stripping of volatile organic compounds
TRANSCRIPT
Stripping of Volatile Organic Compounds
From Refinery Waste Water
Objective The major purpose of this writing is to provide a quick but reasonably accurate
method for sizing a stripper to reduce the concentration of a volatile organic compound
(VOC) in a typical refinery waste water stream down to some specified or acceptable
level. The procedure presented here employs a simple BASIC computer program to
compute the number of theoretical stages using Kremser’s equation. Then certain
correlations and methods are used to determine stripper diameter for cases where sieve
trays are to be used and also cases where random packing might be considered. The
actual number of trays (sieves) or height of packing needed are determined by applying
an appropriate tray efficiency or recommended HETP (height equivalent to a theoretical
plate).
Background Volatile organic compounds (VOC’s) generally exhibit limited solubility
with water but still to the extent that they can be a dangerous contaminant. Common
examples of VOC’s would be benzene, toluene, xylenes, n-hexane (benzene precursor),
cyclohexane (benzene precursor), naphthalene, acetone and the chlorinated hydrocarbons.
The vapor stripping agent is generally steam or basically an inert gas stream such as
refinery tail gas (H2 + CH4) or air. Steam stripping is generally conducted at higher
temperatures than inert gas stripping, usually close to the boiling point of water. Since
the volatility of the organic contaminants is a strong function of temperature, stripping
can be done most efficiently and effectively. This includes the removal of the heavier,
more soluble organics such as phenol that are not readily strippable with inert gas.
Many times steam is not economically available and another source of stripping gas is
sought such as fuel gas (H2 + CH4). The stripper is generally operated at low pressure
and close to ambient temperature. Under these conditions, the removal of the lighter
VOC’s such as benzene is quite effective.
Kremser Equation Strippers for removing VOC’s from waste water are generally
conducted at conditions of nearly constant pressure and temperature and also constant
liquid and vapor flow rate (equal molal overflow). These conditions are closely met
because the VOC’s present in the liquid streams are at the ppm level of concentration.
The top half of Figure 1 shows a simple sketch of a typical stripping column. The
constant liquid and vapor flow rates are designated by the symbols L and V in mols/hr. x
and y denote the mole fractions of the solute species (VOC) in the liquid and vapor
streams. The subscript a refers to conditions around the top of the stripper and subscript
b to conditions around the bottom. ya* is the vapor composition in equilibrium with the
liquid feed stream, and yb* is the vapor composition in equilibrium with the liquid exiting
the bottom.
-2-
The bottom portion of Figure 1 shows some typical equilibrium and (material balance)
operating lines for the VOC stripper. They are both essentially linear because the
equilibrium constant for the VOC and the liquid and vapor rates are basically constant
throughout the entire column. The liquid feed rate, its composition xa and the bottom
terminal compositions (xb, yb, specs) will all be fixed. The inlet vapor composition is
generally very low (yb 0). The minimum possible vapor rate is determined from the
slope of the operating line when it intersects the equilibrium line at the top i.e. when ya =
ya* (a pinch point). By overall solute material balance we would then have,
*
min
(1)a b
a b
x xV
L y y
Theoretically an infinite number of equilibrium stages would be required at this
condition. The next logical step is to increase the vapor rate to some reasonably higher
level than the minimum in order to provide an economic balance between stream flow
rates and some finite number of stages. This is achieved by dropping the top end of the
operating line vertically to a lower vapor composition ya < ya*. This is achieved by
simply increasing the total vapor rate to a desired level of operation. Then the desired
operating V/L ratio is given by,
(2)a b
oper a b
x xV
L y y
For an absorption or stripping column operating at essentially fixed P and T and for
conditions of equal molal overflow, the Kremser equation provides a precise value for the
number of equilibrium (theoretical) stages, N . A detailed derivation of this equation is
presented in Appendix I. The final version of the Kremser equation written in a format
which permits direct evaluation of N is:
*
*
* *
(3)
; ; (4 , , )
b b
a a
b b a a
y yLog
y yN
Log A
Lwhere y K x y K x A a b c
K V
Here the quantity A in the denominator is called the “absorption factor” where K is the
vapor-liquid equilibrium ratio of the VOC in question (K = y/x). Normally, in treating
-3-
or dealing with stripping applications we calculate the stripping factor S which is merely
related to A via the relationship,
1
(5)V
S KA L
Vapor-Liquid Equilibria The level of VOC concentration in either the liquid or vapor
phase is very low and generally in the range of parts per million (ppm). As a result,
Henry’s law can be used to relate the equilibrium concentration between the vapor and
liquid streams. The precise definition of Henry’s law is,
0
(6)i
Si ii solvent
xi
y PH Lim P P
x
Here i is the vapor fugacity coefficient of species i (VOC) in the vapor mixture, and
PsolventS is the vapor pressure of the solvent. At low to moderate pressure and especially
at higher temperatures, the vapor phase can justifiably be treated as being ideal, and i
can be taken to be one. In this case Henry’s law can be expressed as,
(7)i i iy P H x
and the vapor-liquid equilibrium ratio for VOC species i becomes simply,
(8)i ii
i
y HK
x P
In 1983 Tsonopoulos and Wilson (1) studied the mutual solubilities of three C6
hydrocarbons (benzene, cyclohexane and n-hexane) and water at conditions basically at
the three-phase equilibrium pressure. They performed a thermodynamic analysis of their
own experimental measurements plus carefully selected literature data. That portion of
the data which provided the solubility of the hydrocarbons in water was used to calculate
and correlate Henry’s law constants. These values were fitted to an analytical expression
of the form:
2/ (9)
( . deg. ) / .
i
i
Ln H A B T CT D LnT
where T abs temperature is in K and H in MPa mole fr
-4-
Table 1 lists the coefficients to Equation 9 for benzene, cyclohexane and n-hexane in
water for a temperature range extending from the melting point of the VOC hydrocarbon
to the three-phase critical end point. In Table 2 of his paper on the design of steam
strippers for removing VOC’s, Bravo (2) lists some estimates of the values of Hi for
several common VOC’s in water at around ambient temperature (20 deg. C). They are
listed below:
VOC Hi, atm/m.f.
