ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT this early pilot plant production and later production was also tested by Mississippi State College, and Louisiana State University. Satisfactory storage stability has been demonstrated with products made with all of the process variables discussed. Summary
Extensive pilot plant work preceeded the commercial development of a new process (the Stengel process) for manufacturing ammonium nitrate. This process is now in commercial operation at Commercial Solvents Corp., Sterlington, La. The process offers significant investment savings and lower operating costs through reduced personnel and utilities requirements. Since the control of the product moisture is in the reaction equipment, the process is essentially independent of climatic conditions. Acknowledgment
The author wishes to express sincere appreciation to Commercia1 Solvents for permission to present this information. Credit is due t o all Commercial Solvents personnel who were associated
with this project, in particular t o W. 0. Bell, Jr., J. D. Kramer, A. P. Miller, L. A. Stengel, and R. S. Egly. Literature Cited
Burns, J. J., and associates, U. S. Bur. Mines, Rept. Invest. 4944. Elliot, Martin A , Ibid., 4244. Hester, A. S., Dorsey, J. J., and Kaufman, J. T., IND.ENG. CHEM.,46,622(1954). Grant, It. L., and Scott, G. S., U. S.Bur. Mines, Infor. Ciro. 7463,June 1948. AIiller, Phillip, and Saeman, W. C., Chcm. Eng. Progr., 43, 667 (1947). Rous, W.H., and associatee, U. S.Dept. Agr., Tech. Bull. 912, J u n e 1946. Shearon, W.H.,Jr., and Dmwoody, W. B., IND. ENG.CHEM., 45,496 (1953). Stengel, L. A. (to Commercial Solvents Corp.), U. S. Patent 2,568,901 (September 25, 1951). ACCEPTED October 29, 1964. RscBIvEn for review July 30, 1954. presented at the Regional Meeting of the American Institute of Chemical Engineers, Washington, D. C., March 1954.
Thermal Calculations for Sugar Process Engineers HOWARD E. HIGBIE' Deparfmenf of Chemirfry, University o f Piffsburgh, Piffsburgh, Pa.
T
HERMAL properties of gas mixtures have been frequently tabulated as the enthalpies of the individual components (9). Then the total enthalpy or heat content of the mixture is computed by summing, for all components, the product of the enthalpy of the pure component times the fraction of the component present. This procedure is justified x h e n the heat of mixing is negligible; otherwise, the heat contents of the mixtures are not additive. The volume, enthalpy, and free energy changes on forming liquid solutions from their components are not negligible in general, hence workers in the field of theory of solutions have expressed the solution properties in terms of partial quantities (6)-for example, partial molal volume, relative partial molal heat content, and chemical potential. These quantities are defined to be additive so that the specific volume of a solution, for example, is the sum of the products of the mole fractions times the partial molal volumes of the components. The partial quantities are intensive properties of the solution and depend on the composition of the solution as well as on the other variables which determine the value of the total property. The partial enthalpies of water and sucrose in solution provide a convenient basis for engineering calculations of the thermal effects attending changes in these solutions. These changes, which occur in the sugar refining and processing industries, may involve the gain or loss of either component from the solution. A tabulation of the partial enthalpies of water and sucrose is presented in Tables I and 11, for the concentration range from 0 t o 65 weight % sucrose and the temperature range from 32" to 200" F. An enthalpy table for crystalline sucrose has been prepared to cover the same temperature range (Table IV) and an enthalpy table for water vapor over this temperature range (Table 111) has been included for convenience in making computa1
tions. In the following sections a method of preparing these tables is outlined and methods of using the tables for the calculation of the heat effects attending several types of changes are described. The justification for presenting the thermal properties of sucrose solutions as two tables of partial enthalpies rather than aa a single table of the total enthalpy or of the apparent enthalpy can be seen in the relationships between the heat effects and solution changes. The thermal equations can be stated by inspection and the calculations are straightforward. The solution partial enthalpies can be used in conjunction with existing enthalpy tabulations-e.g., the steam tables. A recent communication from Lyle points out that he derived an empirical equation for the enthalpy of sucrose solutions in terms of concentration and temperature (6). Although it wm written without the benefit of more recent heat of dilution and solution data, the equation agrees well with the present tabulation. The Lyle equation does not express the partial enthalpies explicitly so that the calculation of the heat effects accompanying solution, precipitation, and vaporization processes is less convenient than with t h e present tabluation. Development Is Based on Relationships between Partial Quantities and Measurable Quantities
The partial enthalpies of Tables I and I1 as well as the partial specific heats used in their evaluation are defined similarly to the well-known partial molal properties of solutions (6, page 33) except that they have been put on a unit weight rather than a unit mole basis. Thus, the partial enthalpies of water and sucrose in solution are defined by
Present address, 7813 Maple Ridge R d , Bethesda 14, Md.
