INDUSTRIAL AND ENGINEERING CHEMISTRY
770
Vol. 41, No. 4
REACTIOR O F K E T E R E WITH HYDROCYANIC ACID (8, 1 8 )
T h e reaction of ketene with hydrocyanic acid shows the formation of an enolizable kctonitrile (IC)which is subsequently acetylated to form the enol acetate. T h e reactions which occur are represented b y the equations CH*=C=O
+ H C N +CH3COCN +CII2=C(OH)CN
I'II. REACTION OF T C s m m Conversion,
S o catalyst 0.0870 XaOAc
0 . 3 4 , KaOAc 0.457, NaOAc
then CHZ=C(OH)CK f CH2=C=O
TABLE
VI'ITII
HYDROCYANIC ACID
yo
Ketene Ketene Resin t o diYield, % of' IICN Ketene ketene c70 Total 24 40 44 78 6.5 42.5 70 14 74 18.0 70 88 0.1 88 8.7 58 67 2.5 66 30
Average 12 runs 12 runs 7 rnns 12 rnns
Acetoxyacrylonitrile Yield on Ketene,
%
34 60
88 63.5
CHz==C(OCOCH,)CS
I n addition t o a-acetoxyacrylonitrile a small amount of the dimer of pyruvonitrile is also formed 2CHaCOCN -+ C H J C O ~ C ( C N ) ~ Ca-acetoxyisosuccinic H~ dinitrile The dimer can be pyrolyzed a t elevated temperatures or distilled in the presence of basic catalysts such as sodium acetate t o * yield a-acetoxyacrylonitrile and hydrocyanic acid. The reaction of ketene with hydrocyanic acid is carried out by passing ketene into hydrocyanic acid in the presence or absence of diluents, a t -10" to +loo C. Diluents are used mainly to reduce t h e vapor pressure of the hydrocyanic acid and a-acetoxyacrylonitrile itself is a preferred diluent for the reaction. Although considerable reaction is obtained in the absence of catalyst, the highest yields are obtained with a mildly basic catalyst. Anhydrous sodium and potassium acetate are superior t o the alkali cyanides and tertiary nitrogenous compounds as catalysts. I n this reaction a n optimum concentration of catalyst has been observed. With no catalyst or too low a concentration of catal j r s t , diketene is formed in large amounts. With too high a concentration of catalyst the dimerization of pyruvonitrile increases and considerable amounts of a-acetoxyisosuccinic dinitrile are formed. A comparison of average results with and without sodiuni acetate catalyst is reported in Table VII. These runs were carried out operating continuously using the column shown for dilcetene and propionolactone (Figure 1). Unreacled hydrocyanic acid was separated from t h e product by distillation and recycled t o the reactor, The residue was mainly a-acetoxyisosuccinic dinitrile.
a-,~cetoxyisosuccinicdinitrile can be formed alniost t o the exclusion of a-acetoxyacrylonitrile by carrying out the reaction with hydrocyanic acid as a 50% solution in acetic acid a t 0" C. and with 0.370 sodium acetate catalyst. Less than 10% acetic anhydride is formed as a by-product. LITERATURE CITED
Boese, A. B., U. S. Patent 2,108,427 (Feh. 15, 1938). Ibid.,2,382,464 (Aug. 14, 1945). Dommoni, T. F., and Cuneo, J. F., Zbid., 2,411,823 (Nov. 26, 1946).
Gwynn, B. H., and begering, E. F., J . Am. Chem. SOC.,64, 2216 (1942).
Gwynn and Degering, U. S. Patent 2,383,966 (1942). Hurd, C. D., J. Am. Chem. SOC.,55, 275 (1933). Hurd, C. D., Edwards, E. E., and Roach, J. I capillary, and
taT.and tr
0 ; rn = elope.of log qav. us. log 6 ;and %. t a v . / t i .