Carbon tetrachloride 1,183
Chloroform 180
Methylene chloride 125
Trichloroethylene 500
Perchloroethylene 800
1,1,1-trichloroethane 200
1,1,2,2-tetrachloroethane 20
Benzene 240
Ethylbenzene 389
Dichlorobenzene 71
Methyl-isobutyl ketone 7.1
Methyl-ethyl ketone 1.7
Another important VOC that can be found in refinery sour water streams is phenol
(C6H5OH). In 1976 Dr. John Lenoir did a comprehensive literature survey of the
solubility of phenol in water. He came up with his best listing of smoothed data
consisting of the Henry’s law constant of phenol in water as a function of temperature
and liquid phase concentration. We took his listing of the Henry’s law constant at infinite
dilution and fitted those values to an equation of the same form as Equation 9 over the
temperature range of 100 to 300 deg. F. The resulting equation fit which predicts the
tabulated Henry’s constants with a standard deviation of better than one percent is,
2168.458 1158.55 / 0.0000162 27.76904 (10)
deg. / . .
i
i
Ln H T T LnT
where T is in R and H is in psia m f
-5-
BASIC Program Table 2 lists the BASIC program called VOCSTR.BAS which is used
to calculate the number of equilibrium stages for a typical VOC stripper employing either
an inert gas or steam as the stripping agent. Lines 17-25 are reserved for input
information. The definition of these inputs is as follows:
A$ = VOC identity (e.g. benzene, phenol, etc.)
B$ = Liquid phase solvent (water in this study)
P = Average stripper column operating pressure, psia
T = Average stripper column operating temperature, deg. F
GPML = liquid flow rate, gals/min (GPM)
SCFMV = Vapor flow rate, SCFM at 60 deg. F and 1 atm
PPMWI = VOC concentration in the feed liquid, ppmw
PPMWO = VOC concentration in the exit liquid, ppmw
MWG = Average molecular weight of the stripping agent (vapor)
DL = Liquid density, lbm/cuft
MWVOC = molecular weight of the VOC
In lines 30-75 the program computes the molar liquid and vapor flow rates and also the
inlet and exit liquid and vapor VOC mole fractions. In lines 85-105 are calculated the
Henry’s law constant, equilibrium ratio and the absorption factor (AF) for the VOC
component. Lines 110-125 compute ya*, yb
* and finally the number of equilibrium stages
N employing the Kremser equation (Eqn. 3 above). The balance of the program is
devoted to printing out pertinent output and the computation of some other important
quantities.
In lines 160-172 are computed and printed the actual cuft/min (ACFM) of vapor flow at
the operating P and T of the stripper and also the vapor density (ideal gas). Then in lines
195-225, the minimum vapor to liquid molar ratio (V/L)min, minimum vapor rate
(SCFM), actual or operating V/L, and the ratio over minimum V/L are all computed and
printed. The rest of the printout (lines 235-270) consists of data that were inputted
directly. A more detailed description of the output will be covered when we look at two
subsequent illustrations to be provided later.
Sieve Tray Design The first consideration in the design of the VOC stripper is to
determine an appropriate column diameter. The diameter must be sufficient in order to
insure that column flooding or entrainment will not occur. McCabe, Smith and Harriott
(3) provide an excellent discussion dealing with operating vapor velocity limits for sieve
tray columns. In fact, they recommend the specific correlation of J. R. Fair (4) for
calculating flooding conditions for sieve and bubble cap plates. A brief discussion of
flooding (excessive entrainment) phenomena and a summary of the Fair correlation are
presented below.
-6-
The upper limit of velocity in a sieve-tray column is determined by the flooding point or
by the velocity at which entrainment becomes excessive. Flooding will occur when the
liquid in the downcomer backs up to the next plate. This is determined primarily by the
observed pressure drop across the plate and the plate spacing.
A long established empirical correlation for predicting maximum permissible vapor
velocity (at the flood or entrainment point) is expressed by the equation,
, / sec (11)L Vv v
V
u K ft
where uv is the maximum permissible velocity based on bubbling or active area, and Kv
(ft/sec) is an empirical coefficient. Kv is usually evaluated from plant data and correlated
with such typical parameters as plate spacing and the liquid/vapor flow rates. Fair (4) has
amended Equation 11 to include the effect of liquid surface tension. This modified
version is,
0.2
; ( / ) (12)20
L Vv v
V
u K surfacetension dynes cm
A value of = 20 dynes/cm is typical of organic liquids. For water ( = 72 dynes/cm)
the correlation would predict about a 30 percent higher flooding velocity than for the
organics. The correlation is not recommended for liquids of very low surface tension or
for systems which foam easily. Fair and co-workers have developed a graphical
correlation which expresses the coefficient of Equation 12 as a function of tray spacing
and the flow parameter F.P. defined below.
