Coker A.K. Fortran Programs for Chemical Process Design, Analysis, and Simulation
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Physical Property of Liquids and Gases
127
~-A Z O 60oF ~Z O 60oF
8PG =0.66 SPG =0.60
X z OSOoF ~ z O50oF
SPG :0.7 SPG :0.76
A
Z 060oF
SPG =0.66
1
0.9
0.8
0.7
Compressibility
0.6
factor,
Z=PV 0.6
RT 0.4
0.3
0.2
0.1
I I I I I I i I I l
100 600 1000 1600 2000 2500 3000 3600 4000 4500 6000
Pressure,
peie
Figure 2-13. Compressibility factor of natural gases as a function of pressure and
specific gravity.
PROBLEMS AND SOLUTIONS
Problem 2-1
Using the Wilke-Chang relation, determine the value of the infinite-
dilution diffusion coefficient of propane in chlorobenzene at 0~
M B = 112.56 (chlorobenzene), ~t = 1.05 cP,
V A :
74.5(cm3/(g-
mol)) (propane), T = 273.15K and ~) = 1.0.
Solution
The computer program PROG23 calculates the diffusion coefficient
of propane in chlorobenzene at varying molal volume of solute A (pro-
pane). At V A - 74.5(cm3/(g - mol)), the computed value of the diffusion
coefficient, D~ - 1.54 • 10 -5 (cm 2/s).
Problem 2-2
Calculate the diffusion coefficient of allyl chloride (AC) in air at 25~
0.0975cm/s.
and 1 atmosphere. An experimental value is
2
128
Fortran Programs for Chemical Process Design
Solution
Using the correlation of Fuller-Schettler-Giddings, values of atomic
diffusion volumes of ~v from Table 2-3 are:
E v(AC) - 3(C) + 5(H) + C1
= 3(16.5) + 5(19.8) + 19.5
= 78.9
E v(Air) - 20.1
Molecular weight of air,
MwA --
29.0
Molecular weight of allyl chloride, MwB - 76.53
The computer program PROG23 determines the diffusion coefficient
of the gas phase. The computed diffusion coefficient of allyl chloride is
0.0952cmZ/s. Table 2-4 shows the computer output of diffusion coeffi-
cients for the liquid and gas phases.
Table 2-4
Computer Output of Diffusion Coefficients for Liquid and
Gas Phases Diffusion Coefficients for Liquids and Gases
DIFFUSION COEFFICIENTS FOR LIQUIDS AND GASES
DIFFUSION COEFFICIENT OF LIQUID PHASE
MOLAL VOLUME OF DIFFUSION COEFFICIENT
NUMBER SOLUTE A cm^3/g-mol cm^2/s-
1 i0.00 .5130E-04
2 20.00 .3385E-04
3 40.00 .2233E-04
4 60.00 .1751E-04
5 74.50 .1538E-04
6 80.00 .1473E-04
7 i00.00 .1289E-04
8 200.00 .8502E-05
9 400.00 .5609E-05
i0 600.00 .4398E-05
ii i000.00 .3237E-05
12 2000.00 .2136E-05
DIFFUSION COEFFICIENT OF GAS PHASE
DIFFUSION COEFFICIENT: .952273E-01 cm^2/s.
Physical Property of Liquids and Gases
129
REFERENCES
1. Yaws, C. L., Physical Properties: A Guide to the Physical Thermo-
dynamic and Transport Property Data of Industrially important
Chemical Compounds, A Chemical Engineering publication, Chemi-
cal Engineering, McGraw-Hill Publishing Co., New York, N.Y., 1977.
2. Reid, R. C., J. M. Prausnitz, and T. K. Sherwood, The Properties of
Gases and Liquids, 3rd ed., McGraw Hill, New York, 1977.
3. Beaton, C. E and G. E Hewitt, Physical Property Data for the Chemi-
cal and Mechanical Engineer, Hemisphere Publishing Corporation,
New York, 1989.