MODIFICATION O F FLOW EQUATIQN
In ivork in this laboratory on the thixotropy of grease ( 6 )it was found that when a grease is worked continuously a t a given ratc of shear, as by circulation through a capillary, the apparent viscosity a t t h a t rate of shear is related to the time of working, t, by the following equation: = Ct'n
(2)
That i b , M hen 11 is plotted against t on logarithmic scales, a straight line is obtained with slope m, and c is numerically equal to the apparent viscosity when t = 1. I n Figure 2, a typical example of this behavior, obtained by continuously circulating grease B by means of a gear pump and measuring the pressure drop across a capillary in the circulating line, is given. By use of this relationship between viscosity and time, Equation l can be modified in the following nianner so as to take into account the thixotropic change. The average velocity of the grease in a capillary is
When tl is not equal to zero, the equation probably applies only to cases where the rate of shear before entering the capillary is the same as that in the capillary. From this equation it is seen that it' a set of capillaries of constant length-diameter ratios, such af the S.O.D. standard capillaries, is used, the residence time in different capillaries will be the same when the rates of shcar are the. same. Values of both c and m can be determined by capillary measurements alone if capillaries of varying length-diamcter ratios arc used. The most convenient method found for this evaluation is developed in the following manner: The apparent viscosity as calculated by Equation 1 givcs an average or mean value intermediate between the values of the viscosity a t the time of entering the capillary and the time of leaving ,(vev. will refer to the apparent viscosity as calculated for any capillary by Equation 1 or 4,whereas will refer only to valucs calculated for the S.O.D. standard capillaries). The time, tSv., a t which the viscosity is equal to values ealculated by Equation 1 or 4 is shovvii t o be a function of tl, t z , and m as follows: ?sv
=
PLZ I2 S*C(tp-l 2LS - -2LX. 2(m
~
-
tlW+')
+ 1)
Substituting from Equation 2, Mhence ct:".
(3) By combining with the expression S = 4Q/7rRa, Equation I may conveniently be written
p 3 -2LSva R
R S C ( L ~ ~-+t 1'm-1
= __
4L(m
+ 1)
)
But according t o Equation 6. I, = t:! - t - 4L
I--m
hence
(7)
(4) \Then ti = 0, then I , = id, and
TABLE
R$tGf
Ml./Sec. 0.606 0.362 0.195 0.126 0.0750 0.0404 a b
ITr.
ILLUSTRATION O F CONTlNUOUS SOFTESING O F GREASEWIT14 FLOW THqOUGH TUBING' Pressure Drop Across capillary where Capillary Is Preceded by Various Lengths of Tubing, Lb./Sq. In. 61-em. 305-cm. Rate of Shear, Set.-' No tubing tubing tubing Tubing Capillary b 64.1 104 31.0 23.0 19.4 18.5 16.0 62.2 24.7 38.3 10.8 33.5 20.5, 16.0 20.6 17.0 12.8 8.0 21.7 13.4 7.90 12.9 14.8 11.5 7.6 12.6 10.0 5.7 4.22 6.94
Let zequal the fraction by which to multiply tr to obtain tar. Thus
I
For grease A a t 25' C. using 0.25-inch copper tubing. Standard capillary from S.O.D. pressure viscometer.'
Figure 3 is a plot of x versus m, which permits a ready determination of x. The actual determination of m consists of first making pressure-rate measurements using capillaries of different lengthdiameter ratios. The apparent viscosity is then calculated by mean; of Equation 4 and separate curves of apparent viscosity,
~
1
-~
I
~___
_ _ - - _ _ f
I
inch copper tubing (capillaries S and T). Plots of ?tsv. versus tr give straight
1
versus rate of shear, SIplotted for each length-diameter ratio on logarithmic scales. According t o Equation 8, tav. is a constant percentage of tr; therefore, rn may be determined by plotting qav. against tr (logarithmic scale4 and measuring the slope. This is most conveniently done by taking smooth curve values of the apparent viscosity at selected rates of shear and calculating the corresponding values of t, from Equation 6. The value of x corresponding t o m can be read from Figure 3 and used to calculate tav. (Equation 8) and c (Equation 2). Or, c may be determined graphically by shifting the qav. versus tr curves to the left by the factor z and reading at t = 1. TJ~".,
(capillaries K, L, &I, and N ) a t 28' and 38" C., in addition t o the standard capillaries. I n this case the length t o diameter ratio varied from 40 t o 7690. Straight lines are obtained upon plotting these data (Figure 9). The same slope is obtained a t both temperatures and at a11 rates of shear. An-
l0,OOO
EXPERIMENTAL VERIFICATION
