580
INDUSTRIAL AND ENGINEERING CHEMISTRY
low, there is w u d y no use for such a reagent unless the clarifier is operated greatly over capacity. No reagents have been found which have a similar effect on the settling rates in mixtures with low ratios. The pSesence of grits, or sandlike material, has a slightly beneficial effect. IN FLUE KC^ OF CLOUDYOVIRFLOW. Within the limits of experimental error, lime salts and color in the thin juice increased in proportion to the amount of suspended solids in the second carbonation feed. With 0.1% suspended solids, there was a p proximately 0.005 increase in lime salts and 6% increase in color. This amount of suspended solids corresponds to a Kopke clarity reading of about 3. A slightly cloudy clarifier overflow will probably do much less damage to the thin juice than will carbonation a t a lower alkalinity than neoessary. This is substantially in agreement with the results of Stanek and Pavlas (10). CONCLUSIONS FROM EXPERLMENTS
The conclusions apply particularly to California beet juices and to the type of continuous defecation and clari6cation under study: 1. In first carbonation with saccharate milk defecation, the best quality thin juice, as judged by lime salts and color content, is obtained a t low temperatures (at least 70" C.) and at a n alkalinity of 0.130. 2. The lime salts content of the thin juice is increased about 0.010 per hour and the color content about 7% per hour by retention a t 80" C. between first and second carbonation. 3. Titratable alkalinity is the most reliable end point measurement in first carbonation control. The optimum alkalinity for best thin juice quality was found t o be nearly constant a t 0.130 in saccharate milk defecation. This value was practically unaffected by such variables as type and concentration of juice or carbonation temperature (at least in the range 70-90" C.). Clarification is not economically possible at this alkalinity. The measurement of pOH should be superior t o p H in controlling first carbonation in that errors caused by the p H temperature coefficient are avoided. 4. When defecating with milk of lime, the optimum alkalinity in first carbonation is about 0.100 at 80" C. Increasing the concentration of the diffusion juice raises the optimum alkalinity. 5. The difficulty of settling the first carbonation mud increases, in general, with the alkalinity. 6. Under certain conditions, the settling characteristics of clarifier feeds can be improved by the addition of reagents. 7. Lime salts and color in thin juice increase proportionally to the amount of suspended solids in the clarifier overflow.
PRACTICAL OPERATION
With the continuous carbonation system studied, it, is tipparent that in plant-scale practice some sacrifice in thin j u i c ~ quality must be made for clarification and filtration to be performed satisfactorily. While the juice quality is improved by high alkalinities and low temperatures, clarification and filtration are made more difficult. It is apparent that a compromise must be made. At Woodland a medium temperature (SO' C.) ifi cai ried, and alkalinities are kept as high as possible without, preventing clarification. This system of continuous defecation is apparently still capable of improvement. The most complete> defecation will not be obtained until a system is perfected which will permit carbonation at the optimum alkalinity, and still allow satisfactory separation and washing of the carbonation mud. For end point control, the Woodland factory uses an automatic carbon dioxide controller operated by high-temperature glass electrodes. However, frequent alkalinity determination+ are made, and the p H control point is readjusted to give ihe alkalinity desired. Second carbonation control is similar. The recognition of the three types of settling curves for materials in the clarifier enables somewhat more intelligent operation With a known type C curve, the clarification may be greatly improved by lowering the density of the underflow. There is little advantage in this procedure for a type A curve. The advantages of using cow's milk for enhancing settling wlth type A curves were discussed above. ACKNOWLEDGMENT
The helpful supervision of P. W. Alston is gratefully rtcknowledged. LITERATURE CITED
(1) Brewster, J. F., and Phelps, F. P., IND.ENG.CHEM.,ANAL.ED.. 2. 373 (1930). (2) Coe, H.S.,and Clevenger, G. H., Trans. Am. Inst. Mining M r i Engrs., 55,356(1916). (3) Comings, E. w., IND.ENG.CHEM.,32,663(1940). (4) Dedek, J., Facts About Sugar, 34, (Nov.) 42-4, (Dec.) 38 41 (1939). ( 5 ) Kammermeyer, K., IND.ENG.CHEM.,33,1484 (1941). (6) Komers, K., and Coker, K., French Patent 648,450(1928). (7) National Bur. of Standards, Circ. C440, Table 109 (1942). (8) Ibid., Table 119. (9) National Tech. Lab., Circ. 58-4011 (1943). (10) Stanek, V.,and Pavlas, P., L b t y Cukrovar., 52, 313-17 (1934) ,
I
HYDROCARBON GASES. EDWARD G. SCHEIBEL' AND DONALD F. OTHMER Polytechnic Institute, Brooklyn, N. Y .
