Coker A.K. Fortran Programs for Chemical Process Design, Analysis, and Simulation
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Table 2-1
(continued)
2 25.0 23.787
3 50.0 92.665
4 i00.0 761.613
5 150.0 3578.623
6 200.0 11679.780
7 250.0 29846.610
8 300.0 64535.430
9 350.0 124430.400
I0 374.2 165952.400
HEAT-OF-VAPORIZATION OF WATER:0oC-374.2 oC
******************************************************************************
TEMPERATURE oC
HEAT-OF-VAPORIZATION:cal/g
1 .0 606.263
2 25.0 590.540
3 50.0 574.104
4 100.0 538.700
5 150.0 499.026
6 200.0 453.398
7 250.0 398.701
8 300.0 327.819
9 350.0 214.156
10 374.2 .000
Liquid density,
g/cm'3
1.4
1.2
DENSITY glcm'3
--IF--
___A._.
0.8
0.6
0.4
0.2
0 50 1 O0 150 200 250 300 350 400
Temperature. ~
Figure 2-1. Liquid density of water as a function of temperature.
107
108
Fortran Programs for Chemical Process Design
(text continued from page 104)
sharp increase in viscosity as the freezing point is approached. There
are other methods in estimating liquid viscosities of compounds [2].
Figure 2-2 gives a plot of liquid viscosity of water from 0~ to its criti-
cal value of 374.2~ Program Prog21 gives a routine for calculating
the viscosity of liquids. Table 2-1 gives the viscosity of water as a func-
tion of temperature.
Heat Capacity of Liquids
Heat capacity data for liquids are relevant in process design of heat
exchanger equipment and chemical reactors. For example, heat capaci-
ties are needed in the design of liquid-phase chemical reactors that
involve energy input for heating liquid reactants to the reaction tempera-
ture. Alternatively, they are essential when sizing reboilers and condensers
for distillation plant and when rating of heat exchangers in general.
Correlation constants for liquid heat capacity are expressed in a poly-
nomial of the form:
C - A + BT
+ CT 2 -I-
DT 3
P
where
Cp -
heat capacity of saturated liquid, cal/g~
A, B, C, and D - correlation constants for a chemical compound
T- temperature, K
(2-4)
1.8
1.6
1.4
1.2
Liquid Viecosity
cP
0.8
0.6
0.4
0.2
A v Viscosity
0 25 50 1 O0 150 200 250 300 350
Temperature, ~
Figure
2-2. Liquid viscosity of water as a function of temperature.
cp i
374.2
Physical Property of Liquids and Gases
109
Liquid heat capacities are not strongly dependent on temperatures,
except at reduced temperature, (T r = T/Tc), where T r = 0.7 to 0.8. At high
reduced temperatures, liquid heat capacities are large and strongly
dependent on temperature. At the boiling point of most organic compounds,
heat capacities are between 0.4 and 0.5 cal/g.K. However, in this tempera-
ture range, there is no effect of pressure [2]. The computer program
PROG21 uses Equations 2-4 for estimating the heat capacity of liquids.
Table 2-1 shows the heat capacity of water as a function of temperature.
Figure 2-3 shows the heat capacity of water from 0~ to 350~
Thermal Conductivity of Liquids
Liquid thermal conductivities, k L, are required in many chemical and
process engineering applications where heat transfer is prevalent. They
are required to evaluate the Nusselt number hd/k, the Prandtl number
c~/k, and in correlations to predict the idealized condensing film coeffi-
cient based upon laminar liquid flow over a cooled surface. The thermal
conductivity of a saturated liquid is:
k L - A + BT
+ CT 2
(2-5)
where k L = thermal conductivity of saturated liquid, microcal/s.cm.~
A, B, and C = correlation constants
T = temperature, K
1.4
1.2
Liquid
heat 0.8
capacity, Cp
cal/g. C
0.6
0.4
0.2
0
0 25 60 100 160 200 250 300 360
Temperature ~
Figure 2-3. Liquid heat capacity of water as a function of temperature.
~. Liquid Hqktt Capacity
110 Fortran Programs for Chemical Process Design
Values of k L for most common organic liquids range between 250
and 400 ~tcal/cm.s.~ at temperatures below the normal boiling point.
Water and other highly polar molecules have values that are two to three
times larger. Except for water, aqueous solutions, and multihydroxy
molecules, the thermal conductivity of most liquids decreases with tem-
perature. Below or close to the normal boiling point, the decrease is
nearly linear. Methods of computing k L have been reviewed [2]. The
computer program PROG21 gives a routine for calculating k L of liq-
uids, and Table 2-1 shows the results for water. Figure 2-4 is a plot of
thermal conductivity of water from 0~ to 350~
Surface Tensions of Liquids
Surface tension data of liquids are important in many process design
calculations for situations where these is a two-phase interface, e.g.,
two-phase flow, distillation, absorption and condensation. Surface ten-
sion can be expressed as:
I 1 R
T c
-
T (2-6)
~ - G~ Tc _ T~
where (~1 - surface tension at T~~ dynes/cm
T c - critical temperature, K
1800 .