The validity of the equitions developed above has been demonstrated by numerous experiments. A modified form of the S.O.D. viscometer was used in which hydraulic oil was pumped by a Zenith 1/2-B pump at six rates of flow from 0.0404 t o 0.606 ml. per second with a n accuracy of 2%. Three of the conventional pistons and cylinders were manifolded, with the entire apparatus being mounted in a constant temperature air-bath cabinet. The temperature was controlled to 25.0' * 0.3" C. In addition t o the standard S.O.D. capillaries, capillaries cut from copper or steel tubing having length-diameter ratios from 14.1 t o 7690 were used. The latter were calibrated by determining the weight of mercury which could be contained in the capillary itself or, in the cases of the longest capillaries, in representative sections cut from the same coil of tubing. I n all cases the grease t o be tested was charged to the cylinders and stored overnight t o establish temperature equilibrium. Equilibrium pressures at each rate of flow were carefully measured by approaching from both higher and lower pressures. The pressures were read on a calibrated Bourdon gage of appiopriate range. I n cases where a highly thixotropic grease has been stored in a tube for an appreciable length of time, i t is necessary t o pump a t constant rate until the tube is complctely flushed t o reach true equilibrium. The dimensions and pertinent constants for the capillaries used are recorded in Table 111. The characteristics of the greases used may be found in Table IT. The apparent viscosity at each rate of flow for each capillary was calculated using Equation 4. Typical data are given in Table V. These calculated values were plotted on logarithmic scales for each length-diameter ratio, with the rate of shear as the abscissa. Such plots for greases C, D, and E are illustrated in Figures 4 and 5 , respectively. Apparent viscosity values at selected rates of shear were read from these figures and plotted in Figures 6 and 7 against the calculated residence times (Equation 6) corresponding
IO00
v1
3
2 IO
IO0
GREASE D
I
10
100
GREASE E R A T E OF SHEAR, SEC. -1
Figure 5. Apparent Viscosity-Rate of Shear Relation for Greases D and E at 25" C.
INDUSTRIAL AND ENGINEERING CHEMISTRY
774
Vol. 41, No. 4
capillary. The grease passed through an adapter, larger in diameter than the tubing, and Rate of Shear, See.-: then into the capillary, which Pressure, Lb./Sq. 1n.b Capillaries Rate of was smaller in diameter than Flow, Capillary A t o E, Capillary Capillary Capillary Capillary Capillary Capillary C D 1 A B inol. IvU./Seo, 1 E the tubing. 93 272 45 15.3 36 65.9 104 0.606 1400 The viscosity of oil increases 0.362 62.2 39.4 36 12.4 31 78 225 1160 29 10.8 24.7 65 187 21.2 83.5 965 with pressure; therefore, one 0.195 26.4 58 167 860 10.0 21.8 21.7 13.7 0.126 would expect the same to be 62 150 770 8.15 8.6 19.6 23.5 12.9 0.0750 4.39 7 . 7 18.0 47 133 670 21.2 6.94 0.0404 the case with greases. Some Capillaries qualitative tests were madc t o F t o J, Capijlary Capillary CApillary Capillary Capillary Capillary 5 incl. 0 li G H 5 verify this. Grease F was 510 955 pumped through 25 feet of 0.25292 186 277 3770 1900 0. GO6 215 136 207 2250 1137 0.362 385 696 inch copper tubing (capillary 0.196 1210 612 150 97 149 275 490 396 114 " 78 121 784 220 390 P) a t rates of shear of 21, 39, 0.126 0.0750 466 236 87 60 94 170 305 and 65 reciprocal seconds, giv0.0404 251 127 68 47 73 130 233 ing pressure drops of 340, 450, 5 See Tables I and I11 for data on respective capillaries used. b Hydraulia pressure corrected for gage error and piston drag. and 540 pounds per square inch, respectively, a t 25" C. After a pressure relief valve set a t 1000 pounds per square inch was attached on the discharge end of the tubing, the pressure drops across the tubing werc 365,495, and 625 pounds In Y pcr square inch, or an increase of 7y0,IO'%, and 16%, reE 0 1000 n. spectively. I n spite of this pressure effect, which would 5more than offset the temperature effect, the apparent viscosity decreases with increasing capillary length. For practical purposes, i t is probable t h a t the temperature and 5 100 pressure effects up t o a t least 1000 pounds per square inch c may be neglected. t IN CAPILLARIES O F DATAFOR GREASEc AT 25 c. AS DETERMINED TABLE v. PRESHJBE-FLOW VARYING LENGTH-DIAMETER RATIOS"
-
7
8
22
DISCUSSION 10
0. I
To the authors' knowledge, Equation 5 is the first equnI
10
100
1000
IQOOO
RESIDENCE T I M E , SEC.