e
e
Specific Heats and Power Requirements for Compression
T
HE ratio, 7 , of the specific heat a t constant pressure t o the specific heat a t constant volume is an important thermodynamic property of a gas, necessary in calculations of its adiabatic compression and expansion. Edmister ( 2 ) calculated the variation of the isobaric specific heat of hydrocarbons by the use of the residual volume quantity which is defined as t h e deviation of the actual volume from t h a t given by the perfect gas laws. H e expressed the thermodynamic equation for the value of the difference between the isobaric and the isometric specific h a t s in terms of the residual volume function (9). I
Vol. 36, No. 6
Present addresr, Hydrocarbon Research, Ino., New York, N. I'.
This ratio is used to calculate the isentropic work of comprehsion or expansion of a perfect gas, for which the ratio is constant with temperature and pressure variations. York (6) showed that, for actual gases, the correlation gives a n increase of y with increasing temperature and pressure; and the use of a mean valnc would increase the calculated power requirement, whereas the work of compression of a n attual gas is less than t h a t for a perfect gas. H e pointed out t h a t the use of the average y value based on an actual gas cannot be applied t o a n equation derived for a perfect gas, since all the other thermodynamic properties of the system will also deviate from those of a perfect gas and may
June, 1944
I N D U ST R I A L A N D
E N G I N E E R I N G C,H E M I S T R Y
581
t
4
BENZENE
750
ISOBUTANE
ISOBUTYLENE
650$-----{ 0
-40 650
P R O P A NE
-
RROPYLENE
730-
Figure 1. Nomograph for Ratio of Specific Heat of Hydrocarbon Gases The right-hand scale for molecular weight is to be used with the horizontal lines to give appropriate values on the critical constants scale. In using the right-hand scale for a single pure compound of a normal saturated paraffin hydrocarbon, the actual critical constants and the appropriate point indicated on the compound scale are utilized; the correct critical constant may be found from the critical conditions scale. For compounds other than normal saturated paraffins, values are indicated on the right-hand scale which do not correspond to the molecular weights of these compounds; but these values, empirically determined, give correct values in the utilization of the nomograph. For mixtures of two or more compounds, the average molecular weight may be determined, and the point corresponding to this value may be taken on the right-hand scale. The critical conditions may be determined approximately for such mixtures by horizontal projection to the critical condition scale.
average molecular weight. yield a different net reSuch a correlation would sult. T o correct f o r Nomographs and methods of calculation are presented for this deviation, York depend on the molecular determining the ratio of the specific heats of hydrocarbon introduced an “isentropic structure; as developed in gases, the final temperatures attained in a compression or work factor” which is deFigure 1, it is based on expansion, and the theoretical horsepower requirements fined as the enthalpy the normal saturated hyfor compression. These mathematical methods depend change along a constant on correlations of the physical properties of hydrocarbons, drocarbons. It may be entropy path divided by offer a considerable simplificationof the calculations which used within the limits of are rather tedious otherwise, and may be used within the the enthdpy change calcumost engineering work for limits of accuracy required for engineering design. mixtures of hydrocarbon lated by the perfect gas gases encountered in pelaws. The nomograph controleum engineering where structed i n F i-m r e 1, based t h e average molecular on Edmister’s correlation of the ratio of specific heats of various weight is known even if minor amounts of other than hydrocarbon gases, should thus be used in the region where the the normal saturated compounds are involved. For a pure hydrocarbon the corresponding point indicsted on this scale is perfect gas laws apply, For the region where perfect gas laws do used; for a mixture, the average molecular weight is located on not apply, the isentropic work factor must be introduced. This the scale. For the several hydrocarbons of Figure 1 which are quantity is obtained by comparing the actual work requirement not straight-chain saturates, points are indicated on the comwith that calculated for a perfect gas at the same suction tempound scale which give substantially correct results in use of the perature and same compression ratio (7). Thus the value of y nomograph, a l t h p g h these points do not fall on the true molecuto be used in determining and applying this correction factor is given by the nomograph a t the reduced suction temperature and lar weights of these fompounds. a t pressures when the perfect gas laws apply. CORRELATLVG EQUATION For the specific heat ratio in the case of mixtures, the molal average of the values for the individual components has been Edmister (9)calculated the ratio of the specific heats for sevenrecommended. However, the calculation of this average is teen hydrocarbons a t different reduced pressures and temperatedious; a more rapid method where hydrocarbons are involved tures, and found a general correlation of the data according to the would be t o estimate the value from a correlation based on the Equation 1.