January 1955
INDUSTRIAL AND ENGINEERING CHEMISTRY
17
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT crystalline sucrose initially a t 32" F. The heat unit has been taken to be the British thermal unit (B.t.u.) equal to 251.996 International Steam Table calories. Partial Enthalpies of Water and Sucrose. The partial enthalpies of nTater and sucrose in solution, & ( X , T ) and R a ( X , T ) in Tables I and I1 were evaluated as the sums of the enthalpy changes of the processes symbolized in Equations 9 and 10
where H*(M,,M,,T) is the total enthalpy of a solution containing an amount of water M , and of sucrose AI8 a t a temperature T. The weight fraction of sucrose in the solution is X and the partial properties are for the solution specified by ( X , T ) . Then the total enthalpy of the sucrose solution may be written
H*(Ji,,M, T )
=
+
NwRtb(X,T) MaR8(X,T)
R,(X,T) The partial quantities are not directly measurable but they can be evaluated from the specific or apparent quantities if the latter are known as functions of the concentration. These relationships are illustrated below for the case of the partial specific heats. If C$ is the total heat capacity of a sucrose solution then the specific heat is
$.
01'
e,
= [1 -
XI CU,'(O,T)
+x
@CPb
the following expressions, which relate the partial specific heats to the specific heats and to the concentration dependence of the specific heats, result:
(91
R a ( X j T )- R8(X,77" F.)
(10) Since H,(O, 32" F,), the enthalpy of pure water a t 32" F., and H i (32' F), the enthalpy of crystalline sucrose a t 32" F., are zero
(4)
where C,,(O,T) is the specific heat of pure water The partial specific heats are defined by expressions analogous to Equation 1 in which C, replaces H . By combining these n i t h Equation 3 and since
- Hw(O,32" F.)
e (77" F.) - H," (32' F.) -I-H,(O, 77" F.) - e (77" F.) + R8(X,77" F.) - H,(O, 77" F.)
The apparent specific heat of the sucrose in the solution, @Cp,,may be defined by the expressions
Cr,,(O,T) i'll,@CP,
H,(O, 77" F.)
p 8 ( X , T )=
(3)
e,*= M,
=
+ R w ( X ,77" F.) - H,,(O, 77" F.) + R,(X, T ) - R%(X,77" F.)