Figure 6.
Determination of m for Grease C a t 25' C.
other sct of data was available in which grease A was pumped through capillary 1, a 121-cm. length of 0.25-inch copper tubing (capillary R) and 8 572-cm. length of steel tubing (capillary Q ) each having a different diameter. These results fit the new Equation 5 and give lines of constant slope when qav. versus tr is plotted logarithmically (Figure 10). Experiments were designed to prove that the softening of the grease in long tubes was not due in any appreciable degree to tcmperature rise. I n one experiment, grease F was pumped through 25 feet of 0.25-inch copper tubing (capillary P) a t a rate of 0.606 ml. per second (1170 pounds per square inch), and the average temperature of the discharged grease was not more than 1' C. above the initial temperature. I n another experiment, grease C was pumped through capillary E a t the same rate. The equilibrium pressure attained mas 1400 pounds per square inch. The theoretical maximum average temperature rise under these eonditions of flow can be calculated to be 5 " C., assuming R specific heat of 0.5 ( I O ) . Even if no heat were lost to the tubing and air, and the actual temperature rise n-ere as high as 5" C., such a rise could account for less than half of the softening observed. Hersey and Zimmer (6) have pointed out, however, t h a t the temperature rise mould not be uniform across the capillary. If concentrated in a thin film at the wall, the heating would produce a greatly enhanced effect. Actually, the temperature rise, measured by a thermocouple placed close t o the inside wall a t the discharge of the tubing, was less than 1 C., even at this high pressure. Evidently most of the hcat developed is rapidly. dissipated. Furthermore, in the experiment summarized in Table IV, the softening observed could not be accounted for on the basis of temperature rise, even if this were concentrated in a thin film, for the grease was mixed after leaving the tubing and before entering the
tion for the calculation of pressure-flow relations of materials possessing anomalous viscosity which takes into account the thixotropic change in the flowing material, The determination of m does not entail much additional work over t h a t performed in finding the usual apparent viscosityrate of shear relation, and the use of Equation 5 will allow more accurate estimation of the pressure-flow relations in long pipes. For example-in a pipe having a length-diameter ratio of 2000the use of Equation 1 will lead to a n error of +48% in estimating the pressure drop for a grease having a value of m -0.10. For higher values of length-diameter ratio, or of m, the error will be even greater. As evidenced by the behavior of the limited number of grcascs tested, the value of m appears t o vary little with rate of shear or
-
GREASE D In
s_c
5
I
I
I
1
100
d
2 10
GREASE E RESIDENCE TIME, SEC.
Figure 7.
Determination of rn for Greases D and E at 25' C.
INDUSTRIAL A N D ENGINEERING CHEMISTRY
April 1949
775
v)
w 1000
Y
L
TIME,SEC. Determination of m for Grease B at 25' C.
I
I
I
I
I
100
IO00
'","""
I
RESIDENCE
Figure 8.
.
-a
'
10
RESIDENCE TIME, SEC.