4. Gunn, R. D. and T. Yamada, "A Corresponding States Correlation of
Saturated Liquid Volumes," AIChE J., Vol. 17, 1971, pp. 1341-1345.
5. Lychman, E. W., C. A. Eckert and J. M. Prausnitz, "Generalized
Liquid Volumes and Solubility Parameters for Regular Solution
Application," Chem. Eng. Sci., Vol. 20, 1965, pp. 703-705.
6. Yen, L. C. and S. S. Woods, "A Generalized Equation for Computer
Calculation of Liquid Densities," AIChE J., Vol. 12, 1966, pp. 95-99.
7. Andrade, E. N. da C., Phil. Mag., Vol. 17, 1934, p. 497, p. 698.
8. Rao, M. V., K. A. Reddy, and S. R. S. Sastri, "New Method to Find
Surface Tension," Hydrocarbon Process., Vol. 47., No. 1, 1968, p. 151.
9. Hadden, S. T., Hydrocarbon Process, Vol. 45, No. 2, 1966, p. 161.
10. Sprow, E B. and J. M. Prausnitz, Trans. Faraday Soc., Vol. 62, 1966,
p. 1097.
11. Antoine, C., Tensions des vapeurs: nouvelle relation entre les ten-
sions et les temperatures, Compte rend, 1888, p. 107, p. 68, p. 836.
12. Watson, K. M., "Thermodynamics of the liquid State: Generalized
Prediction of Properties," Ind. Eng. Chem., Vol. 35, No. 4, 1943,
pp. 398-406.
13. Huang, E K. and T. E. Daubert, "Extension of Passut-Danner Cor-
relation of Ideal Gas Enthalpy, Heat Capacity, and Entropy," Ind.
Eng. Chem. Process Des. Dev., Vol. 13, No. 2, 1974, p. 193.
14. Yuan, S. C. and Y. I. Mok, "New Look at Heat Capacity Predic-
tion," Hydrocarbon Process., Vol. 47, No. 3, 1968, pp. 133-136,
Vol. 47, No. 7, 1968, p. 153.
15. Tans, A. M. E, "Find Properties of n-Paraffins," Hydrocarbon Pro-
cess., Vol. 47, No. 4, 1968, pp. 169-173.
16. Stull, D. R., E. E Westrum, and G. C. Sinke, "The Chemical Ther-
modynamics of Organic Compounds," Wiley, New York, 1969.
17. JANAF Thermochemical Tables, 2nd ed., NSRDS-NBS 37, June 1971.
130
Fortran Programs for Chemical Process Design
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
Domalski, E. S. and J. Phys. Chem. Ref Data, Vol. 1, 1972, p. 221.
Reid, R. C., et al., "Properties of Gases and Liquids," 3rd ed.,
McGraw-Hill Book Company, New York, 1977, pp. 414-415.
Reid, R. C. et al., "Properties of Gases and Liquids," 3rd ed.,
McGraw-Hill Book Company, New York, 1977, pp. 567-595.
Wilke, C. R. and Chang, E, "Correlation of Diffusion Coefficients
in Dilute Solutions," AIChE J., Vol. 1., No. 2, 1955, pp. 264-270.
Scheibel, E. G., "Liquid Diffusivities," Ind. Eng. Chem., Vol. 46,
No. 9, 1954, p. 2007.
Reddy, K. A. and Doraiswamy, L. K., "Estimating Liquid Diffusivity,"
Ind. Eng. Chem. Fundam., Vol. 6, No. 1, 1967, pp. 77-79.
Chapman, S. and Cowling, T. G., The Mathematical Theory of Non-
uniform Gases, Cambridge Univ. Press, New York, 1961.
Wilke, C. R. and C. Y. Lee, "Estimation of Diffusion Coefficients
for Gases and Vapors," Ind. Eng. Chem., Vol. 47, No. 6, 1955,
pp. 1253-1257.
Fuller, E. N., E D. Schettler, and J. C. Giddings, "A New Method
for Prediction of Binary Gas-Phase Diffusion Coefficients," Ind.
Eng. Chem., Vol. 58, No. 5, 1966, pp. 18-27.
