Paper presented at International Conference of Physics, January 6-9, 2004, Tehran, Iran

1. SEPARATION OF CARBON-13 BY THERMAL DIFFUSION
Gheorghe VÃSARU
Aleea Tarnita, Nr. 7, Apt. 11
CLUJ-NAPOCA, ROMANIA
E-mail: gvasaru@hotmail.com
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 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.
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.
The most important characteristics of a eight-stage cascade consisting of 19
thermal diffusion columns of concentric tube (with an effective length of 4.00 m), placed
in the configuration 8-4-2-1-1-1-1-1 are given. The radius of cold wall was of 1.725 cm
and of hot wall of 0.900 cm, respectively. This system has been constructed and
successfully operated at a mean temperature of 673 K and produces an enrichment of
natural abundance carbon (1.108 % 13C; 98.892 % 12C) of methane, up to the
concentration of 25 % 13CH4.
A thermal diffusion cascade has the advantage of being relatively easy to operate.
However, thermal diffusion is an irreversible process and therefore requires a large
quantity of energy per gram of enriched compound. There is also the disadvantage that the
thermal diffusion column 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 the columns cannot be increased above a certain limit because
temperature inhomogeneity in the hot and cold walls cannot be avoided. For this reasons
even a very large-scale separation plant must be composed of relatively small diameter
columns.
At low production rates, the cost of labor is controlling factor and the thermal
diffusion is an attractive process. Consequently, thermal diffusion is the method of choice
in a 13C- separation plant. Its low productivity is balanced by a simpler and more reliable
operation.
KEYWORDS: Thermal diffusion, isotope separation, carbon-13, methane,
separation phenomena, gases.

2. I. Introduction
The thermal diffusion (TD) 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 TD will be exactly counterbalanced by concentration diffusion.
In a TD 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
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 TD 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 the TD column presents engineering problems associated with
supported heated central elements. At the present time, TD 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.
II. The transport equation
The transport equation for a TD column is:
  Hc(1  c)  ( K c  K d )
dc
dz
(1)
Where  is the total transport of required isotope, H is the coefficient of transport by TD, 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
H  H ' p2
Kc  K' c p 4
(2)

3. Kd is independent of pressure.
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:
 T  2  4


 gr1 h( , R, T1 )
  1
(3)
2   3  2 8
*
 2 D g r1 k c ( , R, T1 )
9!  
1
(4)
2
H
6!
Kd 
Kd  2  D1 r12 k d ( , R, T1 )
(5)
where T is the TD constant,  - the density,  - the viscosity, D - coefficient of
ordinary diffusion, all at the temperature of the cold wall, T 1, g - the gravity constant, r1 Tk
the radius of cold wall, h, kd and kc - shape factors,  = T2/T1, R = r1/r2, T1  1 - the

reduced cold wall temperature, T2 and r2 - temperature and radius of hot wall,
respectively, k - Boltzmann constant and  - the depth of potential well.
III. The equilibrium separation factor
Putting in (1),  = 0, we have
dc
H

dz  2 Adz
c(1  c) Kc  Kd
(6)
the integral of which is


c
 exp 2 A z  z0 
1 c
(7)
or equivalently
c( z) 
1
1  tanh A( z  z0 )
2
(8)
If z0  z  L and c0  c  cL,
where L is the length of the TD column, we have for the equilibrium separation factor the
expression
Qe 
c L (1  c0 )
 exp(2 AL)
c0 (1  c L )
(9)

4. If an efficient tapered cascade is to be designed to enrich an isotope from some
small concentration to some higher concentrations, the TD 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 TD separation factors and the theoretical values
calculated according to Jones and Furry.
The theoretical and experimental separation factors for 13CH4, as function of gas
pressure show that the maximum equilibrium separation factor occurs at a lower pressure.
The separation factor per mass unit, Q *, is given by the equation [6]:
ln Q 
H *L
Kc  K d  K p
(10)
where
H* = coefficient of TD 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.
The H*, Kc and Kd factors can be written as function of pressure and take the form
H *  ap 2
Kc  bp 4
(11)
Kd  c
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]:
b
L

