, two dimensional description of oil shale as it is heated by electromagnetic sources. The model geometry is cylindrical with the radial and axial coordinates describing the position in space. It is possible to use a non-uniform grid in the numerical model for spatial discretization. The model can be used to simulate laboratory studies or simulate actual field tests. The role of the model is to calculate as a function of time and spatial position, the temperatures, pressures, saturations and densities of substances, as well as net energy recoveries. The solid species are described by live independent variables. These are: organics, inert inorganics, dolomite, char and coke. The liquid phase is described by oil variables. The inert gases are combined into a single system which consists of a mixture of steam, H,, CO, CO,, CH,, CH,. The oil is separated into light and heavy ends, each can be either gas or liquid. Various sets of boundary conditions for the temperature and flow can be used in the model. For example, when simulating laboratory experiments it is possible to use adiabatic boundary conditions. The mathematical formulation consists of equations for conservation of species, saturations, capillary pressure, momentum, energy and electromagnetic source term. These equations constitute a system of coupled nonlinear partial differential equations which must be solved numerically. The empirical relations used for a description of the chemical reactions are primarily those of Campbell er a1.14, Burnham”, Braun’ and Sresty6. The permeability relations are derived from the data of Sresty6 and the formulae of Kozeny16. Thermal conductivity and heat capacities are extracted from the data of Dubow and Rajeshwar’ and Braun’, Viscosity data is taken from the work of Jenkins et al.” and Christensonis. The model describes the time evolution of the organic and inorganic materials as the shale is heated. The porosity and permeability are dynamic functions of the shale constituents. The model classifies all organics under

radiation:

J. Baker-Jarvis

and R. lnguva

the bulk name of kerogen (there is no attempt to distinguish between bitumen and kerogen). The inorganic materials consist of a bulk mineral component (primarily quartz), calcite and dolomite and bound water. As the shale is heated the kerogen reacts chemically, yielding gases, char and oil. The carbonates decompose to form gases. It is assumed that the water is released in the form of steam. The RF heating technique requires relatively low operating temperatures for pyrolysis (340-4OO”C) for efficiency. Because of these low temperatures and slow heating rates for in situ heating, coking is a dominant degradation mode for the oil. Cracking reactions are not treated in the present model. Because oxygen will be limited, combustion reactions are neglected in the lowtemperature modelling. Additionally, reactions of evolved carbon with evolved gases at these temperatures are assumed to be minimal’. MATHEMATICAL

MODEL

After Braun’, the following kerogen decomposition:

scheme was assumed

for the

[ 1 kg kerogen]+f, kg char] + [f2 kg oil] + [j, kg CO] + Cf4 kg C&l + [fs kg Hz1+ Lh kg CH41 + IA kg CKI + IX kg hOI where

CH,

are other

coefficients ( ,fi = 0.1709 fi = 0.6585 f3 =0.0106 f4 = 0.0390 f5 = 0.0042 f6=0.0189 f7 = 0.060 1 fe=0.0378

gases

and

A are stochiometric

,?,r;=l [kg [kg [kg [kg [kg [kg [kg [kg

1 char/kg kerogen] oil/kg kerogen] CO/kg kerogen] CO,/kg kerogen] H,/kg kerogen] CH,/kg kerogen] CH,/kg kerogen] H,O/kg kerogen]

Additionally, char is formed by coking. The equations which describe the mass balance of the organics can be written as:

dU, -=

-K,U,

dt

U,(t=O)=

U,,(t=O)=O

$+=f*Ux+g,U,,, Here (K,) constant, kgmp3 of reactions.

u,o

denotes kerogen, (cl) denotes char, g, is a and U~i, denotes densities of substances in shale, K,, denote rate constants for the various The rate constant is given by:

K,=2.81

x 1013 exp(-26390/T)

(s-l)

(3)

The coking reactions were taken from the work of Burnham and Braun’ 5, as was the release of bound water (w): d$=