by the reference state convention, the above expressions are simply algebraic identities. The first term in Equation 9 is the enthalpy change from heating pure water from 32' t o 77' F. and i 8 equal to 45.054 B.t.u. per pound (7'). The first term in Equation 10 is the enthalpy change on heating crystalline sucrose from 32" to 77" F. This i s given in Table IV and is 12.74 B.t.u. per pound. The second term in Equation 10 represents the heat of aolution a t infinite dilution of sucrose in water at 77" F. and is 7.65 B.t.u. per pound (4). The next t o the last terms in Equations 9 and 10 represent the partial enthalpy changes of the water and sucrose accompanying the concentration change from 0 to X. These terms were calculated from the heat of dilution measurements of Gucker, Pickard, and Planck (5). The heat of dilution data may be expressed by the empirical equation
134':4c3g'5
where Q?L, - = a .mIa r e n t relative enthalav of sucrose in solution. -7.05 X 9/5 B.t.u. B.t.u. per pound, and B = A = 342.3 per pound. (The relative heat content of the solution, L, is the specific enthalpy difference between the solution and pure water.) I
"
In general, any of the partial quantities can be evaluated from a knowledge of the specific quantitv as a function of concentration by evpressions similar to Equations 5 and 6. In certain cases the primary data have been expressed in terms of the apparent rather than the specific quantities. In Table 1. Partial Enthalpy of Water in Sucrose Solution, f%(X,T) these cases the partial quantities may Temperature, F. be evaluated by expressions analogous Weight to Equations 7 and 8, which wcre deFraction 32 40 50 60 70 77 80 90 100 rived similarly to Equations 5 and 6 by 0.00 0 . 0 0 8.036 18.070 2 8 . 0 2 0 38.065 45.054 48. 049 58.030 68.009 18.07 28.02 38.07 45.049 4 8 . 0 4 58.02 68,00 0.05 0 . 0 2 8.05 using Equation 4 instead of Equation 3. 38.05 45.030 48 02 58.00 18.07 28.02 0.10 0 . 0 7 8.08 67 98 18.07 18.07 18.01 17.92 17.78 17.56 17.23 16.79 16.21 15.50 14.87
27.99 27.95 27.90 27.78 27.62 27.40 27.10 26.68 26.15 25 52 24.91
38.01 37,95 37.88 37.75 37.58 37.34 37 04 36.64 36.13 35.54 34.98
44.994 44.935 44,848 44.724 44.554 44.323 44.018 43.620 43.121 42.539 41.977
18
67.95 67.89 67.80 67,68 67.51 67.28 66.97
0.15 0.20 0.25 0.30 0.35 0 40 0.45 0.50 0.55 0 60 0.65
0.14 0.22 0.24 0.20 0.10 -0.09 -0.46 -0.98 -1.71 -2.61 -3.68
TTeigIit Fraction
120
130
140
150
160
170
180
190
200
87.973 87.97 87.95 87.91 87.85 87.77 87.64 87.47 87.24 86.94 86.54 86.04 85.46 84.90
97.960 97.95 97.94 97.90 97.84 97.65 97.63 97.46 97.23 96.92 96.52 96.03 95.44 94.88
107.951 107.94 107.93 107.89 107.83 107.74 107.fi3 107.45 107.22 106.91 106.52 106.02 105.44 104.87
117.949 117.94 117.92 117.89 117.82 117.74 117.62 117.45 117.22 116.91 116.51 116.02 116.43 114.87
127.953 127.95 127.93 127.89 127.83 127.75 127.62 127.45 127.22 126.92 126.52 126.02 125.44 124.88
137.966 137.96 137.94 137.90 137.85 137.76 137.64 137.46 137.24 136.93 136.53 136.03 135,45 134.89
147.988 147.98 147.96 147.93 147.87 147.78 147.66 147.49 147.26 146.95 146.55 146.05 145.47 144.91
158.021 158.02 157.99 157.96 157.90 157.81 157.69 157.52 157.29 156.98 156.58 156.08 155.50 154.91
168.066 168.06 168.04 168.00 167.95 1G7.86 167.74 167.56 167.33 167.03 166.63 166.13 165.54 164.19
8.11 8.16 8.12 8.06 7.94 7.72 7.38 7.00 6.25 5.45 4.54
0.00 0.05 0.10 0 15 0.20 0.25 0.30
0.35 0.40 0.45 0.50 0.55 0.60
0.65
57.97 57.91 57.82 57.70 57.53 57.30 56.99 56.60 56.10 55.51 64.95
66,57 66.08 65.49 64.93
F.