Figure 9. Determination of m for Grease F a t 25" andE38'1;C. with temperature. For different types of grease typical values of m will be developed in the course of future work and such values may be used with Equation 5 in routine calculations to afford considerably greater accuracy than can be obtained with Equation 1. For some purposes it may be found more convenient to consider the apparent viscosity as varying with the length-diameter ratio. For example, m can be determined a t any given rate of ~ , the length-diameter ratio. Charts shear by plotting T ~ against could be prepared showing corrections to be applied to results calculated using Equation 1 as functions of the length-diameter ratio and of m. Incidentally, other workers ( l a ) have attributed RESIDENCE TIME, SEC. the variation in apparent viscosity with length-diameter ratio t o Figure 10. Determination of m for Grease A at cnd effects. The data presented here indicate t h a t this variation 25" e. is due t o softening of the grease and that end effects are probably negligible. To permit application of the method to high pressures (above 1000 pounds per square inch) corrections for temExcept in the case where the length-diameter ratio is 40, when perature rise and change of viscosity with pressure must be worked both methods.give similar values, the observed values are in much out. Work must also be done t o evaluate quantitatively the efbetter agreement with data calculated from Equation 5 than with fect on the apparent viscosity of length of storage time previous those calculated from Equation 1. to pumping. I n another check, the rate of flow and the pressure drop of grease, of the type represented by greases A and F, being pumped PRACTICAL APPLICATIONS through 37 feet of 2-inch pipe were observed in plant production. I n the following table the observed pressures are compared with For use in solving pressure-flow problems, the experimental the pressures calculated using values of m and of apparent visdata should be tabulated as plots of c versus S on logarithmic cosity typical of this grease, as proposed earlier: scales. Calculations can then be made as follows:
Calculate X = 4Q/nRa Calculate t, (Equation 6) Read c corresponding to X Calculate P (Equation 5 ) In the study of the pressure effect mentioned earlier, made prior to the development of Equation 5, it was found that the observed pressure drops in capillary P were approximately 30% lower than the values calculated using Equation 1. These have been recalculated using Equation 5 with the following results: Pressure Drop, Lb./Sq. In.-Calculated Observed Equation 5 Equation 1 532 540 785 618 418 450 485 340 329 292 275 43 1 235 251 370
,----
Rate of Flow, R.Il./Seo. 0.606 0.362 0,195 0.126 0.0750
-Pressure, Rate of Flow, Lb./Min. 88 121
Temp., OC. 82 38
Observed 69 57
Lb./Sq. In.Calculated Equation 5 Equation 1 88 72 73 60
I n this last example, grease was taken from a storage tank by a gear pump and discharged through the line. However, in the other examples and in the determination of viscosity by the S.O.D. viscometer, the grease was not passed through a pump, but was forced directly into the capillary or tubing from the storage cylinder. Passage through a pump is the usual case, and as a result some softening will take place in the pump itself (Z), and work must therefore be done in the future t o evaluate this factor. Possibly it can be taken into account as an equivalent time, t l , CONCLUSIONS
A x a check on Equation 5 under conditions approaching practical applications, grease B was pumped through three lengths of 8.75-inch pipe and the pressure drops were measured. Inasmuch as the available apparatus did not permit precise measurements, especially a t the low pressures, the results are considered to agree within experimental error with the calculated values: Pipe
Length, Cm. 84 84 252 252 758 756
LengthDiameter Ratio 40.2
40.2 121 121 362 362
Rate of Flow, Ml./Sea.
4.2 32 4.1 31 3.5 30
-Pressure,
Observed
Lb./Sq. In.--Calculated Equation 5 Equation 1
An equation for the calculation of pressure-flow relations in non-Newtonian fluids which takes into account the thixotropic change in the material has been developed. Numerous tests of the equation have been made using lubricating greases, and the results,are considered to satisfy the equation within experimental error. ACKNOWLEDGMENT
The authors wish to acknowledge the assistance of E. J. Eifert and H. C. O'Brien in viscosity measurements and the continued interest and helpful suggestions of Earl Amott and L. W. McLennan.
776
INDUSTRIAL AND ENGINEERING CHEMISTRY NOMENCLATURE
A
= cross-sectional area of capillary, sq. om.
constant in Equation 2 ” = diameter of capillary, cm. = length of capillary, em. = distance from entrance of capillary that grease travels in time t , cm. m = constant depending on the rate of softening of grease with time when flowing P = pressure, dynes/sq. cm. = 69,000 p , where p is pressure in lb./sq. in. of flow, ml./sec. Q = rate R = radius of capillary, cm. value of the expression 4Q/nR8, termed rate of shear, res = ciprocal see. t = time, see. tl = time of entranceYo capillary, sec. t 2 = time of discharge from capillary, see. t , = residence time in capillary, sec. t,”. = time a t which in the equation q = clm is equal to ?la,.. as calculated by Equation 4 v = volume of capillary, ml. v = velocity, cm./sec. x = ratio t., It, 9 = i p p a r i n t Gscosity, poises 7lm = apparent viscosity, calculated by either Equation 1 or 4, C
qav.