-,,.[

where: P, =4.2 exp( - 62 000/T); All pressures are The reactions MgCa(CO,),

1 -%I[%] x 1O’O exp( -5033/T); k,= 3 x 1O48 and P, = total pressure. in Pa. of dolomite can be expressed as: PO = standard;

+ MgO + CaCO,

+ CO,

FUEL, 1988, Vol 67, July

917

Mathematical

model for in situ oil shale retorting

The heat of reaction

of the carbonates

by electromagnetic

is:

dtJ L= dt

carbonates

MP

K,,=2.5 Equation

are assumed

dolomite.

x 1O’O exp(-29090/T) (5) can be integrated

Ci.,=Ukgexp(

to decompose

CT,, (t = 0) = u;,

where (mg) denotes

and R. lnguva

(104

‘“=ZRT p. = (A + BT)exp(C(P

-K,,U,,

J. Baker-Jarvis

liquids:

H,, = 2.9 x 10” J/kg CO2 The inorganic according to :

radiation:

(s-l)

(6)

to yield:

-/K,,&.r)d:)

(7)

0

The rest of the inorganic materials are assumed to be unaffected by heating. The porosity of the shale depends on the temperature history at a given point in the bed. Initially, the porosity is assumed to be % 1%. As the shale is heated the decomposition of the organics and swelling increases the porosity. The porosity is assumed to be given as a linear function of the shale components:

-D))

(lob)

where: P= the pressure; M = the molecular weight; R= the gas constant; T = the temperature; and Z = the compressibility factor. The density of the liquid oil is assumed to be temperature dependent with A, B, C and D constants which are fit empirically. A capillary pressure is also assumed between gas and liquid. The sum of the saturations of oil and gas must equal unity. The fluid species equations characterize the time evolution of the gases and oil. In the present model gases are separated into inert and gaseous oil. The inert gas satisfies the following equation:

&,@S,p,)+v-(l&j)= $ fiU,Kk+dU,/dt+&i i=3

(11)

where: S,, ug, lgi, and pg are the saturations, velocities, sources and densities of the gas phase. The liquid oil is separated into light and heavy oil. The light oil can be present in either liquid or gas phases and the heavy oil is assumed to remain in liquid form. The species equation for the light oil (lo) can be written as:

=(I-@f$kUk+z,,,

(12)

where S,, S,, are the saturations, ui are the velocities, Yi are the mole fractions of the gases, Xi are the liquid mole fractions of the light and heavy oil, 6 is the fraction of oil that is heavy, and pO, pg are the densities of the oil and gas phases. The heavy oil (ho) satisfies: where pts denotes densities of substances and E is the initial porosity and can include effects of swelling. The absolute permeability of the shale is also a function of the temperature history. In this model the permeability is defined in each region in the shale as a function of the porosity. Initially, the shale permeability is about 10m4 Darcy. As it is heated the permeability increases to around 0.1-0.5 Darcies. The global evolution of the permeability with temperature for varying grades of shale has been determined experimentally’j. The usefulness of Sresty’s data is limited since the measurements are for bulk permeabilities of the total shale sample, whereas this model needs as an input a local permeability. To express the temperature evolution of the permeability as a function of the organic content, various functional relationships were tried and the formula16 given below produced good results:

;(“IX”“S””

K,‘C(l

_@)Z

+6

(9)

The total permeability can be written as a product of the absolute and relative permeabilities. The peremability of the oil shale is generally a very complicated function of many variables and may vary drastically from shale to shale depending on the shale microstructure. Equation (9) is an attempt to model the permeability in a simplified form. In addition, density relations are needed for gases and

918

FUEL, 1988,

Vol 67, July

+ YhOP&

= Gf,KkUk +Iho (13) The total mass of the system is conserved in that the sum of all the rate and species equations yields an equation of bulk continuity. We also need relationships between the various species of gases and oils: K+&+yhO=l

(14)

X,,+Xho=l

(15)