0.5
. . (13)V
L
LF P
V
where L/V is the ratio of mass flow rate of liquid to vapor. L and V are the liquid and
vapor densities generally expressed in units of lb/cu ft. The graphical correlation is
applicable to both sieve and bubble cap plates. This graph appears as Figure 18-30 on
Page 515 of the textbook by McCabe et. al. (3).
For safe column operation it is best to use a value of Kv that is around 75 percent of the
value determined from the above correlation. This will then provide an operating
superficial vapor velocity (Eqn. 12) that is safely below that which would initiate
flooding or entrainment. This velocity in turn will then permit us to determine an
appropriate column diameter.
-7-
A very typical overall tray efficiency that if often employed for stripping applications
such as the removal of dilute VOC concentrations in water is around 25 percent. This is
basically the same efficiency value that is used for the design of sour water strippers in
general.
Random Packing Design For illustrating the use of random packing in the sizing and
design of a VOC stripper, we have chosen Intalox Metal Tower Packing ( IMTP)
developed by the Norton Company (5). The computation procedure for maximum vapor
flow capacity using the IMTP packing was essentially developed by Strigle (6,7).
The correlation uses the same flow parameter F.P. (Eqn.13) as is used for the sieve tray
correlation. The vapor load in a column is expressed in terms of the C-factor Cs and is
defined by the expression,
, / sec (14)Vs s
L V
C v ft
The C-factor is basically the superficial vapor velocity corrected for the gas and liquid
densities. In another sense, it is a column capacity factor, in that it is used to correlate
what vapor flow rates or vapor velocities will initiate flooding or liquid entrainment.
In the work that led to the development of high void fraction packing e.g. IMTP packing,
it was found that vapor velocities could be increased to such a high rate that significant
liquid entrainment was produced without producing a corresponding high pressure drop.
This entrained liquid was carried up the column resulting in a drop of separation
efficiency at vapor velocities that were still below the packing’s maximum hydraulic
capacity (flood point). The Maximum operational Capacity (MOC) is defined as the
point at which the separation efficiency starts to decline appreciably. The MOC is not
identical to flood, but it commonly occurs at about 90 percent of the flood point.
For this correlation we replace the C-factor Cs with the term Cmoc in Equation 14. By
experimentation, Strigle (6,7) reported the MOC of IMTP packing for many systems. He
prepared a plot of a factor identified as Cuncorr.,moc as a function of the flow parameter for
IMTP packings of sizes # 25, #40, #50 and #70. We cannot present this graph here
because of proprietary reasons. Cuncorr.,moc represents the capacity factor for the specific
conditions where:
, 20 /
cos , 0.20L
Surfacetension dynes cm
liquid vis ity cps
-8-
Strigle’s data indicates that the maximum increase of Cmoc is 8 percent for liquids with
higher surface tension. Hence for water which has a surface tension in the range 60-73
dynes/cm range, Cmoc is increased by 8 percent. In addition he found the Cmoc value at
fixed flow parameter varies as the liquid viscosity to the –0.11 power. Upon correcting
the C-factor at MOC for liquid viscosity and for the maximum effect of surface tension
(aqueous systems), we get:
0.11
.,
0.20(1.08) (15)moc uncorr moc
L
C C
For a safe design, it is recommended that the vapor rate at the highest loaded point in the
packed bed should not exceed 75 percent of the predicted Maximum Operational
Capacity (Eqn. 15). Therefore the following equation was recommended for sizing the
tower diameter when IMTP packing is employed:
0.75 (16)L Vs moc
V
v C
Illustration 1 We are asked to provide an appropriate design of a stripper for reducing the
concentration of benzene in a waste water stream from 700 ppmw (parts per million by
weight) down to 1 ppbw (parts per billion by weight). The liquid flow (feed) rate is to be
constant throughout the stripper at 300 gpm. The average operating pressure and
temperature of the stripper will be 70 psia and 85 deg. F respectively. The stripping gas
to be employed for this service is a benzene-free hydrogen-methane rich ethylene plant
tail gas with a molecular weight of 10.28. We are specifically asked to choose a
reasonably economic gas rate (SCFM) and look at the following two options as far as the
column (stripper) internal hardware is concerned:
a. Sieve trays with an 18-inch tray spacing and 25 % overall tray efficiency
b. No. 50 intalox metal tower packing (IMTP)
Sieve tray design: In order to be able to select an appropriate design gas rate, we need to
first establish a relationship between the number of theoretical (equilibrium) stages and
gas rate. Program VOCSTR.BAS (Table 2) was run for a host gas rates. A summary of
the program input is as follows:
A$ = BENZENE GPML = 300
B$ = WATER SCFM = 700, 850, 1000, 2000, 3000, 3700
P = 70 PPMWI = 700
T = 85 PPMWO = 0.001
-9-
MWG = 10.28
DL = 62.17
MWVOC = 78.1
In Lines 90 to 95 of the program, the coefficients listed in Table 1 for benzene in water
are used to compute the Henry’s law constant H and equilibrium constant K. For
example with a gas rate of 1000 SCFM the program computes:
xa = 1.615109 E-04 ; xb = 2.3073 E-10
yb = 0 ; ya = 8.483463 E –03
H = 5461.8 psia ; K = 78.026
L = 8302.3 Lbmoles/hr ; V = 158.06 Lbmoles/hr
N = 31.2 equilibrium stages
The minimum gas rate (infinite stages) is computed in Line 208 using Equation 1 of the
text. (V/L)min = 0.012816 and therefore:
min
379.6(0.0128163)(8302.3) 673.
60SCFM SCFM
A more complete listing of the output for this run is attached to Table 2.