Standing, M. B, and D. L. Katz, "Density of Natural Gases," Trans.,
AIME, Vol. 146, 1942, pp. 140-149.
EL-Gassier, M. M., "Fortran Programs Computes Gas Compres-
sion," Oil Gas J, July 13, 1987, p. 88.
Gopal, V. N., "Gas Z-factor Equations Developed for Computer,"
Oil Gas J, August 8, 1977, p. 59.
Takacs, G., "Comparing Methods for Calculating Z-factor," Oil Gas
J, May 15, 1989, pp. 43-46.
Awoseyin, R. S., "Programs Integrates Pressure Loss for Single and
Two-phase Pipelines," Oil Gas J, June 23, 1986, p. 33.
I00
ii0
120
125
PROGRAM PROG21
*************************************************************
THIS PROGRAM CALCULATES THE PHYSICAL PROPERTIES OF WATER
AT A TEMPERATURE RANGE FROM 0oC TO 500oC. THE CRITICAL
TEMPERATURE=374.12oC.
THE PROGRAM WILL CALCULATE THE FOLLOWING PHYSICAL PROPERTIES
1. DENSITY DEN g/cm^3.
2. VISCOSITY VIS cP
3. HEAT CAPACITY HC cal/g.oC.
4. THERMAL CONDUCTIVITY THER (micro-cal /s.cm.K)
5. SURFACE TENSION ST dyne/cm.
6. VAPOR PRESSURE VP mm Hg.
7. HEATS OF VAPORIZATION HV cal/g
*************************************************************
DIMENSION T(I:50), DEN(I:50), VIS(I:50), HC(I:50)
DIMENSION THER(I:50), ST(I:50), TK(I:50), VP(I:50), HV(I:50)
INTEGER N
OPEN FILE TO PRINT THE RESULTS
OPEN (UNIT = 1, FILE = 'PRN')
INPUT THE NUMBER OF DATA AND THE VALUES OF THE TEMPERATURE
FOR WHICH THE PHYSICAL PROPERTIES ARE CALCULATED.
DATA N /i0/
DATA T(1)/0.0/, T(2)/25.0/, T(3)/50.0/, T(4)/100.0/
DATA T(5)/150.0/, T(6)/200.0/, T(7)/250.0/, T(8)/300.0/
DATA T(9)/350.0/, T(I0)/374.2/
WRITE (1, 100)
FORMAT (//, IH , 25X, "PHYSICAL PROPERTY DATA OF WATER',
/1H ,78(1H*))
WRITE (i, ii0)
FORMAT (//, 40X, 'TEMPERATURE oC')
DO I = i, N
WRITE (i, 120) I, T(I)
FORMAT (30X, I2, 10X, F8.2)
END DO
WRITE (1, 125)
FORMAT (78(IH-))
CONVERT THE TEMPERATURE FROM DEGREE CENTIGRADE TO KELVIN.
