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.

crkoppany@aol.com