2
a 2 p log Q*
c
Lp 2

a 2 log Q*
(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 maximum separation
When the gas pressure in a TD is adjusted to achieve maximum separation, the
coefficient of convective remixing, Kc, is equal to the coefficient of diffusive remixing,
Kd [7]

5. IV. Heat losses
Heat is removed in four ways from the heating element in a TD 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 sheath to the cold jacket end fittings [7].
Convection and conduction through the gas are essential for the operation of a TD
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 TD.
The amount of heat radiated from the heater and the amount conducted through the
spacers and sheath can be determined from power input and heater sheath temperature
with an evacuated column.
V. Separation of 13C
1). 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
13
C are 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 13C 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.
Conclusion: TD was found to be the 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 CO2/carbamate chemical exchange process are eliminated, for
moment, from consideration.
Today, 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 that uses 13C. Recently, the US FDA gave approval for
clinical use of the 13C Urea Breath Test for the detection of the ulcer-causing bacterium
Helicobacter pylori (H.pylori). This new breath test is safer, simpler, and more accurate
than other tests which diagnose H. pylori infection. It requires the patient to blow into a

6. collection device for a pre-dose sample, drink the dissolved urea, and exhale into a
collection device after 30 minutes. This test does not require blood samples, endoscopy, or
other uncomfortable and expensive procedures for the patient.
The breath test is an exceptional method of diagnosis because it has better
specificity and accuracy than most other methods of detection, and it is the only test
developed for non-invasive detection of H.pylori in the stomach. Blood tests cannot
reliably detect current infection because they continue to detect antibodies as long as a
year after exposure or previous infection. The 13C-urea breath test finally gives doctors a
non-invasive tool for accurate diagnosis of H-pylori infection in the stomach.
Using labelling chemical compounds with the enriched stable isotope 13C, others
enriched stable isotopes or markers, has the advantage of eliminating the need for use of
radioactive materials. Researchers use stable isotopically labeled compounds in place of
common chemicals to trace the isotope marker through reactions and into final products,
including the determination of metabolic pathways. It is this process at work in the 13Curea breath test.
The H.pylori bacteria produce enhanced level of urease, a urea-metabolizing
enzyme. One of the reaction products is CO2. By labeling the urea with highly enriched
13
C, it is possible to measure the levels of 13CO2 exhaled by the patient. People infected
with H.pylori bacteria have higher levels of 13 C. The results are detected by a mass
spectrometer to make the diagnosis of bacterial infection [10].
With US regulatory clearance and approval, millions of people will benefit, as the
breath test becomes the routine diagnostic tool for ulcer in doctor’s offices and hospitals.
Thus, stable isotopes and particularly the 13C labeled compounds, are of great importance
for research laboratories and commercial applications, including practical and beneficial
uses such as diagnosis of disease and mitigation of human suffering.
2). Separation of 13C by TD
A TD cascade has the advantage of being relatively easy to operate. However, TD
is an irreversible process and therefore requires a large quantity of energy per gram of
material separated. There is also the disadvantage that the basic TD 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 TD columns cannot be increased
above a certain limit because temperature inhomogeneities in the hot and cold walls
cannot be avoided. For these reasons even a very large-scale TD plant must be composed
of relatively small diameter TD columns.
The technical characteristics of our standard TD column is given in Table 1 [1112].
One of the most persistent problems encountered in the 13C TD cascades 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 different methane TD cascades for enrichment of 13C 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

7. to product withdrawal, respectively. Parameters of methane TD cascade are given also in
Table 1.
Table 1. Parameters of methane TD cascade:
Physical properties of methane (at T1 = 295 K):
Density,  (g/cm3)
6.626x10-4
Viscosity,  (g/cm s)
1.110x10-4
Ordinary diffusion, D (cm2/s)
0.215
TD constant, T
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
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 concentration of 25 % 13C (g 13C/a): 33
This cascade was set up with an appropriate system for feed purification, pressure
control, waste and product withdrawal, impurity control and removal, and interstage gas
circulation. In the feed system, methane of 97.4 % purity was further purified up to 99.85 99.88 % by pumping volatile impurities, at liquid nitrogen temperature. 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.
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