1600 .
1400
Thermal 1200 -
conductivity
of
liquid,
1000 .
/
~cal/s.cm. C
800 .
600 .
400 .
200 -
Figure 2-4. Thermal conductivity of water as a function of temperature.
o I I I I ! ' :
0 50 1 O0 150 200 250 300 350
Temperature,
~
Physical Property of Liquids and Gases 111
T = temperature, K
R- correlation parameter
For water, the temperature range for which surface tension is valid is:
Temperature range 0~ to 100~ cy~ = 71.97
Temperature range 100~ to 374.2~ cy~ = 58.91
T~ = 298.16 K, R = 0.8105 for 0~ to 100~
T~ = 373.16 K, R = 1.1690 for 100~ to 374.2~
The surface tension has been correlated with other physical param-
eters such as liquid compressibility, viscosity, molar fractions, and the
refractive index. Rao et al. [8] developed a linear relationship between
the surface tension at normal boiling point (log Ob) and the reduced
boiling point temperature
(Tbr).
Hadden [9] presented a nomograph for
hydrocarbons that enables rapid calculation of cy. For cryogenic liquids,
Sprows and Prausnitz [10] introduced the equation
o : o 0 (1 - T r )P (2-7)
where o- surface tension, dyne/cm
o 0 and p were determined by a least-squares analysis of the measured
data. The computer program PROG21 gives a routine for estimating the
surface tension of liquids, and typical results for water are shown in
Table 2-1. Figure 2-5 demonstrates the surface tension of water from
0~ to its critical value of 374.2~ In general, the surface tension of a
liquid in equilibrium with its own vapor decreases with temperature
and becomes zero at the critical point. In the reduced temperature range
0.45 to 0.65, o for most organic liquids range from 20 to 40 dyne/cm.
For water, o = 71.97 dyne/cm at 25~
Vapor Pressure
Vapor pressure data, Pv, of pure components are important in calcula-
tions relating to vapor-liquid phase equilibria, e.g., in the simplest case
to predict the pressure in a closed vessel containing a specific liquid or
mixture of liquids. Pv data are required for bubble point and most dew
point computations. These values are used in flash calculations involv-
ing mass transfer operations. Clearly the design of pressure require-
ments for storage equipment requires knowledge of the vapor pressure
of the components as does the design of appropriate pressure relief
112 Fortran Programs for Chemical Process Design
80
70
60
A
V
---m--
m
Surface tension,
dynelcm.
50
Surface tension,
dynelcm.
30
20
10
0
0 25 50 100 150 200 250 300 350
Temperature,
~
Figure
2-5. Surface tension of water as a function of temperature.
374.2
systems. The vapor pressure of the saturated liquid as a function of tem-
perature is
B
log Pv - A +- + C log T + DT + ET 2 (2-8)
T
where Pv - vapor pressure of the saturated liquid, mm Hg
A, B, C, D, and E -correlation constants for the chemical compound
In the table of vapor pressure, there are values for the acentric factor
co, which is:
co=-logP~-l.0at T r =0.7 (2-9)
where reduced pressure Pr = P/Pc
reduced temperature T r = T/T c
The acentric factor is used in thermodynamic correlations involving
fugacity, compressibility factor, enthalpy, fugacity, and virial coefficients.
The computer program PROG21 provides a routine for estimating the
vapor pressure, and Table 2-1 shows Pv of water as a function of tem-
perature. Figure 2-6 shows the vapor pressure of water as a function of
temperature to its critical value of 374.2~ For water, deviations of less
Physical Property of Liquids and Gases 113
180000
160000
140000
120000
Vapor prenure,
Pv, 100000
mm Hg
80000
60000
40000
20000
A
--m--
Vapor Preeeure,
Pv,
0 28 50 100 180 200 280 300 350 374.2
Temperature,
OC
Figure 2-6. Vapor pressure of water as a function of temperature.
than 0.5 % are experienced among the other methods. An equation often
used to estimate the vapor pressure is the Antoine [ 11 ] equation.
B
In Pvp - A - (2-10)
T+C
The constants A, B, and C for many compounds are in the data bank
of some simulation design packages. Alternatively, these are found in
texts such as Reid
et al
[2]. Equation 2-10 is only applicable for pres-
sures with ranges from 10 to 1500 mmHg. Reid
et al
[2]. and Beaton
and Hewitt [3] have discussed other methods in estimating vapor pres-
sure of compounds but none appears to offer any specific advantage.