Temperatuie,
Thus the partial quantities can, alternatively, be evaluated from a knowledge of the apparent quantity and of its concentration dependence. In this enthalpy tabulation the standard or reference state has been chosen to be liquid water and crystalline sucrose a t 3 2 " F. Then, for example. Equation 2 represents the amount of heat absorbed in making up the specified solution from liquid water and
47.99 47.93 47.84 47.72 47,55 47.32 47.01 46.61 46.12 45 53 44.97
110 77,990 77.98 77.96 77.93 77.87 77.78 77.66 77.49 77.26 76.95 76.56 76.06 75.47 74.91
I N D U S T R I A L AND E N G I N E E R I N G CHEMISTRY
Vol. 47, No. 1
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT Table II. Partial Enthalpy of Sucrose in Sucrose Solution, Weight Fraction 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65
32 5.51 4.56 3.66 3.32 3.01 2.88 2.92 3.12 3.46 3.93 4.50 5.15 5.83 6.43
40 7.43 6.86 6.32 6.18 6.05 6.06 6.20 6.44 6.80 7.25 7.78 8.36 8.96 9.48
50 10.27 10.07 9.89 9.93 9.99 10.14 10.36 10.65 11.02 11.46 11.95 12.47 12.99 13.43
77 80 20.387 21.72 20.602 21.93 20.835 22.16 21.086 2 2 . 4 2 21.361 22.69 21.659 22.99 21.985 23.31 22.331 23.66 22.719 24.05 23.135 24.46 23.573 24.90 24.024 26.35 24.454 25.78 24.803 26.13
18.60
18.92 19.26 19.65 20.06 20.50 20.96 21.40 21.75
90 26.20 26.41 26.65 26.90 27.17 27.47 27.80 28.14 28.53 28.95 29.38 29.83 30.26 30.61
F.
130
140
G(X,T) 150
160
H", (TI, B.t.u./Lb.
180
190
66.41 66.20 66.65 66.90 67.17 67.47 67.80 68.14 68.53 68.96 69.38 69.83 70.26 70.61
71.66 71.87 72.11 72.36 72.63 72.93 73.25 73.60 74.00 74.40 74 84 75.29 75.72 76.07
77.3 54 5 77.79 78.04 78.31 78.61 78.93 79.28 79.87 80.08 80.52 80.97 81.40 81.75
C,(X, 32" F.) = 1.0074 B.t.u./(lb.)(" F.)
EX
190 200
Rw(X,T)
- R,(X,
77" F.) =
By making use of equations analogous to Equations 7 and 8, the following empirical equations can be written:
i:
e-
-X2
d+L,(X, 77" F.) dX
s'
77" F. =
R a ( X , T )- Pe(X,77" F.)
H,(O,T)
1
- H,(O,
77" F.) (17)
=i
d+L,(X, 77" F.)
sT sT
77' F. 77' F.
Cp,(X.T) dT
(13)
?p,(X,T) dT
(14)
+ CX + D T X
-
The quantity, R,(O,T) Rw(O,77" Fa),is well known ( 7 ) . At temperatures below 77" F. the solution specific heats were assumed to be linear between the value a t 32" F. given by Equation 16 and the value a t 77' F. given by Equation 15. This gave an equation giving the specific heat of the solution as a function of X and T . Then, by using Equations 5 and 6, empirical equations were written to give the partial specific heats as functions of X and T , and these TTere used to evaluate the integrals of Equations 13 and 14.
B,(X,T)
The evaluation of the integrals in Equations 13 and 14 requires a knowledge of the partial specific heats as a function of temperature a t each concentration. The partial specific heats at a given temperature can be obtained from specific heat-concentration data using Equations 5 and 6 . There are data relating the specific heats of sucrose solutions to the concentration a t 32", 68", 122', and 176" F. Yanovskii and Arkhangelslrii (10) made measurements at the three higher temperatures and expressed their results in an empirical equation
C,(X,T) = C,(O,T)
+ D T ] dT
(11)
The last terms in Equations 9 and 10 are the partial enthalpy changes attending the temperature changes from 77" F. to T. These are given by Lewis and Randall (5, page 45).
R a ( X , T )- a ( X , 77" F.)
C
p [ T z - (77"F.)2] (18)
@L + X[1 - XI
R,(X, T ) - R,(X, 7 7 " F.) =
(16)
C,(O, T)dl'
77" F.
