1444
TNDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 43, No. 6
K = n = P = P“ =
equilibrium ratio Y/X mole fraction of a component in system pressure, pounds per square inch absolute vapor pressure, pounds per square inch absolute X = mole fraction of a component in coexisting liquid phase Y = mole fraction of component in coexisting gas phase
Subscripts 1 signifies methane 4 signifies n-butane 10 signifies decane LITERATURE CITED
Benedict, M., Webb, G. B., and Rubin, L: C., J. Chem. Phys., 10, 747-58 (1942).
Bridgeman, 0. C., J . Am. Chem. Soc., 49, 1174-83 (1927). Lewis, G. N., Proc. A m . Acad. Arts Sei., 43, 273-93 (1907). Olds, R. H., Ph.D. thesis, California Institute of Technology, 1947.
Olds, R. H., Reamer, H. H.. Sage, B. H., and Lacey, T.V. N , JND. ENG.CHEM.,36, 2 8 2 4 (1944). Olds, R. H., Sage, B. H., and Lacey, W. N., to be published ill Research Volume of Production Division, ilmerican Petroleunl Institute. Reamer, H. H., Fiskin, J. M., and Sage, B. H., IND.Exci. &EM.,
41,2871-6 (1949).
Reamer, H. H., Olds, R. H., Sage, B. H., and Lacey, W. N., Figure 10.
Equilibrium Ratio for Decane at 280” F
coexisting phases were established. Table VI11 makes comparisons of Borne directly measured values of the composit,ions of each of the coexisting phases with corresponding data obtained by interpolation of the values in Table VII. The experimentally determined results, for the same pressure and value of composition parameter, show an average deviation of 0.004 mole fracfion from the smoothed data presented in Table VIII. ACKNOWLEDGMENT
This paper is a contribution from American Petroleum Institute Research Project 37, located at the California Institute of Technology. The assistance of Elwood Rogers in the experimental program, and R. H. Oldb, H. F. Johnston, and Betty H. Tieridall in the smoothing of the data is acknowledged. NOMEYCLATURE
C,, = composition parameter in homogeneous region C, =- -omposition parameter in heterogeneous region
Ibid., 34, 1626-31 (1942).
Reamer, H. H., Sage, B. H., and Lacey, W. N., American Documentation Institute, Washington, D. C., Document 3212 (1950).
Reamer, H. H., Sage, B. H., and Lacey, W. N., IND.ENG CHEM.,38, 986-9 (1946). Ibid., 39,77-82 (1947). Sage, B. H., Hicks. B. L., and Lacey, W. N., Ibid., 32, 1085 92 (1940).
Sage, B. H., and Lacey, W. N.,Trans. Am. Inst. Mining Met. Engrs., 174, 102-20 (1948).
Sage, B. H., and Lacey, W. N.,Tians. A m . Inst. Mining Met. Engrs., 136, 1 3 6 6 7 (1940).
Sage, B. H., Lavender, H. M., and Lacey, W. N., IND.Eivr:. CHEM.,32,743-7 (1940). Shepard, A. F., Henne, A. L., and Midgley, T., Jr., .I. Brn Chem. SOC., 53, 1948-68 (1931). RECEIVEDMarch 9, 1950.
Paper 54 in the series “Phase Equilibria in Hydrocarbon Systems.’’ References t o papers 1 to 50 will be found in IND.ENG.CHEM., 41, 474 (1949). For detailed tables supplementary to this article (9)order Document 8212 from the American Documentation Institute, 1719 N St., N . W . , Washington 6, D. C . . remitting $1 for microfilm which yields images 1 inch high on standard 35-nlm. motion picture film or $3.30 for photocopies 6 by 8 inches which are readable without optical aid.
Nomograph for Calculating Contact Time for Vapor-Phase Reactions JOHN N. PATTISOS Rattelle Memoriul Institute, Columbtcs. Ohio
Contact time is the time of reaction and as such is a very important factor in the comparison of the results of vaporphase reactions. Most workers in the fields of kinetics and catalysis make frequent calculations of this type. A nomograph for the determination of contact time has been prepared for their convenience. The derivation of the equation for the calculation of contact time is given. The use of the nomograph is explained and illustrated by a typical example. The nomograph will serve as a time saver for those who are working with vapor-phase reactions.