Figure 2 provides a plot of the number of theoretical stages Ntheo versus the SCFM vapor
rate from 673 (min) to 3700 SCFM. A reasonable economic balance between Ntheo and
gas rate would be to choose 10 theoretical stages at a gas rate of 2500 SCFM.
Next we use the correlation of Fair (4) to size the stripper diameter for sieve trays with an
18-inch tray spacing.
Physical properties at 85 deg. F and 70 psia:
v = 0.123 lb/cuft from the program (ideal gas law)
L = 62.17 lb/cuft taken from the steam tables of Keenan and Keyes (8)
= 70.0 dynes/cm taken from Yaws (9)
L = 0.80 cps taken from Yaws (9)
-10-
Liquid and vapor mass flow rates:
0.5 0.5
(300)(60)(62.17) / 7.48 149,600 /
(2500)(10.28)(60) / 379.6 4062 /
149,600 0.123( .13)
4062 62.17
1.638
V
L
L lbs hr
V lbs hr
LFlowParameter Eqn
V
For an 18-inch tray spacing, we read from Figure 18-30 (Page 515) of Mc Cabe et. al. (3):
Kv = 0.07
To insure that we obtain a superficial vapor velocity below the point where flooding or
entrainment begins, let us use a value of Kv that is 75 percent of the value read above
from the figure.
Kv (operation) = (0.75)(0.07) = 0.053
Then from Eqn. 12 we calculate the operating superficial vapor velocity:
0.2
0.
62.17 0.123 70.0( .) (0.053)
0.123 20
(0.053)(22.46)(1.285) 1.53 / sec
40629.173 / sec
(0.123)(3600)
9.173( ) 6.0 . .
1.53
(4)(6.0)( . .)
3.1416
v
cs
t
u oper
ft
Gas volumetric flowrate cuft
A column sq ft
D col dia
5
2.8 ( 3 )ft usea ft diameter
For a sieve tray column requiring 10 theo. stages with a 25 percent efficiency, we would
install 10/0.25 or 40 sieve trays. So our final sieve tray design here for Illustration 1
consists of:
40 actual sieve trays with an 18-inch tray spacing placed in a
3.0 foot diameter vessel.
-11-
No. 50 IMTP packing: For the same vapor and liquid flow rates and theoretical stages,
we now wish to determine the tower diameter and height of packing required for a
stripper filled with No. 50 IMTP random packing. The flow parameter (Eqn. 13) is the
same, F.P. = 1.638. Then, from the proprietary plot developed by Strigle (6,7), we read,
., 0.17 / secuncorr mocC ft
Next Eqn. 15 is used to correct for liquid viscosity and the maximum effect of surface
tension:
0.11
0.20.17 1.08 0.158 / sec
0.8mocC ft
To provide a safe design (avoidance of flooding), let us use a value of Cmoc that is 75
percent of the above value.
0.5
0.75 0.158 0.118 / sec
62.17 0.123: 0.118 2.650 / sec
0.123
9.173 / sec3.461
2.65 / sec
(4)(3.461)2.1
3.1416
s
cs
t
C ft
Superficial velocity v ft
cuftA sq ft
ft
D ft
For this design it would be wise to select a 2.5 ft diameter column packed with No. 50
IMTP.
Norton (5) and Strigle (6,7) list the following HETP (height equivalent to a theoretical
plate) values for IMTP random packing:
HETP, inches
IMTP No. 40 28
IMTP No. 50 36
IMTP No. 70 48
-12-
It may recalled previously, that 10 theoretical stages were required to reduce the benzene
content of the waste water from 700 ppmw down to 1 ppbw. Therefore, if No. 50 IMTP
is employed, then the height of packing needed in this design would be:
Height = (10)(36)/12 = 30 feet.
For a sound design, whereby liquid channeling would be avoided, the column should be
divided into two 15-foot packed sections with liquid redistributors placed in between.
Illustration 2 For the second design case we wish to size a stripper which will reduce the
concentration of phenol in a waste water stream from 55 ppmw down to 13.5 ppmw.
Once again the liquid (feed) rate throughout the column is constant. In this case, the
liquid rate is 63.6 gpm. The average operating pressure and temperature of the stripper
will be 30 psia and 250 deg. F (sat.). The stripping vapor to be used here is saturated
steam at 30 psia and 250 deg. F, obviously, with a molecular weight of 18.02. As in the
first illustration we are asked to find a reasonably economic gas rate and look at two
options as far the stripper internals are concerned.
a. Sieve trays with an 18-inch tray spacing and 25 % overall tray efficiency
b. No. 50 intalox metal tower packing (IMTP)
Sieve tray design: Once again we ran Program VOCSTR.BAS for a host of selected gas
rates in order to first establish the relationship between the no. of theoretical stages and
gas (vapor) rate. Program input for Illus. 2 was as follows:
A$ = PHENOL GPML = 63.6
B$ = WATER SCFM = 4300, 4500, 5000, 5300, 5600
P = 30 PPMWI = 55
T = 250 PPMWO = 13.5
MWG = 18.02
DL = 58.8
MWVOC = 94
In Lines 90 through 95 of the program Equation 10 is use directly to compute the Henry’s
law constant and equilibrium constant for phenol in water at the average conditions of P
and T in the column. For example, for a gas rate of 5000 SCFM the program computes
and prints out the following (See Table 3 for program listing and output):
xa = 1.054362E-05 xb = 2.587979E-06
yb = 0 ya = 1.67575E-05
-13-
H = 56.731 psia K = 1.891
L = 1664.7 Lbmoles/hr V = 790.3 lbmoles/hr
N = 4.