DO I = i, N
TK(I) = T(I) + 273.16
END DO
131
C
ii
130
140
150
155
C
22
160
170
180
185
J = 1
GO TO (ii, 22, 33, 44, 55, 66, 77), J
CALL THE PROGRAM TO CALCULATE THE DENSITY OF WATER
CALL PROGI (T, DEN, N)
WRITE (i, 130)
FORMAT (//, 1H , 25X, 'DENSITY OF WATER: 0oC - 374.2oC'
/IH , 78
(
IH* ) )
WRITE (i, 140)
FORMAT (/,20X, ' TEMPERATURE oC', 10X, 'DENSITY g/cm.^3 9
/, 78(IH-),/)
DO I = i, N
WRITE (I, 150) I, T(I), DEN(I)
FORMAT (10X, I2, 10X, F6.1, 10X, F12.3)
END DO
WRITE (I, 155)
FORMAT ( 78 (IH-) )
J = J + 1
IF (J .EQ. 2) THEN
GO TO 5
ELSE
GO TO 900
ENDIF
CALL THE PROGRAM TO CALCULATE WATER VISCOSITY
CALL PROG2 (TK, VIS, N)
WRITE (i, 160)
FORMAT (//, IH , 25X, 'VISCOSITY OF WATER: 0oC -
/IH ,78(IH*))
WRITE (I, 170)
FORMAT (/, 20X, 'TEMPERATURE oC', 10X, 'VISCOSITY
/, 78(1H-),/)
DO I = i, N
WRITE (i, 180) I, T(I), VIS(I)
FORMAT (10X, I2, 10X, F6.1, 10X, F12.3)
END DO
WRITE (i, 185)
FORMAT (78(IH-))
J = J + 1
IF (J .EQ. 3) THEN
GO TO 5
ELSE
GO TO 900
ENDIF
374.2oC'
cP' t
132
C
33
190
200
210
215
C
44
220
,
230
240
250
255
CALL THE PROGRAM TO CALCULATE HEAT CAPACITY OF WATER
CALL PROG3 (TK, HC, N)
WRITE (i, 190)
FORMAT (//, IH , 25X, 'HEAT CAPACITY OF WATER: 0oC - 350oC',
/IH ,78(IH*))
WRITE (I, 200)
FORMAT (/, 20X,'TEMPERATURE oc',IOX,'HEAT CAPACITY cal/gm.oC'
/,78(IH-),/)
DO I = i, N-I
WRITE (1,210) I, T(I), HC(I)
FORMAT (10X, I2, 10X, F6.1, 10X, F12.3)
END DO
WRITE (i, 215)
FORMAT (78(IH-))
J = J + 1
IF (J .EQ. 4) THEN
GO TO 5
ELSE
GO TO 900
ENDIF
CALL THE PROGRAM TO CALCULATE THE THERMAL CONDUCTIVITY OF WATER
CALL PROG4 (TK, THER, N)
WRITE (i, 220)
FORMAT (//, 25X, "THERMAL CONDUCTIVITY OF WATER: 0oC - 350oC',
/1H
, 78(1H*))
WRITE (i, 230)
FORMAT (/, 20X, "TEMPERATURE oC', 5X,'THERMAL CONDUCTIVITY',\)
WRITE (1, 240)
FORMAT (' micro-cal/s.cm.K', /, 78(IH-), /)
DO I = i, N-I
WRITE (i, 250) I, T(I), THER(I)
FORMAT (10X, I2, 10X, F6.1, 10X, F12.3)
END DO
WRITE (1, 255)
FORMAT (78(IH-))
J = J + 1
IF (J .EQ. 5) THEN
GO TO 5
ELSE
GO TO 900
ENDIF
CALL THE PROGRAM TO CALCULATE THE SURFACE TENSION OF
WATER (Page 219, Yaws et. al.)
133
55 CALL PROG5 (TK, ST, N)
WRITE (i, 260)
260 FORMAT (//, IH , 25X, 'SURFACE TENSION OF WATER: 0oC - 374.2oC',
* /1H ,
78(1H*))
WRITE (1, 270)
270 FORMAT (/, 20X, 'TEMPERATURE oC' ,10X, 'SURFACE TENSION:dyne/cm. ',
* /, 78(1H-),
/)
DOI= i, N
WRITE (i, 280) I, T(I), ST(I)
280 FORMAT (10X, I2, 10X, F6.1, 10X, F12.3)
END DO
WRITE (i, 285)
285 FORMAT ( 78 (IH-) )
J= J+ 1
IF (J . EQ. 6) THEN
GO TO 5
ELSE
GO TO 9OO
ENDIF
CALL THE PROGRAM TO CALCULATE THE VAPOR PRESSURE OF
SATURATED LIQUIDS (PAGE 214 Yaws et. al. )
66 CALL PROG6 (TK, VP, N)
WRITE (I, 290)
290 FORMAT(//, IH , 25X, 'VAPOR PRESSURE OF WATER: 0oC - 374.2 oC',
* /1H , 78(1H*))
WRITE (i, 300)
300 FORMAT (/,20X,'TEMPERATURE oC', 10X,'VAPOR PRESSURE: mm Hg',
* /, 78(1H-),
/)
DO I = i, N
WRITE (i, 310) I, T(I), VP(I)
310 FORMAT (10X, I2, 10X, F6.1, 10X, F12.3)
END DO
WRITE (i, 315)
315 FORMAT (78(IH-))
J = J + 1
IF (J .EQ. 7) THEN
GO TO 5
ELSE
GO TO 9O0
ENDIF
CALL THE PROGRAM TO CALCULATE THE HEATS OF VAPORIZATION
(PAGE 204 , Yaws et. al.)