Here the sum over X and Y are the constraints that the sum of all the mole fractions of the oils gases are unity. The mole fractions of light and heavy oils in vapour and liquid phase are given as: r,, = KX,,

CD3

+ @Yt&P,) + VVll,P&

(16)

yho= KX,,, (17) where K represents equilibrium constants.’ For disappearance or appearance of the oil phases the pseudoequilibrium ratios” are used. This technique allows a small amount of all phases to always remain and eliminates the need for variable substitution. The momentum equation for flow in porous media is approximated by Darcy’s Law: = i$= -+P+pig]

(18)

Mathematical

model for in situ oil shale retorting by electromagnetic radiation: J. Baker-Jarvis and R. lnguva 500

and the gas viscosity

is given by:

v,=[A+BT+CT2] 0.8

20

G 0,

_; (u -

CQ

5

Y

f G 0.4

10

200

g

(22)

The thermal conductivity is assumed to be a function of the amount of organics in the shale (see Dubow and Rajeshwar”). Also, since the shale is layered the anisotropic nature of the thermal conductivity must be input 20,21. Effective values for thermal conductivity are used for heat flow parallel and perpendicular to the bedding planes (assumed layered in a periodic fashion):

E

(23) 0

0

1

I

I

I

I

I

I

I

4

where: n, = the volume fraction of layers of type one. The thermal conductivities of those layers is given by:

0 8

HOWS

Figure 1 Typical sample is heated5

example

of how the dielectric

properties

vary as a

where: (i) =gas or oil phase; g = the total permeability tensor; g = the gravity vector. Consider now the energy balance for the gas-liquid-solid system. The energy balance includes effects of convection, conduction and sources. Some simplifying assumptions are necessary for the modelling. Since the electromagnetic heating is relatively constant over the region of interest and since velocities and pore size are small, to a good approximation the temperatures of the gas, liquid and solid are equal at any point in space. We can write a bulk energy balance equation:

+ tckUkT, + (Cinorg

Uinorg

T,

+

(Gv uw

T,

+(Cch,,Cicha,T)+V.(PoCpoTv,+PgC,TDg) =V.(7.VT)+g(r,t)+H,+H,,+H,

(19)

where: T = the-temperature above the initial resource temperature; x= the thermal conductivity tensor; c~,~)= specific heats; g(r,t) = the electromagnetic source term which for a monopole applicator the space distribution is worked out later and Ha, are the heats due to reactions. A constitutive relation is also needed to express the electromagnetic source in terms of the frequency of the applied fields and properties of the medium: -g(r,t) = 1/2E.J = 1/2cus”[E1’ (watts/M3) (20) where w = the angular frequency; E”= the imaginary part of the dielectric constant; and E= the electric field. In general the source term is a function of radial distance in the shale (attenuation length) and also temperature dependent, since as the shale is heated the electrical properties of the shale change (see Figure I). The electrical dissipative source term g(r,t) has units of watts/m3 of shale. The present source being used is that of a monopole applicator. The viscosities are temperature dependent. For the liquid oil phase the viscosity is: V, = A exp(B/T)

(21)

The specific heats depend and temperature:

both on shale grade (gal/ton)

cP= (AT + B)(C + DX)

(25)

where: X = the grade of the shale in gal/ton; and T = the temperature in K; cP is specific heat. The total model then consists of a system of coupled equations for the unknowns Xho, Xl,, Y,,, Y&,Yi, Ss, S,, P,, T, U[k,, U&l,, qmgJ* U,, up, uo, g(r,t). The equations can be solved by a finite difference scheme to yield predictions for the time and space evolution of the temperature, pressure, saturation and oil yields. To complete the mathematical model we need appropriate boundary conditions for the fluids and temperatures on the bounding surfaces. In the present model the normal velocity components of the gases and oil are specified as zero on the outer boundaries. At the well bore it is possible to specify the pressure, or flow, or a convective flow condition given by: vvfell(i)

=F[Patm

-Pi]

where: h=an empirical constant; and i denotes the velocity of the component (gas or oil). For the temperature flux on the boundaries we may write a convective boundary condition : -(;iVT)%=H(72:-

T)

(27)

where H and T, are constants.

