This paper gives a short overview of the theoretical and practical aspects of a thermal diffusion column, of the most important applications of 13C and describes a thermal diffusion cascade for enrichment of this isotope.

1. SEPARATION OF CARBON-
13 BY THERMAL
DIFFUSION
GHEORGHE VASARU
Aleea Tarnita, Nr. 7, Apt. 11
400649 CLUJ-NAPOCA, ROMANIA
E-mail: gvasaru@hotmail.com

2. ABSTRACT
 In the selection of a process gas for use in the separation of 13C by
thermal diffusion, methane is a first candidate because of its low
molecular weight. Generally, the process equipment to be employed for
this separation consists of concentric tube columns with calrod heaters,
which are normally operated at a mean temperature no more than 673
K because methane decomposes at greater temperatures.
 This paper gives a short overview of the most important
applications of 13C and describes a thermal diffusion cascade for
enrichment of this isotope.
 Successively, the results of calculations of the transport coefficients H
and K for a concentric tube column, operated with methane as process
gas, are presented. Static separation factor at equilibrium vs gas
pressure has been calculated for various molecular models. The
experimental separation factors for different gas pressures were found
to be consistent with those calculated for the inverse power repulsion
model and the Lennard-Jones (12,6) model.

3. Thermal Diffusion Process
 The thermal diffusion process is based on the fact that molecular
diffusion can be caused by a temperature gradient. In general, if
two gases are exposed to a temperature gradient between two
surfaces, the gas with the lower molecular weight will tend toward
the hotter surface. The two gases will separate until a concentration
gradient occurs resulting in concentration diffusion of equal
magnitude in the opposite direction. Under equilibrium conditions
the rate of transfer of the light molecules towards the hot surface
resulting from thermal diffusion will be exactly counterbalanced by
concentration diffusion.
In a thermal diffusion column the relatively small separation factor
is multiplied by the effect of convection currents resulting from the
temperature gradient. The heavy molecules, which tend toward the
cold surface, are swept to the bottom of the column while the light
molecules at the hot surface are swept toward the top of the
column. The maximum separation is limited by the concentration
diffusion that is eventually set up in the axial direction as a result of
the separation itself.

5. Thermal Diffusion Process (Cont’d)
 This transport phenomena makes available enriched isotopes which
either cannot be provided by other separation methods or are more
costly when prepared by alternate means with emphasis on
concentrating isotopes of the inert gases. The heaviest and lightest
isotopes in such mixtures can easily be enriched to any desired
concentration if a proper thermal diffusion cascade is constructed
[1- 4]. A cascade to enrich an isotope of other than the greatest or
least mass in a mixture of three or more components become more
complicated in arrangement and offers design problems relative to
length, width and flow rates.
Construction of thermal diffusion column presents engineering
problems associated with supported heated central elements. At the
present time, thermal diffusion columns are designed to use
standard, commercial tubular heaters or wire heaters with an
effective length of some meters. To conserve space, 12 to 19
columns are enclosed in a common water jacket. Thus, individual
columns can be interconnected externally to give any desired shape
of cascade. Within the same bundle, some columns can be used for
enriching one isotope, while at the same time other columns are
being used to enrich a different isotope.

6. The Transport Equation
The transport equation for a thermal diffusion column is:
(1)
where t is the total transport of required isotope, H is the
coefficient of transport by thermal diffusion, c is the fractional
molar concentration of the required isotope, Kc is the
coefficient of transport by convection currents, Kd is the
coefficient of transport by ordinary diffusion, and z is the axial
coordinate of the column. Kc and Kd are named also as
convective and diffusive remixing coefficients, respectively.
According to the Jones and Furry theory [5], H and Kd are
functions of pressure; thus
(2)
Kd is independent of pressure.

7. The Transport Coefficients for Cylindrical Case
The transport coefficients for the cylindrical case of a TD
column and for the Lennard-Jones (12-6) molecular model are
given by the following expressions:
(3)
(4)
(5)
where aT is the TD constant, r - the density, h -- the viscosity,
D - coefficient of ordinary diffusion, all at the temperature of
the cold wall, T1, g - the gravity constant, r1 - the radius of cold
wall, h, kd and kc - shape factors, q = T2/T1, R = r1/r2, -
the reduced cold wall temperature, T2 and r2 - temperature and
radius of hot wall, respectively, k - Boltzman constant and e -
the depth of potential well.

8. Equilibrium Separation Factor
Putting in (1), t = 0, we have
(6)
the integral of which is
(7)
or equivalently
(8)
If z0 £ z £ L and c0 £ c £ cL,
where L is the length of the thermal diffusion column, we have
for the equilibrium separation factor the expression
(9)

9. The Separation Factor per Mass Unit
The separation factor per mass unit, Q*, is given by the
equation:
(10)
where
H* = coefficient of thermal diffusion transport per
unit mass,
Kc = coefficient of convective remixing,
Kd = coefficient of diffusive remixing,
Kp = coefficient of parasitic convection
L = length of column
The coefficient of parasitic remixing, Kp, arises due to
unknown inaccuracies within the column such as nonuniform
surface temperature distribution and imperfect centering of the
heater.