8. destroyed 13. For removing these impurities a TD column was provided, column 19,
placed at the bottom of the cascade. The level of impurities was detected with a thermalconductivity 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 inter stage gas circulation, hermetical 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 TD 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 TD column having a
single cooling jacket in a bundle system, maintained at the temperature of 293 K. The
operating pressure was 1.05 at.
References:
1.Vãsaru G., Râp I.: Thermal Diffusion. A Bibliography (Period 1856- 1966),
Bibliographical Series No. 28, STI/PUB/21/28, IAEA Vienna, Austria, 1968,
1650 refs., 345 pp.
2. Vãsaru G.: Thermal Diffusion Bibliography (Period 1965 - 1995), ITIM, ClujNapoca, Romania, and Nagoya University, Japan, April 1996, 1781 refs, 223 pp.
3. Vãsaru G. et al.: Thermal Diffusion Column. Theory and Practice with
Particular Emphasis on Isotope Separation, VEB Deutscher Verlag der
Wissenschaften, Berlin, Germany, 1969, 210 pp.
4. Vãsaru G.: Separation of Isotopes by Thermal Diffusion, USERDA, ERDA-tr-32,
Distribution Category UC-22, Translation Series, USERDA Technical Information
Center, Oak Ridge, TN, USA, 1975, 376 pp.
5. Jones R. C., Furry W.H.: Rev. Mod. Phys., 18, p. 151, 1946
6. Butler T. A., et al.: Report ORNL-3607, Oak Ridge Natl. Lab., 1964
7. Butler T. A., et al.: Report ORNL-3815, Oak Ridge Natl. Lab., 1985
8. Schwind R.A.: Chem. & Process Eng., p. 75, July 1969
9. Cambridge Isotope Laboratories Inc.: CIL Expands 13C Production Capacity,
1998
10. ISOTEC, Inc.: What’s New? , Isotec Inc. Leads the Way in Providing 13C-urea for
Ulcer Breath Test, Press Release, Oct. 8, 1996
11. Vãsaru G., et al.: Separation of 13C by Thermal Diffusion, Stable Isotopes in Life
Sciences, IAEA Vienna, p. 39, 1977
12: Muller G., Vasaru G.: Isotopenpraxis 24, 11/12, p 455, 1988
13. Rutherford W.M., Keller W.M.: J. Chem. Phys., 44, 2, p.723, 1966
Other monographs and bibliographies published by us in the field of isotope separation:
1. Vãsaru G.: Method of Separating Stable Isotopes, Report MLM-1296 (tr.) TID4500 (44th. Ed) UC-22 Isotope Separation USAEC, Mound Laboratory, Miamisburg,
Ohio, USA, 1965, 112 pp.

9. 2. Vãsaru G., Thermal Diffusion in Isotopic Gaseous Mixtures, Fortschritte der
Physik, 15, 1, p.1, Akademie-Verlag, GmbH Berlin, Germany, 1967, 112 pp.
3. Vãsaru G.: Les isotopes stables, CEA¬BIB-136, CEN-Saclay, France, 1970, 370 pp.
4. Vãsaru: G. et al.: Deuterium and Heavy Water. A Selected Bibliography,
Elsevier Scientific Publishing Co., Amsterdam, Holland, 1975, 806 pp.
5. Vãsaru G., Zirconium and His Implications in the Construction of the Nuclear
Power Reactors, Editura Tehnica, Bucharest, Romania, 1989, 184 pp.
6. Vãsaru G.: Tritium Isotope Separation, CRC Press Inc., Boca Raton, Florida, USA,
1993, 304 pp.