R8(X,77' F.) - R8(0,77" F.) =
(15)
where C = -0.6359 B.t.u. per (pound) ( ' F.) and D = 0.001019 B.t.u. per (pound) (' F,). January 1955
+ +P X 2+ GX3
= R,(O, T ) - R,(O, 77" F.) + C [ T - 77" F.] + T x ] { A + 2B 342.3 [z]/ -X
-
200
where E = -0.7861, P = 0.5666 and G = -0.4767 B.t.u. per (pound)( ' F.). Accordingly, the following procedures were used for the evaluation of the integrals in Equations 13 and 14. At temperatures above 77" F. Equation 15 was combined with Equation 5 or 6 to give integrable expressions to substitute in Equations 13 and 14. This lead to the following empirical equations:
1141.9 1145.8
fE,(x,77" F.) - R,(O, 77" F.) =
__
170
Anderson ( 1 ) made measurements near 32' F. and found that the linear dependence of the specific heat on weight fraction no longer held a t this temperature. H i results may be represented by the empirical equation
Enthalpy of Water Vapor, H;(T),
Table 111. Temp.,
70 17.42 17.61 17.81 18.05 18.31
60 13.60 13.65 13.72 13.89 14.08 14.32 14.60 14.92 15.31 15.73 16.19 16.67 17.13 17.52
Temperature, F. 100 110 120 30.84 35.49 3 1 . 0 5 35.70 31.28 35.94 31.54 36.19 31.81 36.48 32.11 36.76 32.43 37.08 32.78 37.43 33.17 37.82 33.59 38.24 3 4 . 0 2 38.67 34.47 39.12 34.90 39.55 3 5 . 2 5 39.90
- R,(X,
77" F.) = C,(O, 77" F.)[T
[C,(O, 77" F.)
- C,(O,
32' F.)
- 77" F.] 4-
+ F X 2 + 2 GX3]X IT
- 77" F.]* 90
R 8 ( X , T )- R6(Xl77" F.) = [C,(O, 77" F.) [T
- 77" F.] +
+ C + 77" F. D ] X
[Cp(0, 77" F.) - Cp(0, 32" F.)
E - 21"X
(19)
+ C + 77D -
77" F.]' + F - 3G X 2 + 2GXa] [T - 9o
(20)
Water Vapor. The values of the enthalpy of water vapor, HL( T), are well known ( 7 )and are given in Table IIT of this paper for convenience in making computations. Crystalline Sucrose. Enthalpy of crystalline sucrose, H:( T), was evaluated through the expression (5, page 45)
INDUSTRIAL AND ENGINEERING CHEMISTRY
19
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT
Table
IV.
Temp.,
where Cgb (7') is the specific heat of crystalline sucrose. This quantity has been measured below room temperature by Parks, Huffman, and Barmore (8) and the measurements were extended to higher temperatures by Anderson, Higbie, and Stegeman ( 2 ) . The latter authors have written an empirical equation expressing both sets of data over the temperature range of intere-t in this work.
Cis (T)= H
+J
[ T - 77" F.]
+ K [ T - 77"
F.12
Enthalpy of Crystalline F.