INDUSTRIAL AND ENGINEERING CHEMISTRY
582 Y =
1 4 - C(r7 - I )
that the critical temperatures and critical pressures are dependent upon the respective molecular weights of the members of the homologous paraffin series. Furthermore, the critical conditionb for other hydrocarbon gases or mixtures of such gases may bt assumed to be approximately those of the paraffin gas having the same molecular weight as the molecular weight' or average molecular weight of the gas in question. These may be indicated on w scale having one set of cahhrations for the molecular weights hydrocarbons, another scale for the correqponding critical ternperatures, and still another v a l e for the correiponding critical pressures. Since it i i desired t o indicate, in addition to thew three calibrations, another for individual compounds, the t n ~
(1)
where y = ratio of specific heats for any hydrocarbon C = constant for each hydrocarbon yr = ratio of specific heats of reference substance (taken as propane) a t same reduced pressure and temperature conditions Figure 1 was based on the empirical correlation of the values of for the reference substance and Equation 1. The nomograph facilitates interpolation of the reduced temperature lines. This i s a little difficult t o accomplish accurately on the original correlation which had a maximum deviation of 44; from t h e y
"E "C.
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Vol. 36, No, 6
's
50 0
c 11.07
800i400 700
6ooZ300
N400
200
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2
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1.13 1.14
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RATIO 4 5 I+,#'
, ' " ' II
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(21 6
,
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0.2 RATIO
Figure 2. Noinograph for Determining Final 'remperature for Adiabatic Expansion and Compression 4 drafting triangle is placed 80 that one leg intersects t w o proper values of compression ratio and of y, ratio of specific heats, a n d the other leg intersects the given temperature on one of the srales. The desired temperature is read on other scale.
cdculated valuP2, although most points dgrerd M ithin 17;. T h e nomograph gives values of the ratio of specific heats n hich check> the original correlation as accurately as it could be read over most of the range. However, a slight deviation in the nomograph is detected at the calibrations on the reference line between 2 and 0. In this region, the original correlation shows t h a t y increacei greatly with the reduced pressure. Therefore, while the actual values of y have an error as great as 10yc,tke accuracy based on the reduced pressure scale is within 2 t o 3 9 . The unreliability in this region was appreciated (3); no attempt vivas made t o extrapolate many of the curves over t o the entire range given. Thus, the nomograph should not be extrapolated in this direction beyond the limits indicated. Alqo ureful in a graphical yepresentation 1s the baiic relatioil
lines uri the right of Figure 1 are wed t o carry these four seta oi calibmtions, and any calibration may be read corresponding t,ci one on the other xa,le by drawing a horizontal line between the:
two scales. This is simplified by the horizontal rulings betweeri these scales. This correlation of critical conditions t o molecular weight is correct within the accuracy of the rest of the nomclgraph. T o determine the ratio of the specific heats of a gas at s n y temperature and pressure, the corresponding reduced tempera,turcs and pressures are calculated (or found by nomographs sucf. as those of Othmer, 6); and a line is projected through these values on the T Rand PR scales a t the left of the nomograph to an intersection with the reference line. Through this point, on t h e i.c,ference line, a second line is projected t,o t h e point on the*scaJc
INDUSTRIAL AND ENGINEERING CHEMISTRY
lune, 1944
at the extreme right which corresponds t o the gas in question. The intersection of this line with the CP/CVscale gives the desired value of t h e ratio. T o apply this method t o mixtures of gases, it is necessary t o use the correlation of critical temperature and pressure on the basis of molecular weight. From the compound scale a horizontal line is followed t o the critical conditions scale, and the critical pressure and temperature of a gas of this molecular weight are read from the right- and left-hand sides of the line, respectively. The reduced temperature and pressure are calculated and applied t o the T Rand P R scales t o locate a point on the reference line, a line is projected from this point t o the molecular weight scale on the extreme right, and the value of the ratio is read on the CP/CV scale as before. The use of this nomograph can be illustrated by the solution of the problem given by Edmister ( 3 ) . The value of y for propylene a t PR = 0.555 and T R = 0.95 is determined, as shown in the insert sketch of Figure I, t o be 1.53. This checks the value of 1.525 given by Edmister. (Here the point for propylene used does not correspond t o its molecular weight, as noted above.)
583
The previous formulas refer only t o perfect gases. For power requirements of actual gases, t h e isentropic work factor of York (6) must be included, together with the actual specific heat:
where M = molecular weight of gas C p = specific heat of gas, B.t.u./lb.