The minimum gas rate (infinite stages) once again is computed in Line 208 (Eqn, 1)
where (V/L)min = 0.3990126:
min
379.6(0.3990126)(1664.7) 4202.
60SCFM SCFM
In Figure 3 we have plotted the number of theoretical stages versus vapor rate from 4200
to 6000 SCFM. In this case a reasonable economic balance between Ntheo and gas rate
would be to choose 5 theoretical stages at a gas rate of 4750 SCFM.
Sieve tray column diameter using the Fair (4) correlation with 18-inch tray spacing.
Physical properties at 250 deg. F and 30 psia (taken from the same sources as for
Illustration No. 1:
V = 0.071 lb/cuft
L = 58.8 lb/cuft
= 51.0 dynes/cm
L = 0.24 cps
Liquid and vapor mass flow rates:
0.5
0.5
(63.6)(60)(58.8) / 7.48 30,000 /
(4750)(18.02)(60) / 379.6 13,530 /
( .13)
30,000 0.0710.077
13,530 58.8
V
L
L lbs hr
V lbs hr
LFlowParameter Eqn
V
For an 18-inch tray spacing, we read from Figure 18-30 (Page 515) of McCabe et. al. (3):
KV = 0.27
-14-
Then KV (oper.) = (0.75)(0.27) = 0.203 ft/sec
And by Eqn. 12, the operating superficial vapor velocity is:
0.2
0.5
58.8 0.071 51( .) 0.203
0.071 20
0.203 28.761 1.206 7.04 / sec
13,53052.934 / sec
0.071 3600
52.9347.519
7.04
4 7.5193.09 ( 3.5 )
3.1416
v
cs
t
u oper
ft
Gas volumetric flowrate cuft
A sq ft
D ft usea ft diameter
For a sieve tray column requiring 5 theo. stages with a 25 percent efficiency, we would
install 5/0.25 = 20 actual sieve trays. The final design for this phenol stripper (Illus. 2)
consists of:
20 actual sieve trays with an 18-inch tray spacing placed in a
3.5 foot diameter vessel.
No. 50 IMTP packing design:
Here we have the same liquid and vapor flow rates and number of equilibrium stages as
computed above for the sieve tray design. We desire to determine the column diameter
and height of No. 50 IMTP packing required for this phenol stripping service. The flow
parameter is the same i.e. F.P. = 0.077. From the maximum capacity chart developed by
Norton (5) and Strigle (6,7) we read:
Cuncorr. moc = 0.37 for No. 50 IMTP
Next Eqn. 15 is is used to correct for liquid viscosity and the maximum effect of surface
tension:
0.11
0.200.37 1.08 0.392 / sec
0.24mocC ft
-15-
To provide a sound design (avoidance of flooding) we choose to use a value of Cmoc that
is 75 percent of the above value.
0.75 0.392 0.294 / sec
58.8 0.071: 0.294 8.456 / sec
0.071
52.936.26
8.456
4 6.262.82
3.1416
s
cs
t
C ft
Superficial velocity v ft
A sq ft
D ft
For this phenol stripping design, we should at least employ a 3.0 ft diameter column
packed with No. 50 IMTP packing.
As we saw previously (little chart on page 11) No. 50 IMTP has an HETP of 36 inches.
Therefore for 5 theoretical stages (at 4750 ACFM vapor rate) the height of packing
needed would be:
Height = (5)(36)/12 = 15 feet.
In this case a single 15-ft long packed section would be installed.
Multi-VOC’s(Solutes) If more than one VOC is present in the aqueous phase, then we
would run Program VOCSTR.BAS for each VOC by itself to see how many equilibrium
stages would be needed to reduce its concentration down to the prescribed (design) ppm
level. This calculation would be conducted at the total liquid and vapor flow rates using
the specific Henry’s law constant for that particular VOC. The VOC which requires the
largest number of theoretical stages would produce the controlling design case.
This would seem to be a reasonable approach because these VOC’s (solutes) are present
in the liquid at very low concentration. As far as the VLE or Henry’s law correlation is
concerned, the solute molecules basically “see” only solvent (water) molecules and rarely
one another.
16-
List of References
1. Tsonopoulos, C and Wilson, G.M., “High Temperature Mutual Solubilities of
Hydrocarbons and Water”, AIChE Journal, Vol. 29. No. 6, Page 990,
(November, 1983).
2. Bravo, J.L., “Design Steam Strippers for Water Treatment”, Chemical Engineering
Progress, Page 56 (December, 1994).
3. McCabe, W.L., Smith, J.C., and Peter Harriott, “Unit Operations of Chemical
Engineering”, 4th Edition, McGraw-Hill Book Co., Page 515 (1985).
4. Fair, J. R., Pet. Chem.. Eng. Vol. 33 (10):45 (1961).
5. Norton Chemical Process products, “Intalox high Performance Systems”,
Bulletin IHP-1, (1987).
6. Strigle, R.F., “Random Packings and Packed Towers”, Gulf Publishing Co,
(1987)
7. Strigle, R.F., “Packed Tower Design and Applications – Random and Structured
Packings”, 2nd
Edition, Gulf Publishing Co., (1994).
8. Keenan, J.H., Keyes, F.G., Hill, P.G., and Moore, J.G., “Steam Tables”, John Wiley
& Sons (1960).
9. Yaws, C.L., “Physical Properties – A Guide to the Physical Thermodynamic and
Transport Property Data of Industrially Important Chemical Compounds”, McGraw-
Hill Publishing Co. (1977).