NUMERICAL

SCHEME

Equations (12), (13) and (19) were discretized in the spatial coordinate only, so that the problem then was reduced to solving a set of coupled, first order, ordinary differential equations in time. After running the model, various interesting quantities were plotted. Oil yields were plotted by a knowledge of saturations, porosities, coke and kerogen concentrations at each point in the shale. The yields were normalized to the calculated potential oil in the shale.

FUEL,

1988,

Vol 67, July

919

Mathematical

model for in situ oil shale retorting by electromagnetic radiation: J. Baker-Jarvis and R. lnguva are fairly close when considering the scale on which they are plotted. It seems that numerical dispersion has affected the temperature profiles to a lesser degree than the saturations. This is probably due to the fact that the relatively constant heating rate produces temperature profiles which have small thermal gradients.

r----10

z Figure 2 A large scale retort. The system consists of a well bored into the shale bed and an antenna inserted in the wellbore. The region enclosed by the dashed lines is the region heated by the antenna. The first set of plots assume the shale to be layered in a periodic fashion, alternating from high (33 gal ton-‘) to low (5 gal ton-‘) concentrations of shale. It is assumed that the fields are confined by use of some waveguide-like technique to the enclosed region

LARGE

SCALE

6

E

I

w

J

SIMULATION

As an application of the model, an idealized commercial run has been simulated. The geometry consists of a well bored in the shale (Figure 2). In this idealized simulation it is assumed that the heating source is uniform within the retort region. The simulation is idealized in that there has not been sufficient experimental research to yield accurate estimates of some of the input physical parameters such as the relative permeabilities and absolute permeabilities. As a first approximation the following relations for the permeabilities were used; P,* = (1 -&J2, Pro = So2. Figures 3 to 5 show the evolution of various quantities with time for an average heating rate of 054°C h-’ and an initial porosity of 1%. In this case the shale grade varies in the bed in the periodic fashion for a maximum of 33 to 5 gal ton-‘. It can be seen that the effects of layering on the temperature profile is minimal. The layering can be seen quite clearly in the plots for organics, coke and char. Figure 5 shows the evolution of the oil as the shale is heated. Note that the oil yield is normalized to the calculated potential oil in the shale. To study the effects of grid size on the model results a series of tests were run. In these tests the region heated was held fixed whereas the number of spatial grid blocks were varied. The average heating rates were 21°C h- ’ until 39O”C, and thereafter the source was turned off. In Figure 6 gas saturations and temperatures are plotted for 63 grid blocks (dashed lines), 48 grid blocks (+lines), and 35 grid blocks (solid lines). The saturation and temperature profiles are functions of radial distance in the shale for a fixed z coordinate. The z coordinate used was the centre of the heated region. It can be seen that for 63 and 48 grid blocks the saturations are almost identical, whereas at 35 grid blocks the solutions diverge. The origin of the numerical dispersion is spatial truncation error and the effects of upstream weighting in the relative permeability terms. For the temperatures all the solutions

920

8

\1

FUEL, 1988, Vol 67, July

01 0

I

I

1

I

2

4

6

8

10

li

161 \

10 -

z

8-

6-

/

,

0 0

2

4 Temperature

6 r (m) contours

8

10

‘b I 12

(“C)

Figure 3 Simulation of themperature profiles (“C) for a full scale commercial retort after (a) 10 days and (b) 40 days heating. The dimensions of the retorted shale are IOm in radial direction and 10m in vertical direction (cylindrical symmetry). The heating rate is O.WC h-’ and the frequency of the input power is 2 x IO6 Hz with attenuation length of 16Om