AHs = change in enthalpy along a n isentropic path The methods of calculating this factor were fully discussed by York (6) who recommended t h a t the calculation be based on the value of y a t t h e suction conditions of t h e compressor. The convenience in using the nomograph5 in evaluating t h e (2’2 - T1) term in Equation 4 is evident. APPLICATIONS
ADIABATIC EXPANSION AND COMPRESSION O F A PERFECT GAS
The ratio of specific heats obtained from Figure 1 is used t o calculate the outlet temperature for a n adiabatic expansion or compression of a perfect gas in t,he following relation: v - 1
where Tz = outlet temp. T I = inlet temp.
PZ = outlet pressure
PI = inlet pressure
A nomograph is constructed (Figure 2 ) from which the outlet temperature can be determined from the values of y , T I , and Pg/PL, the compression or expansion ratio. Figure 2 is the set square type, and either compression or expansion operations may be readily calculated with it. For compression, it is used by adjusting a right triangle so t h a t one leg passes through the proper values on both the y scale and on the compression ratio scale; the other leg passes through the desired value on the scale ’corresponding t o t h e temperature at lower pressure (inlet). The resultant outlet temperature is given by the intersection of the latter leg with the scale corresponding t o the temperature at higher pressure (outlet). For expansion calculations the lower calibrations on the horizontal scale giving the expansion ratio are used, the inlet temperature value is set on the temperature at higher pressure scale, and the exhaust temperature value is found on the temperature at lower pressure scale. The value of y used in Equation 2 is t h a t at the inlet conditions since, as previously mentioned, this equation requires a constant value of y. The theoretical power requirement in a single-stage adiabatic compression, based on perfect gas law relation, is:
where PI = pressure a t inlet, Ib./sq. in. Vi = volume of gas compressed, cu. ft./min. When the nomograph is used t o calculate the exhaust temperature, a more convenient form of Equation 3 is: h.p. = 0.007808 --?L (Tz 7-1
- Ti)
where h.p. = horsepower required per lb. mole/hr. of gas compressed
PROBLEM. A gas which consists substantially of a mixture of normal saturated hydrocarbons and has an average moIecular weight of 40 is t o be compressed adiabatically from 15 pounds per square inch absolute at 50” F. t o 100 pounds absolute. The outlet temperature and the theoretical horsepower required t o compress 300 moles (12,000 pounds) per hour of this gas is desired. Perfect gas laws will be assumed to hold for this case. This example is worked out according to the insert sketches i n Figures 1 and 2. For a gas of 40 molecular weight, P, = 639 and T o = 635” R. Thus a t inlet conditions, P R = 0.023 and T R = 0.804; and from Figure 1, y = 1.150. The compression ratio is 6.67 and, from Figure 2, the outlet temperature is found t o be 192 F. GENERAL. Figure 1 was constructed to determine y for hydrocarbons. For other gases or vapors, such as air and steam, when y is known (1, 4, Figure 2 may be used t o determine t h e outlet temperatures; the related methods of calculation described may be applied for the determination of tlhe theoretical power required. O
LITERATURE CITED
Dorsey, N. E., “Properties of Ordinary Water-Substance”, pp. 110,262,264, New York, Reinhold Pub. Corp., 1940. Edmister, W. C., IND.ENQ.CHIN.,30,352 (1938). Ibid., 32, 373 (1940). Ellenwood, F. O., Kulik, N., and Gay, N. R., Cornel1 Univ. Expt. Sta., Bull. 30, 9 (1942). Othmer, D. F., IND.ENQ.CHEM.,34, 1072 (1942). York, Robert, Jr., Ibid., 34,535 (1942). York, Robert, Jr., private communication, 1943.
Recovery of Sulfur from Sulfur Dioxide in-Waste Gases-Correction Attention has been called to a n error in our paper which AND ENGINEERING appeared in the April issue of INDUSTRIAL CHEMISTRY(pages 329 t o 332). Equilibrium constants K in Table 11, Equation 6, should read 0.1,0.4, and 0.7 for 150°, 200”, and 250’ C., respectively. On page 330, t h e last sentence of t h e second paragraph under “Thermodynamic Considerations” should read: “Inspection of the free energy values for reaction 6 seems to show t h a t diatomic sulfur is not seriously involved in t h e second step of the process.” T. F. DOUMANI, R. F. DEERY, AND W. E . BRADLEY UNIONOIL COXPLNY O F CALIFORNIA WILMINQTON, CALIF.