32 40 60 BO 70 77 80 90 100 110 120 130 140 150 160 170 1 a0 190 200
(22)
where H = 0.2971 33.t.u. per (pound)(' F.) J = 6.398 X lo--' I3.t.u. per (pound)(" F.)2 K = 4.59 X lo-' I3.t.u. per (pound)(' F.)3
Sucrose, @(T)
I I : ( T ) , B t u /Lb. 0.00 2.173 4,944 7.777 10.672 12.736 13.630 16.658 19.74 22.89 26.11 29,40 32.76 36.19 39.69 43.25 46.90 50.61 54.40
Equation 22 was used directly to evaluate the integral in Equation 21 and the results are collected in Table IV. Sample Problems Illustrate Calculation of Thermal Effects of Changes in Sucrose Solutions
Tables Are Most Accuraie at Dilute Solution and near Room Temperature
The relationships developed in this paper are used for computing the thermal results of changes in sucrose solutions. These The major source of uncertainty in Tables I arid I1 arises in changes include the addition of water or sucrose to a mwose soluthe evaluation of the partial specific heat-temperature integrals tion, the evaporation of water from a nonsaturated solution, and of Equations 13 and 14. Since these integrals represent an the evaporation of water 1% ith concurrent crystallization of sucroBe increasing fraction of the partial enthalpy value as the teinperafrom a saturated so'lution. It is possible t o calculate the heat that ture goes up or down from 77" F. the absolute accuracy of the must be absorbed to maintain constant temperature during all, tables depends on temperature. The solution specific heat data of these changes. I t is also possible to calculate the final teinwere obtained a t rather wide temperature intervals and the perature resulting from the addition of either water or 8ucrose to data a t high temperatures have not been confirmed. An estithe solution in the absence of heat exchange with the surroundings. mate of the accuracy of the date of Yanovslrii and Arlrhangelskii The general procedure for calculating the isothermal heat as expressed by Equation 15 niay be made by comparing them absorption is to evaluate the total enthalpy of the reactants bewith the highly precise results of Guclrer, Piclrard, and Planclr fore the change and that of the products of the change using at i i O P. obtained from heat of dilution measurements at neighEquation 2. The enthalpy of the products minus that of the boring temperatures. reactants is equal to the heat absorption required to maintain constant temperature. The general procedure for calculating Solution Specific Heats aL77O F., B.t u./(Lb. ' F.) the final temperature resulting from adiabatically mixing water Yanovskii and Arkhangelskii ~(IO) Gucker, Picksrd, and Planck ( 8 ) with sucrose or with a solution is somewhat more comX CP, % c, 3% GB CP plicated. I n this case the over-all change niay be analyzed into 0,4409 0.942i 0.9983 0,4439 0.9424 0.9983 0.1 0.4409 0.7783 0 7782 0.9983 0.4530 an equivalent series of changes including an isothermal change. 0,9950 0.4 0.9983 0.4409 0.G639 0.4628 0.6718 0.9845 0.6 The individual heat effects are computed and the final temperature is chosen EO that the sum of the individual heat effects L Thus the use of the Panovskii and Arlchangelslrii equation inzero. troduces an error of about 1.1%in the solution specific heats at, Isothermal Solution of Sucrose in Sucrose Solution, Con77" F. and a t the high concentrations. If a 3% uncertainty is sider the addition of a quantity of crystalline sucrose, A M , , a t ascribed to these data over the entire temperature range the temperature T to a quantity of sucrose solution M a t the aame partial enthalpies will have the following uncertainties: temperature. The heat that must be absorbed to maintain constant temperature is the difference hetween the enthalpy of the Cstd. Enthalpy Uncertainties. B t.u /Lb. Temp., F. final solution and that of the initial solution plus that of the Hw(X,T) Rd.Y,T) crystalline sucrose. By Equation 2 the enthalpy of the final 11.3 10.4 32 solution is 0.8 0 3 50 77 90 150 200
0.03 0.3 2.1 3.6
0.0.5
P O
1.8
The greatest uncertainty n ill be in the values a t high conce~itrntion and a t temperatures far removed from 77" F. S e a r room temperature and in dilute solution the accuracy will be higher than this tabulation indicates. I n spite of the magnitude of the uncertainties in the absolute values of the partial enthalpies the tables have been written to within rt 0.01 B.t.u. per pouiid of the values given by the empirical equations. This has been done because computations will frequently involve enthalpy differences over rather narron temperature intervals and these diffcrences will be less uncertain than the absolute values. The values of the enthalpy of crystalline sucrose (Table IV) are estimated to have an uncertainty of about 0.5%. while the errors in Table I11 can he considered negligible in the present tabulation. 20
[JL
0.2
+ A X l , ]{ [I - X,] R o ( S f > T+)XjB, ( X j , T ) }
Siiiiilarly, the enthalpy of the initial solution pIus that of the crystalline sucrose is A I ( [I
- X,]Ei,,(X,,T) + x"L7b(X*>T)) + 4MJR (T)
The isothermal heat absorbed
Q
IS the
differencc
+ L W , ] ( [ ~- X j ] lYt