c
OKTSCT time, as used in most work dealing with vapor-
phase catalysis, is defined as the time that the reactants are in contact with the catalyst. The time will vaiy from one molecule to another in a given system A fen- may pass rompletplv through the catalyst zone n-ithout coming in contact with the catalyst, whereas others may remain on the catalyst after reacting, and further react to form by-products. Because it is impractical to determine the contact time for each molecule, the average contact time is used for all the material fed. From the above definition, it can be seen that contact time has much more significance than ordinarily used terms expressing
1445
INDUSTRIAL AND ENGINEERING CHEMISTRY
June 1951 G
F
M
P
X
T
L
C
0.051000:
0.1-
25 9007
20
800-
0
I n case the reaction zone is partly filled with catalyst, there will be less free space and the contact time will be reduced accordingly. Letting F = the per cent of free space in the catalyst,
7000.5
600-
20
I 8
500
30
I
Y 4c d
2
m5c
3
W
4
I&a 6C
7(
e e
8( 9(
€
lo(
I(
1--0
I g
z
-5
?.!t 3001 cn k-
3 i!
8
-I5
a
8 a
: 200-
-
Po
-10
-
%
a
-2 5 13.0 L3.5 i-40
a
W
If a change in volume occurs during the reaction, this will alter the contact time. An integration of the rate equation is necessary to correct accurately for this effect, but an average of the amount of gas entering and leaving the reactor is more often used for the sake of simplicity. Using the perfect gas law to calculate the a v e r a g e v o l u m e of t h e reactant gases a t reaction conditions,
3( 4( 54 6(
-233
81
-25'
IO'
and
I
G = W s in + Mols out 2 Mols in
-
20 30
40 5c 60 F - M ( P t 14.7) G * L ( T+ 273)
= 33.5.
Figure 1. Nomograph
feed rate as gallons per hour, barrels per minute, and space velocity. Changes in feed composition can have a pronounced effect upon the time the feed spends in the catalyst zone, because, no matter what the liquid volume may be, 1 mole of any feed in the gap phase occupies approximately the same volume. Temperature, pressure, and the amount of reaction taking place also exert an effect upon the contact time. None of the above variables is considered in the values given for space velocity or gallons per hour fed. I n addition, use of gallons per hour does n o t take into account the volume of catalyst used.
KEY
where ni and no are the number of moles of reactants in, and product out of thereactor, respectively. O' Upon s u b s t i t u t i o n of more commonly used terms such as L , the liquid hourly cp to p0 find X, space velocity (the volume x, to P find e of liquid f e d p e r h o u r C= Coniact Time divided b y the bulk volume of the catalyst), M , the molal volume of the feed in milliliters (at the temperature at which L was determined), G, the volume-change factor, (moles in moles out)/2 moles in, and T in degrees centigrade, and conlbilling the constants, L to M find X I
XI !O T find CAP CAP = Contact Time if F = 60% , G = 1.0 and P = lotm. CAP to F find Xz: X2 to G find Cp C p ~ C o n t a c tTime it P= I otm.
+
If it is desired to use gallons per hour per cubic foot of catalyst instead of the usual space velocity, the constant is 4.48 instead of 33.5. The nomograph (Figure 1) will be found useful for solving the above equation.
DERIVATION OF THE EQUATION
If a volume of gas, Ti,, a t reactor conditions passes through a reactionzone, V,, in a unit of time, the contact time, C, will be determined as follows:
HOW TO USE THE NOMOGRAPH
The scales must be used in the order shown in the key. A straightedge is used to connect the value for space velocity, L ,
INDUSTRIAL AND ENGINEERING CHEMISTRY
1446
with AI, the molal volume of the feed. The point where the straightedge crosses the X scale, zl, is marked. The straightedge is now placed so as to connect z1 with ?”, the reaction temperature, and Cap is marked where the C scale is crossed. Cap is the contact time, assuming that the free space, F , is G070J that. no change in volume occurs as a result of the reaction, and that the pressure of the reaction is 1 atmosphere. These assumptions will be true, or nearly so, in many cases, and no further calculations will be necessary. If these assumptions are not true, corrections can easily be applied by joining Cap to the free space, F , with a straightedge to find 22, followed by joining zp and G (volume-change factor) with a straight line. W-here this line crosses C, the contact time, C p , is found. If the pressure of the reaction is 1 atmosphere, this will be the true contact time. If not, C p and Po are joined with a straight line to find z3,followed by joining the pressure of the reaction, P , and z3to find C, the true contact time. The pressure correction can be made before the correction for free space and volumechange factor if desired, as it operates independcntlg of them. DISCUSSION
The ranges of the scales used were chosen to cover most cases encountered. The units in which the scales are calibrated mere chosen for simplicity and general utility. The L scale is calibrated in both liquid hourly space velocity and its equivalent in gallons per hour per cubic foot of catalyst. This scale may be found useful for the direct conversion of these two units. M , the molal volume of the feed, is the volume of feed (milliliters) equivalent to 1 gram mole. It can be calculated by dividing the molecular weight of the feed by the density a t the same temperature at which V is measured. In case the feed is not pure, the average molecular weight must be used, as shon-n in the example. I n case two or more liquids are being fed to the reactor simultaneously, the average molal volume is calculated a s though the feed &-ere one mixture, and the combined space velocity must be used. In many reactions there is little, or no, change in the number of moles in the converter. I n cases of this sort, G is unity. For accurate work, G should be determined as closely as possible, but, in many cases, where the order of magnitude is the chief interest, G may be assumed to be 1. Only in a few instances will the error of this type be serious, such a s in the production of ethylene from ether, in which a large change in the number of moles occurs and nearly complete conversion per pass is obtained.
