Continuous Separation of Gaseous Mixtures
by Fractional Diffusion through Porous Membranes KARL ISAMMERMEYER AND HENRY T. WARD Drexel Institute of Technology, Philadelphia, Penna.
The separation of gas mixtures by diffusion through
well below the mean free paths of the gaseous molecules in question, the latter being about 6 X 10+ and 18 X 10-6 em. for carbon dioxide and hydrogen, respectively, a t standard conditions. Under these conditions the membrane would have a perfect efficiency. The fact that the mean free path of gases increases directly as the pressure decreases has been taken advantage of in the work on isotope separation, and it is in this field that the experimental technique for the separation of gaseous mixtures by means of porous membranes has been brought to a high degree of perfection. The contributions of Hertz (7, 9 ) , RIulliken and Harkins (16), Langer (11), and Wooldridge and Smythe (19) are outstanding examples of what has been accomplished in recent years. When the diffusion process is carried out a t atmospheric pressure with ceramic materials as membranes, there will be a great number of pores which are so large that mass motion of appreciable quantities of the gas will take place in accordance with Poiseuille’s law and the degree of separation will be lowered accordingly. From these considerations an equation has been set up which expresses the amount of any one gaseous constituent diffusing through a membrane as the sum of the amount obtained by molecular diffusion and by the attendant mass motion through the larger pores. The equation is as follows:
porous membranes was investigated for the systems nitrogen-carbon dioxide and hydrogencarbon dioxide. Equilibrium curves were established for composition of feed vs. product. The theoretical interpretation involves the sum of molecular diffusion and mass motion in fluid flow. The results are compared with those of membrane diffusion with atmolysis. The literature and commercial and economic aspects are discussed.
HE work of Graham (6),master of the mint, is almost T without exception the basis upon which numerous later investigations on the diffusion of gases are founded. Graham, in his original publication which appeared in 1863, interpreted with remarkable keenness of conception the fundamental relations involved in the diffusion of mixtures of gases through porous membranes. Graham’s law may be written as:
= moles of gas diffusing per unit time and area A p = partial pressure difference over membrane T = absolute temperature
where N
M D,
L
= = =
molecular weight of diffusing gas proportionality factor; diffusion constant thickness of membrane
where Arl = total moles of constituent 1 diffusing per unit time and unit superficial membrane area D l = D,/L = coefficient of molecular diffusion which includes the unknown effective thickness of the membrane D, = a constant for any one system of gases ap1 = partial pressure drop of constituent 1 over the membrane MI = molecular weight of constituent 1 N, = total moles of feed gas per unit time and area A’, = total moles of product gas per unit time and area
This law was formulated primarily from results obtained on the diffusion of gas mixtures through a graphite plate, which Graham aptly calls “a pneumatic sieve which stops all gaseous matter in mass, and permits molecules only to pass”. When the law is applied t o “molecular diffusion”, deviations from the law are to be expected when this molecular diffusion becomes in part effusion. Graham recognized this fact when experimenting with stucco, stoneware, and clay pipes, and states that the use of membranes made of such materials results in a “mixed phenomenon”. Occasionally investigators (1, 6,17) report that their results are not in agreement with Graham’s law, but it is possible that the conditions under which their work was carried out were such that this law did not apply.
c = - Bd2 -x 321
A
-
(mol. vol. at standard conditions) essentially a membrane constant where g = gravitational constant = diameter of pores (unknown) d I = length of pores (unknown) A = total cross-sectional area of flow (unknown) AP = total pressure drop over membrane Pa”. = average pressure, atmospheres Yf, = mole fraction of constituent 1 in feed gas pf = viscosity of feed gas
Theoretical Interpretation of Mixed Flow
The use of the factor log N f / N * in combination with Graham’s law is indicated by the theoretical developments of RIulliken and Harkins (16).
Molecular diffusion through a membrane is the process where mass motion of the gas as such is absent, which is the case when the diameters of the pores of the membrane are 414
April, 1941
INDUSTRIAL AND ENGINEERING CHEMISTRY
475
To apply Equation 2, it is necessary to determine factors D,and C experimentally from two or more diffusion runs. It has been possible to check the validity of the equation by a limited number of experimental data developed in the present investigation, and the results will be presented in the discussion of the system nitrogen-carbon dioxide.