Enthaply of Vaporization
The enthalpy of vaporization, AH v, is also termed the latent heat of
vaporization. AH v is the difference between the enthalpy of the satu-
rated vapor and that of the saturated liquid at the same temperature. The
enthalpy of vaporization data is used in process calculations such as the
design of relief systems involving volatile compounds. In distillation,
heat of vaporization values are needed to find the heat loads for the
reboiler and condenser. Watson [12] has expressed a widely used corre-
lation in calculating AH v.
114
Fortran Programs for Chemical Process Design
[ ]R
T c -T
AH v -AHvl T c_T 1
where AH v - heat of vaporization at any temperature cal/g
AHv~ - heat of vaporization at T~, cal/g
Tc- temperature, K
R - characteristic constant for the chemical - 0.38
(2-11)
AH v decreases with temperature and is zero at the critical point. The
computer program PROG21 incorporates a routine for estimating AH~,
and Table 2-1 shows the results of water as a function of temperature.
Figure 2-7 shows the heat of vaporization of water as a function of tem-
perature. The shape of this plot agrees with most other enthalpy of
vaporization data.
Heat Capacities of Gases
The heat capacity of gases is essential for some process engineering
design, e.g., for air-cooled heat exchanger and for gas-phase chemical
0
reactions. Here, in the latter case the heat capacities, Cp, for gases are
required to determine the heat necessary to bring the chemical com-
0
pound increase to the reaction temperature. Cp is also used in the rating
Heat of vaporization,
cailg
700 -
600 J
500 -
400 -
300 -
200 -
100 -
0
0
I I 'I
~r Heat of vaporization, oal/g
---B--
v
26 50 100 150 200 250 300 350 374.2
Temperature,
OC
Figure
2-7. Heat of vaporization of water as a function of temperature.
Physical Property of Liquids and Gases
115
of heat exchangers and energy balance computations. The heat capacity
of a mixture of gases may be found from the heat capacities of the indi-
vidual components contained in the mixtures.
0
The correlation for Cp of the ideal gas at low pressure is a third-
degree polynomial, which is a function of temperature.
0
Cp
--
A + BT
+ CT 2 -t-
DT 3
(2-12)
where C o- heat capacity of ideal gas at low pressure, cal/gmol.K
P
A, B, C, and D = constants for the chemical compounds
T = temperature, K
The correlation coefficients A, B, C, and D can be determined using
a least square fit of the experimental data, as discussed in Chapter 1.
Huang and Daubert [ 13] published constants for a fourth-order polyno-
mial for heat capacities of many hydrocarbons. Yuan and Mok [ 14] used
0
an exponential temperature function to correlate C p with temperature
and provided constants for many hydrocarbons and nonhydrocarbons.
Tans [15] produced a nomograph that allows a rapid approximation of
0 0
C p for paraffins. A compedium of C p as a function of temperature for
several hundreds of organic compounds is given by Stull
et al.
[ 16] and
0
in JANAF [ 17] tables. PROG22 provides a routine for estimating Cp of
gases, and Table 2-2 shows results of carbon dioxide. Figure 2-8 is a
plot of C o with temperature for carbon dioxide.
P
Heats of Formation
Heats of formation, AHf ~ for individual chemicals involved in chemi-
cal reactions are important to find the heat of reaction, AH~, and associ-
ated heating and cooling requirements. If AH~ < 0, then the chemical
reaction is exothermic and will require cooling. If AH~ > 0, the reac-
tion is endothermic and heating is therefore required.
The correlation of AH~of the ideal gas at low temperature is based
on a series expansion in temperature and is expressed as:
AH~ - A + BT
+ CT 2
(2-13)
where AH~ - heat of formation of ideal gas at low pressure, kcal/g-mol
A, B, and C - corellation constants
T = temperature, K
(text continued on page 118)
Table 2-2
Computer Output of Physical Properties of Gases
PHYSICAL PROPERTY DATA OF GASES
******************************************************************************
TEMPERATURE RANGE (300 - 1500K)
1 300.00
2 400.00
3 500.00
4 600.00
5 700.00
6 800.00
7 900.00
8 I000.00
9 ii00.00
i0 1200.00
Ii 1300.00
12 1400.00
13 1500.00
HEAT OF FORMATION OF METHANE
******************************************************************************
TEMPERATURE K HEAT
OF FORMATION
kcal/mol
1 300.0 -17.962
2 400.0 -18.676
3 500.0 -19.320
4 600.0 -19.894
5 700.0 -20.398
6 800.0 -20.832
7 900.0 -21.196
8 i000.0 -21.490
9 ii00.0 -21.714
I0 1200.0 -21.868
ii 1300.0 -21.952
12 1400.0 -21.966
13 1500.0 -21.910
THE FREE
ENERGY OF FORMATION OF ETHYLENE kcal/mol.
******************************************************************************
TEMPERATURE K FREE ENERGY OF FORMATION:kcal/mol
1 300.0 15.830
2 400.0 17.640
3 500.0 19.450
4 600.0 21.260
5 700.0 23.070
6 800.0 24.880
7
900.0 26.690
116