-17-
General Nomenclature
A Absorption factor or reciprocal of the
stripping factor, 1/S, defined by Eqn. 4c
A/, B, C, D Coefficients for Eqn. 9
Acs Cross-sectional area of a tower, sq ft
Cs C-factor defined by Eqn. 14 for random
packed towers, ft/sec
Cuncorr.,moc Packing C-factor or capacity factor for
= 20 dynes/cm and L = 0.20 cps, ft/sec
Cmoc Packing capacity factor corrected for
effect of surface tension and liquid
viscosity, ft/sec
Dt Tower diameter, ft
H Henry’s law constant for VOC or solute
in the aqueous phase, units of pressure/m.f.
K Vapor-liquid equilibrium ratio of the VOC
Kv An empirical coefficient present in either
Eqns. 11 or 12, sieve-trayed towers, ft/sec
L Mass flow rate of liquid, lbmols/hr
N Number of equilibrium stages
P System total pressure, psia or atm
Pssolvent Vapor pressure of the solvent, psia or atm
S The stripping factor, defined by Eqn. 5
SCFM Standard cubic feet of gas flow per minute
At 60 deg. F and 1 atm
-18-
Nomenclature Cont.-
T System temperature, deg. F, R or K
uv or vs Maximum permissible superficial gas
or vapor velocity
V Vapor or gas mass flow rate, lbmols/hr
xi Mole fraction of VOC (i) in the
liquid phase
xa Mole fraction of VOC in the liquid feed
to the column
xb Mole fraction of VOC in the liquid exiting
the bottom of the column
yi Mole fraction of VOC (i) in the vapor phase
ya Mole fraction of VOC in vapor exiting
the top of the column
yb Mole fraction of VOC in vapor feed to the
column (generally equal to zero)
ya* Mole fraction of VOC in equilibrium with
the liquid feed stream (xa)
yb* Mole fraction of VOC in equilibrium with
the liquid exiting the bottom of the column
Greek Letters
i Vapor fugacity coefficient of species i
(VOC) in the vapor mixture
L Liquid density, lbm/cu ft
-19-
Nomenclature Cont.-
V Vapor density, lbm/cu ft
Liquid surface tension, dynes/cm
L Liquid viscosity, cps
Subscripts
i VOC or solute i.d.
min. Minimum
solvent designates the solvent (usually water)
-20-
Appendix I
Formal Derivation of the Kremser Equation
First of all, let us consider an arbitrary theoretical stage n as shown in the top (left)
portion of Figure 1. For conditions of constant molal overflow and constant solute
(VOC) equilibrium constant K, we can write a simple material balance with respect to the
solute or VOC itself:
1 1 ( 1)n n n nV y L x V y L x I
The liquid composition can be substituted for using the equilibrium constant expressed
as,
11. 1
nn n n
n nn n
yy K x or x
K
y ywhereby Eqn I becomes V y L V y L
K K
Next the above expression is divided through by V to give,
11
n nn n
y yL Ly y
V K V K
Equation 4c of the text defined the absorption factor as A = L/KV. As a result, after
rearrangement and substitution of the above relation for A, the material balance equation
can be written as,
1 11 0 ( 2)n n ny A y A y I
Equation I-2 is a finite difference equation which is next to be solved subject to the two
boundary conditions:
*
1
0
1
n o a a
n N b
n y y y K x
n N y y y
-21-
The assumed solution form for Eqn. I-2 is,
n
ny C wheren anyarbitrary stagen
Upon substitution of this assumed solution form, Eqn. I-2 becomes,
1 1
1
2
(1 ) 0
exp :
(1 ) 0
n n n
n
C A C AC
Division through by C readily yields the quadratic ression
A A
This expression is readily solved using the quadratic formula:
2
1 1 4 1 (1 )
2 2
1
A A A A A
whereby or A
Since the original finite difference equation is linear, our general solution becomes,
1 1 2 2 1 2
1 2
(1) ( )
( 3)
n n n n
n
n
n
y C C C C A
or y C C A I
Now we apply the two specified boundary conditions above in order to evaluate the
constants C1 and C2:
* 0
1 2 1 2
1
1 2
a
N
b
y C C A C C
y C C A
Next we substitute for C1 into the second expression above,
* 1
2 2
*
2 1 1
N
b a
b a
N
y y C C A
y ywhereby C
A
-22-
* * 1* *
1 2 1 1
* 1 *
1 1
1 1
: ( 4)1 1
N
b a a ba a N N
Nna b b a
n N N
y y y A yThen C y C y
A A
y A y y yOur solution then becomes y A I
A A
Equation I-4 applies to any arbitrary theoretical or equilibrium stage n. Now if we apply
this equation specifically to the bottom stage N whereby,
*
* 1 **
1 1
* 1 * * 1 *
,
1 1
n N b
NNa b b a
b N N
N N N N
b b a b b a
when n N y y y
y A y y yy A
A A
or y A y y A y y A y A
If we divide the above expression through by AN and rearrange the result, we get,
*
* * *
*
* * *: ( 5)
b b
a b b aN
b bN N
a b b a
y yy A y A y y
A
y ySolving for A A I
y A y A y y
Equation I-5 can be further simplified by performing a solute material balance around the
entire column (see Figure 1):
* *
* *
* *
, / /
( 6)
,
a b b a
a a b b
a bb a
a b b a
L x V y L x V y
However x y K and x y K
y yTherefore L V y L V y
K K
L Lor y y y y I
K V K V
Lbut A the absorption factor
K V
-23-
Next the absorption factor is incorporated into Equation I-6 and the result solved for ya to
give,
* * ( 7)a b b ay y A y A y I
Now we can insert Equation I-7 into the denominator of Equation I-5:
*
*
N b b
a a
y yA
y y
Upon taking the logs of both sides of the above expression and then solving for N, we
arrive at the final form of the Kremser equation:
*
*
( 8)
b b
a a
y yLog
y yN I
Log A
Equation I-8 corresponds to Equation 3 of the text.