Mathematical

model

for in situ oil shale retorting I

16

by electromagnetic

I

J. Baker-Jarvis

and R. lnguva

number of other dipoles inserted nearby it is possible to obtain a relatively uniform heating pattern. For a monopole of length L orientated along the z axis (see Figure 7) the current has only a z component. From Maxwell’s equations the vector potential can be obtained:

100

100

radiation:

L

A,=-

P

dz’ I,(z’)K(r,r’)

4x s -L

where the kernal 2

K is given by: It

8-

K(r, r’) = 1/2n

exp( - ikR(tI)/R(@dtI

(29)

R = ((z - z’)’ + p2 + u2 - 2ap cos /I)“’

(30)

s -n

with

where:

z = the observation point; p = radial coordinate; radius; and /I = the angle between p and p’; I =current; p = permeability. However, for the field calculations the reduced or average kernal was used to reduce computation time: a = the antenna

0

a

2

16

4

6

,.,.,

I

8

10

12

K = exp( - ikR)/R

(31)

R=((z-z’)‘+~~)~‘~

(32)

._”

000

200

1

3Kl-3oo~l

141-300-300

This approximation is valid for thin antennas and introduces error in the field calculations only for points extremely close to the antenna. The vector potential is given by: L

dz’ Z,(z) exp( - ikR)/R

A, = &

(33)

s 10 -

The electric field can then be obtained 2

from:

8-

E, = -;

/ dz’l(r.)[$;]K(R) -L

60.8

0.7

0.6

r 0-N Figure 4 (a) Organic content remaining in the shale at (a) 10 and (b) 40 days (kg me3). The shale was layered periodically with layers of high and low organic content

D E 0.5 B P ; 0.4 0 z 8 0.3 & 0 0.2

HEATING

USING

A MONOPOLE

ANTENNA

A simple heating applicator is the monopole (or dipole) antenna (see Figure 7). This consists of a ground plane and a tubular conductor inserted into the shale bed. The advantage of a dipole for heating applications is the simplicity of insertion and that when phased with a

0.1 0

I

5

.

,

. 1

10

,

I

,

I

15

,

.

I

20

.

I

,

25

,

,

,

30

,

,

,

,

,

35

,

,

,

,

40

,

,

,

45

Time (days) Figure 5 simulation

Oil yield as a function

of time for the above

large scale

FUEL, 1988, Vol 67, July

921

Mathematical

model

for in situ oil shale retorting

by electromagnetic

excitation

‘.O(,

radiation:

J. Baker-Jarvis

and R. lnguva

is that of a TEM mode given by: (38)

where: L(= the monopole radius; b= the outer coaxial radius; and p= the radial coordinate. The following assumptions were made: 1. The averaged kernal was utilized. 2. The antenna is assumed to have no conductive losses. 3. The antenna is assumed to be electrically thin (L/a > 60). Pocklington’s integral length 2L is given by L

E, = l/iwe 0.5L

I

’

I

I

I

I

I

I

10

for an

1

antenna

a9qz,zy +k'K(z,z') I(z’)dz’dtI

a22

L

I

1 .o

equation23

of

(39)

where: E, = excitation field. Pocklington’s equation was solved numerically using the method of moments to obtain the current on the antenna and then Equations (34) and (36) were integrated numerically to find the field distribution in the shale, which was then put into Equation (20) to give the power distribution pattern (an example of the power distribution is given in Figures 8 and 9).