134
77
320
330
340
345
900
CALL PROG7 (TK, HV, N)
WRITE (i, 320)
FORMAT(//, 1H ,25X,'HEAT-OF-VAPORIZATION OF WATER:0oC-374.2 oC',
/1H
, 78 (1H*))
WRITE (1, 330)
FORMAT (//, 20X, ' TEMPERATURE oC ', 10X, "HEAT-OF-VAPORIZATION: cal/g ',
/, 78(IH-), /)
DO I = i, N
WRITE (i, 340) I, T(I), HV(I)
FORMAT (10X, I2, 10X, F6.1, 10X, F12.3)
END DO
WRITE (i, 345)
FORMAT ( 78 ( IH- ) )
J=J+ 1
IF (J 9 EQ. 8) THEN
GO TO 900
ELSE
ENDIF
CONTINUE
FORM FEED THE PRINTING
PAPER
TO TOP OF THE NEXT PAGE.
WRITE (i, *) CHAR (12)
CLOSE (UNIT = i)
STOP
END
**************************************************************
THIS PROGRAM CALCULATES THE DENSITY OF WATER FROM
"PHYSICAL PROPERTIES BY C.L. YAWS et. al. PAGE 222.
***************************************************************
SUBROUTINE PROG1 (T, DENL, N)
DIMENSION T(I:50), DENL(I:50), TR(I:50), SUM(I:50)
INTEGER N
CRITICAL TEMPERATURE : TC=374.2
CALCULATE THE REDUCED TEMPERATURE : TR=T/TC
TC = 374.2
DO I = 1, N
TR(I) = T(I)/TC
END DO
CORRELATION CONSTANTS OF WATER
A = 0. 3471
B = 0. 2740
CALCULATE THE DENSITY OF WATER
DOIOI=I, N
135
i0
SUM(I) = (1.0 -
TR(I))
IF (SUM(I) .EQ. 0.0) THEN
DENL(I) = A*B
ELSE
SUM(I) = SUM(I)**0.2857
DENL(I) = A*(B**(-SUM(I)))
ENDIF
CONTINUE
RETURN
END
*************************************************************
THIS PROGRAM CALCULATES THE VISCOSITY OF WATER FROM
0oC TO 374.2oC PAGE 213, YAWS et. al.
*************************************************************
SUBROUTINE PROG2 (TK, VISI, N)
DIMENSION TK(I:50), VISI(I:50), VIS2(I:50)
INTEGER N
CORRELATION CONSTANTS OF WATER
A = -i0.73
B = 1828.0
C = .01966
D = -.00001466
CALCULATE THE VISCOSITY
DO I = i, N
VIS2(I) = A + (B/TK(I)) + (C*TK(I)) + (D*TK(I)**2)
VISI(I) = 10**(VIS2(I))
END DO
RETURN
END
***************************************************************
THIS PROGRAM CALCULATES THE HEAT CAPACITY OF WATER FROM
0oC TO 350oC (PAGE 221 Yaws et. al.)
***************************************************************
SUBROUTINE PROG3 (TK, HCI, N)
DIMENSION TK (1:50), HCI (1:50)
CORRELATION CONSTANTS OF WATER
A = 0.6741
B = .002825
C = -.000008371
D = .000000008601
CALCULATE THE HEAT CAPACITY
DO I = 1, N
HCI(I) = A + (B*TK(I)) + (C*TK(I)**2) + (D*TK(I)**3)
END DO
RETURN
136