Experimental Diffusion through Membranes The present investigation deals with the diffusion of essentially binary gaseous mixtures through commercially available porous membranes in order to determine “flow equilibrium” diagrams for several combinations of gases. An auxiliary gas or vapor on the diffusate side of the membrane to sweep away the diffused gas was not employed. Such an auxiliary gas, either in combination with a porous membrane or simply with a perforated separating partition, has been used by many investigators with considerable success (8, IS, 14). Information on the fractional diffusion of gases through porous membranes without the use of a sweeping agent is nonexistent for the case of continuous separation a t or near atmospheric pressures. All of the isotope work has been carried out a t very low pressures, in the neighborhood of 0.5 mm. of mercury, and in most instances batch operation in a closed system has been used. Riesenfeld and Chang (16) worked with carbon dioxide-oxygen mixtures, but also a t a high vacuum, so that their results are in no way on a comparative basis. The experimental work covered in this paper deals with the gas mixtures nitrogen-carbon dioxide and hydrogen-carbon dioxide. I n each case the composition of the mixtures was varied over a sufficiently wide range to permit the establishment of flow-equilibrium curves which are analogous to the liquid-vapor composition curves of binary mixtures. These curves apply only to the respective membranes used in the investigation. A diagram of the diffusion cell and necessary measuring devices is shown in Figure 1. The diffusion cells were Alundum extraction thimbles, manufactured by the Norton Company. Since these thimbles in general were too coarse to permit any degree of separation, the commercial grades were modified by alternate soaking in barium chloride and sulfuric acid to precipitate barium sulfate in the pores and decrease the permeability. The permeability rating of the cells was obtained by the Norton Company’s laboratories, using a Uehling instrument, and are as follows: Type of Cell Extraction thimble V F Extraction thimble M Extraction thimble h‘I2
Relative Permeability, Cc./Min./Sq. In. 7.66 11.92 11.42
The desired gas composition was adjusted in gas storage tank
A (Figure 1) at about 40 pounds per square inch gage pressure,
and the upstream operating pressure was regulated by control valve B. The gas passed through cell C, which consisted of the membrane (Alundum extraction thimble) enclosed in a jacket and of connections for feed, waste, and product gas. The waste as that is, undiffused gas-was drawn from the inside of the ul;! dum cell and collected in samplers D, and the prodiict gas was removed from the space surrounding the membrane and collected in samplers E . The experimental rocedure consisted in flushing the apparatus by operating wit\ by-passes for the product and waste gas for about 1 t o 1.5 hours. This initial operating period served mainly to displace any air or residual gas from the previous run. ‘The next step was to switch the product and waste gas into preliminary sampling bottles DIand ELto permit final adjustment of .the product and waste gas rates. ThiR second period was usually
FIGURE1. DIAGRAM OF EXPERIMENTAL APPARATUS 45 to 60 minutes, in which time flow e uilibrium was thoroughly and Ez, were connected established. The final sample bottles, in parallel with the preliminary bottles, and only a few seconds of manipulation were required t o switch over. In the actual test period sufficient gas samples were collected t o permit the running of check analyses on each sample. All samples including a feed sample, were analyzed by conventional methods for the respective constituents as well as oxygen. The determination of oxygen served primarily as a check for air leaks, when the downstream side of the membrane was operated below atmospheric pressure. All possible precautions were taken to eliminate sources of errors when working with gas mixtures containing carbon dioxide as one of the components. According to Venable and Fuwa (18) the solubility of carbon dioxide in rubber is appreciable; in fact, a given volume of rubber may dissolve an equal volume of carbon dioxide. Workers in microchemical analysis are well aware of this phenomenon, and try to prevent its occurrence as much as possible by vacuum impregnation of the rubber parts with a mixture of paraffin wax and vaseline. All rubber parts in the apparatus were therefore treated in this manner, and connections where rubber tubing had to be used were held t o a minimum. The relatively high solubility of carbon dioxide in acidified water, which was used as a sealing liquid in the samplers, is a further possible source of error but can largely be overcome by using liquid saturated with the gas.
’b,
System Nitrogen-Carbon Dioxide All of the diffusion experiments were carried out with cell M, an Alundum thimble. The pressure drop over the membrane varied from 8.4 to 17.8 inches of mercury, and the ratio Nf/N* varied from 3.30 to 4.54, with the exception of one run which gave 9.28. The flow-equilibrium curve is shown in Figure 2. It might be expected that both the flow rate, which is determined by the pressure drop, and the ratio of feed to product would affect the degree of separation. However, the range of pressure drop and the variations in ratio of feed to product used apparently did not affect the degree of separation t o a noticeable extent. Therefore only one curve was drawn through the experimental points. This does not mean that the same behavior should be expected with different membranes, nor perhaps with greater variations of the factors in question. The differences in composition between feed and product are small but definite. The number of cells for successive separations can be obtained graphically by proceeding in a stepwise manner from the feed composition to the desired product composition, as the product composition of any cell becomes the feed composition for the succeeding cell. As Figure 2 indicates, about twenty-three cells in series would be necessary to obtain enrichment from 20 to 80 per cent nitrogen. While this is a fairly large number of cells, it is possible that more suitable membranes would require an appreciably lower number of cells for the same degree of enrichment.
INDUSTRIAL A N D ENGINEERING CHEMISTRY
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Table I gives the analyses of feed, product, and waste of the six runs used to establish Figure 2. I n five of the runs sufficient data were obtained to make complete material balances and to calculate the factors D1and C in Equation 2. This information is also given in Table I.
TABLEI. DIFFUSION OF NITROGEN-CARBOX DIOXIDEMIXTURES THROUGH CELL Ma Run No.
yo increase NZ (based on N z content of feed)
A P , in. H pa”., In.
Temp.,
8,F.
N p # cc. produot/min.
I
I1
I11
IV
v
VI
1.1 77.8 21.1
1.7 61.8 36.5
1.6
1.8
46.6 51.8
1.8 53.1 45.1
41.8 56.4
2.6 24.9 72.5
2.0 79.6 18.4
3.0 63.8 33.2
1.6 49.1 49.3
56.4 42.1
1.5
2.2 44.3 53.5
2.8 27.4 69.8
0.8 74.4 24.8
1.3 61.5 37.2
1.6b 46.3b 52.lb
1.5b 52.lb 46.4b
1.8 39.7 58.5
2.7 24.0 73.3
2.3 9.4 29.4 75 5.0 3.40 6.36 5.57 1.47 1.46
3.2 5.4 8.4 16.1 22.4 30.3 76 75 6.3 20.6 9.2s 9.52 4 . 0 2 10.11 4.66 8.06 2.10 10.16 2.23 7.48
6.2 7.6 34.0 74
... ...
6.0
14.8 27.5 79.5 9.6 3.70 4.23 5.10 5.12 6.11
10.0 15.1 26.5 79.5 11.4 4.54 3.12 2 95 i.95 7.06
X