3gol

Experiments with u monopole In conjunction with Western Research Institute we recently performed a number of experiments using a monopole to heat small blocks of shale at 2.45GHz to calibrate both our field models and the heat-mass transfer model. In these tests, blocks of western anvil points oil shale were heated by a monopole antenna inserted into

F 1 .o

10.0

,

-. .-__---

r(m) Figure 6 Radial saturation profiles (a) and radial temperature profiles (“C) as the number of grid points is varied in a large scale simulation. The axial coordinate is located in the middle of the retort. Number of grid blocks: -----,35; +-+-+-,48, ---,63

(35) -L

The derivatives yield :

of K can be calculated

a2K (z-z’)(p-p’) apaz

-2zz

2ik :[-+-)I R3 a2K ~- = lexp( a2 47c +i In

922

the

3

(36)

R4

Z

A!il

k (1+k2(z-~‘)2 - ix R2

3k(z - z’)” + 3(z - z’)2

calculations

to

erp(-ikR)/R[ik($+$)

- ikR)lR

R3

analytically

R4 it was

’

1

assumed

FUEL, 1988, Vol 67, July

e

P

(37) that

the

input

k----a4 Figure 7

A monopole

antenna

with ground

plane

Mathematical

model for in situ oil shale retorting by electromagnetic radiation: J. Baker-Jarvis and R. lnguva cracks in the bed (at least when the block is not constrained radially), thus limiting the need for blasting and enhancing the recovery. Future modelling should include more information on Pressure

Pressure

-2L

Figure 8

2L

X

Typical

power contour

for a monopole

antenna

/

b-46.4

cm -4

Shale block

Figure 10 applicator

Radio frequency

heating of a shale block using a monopole

0 15

/737

Jl 33

d 23

22

17.8’

Figure 9

Power

distribution

around

. 1

a monopole

26

25

.

the middle of the block (Figure 10). The monopole heating system is shown in Figure I I. In Table 1 the input parameters used are summarized. In Figure 12 the experimental results at various thermocouple positions are compared with the model results. The temperature distributions predicted by the model compare reasonably well with experimental results. It was noticed that overheating occurred at the input point and near the antenna. This overheating problem was due to the near fields around the antenna. Little oil was recovered in this test because of the relatively low temperatures obtained.

.

2.8

32 .

31 .

:

;

24 .

4’ 29 .

1

13

21

. 5

i

:7

30 .

z6’* ‘5.12”-

CONCLUSIONS The model appears to be numerically stable for the cases tested. For the geometries studied it appears that oil may be recovered at ~200 kw/h of electricity ner barrel of recovered oil. To enhance recovery, sweep gases could be injected at various points in the heated region. Another advantage of the r.f. heating process is that it produces

u

7.69”

1’0 ;1

19 . l

Figure

11

Thermocouple

positions

FUEL,

1;

18

20m

in shale block

1988,

Vol 67, July

923

Mathematical Table I

Summary

model

for in situ oil shale retorting

by electromagnetic

of input parameters 0.5 x 0.5 x 0.5 m

Block size Frequency Power level Shale grade Thermal data Viscosity Density data Equilibrium coefficients Reaction kinetic parameters

450 MHz 2200 W 23 GPT reference reference reference reference reference

1I 18 24 24 15

radiation:

J. Baker-Jarvis

and R. lnguva

the flow of the oil in the shale. That is, one would expect that some of the oil would be trapped in the shale in regions of low permeability. The experimental studies performed by Sresty6 were too small to see the effects of oil trapping, and were probably performed on selected samples of shale. In the comparison of the model with experiment we see in Figurr 12 that the model performed reasonably. In Figure IZa, d and f the model deviated from the

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FUEL, 1988, Vol 67, July

measurements

in a shale block

(-0-W)

for various

(a) 1;

Mathematical

model

for in situ oil shale retorting

by electromagnetic

radiation:

J. Baker-Jarvis

and R. lnguva

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experiment. The reason for this is that all the thermocouples were very near the antenna and the present field model is not good close to the monopole.

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through the Laramie RP20-85LC11060.