10. Transport Coefficients vs Pressure
The H*, Kc and Kd factors can be written as function of pressure and
take the form
(11)
where a, b, and c are constants determined by column geometry and
temperature and by properties of the gas. The ratio b/a and c/a can be
determined from the equilibrium data, but a different kind of
experiment must be performed to estimate a and allow calculation of b
and c. These ratios may be computed from the equations [6]:
(12)
where
p = gas pressure at which the maximum separation factor occurs,
Q* = separation factor per unit mass at the maximum in the curve.
Pressure at the maximum separation.
When the gas pressure in a thermal diffusion column is adjusted to
achieve maximum separation, the coefficient of convective remixing, Kc,
is equal to the coefficient of diffusive remixing, Kd,

12. Heat Losses
 Heat is removed in four ways from the heating element in a thermal
diffusion column: by radiation from the heater, by convection
currents in the gas, by conduction through the gas, and by
conduction through the spacers between the heater and the cold
wall and lengthwise through the heater sheets to the cold jacket end
fittings [7].
 Convection and conduction through the gas are essential for the
operation of a thermal diffusion column, but if the heat loss via
radiation or direct conduction through the spacers can be
decreased, the over-all economy of operation will increase.
Theoretical and experimental investigations of heater temperature
and various modes of heat transfer to the cold wall were undertaken
to better understand column operation and to increase the
efficiency and economy of isotope separation by thermal diffusion.
 The amount of heat radiated from the heater and the amount
conducted through the spacers and sheets can be determined from
power input and heater sheath temperature with an evacuated
column.

13. Tapered Cascade
 If an efficient tapered cascade is to be designed to enrich an
isotope from some small concentration to some higher
concentrations, the thermal diffusion characteristics of a given
column system must be determined. These characteristics can be
computed theoretically. To test the validity of this theory, a series
of experiments was performed to determine the agreement between
observed values of thermal diffusion separation factors and the
theoretical values calculated according to Jones and Furry theory.
 The theoretical and observed separation factors for 13CH4, as
function of gas pressure show that the maximum equilibrium
separation factor occurs at a lower pressure.

14. Comparison of Separation Methods
 Research needs for 13C include nuclear bombardment studies, tracer
studies on chemical reaction and biological processes and clinical medicine
studies.
 Most molecules of biological interest are large and complex. Synthesis
with 13C requires several reactions each having a relatively low yield.
Consequently, the several grams of 13C would be required to synthesize 1 g
of a carbon biological molecule. Thus, if 13C is to be a practical tool in
biological research, it must be available in larger quantities at a lower cost.
 For producing large quantities of enriched carbon-13 from natural
abundance carbon (1.1 % 13C and 98.9 % 12C), R.A.Schwind [8] performed an
economic evaluation of four methods: thermal diffusion, distillation, gaseous
diffusion and chemical exchange. These processes were chosen because
they are only ones for which enough laboratory and production knowledge is
available to design large production facilities. From this study, the relative
production cost per gram of 13C of a mixture containing 60 % 13C was obtained
as a function of the production rate for each of these methods. The cost
figures were based on an amortization of the capital equipment cost over a
period of 10 years.

15. Practical Conclusions
 The practical conclusions are as follows: Thermal diffusion was
found to be most economical method for the production rates below
100 g/a; CO distillation should be used for production rates above
200 g/a. The gaseous diffusion and the CO
 The world’s largest unit for 13C production is located in Xenia,
Ohio, at Cambridge Isotope Laboratories Inc [9] This plant has been
in continuous operation since 1990 producing 99 % 13C at a rate of
30 kg/a. After the current expansion in 1997, the plant capacity has
been increased to 120 kg/a. The recent increased interest in this
unique isotopic material follows regulatory approval of the first
diagnostic test which uses 13C. Recently, the FDA gave approval for
clinical use of the 13C Urea Breath Test for the detection of the
ulcer-causing bacterium Helicobacter pylori. This new breath test is
safer, simpler, and more accurate than other tests which diagnose
Helicobacter pylori infection. In this breath test, the patient drinks a
solution of non-radioactive 13C Urea and then breathes into a
collection device. The test takes only thirty minutes; can be
performed in a doctor’s office; avoids the need for stomach
endoscope with biopsy an is more accurate than blood tests.

16. Separation of 13C by Thermal Diffusion
Practical Aspects (I)
 A thermal diffusion cascade has the advantage of
being relatively easy to operate. However, thermal diffusion
is an irreversible process and therefore require a large
quantity of energy per gram of material separated. There is
also the disadvantage that the basic thermal diffusion
column cannot be scaled up. The gap between the hot and
cold walls cannot be increased because the separation
factor is proportional to the temperature gradient and there
is a practical limit to the obtainable temperature difference.
The diameter of thermal diffusion columns cannot be
increased above a certain limit because temperature in
homogeneities in the hot and cold walls cannot be avoided.
For these reasons even a very large-scale thermal diffusion
plant must be composed of relatively small diameter thermal
columns. A simplified scheme of our standard thermal
diffusion column are given in Fig. 1.