(7)
1+2+l
The per cent of free space in the catalyst will not always be known, and, in plant operations, a sample is not always handy for its determination; therefore, some typical values are given as determined by liquid displacement using hexane. Type of Carrier A 1um ina Silica gel Carborundum Clays Diatomaceous earth Filtros
Some Typical Values Obtained 56 34 50 57 70 58
58 48 64 60
67
..
67
70
.. 62 .. ..
..
52
58
.. ..
67
6i
..
..
..
Vol. 43, No. 6
the reactor used. Some workers (1, 2 ) prefer simply to use a constant value of 60 or 70 for F. From the above values, it would appear that 60 would be the best value for use, if nothing is known about the catalyst. Therefore, this assumption has been made in setting up Cap, As values for the molal volume, feed rate, etc., are determined in terms of the scales on this nomograph, it will be found convenient to mark them on the scale at the appropriate place, thus saving time in subsequent calculations in which they may be involved. The chart has been designed to be as versatile as poesible; however, the needs of a single individual using the chart mill be found to be rather limited in most cases-Le., he will not have many converter sizes, temperatures, or many different feed compositions to consider. As soon as these “usual” values have been marked on the chart, the effect of the variation of any one value can be quickly determined. EXAMPLE
Ethyl alcohol is fed a t the rate of 390 gallons per hour to a converter containing about 313 cubic feet of alumina catalyst. Atmospheric pressure is used and the catalyst temperature is 390” C. The ethyl alcohol is completely dehydrated to ethylene and r+ater. The feed rate, L , is 390/313 = 1.25 gallons per hour per cubic foot of catalyst, which is equivalent to L.H.S.V. 0.166. The by volume; therefore, 100 alcohol used way 190-proof or ml. would contain 95 X 0.789/46 = 1.63 moles of alcohol plus 5 X 1/18 = 0.28 mole of w-ater, or 1.91 moles; therefore, the molal volume of the feed is 100/1.91 or 52.4 ml. By connecting these two values, z1 is located. The straightedge is now placed on z1 and 390” C. on the T scale and Cap is found to be 12.5 seconds. This catalyst contains 567, free space and, as can be seen from the equation, a large change in volume occurs in the reaction zone:
CzH,OH --+ CIH,
+ HzO
(9)
In this case, 100 1111. of feed would give 2 X 1.63 or 3.26 moles of product plus 0.28 mole of water which was unaffected, or a total of 3.54 moles out for 1.91 in.
If we now connect C,, (12.4 seconds) with 56Y0 on the F scale, lye get z2. Kest, 1.43 on the G scale is connected to x2 and, where the straightedge crosses C, we find C p equal to 8.1 seconds, which is the contact time in this case, because the reaction was a t atmospheric pressure. ACCURACY
The chart itself is accurate t o about 1%; however, in considcration of the usual accuracy of data of this type, the final values of C should easily be within * 10% of the true value and can easily be better if care is taken in obtaining the data and in the computations. For locating differences in contact time, where wveral of the factors are the same, some of the error will be canceled and greater accuracy ail1 be obtained.
..
Theoretically, changes ia mesh sizes have no effect on the per cent of free space, but in practice it is found that the larger particles do not pack a s well as they should in small tubes. For the most accurate work the free space should be determined in
LITERATURE CITED
(1) Berkman, Morrell, and Egloff, “Catalysis,” pp. 1061, 1064, New York, Reinhold Publishing Corp., 1940. ( 2 ) Rogers, C. U.,Mellon Institute, private communication.
RECEIVED September 14, 1950.