Projects

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REFERENCES ACKNOWLEDGEMENTS The authors wish to acknowledge the continual support and encouragement of Dr William Little, Dr Chang Yul Cha, Mr Norm Merriam, V. K. Saxena and Dennis Moore. This project has been supported from a grant

1

2

Braun, R. L., ‘Mathematical Modeling of Modified In-Situ and Aboveground Oil Shale Retorting’, Report No. UCRL-53119, Lawrence Livermore Laboratory, 1981 Travis, T. J., Hommert, P. S. and Tyner, C. E. ‘A Two Dimensional Numerical Model of Underground Oil Shale Retorting’, Las Alamos Laboratory Report, 1982

FUEL, 1988, Vol 67, July

925

Mathematical 3 4

5

6

926

model for in situ oil shale retorting by electromagnetic radiation: J. Baker-Jarvis and R. lnguva

Coats, K. H. SPEJ 1980, 20, 363 Bridges, J. A., Tallove, A. and Snow, R. H., ‘Net Energy Recoveries for the In-Situ Dielectric Heating of Oil Shale’, Proceedings of the 1lth Oil Shale Symposium, Colorado School of Mines, Golden, Colorado, 1976 Bridges, J. E., Enk, J., Snow, S. H. and Sresty, G. C., ‘Physical and Electrical Properties of Oil Shale’, 15th Oil Shale Symposium Proceedings, Colorado School of Mines, Golden, Colorado, 1982 Sresty, G. C., ‘Kinetics of Low Temperature Pyrolysis of Oil Shale by the IITRI RF Process’, Proceedings of the 13th Oil Shale Symposium, Colorado School of Mines, Golden, Colorado, 1979 Sarapuu, E. Quart. Cola. Sch. Mines 1965, 60(4) Erodskaya. B. K., ‘Use of Electric Current for the Purpose of Preparing Oil Shale Layers for Underground Strip Mine Gasification’, NSF, Washington DC _ Fisher. S. T.. ‘Processing of Solid Fuel Deposits bv Electrical Induction Heating’, IEEETransactions of Inhustrialelectronics and Control Instrumentation, February 1980, IECI-27, No. 1 Abernathy, E. R., ‘Production Increase of Heavy Crude Oils by Electromagnetic Heating’, Paper No. 37007, Ann. Tech. Meeting of Pet. Sot. of CIM, Calgary, Alberta, Canada, 1974 Dubow, J. and Rajeshwar, K., ‘Thermophysical Properties of Oil Shales’, Final Technical Report No. EF-77-5-03-1584(DOE), 1979

FUEL, 1988, Vol 67, July

12 13 14 15 16 17 18 19 20 21 22

23 24

Wall, E. T., Damraurer, R., Lutz, W., Bies, R. and Cranney, M. Thermcrl Hydrocarbon Chemistry 1978, 330 Raytheon Patents 4,196,329,4,320,801,4,135,579 by Rowland; 4,301,865, 4,140,179 by Kasevich; 4,193,451 by Dauphine Campbell, J. H., Koskinas, G. J. and Stout, N. D. In Situ 1980.2, I-15 Burnham, A. K. and Braun, R. L. In Situ 1985,9( 1). l-23 Bear, J., ‘Dynamics of Fluids in Porous Media’, Elsevier Press, NY, 1972 Jenkins, G. R. and Kirkpatrick, J. W. J. CLm. Petrol. MarchJune, 1979, 18(1). 60 Christenson, R., ‘Viscosity Characteristics of Bitumen’, Musters Thesis, University of Wyoming, 1980 Abou-Kassem, K. and Aziz, K. J. Pet. Tech. 1985, 37, 1661 Baker-Jarvis, J. R. and Ramarao Inguva J. Heat Transfer 1985, 107, 39 Baker-Jar+, J. R. and Ramarao Inguva Fuel 1984.63, 1726 Gear, C. W. ‘Numerical Initial Value Problems in Ordinary Differential Equations’, Prentice-Hall, Englewood Cliffs, NJ, 197 1 Stutzman, W. L. and Thiele, G. A., ‘Antenna Theory and Design’, John Wiley and Sons, NY, 1981 Youngren, G. K., ‘Development and Application of an In Situ Combustion Reservoir Simulator’, SPE, February 1980, pp. 3951