17. The standard thermal diffusion
column of concentric tube type:
 1,15 – electrical contact rods;
2,14 – connecting tubes (brass);
 3,4 – textolyte insulators;
 5 – flange (stainless steel);
 6,10 – rubber gaskets;
 7 – cold wall;
 8 – hot wall;
 9 – spacer;
 11 – lower end of the hot wall;
 12 – bellows;
 13 - flange (copper).

20. Separation of 13C by Thermal Diffusion
Practical Aspects (II)
 At low production rates, the cost of labor is the controlling factor and the thermal diffusion
is an attractive process.
 One of the most persistent problems encountered in the 13C thermal diffusion
cascade is decomposition of the process gas (methane) into free hydrogen and carbon.
Since this decomposition could be catalyzed by the surface of central heater, a series of
experiments was conducted to evaluate methane decomposition on various metal surfaces
Using a heater made by swaging a soft aluminum sheath over the standard stainless steel
calrod, no perceptible decomposition of methane was observed at 673 K.
 The performances of several methane thermal diffusion cascades for 13C enrichment
from natural abundance was calculated. To guide current laboratory operations, various
arrangement of the existing 19-column cascade were evaluated. From the six alternatives
we have selected the cascade arrangement of 8-4-2-1-1-1-1-1 columns per stage from
feed to product withdrawal, respectively, Fig. 2 [10]. This cascade was set up with an
appropriate system for feed purification, pressure control, waste and product withdrawal,
impurity control and removal, and stages gas circulation. In the feed system, methane of
97.4% purity was further purified by pumping volatile impurities, at liquid nitrogen
temperature, up to 99.85 - 99.88%. After purification, the methane was stored in a high-pressure
bottle from which it was fed through a special system into the feed reservoir.
Waste, i.e. depleted methane in 13C was withdrawn from the feed reservoir and stored as
methane of high purity.
 Enriched methane in 13C was removed continuously from the bottom of the seven stages
and stored in a calibrated reservoir.

21. Separation of 13C by Thermal Diffusion
Practical Aspects (III)
 The methane used as feed gas was not completely free of impurities such as nitrogen,
carbon dioxide and ethane. These impurities introduced with the feed material in cascade
are transported at a high rate towards the bottom of the cascade where they accumulate. If
these are not removed continuously, the fairly sharp interface between methane and
impurities rises rapidly and the effectiveness of the separation system is destroyed [11].
For removing these impurities a single column was provided, column 19, placed at the
bottom of the cascade. The level of impurities was detected with a thermal-conductivity
cell placed at the bottom of the column 19. For reference the enriched methane from the
bottom of the seven stage was used. The signal of these sensors was a direct measure of
the methane purity in the column. Impurities were withdrawn from the bottom of column 19
through a calibrated leak.
 For interstage gas circulation, hermetically sealed compressors was used. Allowing only
one column at a moment, in each stage, to be open to the compressor-driven loop
obviated the parasitic gas circulation. The columns in stages 1 - 3 were alternately opened
to the circulation manifold by solenoid valves operated by an electronic programmer.
 The control of enriching during the transient period has been performed by mass
spectrometry.
 The cascade was operated at the temperature of 673 K, all 19 thermal diffusion column
having a single cooling jacket in a bundle system, maintained at the temperature of 293 K.
The operating pressure was of 1.05 at.

25. Parameters of the Methane Thermal Diffusion
Cascade
 Physical Properties of Methane (at T1 = 295 K):
 Density, r (g/cm3) 6.626x10 -4
 Viscosity, h (g/cm.s) 1.110x10 -4
 Diffusivity, D (cm2/s) 0.215
 Thermal diffusion constant, aT 0.00678
 Carbon Isotopes: 12C (98.892%); 13C (1.108%)
 Target: The enrichment of 13C at the concentration of 25% 13CH4
 Geometric Parameters and Operating Conditions:
 Radius of cold wall, r1 (cm) 1.725
 Radius of hot wall, r2 (cm) 0.900
 Column length, (cm) 400
 Temperature of the cold wall, T1 (K) 295
 Temperature of the hot wire, T2 (K) 673
 Operating pressure, p (at) 1.04
 Power consumption per column (kW) 1.7
 Materials: hot wall: stainless steel; cold wall: brass
 Transport Coefficients (LJ model):
 H (g/s) 4.50x10 -5
 Kc (g.cm/s) 2.40x10 -2
 Kd (g.cm/s) 1.37x10 -3
 Qe (exp.) per column 2.00
 Cascade: 19 columns of concentric tube type in 8 stages
 Cascade Configuration (Staging from the waste end): 8-4-2-1-1-1-1-1
 Production: 13CH4 at the concentration of 25% 13C (g 13C/year): 33

26. Thank you!

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