-24-
Table 1 File: VOC.XLS
Henry's Constants for C6 Hydrocarbons in Water
Ln Hi = A + B/T + CT**2 + D Ln T
Hi in Mpa/m.f. and T in deg. K
Temp. Range
Low* High** Low high
Hydrocarbon A B C D deg. K deg. K deg. F deg. F
Benzene 132.977 -9463.47 -1.50638E-05 -16.9273 278.69 541.7 41.942 515.36
Cyclohexane 244.272 -13539.9 -2.03342E-06 -33.6554 279.70 529.4 43.76 493.22
n-hexane 413.539 -21622.5 -1.26465E-06 -58.2501 177.50 496.7 -140.2 434.36
* HC melting point, deg. K
** Three-phase critical end point, deg. K
Coefficients A through D are taken from the work of Tsonopoulos and Wilson (1)
Table 2 - Illus. 1 Benzene Stripping Case
5 REM THIS PROGRAM RATES A STRIPPING COLUMN
10 REM FOR REMOVING A (VOC) FROM WASTE WATER
15 REM USING FLUE GAS OR STM UNDER ISOTHERMAL-ISOBARIC CONDITIONS.
17 READ A$, B$
18 LPRINT A$, B$
19 LPRINT
20 READ P, T, GPML, SCFMV, PPMWI, PPMWO
25 READ MWG, DL, MWVOC
30 LW = GPML * DL * (60 / 7.48)
32 L = LW / 18.02
35 V = (SCFMV / 379.6) * 60
40 XA = (PPMWI) * (.000001) * (18.02 / MWVOC)
45 XB = (PPMWO / PPMWI) * XA
50 YB = 0
55 YA = (L / V) * (XA - XB) + YB
60 LPRINT "STREAM VOC MOLE FRACTIONS"
65 LPRINT
70 LPRINT "LIN", "LOUT", "VIN", "VOUT"
75 LPRINT XA, XB, YB, YA
80 LPRINT
85 TR = T + 459.7
87 TK = TR / 1.8
90 LNH = 132.977 - 9463.47 / TK - 1.50638E-05 * TK * TK - 16.9273 *
LOG(TK)