D L I
Vol. 41, No. 4
from data talcrn only with 8.O.D. standard caoillaries. poises = apparent v i s c o d y , calculated by Equation 1 or 4 using any capillary, poises LITERATURE CITED
(1) Arveson, M. H . , IND. ENG.CHEM.,24, 7 1 (1932) ; 26, 628 (1934). Beerbower, A., Rproule, L. W..Pathevg, J. B., and Zimmev, J. C., Inst. Spokesman, 6, No. 8, 9 (1942); No. 10, 11 (1943). (3) Blott, J. F. T., and Samuel, D. L., IND.ENG.CIIEX., 32, 08 (2)
(1940).
‘(4) Brunstrum, L. C., Adania, E. W.,arid Ziegler, E. E., Znst. Spokesman, 9, No 3 , 4 (1946). (5) Hersey, M. D., and Zimmer, J. C., J . A p p l i e d Phys., 8, 359 (1937). (6)
McLennan, L. K.,and Smith, G. H., A.S.T.M. Bull., 152, 123
(1948). (7) &looney, M., J . Rheol., 2, 210 (1931). (8) Roehner, T.G., and Robinson, R. C., Znst. h’pokesman, 10, No.
.-
1 2 (1947). -.,
(9) (10) (11) (12)
Sproule, L. W.,Zbid., 8, No. 11, 12 (1945). Tollenaar, D., and Bolthof, H., IND. ERG.CHmr., 38,851 (1946) Zimmer, J. C.,lnst. Spokesman, 7,No. 12; 8, No. 1 (1944). Zimmer, J. C., andPatberg, J. B., Ibid., 9, No. 5 (1945).
RECEIVED January 26, 1948.
Power Savings in Process
Refrigeration FREDERICK CARRI 25 Arkwright Road, London, N.W.3, England
A distinctionis drawn between the requirements of cold storage or space refrigeration duties, and of duties occurring in the chemical process industries. Analysis of the performance of different refrigeration cycles suggests the use of a variation of the vapor compression cycle, on which calculated data are presented. EFRIGERATION systems are required t o perform duties vrhich may be divided into two main classes. The f i s t type of duty consists of the transference of heat from a constant low temperature to a constant high temperature; in the second type of duty, such as occurs in cooling a liquid of finite specific heat, the heat is removed at a varying temperature, and may also be required to be delivered at a varying temperature. The first type of duty occurs in cold storage applications (space refrigeration); the second type occurs frequently in the chemical process industries (process refrigeration).
source a t a higher temperature than itself; in this process i t boils and more vapors are evolved. Compression of the vapors from the chiller by the. compressor, E, and delivery t o the condenser complete the cycle. This cycle performs a space refrigeration duty; the heat is absorbed a t the constant boiling temperature of the liquid in the chiller, and is delivered at the constant condensing temperature of the vapor in the condenser. If such a cycle could be operated under thermodynamically reversible conditions, the relation between heat and work quantities would be given by Equation 1.
I -
t
F=+
I
SPACE REFRIGERATION
Space refrigeration duties are conveniently and efficiently performed by systems in which heat removal is effected by means of a boiling liquid refrigerant; the vapor compression system is t h e most widely used of these. Figure 1 is a diagrammatic flowsheet of such a system.
A refrigerant vapor-for instance, ammonia-is delivered under pressure t o a condenser, A , in which i t is condensed, and heat is removed by cooling water. The condensed liquid is accumulated in a receiver, B, from which i t is allowed t o expand through a valve, C, into a chiller D. The receiver liquid being saturated, expansion is accompanied by partial vaporization and a fall of temperature. The cold liquid remaining in the chiller may then be employed as a refrigerant, absorbing heat from a 1
Present address, Polymer Corporation, Sainia, Ontario, Canada.
HEAT-
Figure 1. Diagrammatic Flow Sheet of Vapor Compression System