92 H = 145.04 * (EXP(LNH))
95 K = H / P
100 LPRINT "H,PSIA/MF AND K="; H, K
105 AF = L / (K * V)
110 YAST = K * XA
115 YBST = K * XB
120 NUM = (YB - YBST) / (YA - YAST)
125 N = LOG(NUM) / LOG(AF)
130 LPRINT
132 LPRINT "P,PSIA AND T,F="; P, T
133 LPRINT
135 LPRINT "GPM", "SCFMV="; GPML, SCFMV
137 LPRINT
140 LPRINT "M/H LIQ AND M/H VAP="; L, V
142 LPRINT
145 LPRINT "NO. OF THEO. STAGES="; N
150 LPRINT
160 ACFMV = SCFMV * (TR / 520) * (14.7 / P)
165 LPRINT "ACFM OF VAPOR="; ACFMV
167 LPRINT
170 DV = (MWG * P) / (10.731 * TR)
171 LPRINT
172 LPRINT "VAPOR DENSITY,LB/CUFT="; DV
173 LPRINT
190 LPRINT
195 LPRINT "MIN V/L"
197 LPRINT
200 VLMIN = (XA - XB) / (YAST - YB)
205 LPRINT "MIN. MOLAR V/L="; VLMIN
206 LPRINT
208 VMIN = (VLMIN) * L * 379.6 / 60
210 LPRINT "MIN VAPOR RATE, SCFM="; VMIN
212 LPRINT
215 LPRINT "OPER. MOLAR V/L="; V / L
220 LPRINT
225 LPRINT "RATIO OVER MIN. V/L="; (V / L) / VLMIN
230 LPRINT
235 LPRINT "M.W. OF GAS AND LIQ. DENS. LB/CUFT="; MWG, DL
240 LPRINT
242 LPRINT "MW OF VOC="; MWVOC
245 LPRINT
250 LPRINT "VOC PPMW-IN AND PPMW-OUT="; PPMWI, PPMWO
260 LPRINT
270 LPRINT "AVG. P(PSIA) AND T (DEG. F) OF TOWER="; P, T
490 DATA BENZENE,WATER
500 DATA 70,85,300,1000,700,0.001
510 DATA 10.28,62.17,78.1
999 END
Output For V = 1000 SCFM
BENZENE WATER
STREAM VOC MOLE FRACTIONS
LIN LOUT VIN VOUT
1.615109EE-04 2.307299E-10 0 8.483463E-03
H, PSIA/MF AND K = 5461.793 78.02561
P,PSIA AND T,F = 70 85
GPM SCFM = 300 1000
M/H LIQ AND M/H VAP = 8302.272 158.0611
NO. OF THEO. STAGES = 31.18374
ACFM OF VAPOR = 219.975
VAPOR DENSITY, LB/CUFT = .1231101
MIN V/L
MIN. MOLAR V/L = 1.281629E-02
MIN VAPOR RATE, SCFM = 673.1845
OPER. MOLAR V/L = .0109383
RATIO OVER MIN. V/L = 1.485477
M.W. OF GAS AND LIQ. DENS. LB/CUFT = 10.28 62.17
MW OF VOC = 78.1
VOC PPMW-IN AND PPMW-OUT = 700 .001
AVG. P(PSIA) AND T (DEG. F) OF TOWER = 70 85
Table 3 - Illus. 2 Phenol Stripping Case
5 REM THIS PROGRAM RATES A STRIPPING COLUMN
10 REM FOR REMOVING A (VOC) FROM WASTE WATER
15 REM USING FLUE GAS OR STM UNDER ISOTHERMAL-ISOBARIC CONDITIONS.
17 READ A$, B$
18 LPRINT A$, B$
19 LPRINT
20 READ P, T, GPML, SCFMV, PPMWI, PPMWO
25 READ MWG, DL, MWVOC
30 LW = GPML * DL * (60 / 7.48)
32 L = LW / 18.02
35 V = (SCFMV / 379.6) * 60
40 XA = (PPMWI) * (.000001) * (18.02 / MWVOC)
45 XB = (PPMWO / PPMWI) * XA
50 YB = 0
55 YA = (L / V) * (XA - XB) + YB
60 LPRINT "STREAM VOC MOLE FRACTIONS"
65 LPRINT
70 LPRINT "LIN", "LOUT", "VIN", "VOUT"
75 LPRINT XA, XB, YB, YA
80 LPRINT
85 TR = T + 459.7
90 LNH = -168.458 - 1158.55 / TR - 1.6222E-05 * TR * TR + 27.76904 *
LOG(TR)
92 H = EXP(LNH)
95 K = H / P
100 LPRINT "H,PSIA/MF AND K="; H, K
105 AF = L / (K * V)
110 YAST = K * XA
115 YBST = K * XB
120 NUM = (YB - YBST) / (YA - YAST)
125 N = LOG(NUM) / LOG(AF)
130 LPRINT
132 LPRINT "P,PSIA AND T,F="; P, T
133 LPRINT
135 LPRINT "GPM", "SCFMV="; GPML, SCFMV
137 LPRINT
140 LPRINT "M/H LIQ AND M/H VAP="; L, V
142 LPRINT
145 LPRINT "NO. OF THEO. STAGES="; N
150 LPRINT
160 ACFMV = SCFMV * (TR / 520) * (14.7 / P)
165 LPRINT "ACFM OF VAPOR="; ACFMV
167 LPRINT
170 DV = (MWG * P) / (10.731 * TR)
171 LPRINT
172 LPRINT "VAPOR DENSITY, LB/CUFT="; DV
173 LPRINT
190 LPRINT
195 LPRINT "MIN V/L"
197 LPRINT
200 VLMIN = (XA - XB) / (YAST - YB)
205 LPRINT "MIN. MOLAR V/L="; VLMIN
206 LPRINT
208 VMIN = VLMIN * L * 379.6 / 60
210 LPRINT "MIN VAPOR RATE,SCFM="; VMIN
212 LPRINT
215 LPRINT "OPER. MOLAR V/L="; V / L
220 LPRINT
225 LPRINT "RATIO OVER MIN. V/L="; (V / L) / VLMIN
230 LPRINT
235 LPRINT "M.W. OF GAS AND LIQ. DENS. LB/CUFT="; MWG, DL
240 LPRINT
242 LPRINT "MW OF VOC="; MWVOC
245 LPRINT
250 LPRINT "VOC PPMW-IN AND PPMW-OUT="; PPMWI, PPMWO
260 LPRINT
270 LPRINT "AVG. P(PSIA) AND T (DEG. F) OF TOWER="; P, T
490 DATA PHENOL,WATER
500 DATA 30,250,63.6,5000,55,13.5
510 DATA 18.02,58.8,94
999 END
Output for V = 5000 SCFM
PHENOL WATER
STREAM VOC MOLE FRACTIONS
LIN LOUT VIN VOUT
1.054362E-05 2.587979E-06 0 1.67575E-05
H,PSIA/MF AND K = 56.73096 1.891032
P, PSIA AND T,F = 30 250
GPM SCFM = 63.6 5000
M/H LIQ AND M/H VAP= 1664.674 790.3055
NO. OF. THEO. STAGES= 3.995301
ACFM OF VAPOR = 3343.779
VAPOR DENSITY, LB/CUFT = 0.0709841
MIN V/L
MIN. MOLAR V/L = .3990126
MIN VAPOR RATE, SCFM = 4202.336
OPER. MOLAR V/L = .4747508
RATIO OVER MIN. V/L = 1.189814
M.W. OF GAS AND LIQ. DENS. LB/CUFT = 18.02 58.8
MW OF VOC = 94
VOC PPMW-IN AND PPMW-OUT = 55 13.5
AVG. P(PSIA) AND T (DEG. F) OF TOWER = 30 250
AUTHOR’S BACKGROUND
Dr. Charles R. Koppany is a retired chemical engineer formerly employed by C F Braun
& Co/ Brown & Root, Inc. from 1965 to 1994. While at Braun he served in both the
Research and Process Engineering departments. Dr. Koppany has also done part-time
teaching in the Chemical Engineering Departments at Cal Poly University Pomona and
the University of Southern California. He holds B.S., M.S. and PhD degrees in Chemical
Engineering from the University of Southern California and is a registered professional
engineer (Chemical) in the state of California.