MODIFICATION OF CARBON BED SIZING


                         ALGORITHM 'BED.SIZE'
FINAL REPORT
                             A Report Prepared For:




                                USEPA OAQPS EAB



                            RESEARCH TRIANGLE PARK



                                   N. C., 27709
                                      Prepared By:


                      CHAS,  T,  MAIN,  INC,

                                     Charlotte, NC

                                     JULY 14, 1988
                                           (AIAIIV]
                                           >	IWtk'l	'
1893

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MODIFICATION OF CARBON BED SIZING ALGORITHM "BED SIZE"
Prepared for:
USEPA OAQPS EAB
Research Triangle Park,
N.C., 27709
Prepared by:
W. L. Klotz
Chas. T. Main, Inc.
Charlotte, N.C.
28224
July 14, 1988

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TABLE OF CONTENTS
SUMMARY AND RECOMMENDATIONS ..........................................
1.0 INTRODUCTION[[[
2.0 BREAKTHROUGH PREDICTION ................ ..................... ....
3.0 STEAM REGENERATION HEEL PREDICTION ..............................


3.1 REGEN Predictions................................ . . . . . . . . . .
4.0 VENDOR CONTACTS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.0 RESULTS AND CONCLUSIONS.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.0 REFERENCES
APPENDIX A
.......... .................................... ........
APPENDIX B

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LIST OF TABLES
1.
Breakthrough Curve Data Analysis............................ 7
LIST OF FIGURES
1.
LB STEAM/LB SOLVENT VS. STEAMING TIME.................. .... 15
2.
RELATIVE ORGANIC LOAD REMAINING VS. STEAMING TIME...... .... 16
3.
LB ORGANIC REMOVED / LB CARBON VS. STEAMING TIME ....... ... 17
ii

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of ~W\
~~~O( ~
~'
SUMMARY AND RECOMMENDATIONS
The program BED_SIZE for sizing carbon beds has been reviewed in
regard to available experimental and vendor data for dynamic breakthrough
from the literature. Any predictive approach relating to carbon may be
expected to show at least a 30 per cent variability simply because of the
variable nature of the manufactured carbon product itself. BED SIZE has
been validated within these limits for low inlet concentrations of an
organic solvent, less than 300 ppm, but overestimates bed length for
higher concentrations. It has been found that BED_SIZE provides a basis
for the rule of thumb factor of 2 used by vendors, as a result of this
overestimation, in conventional bed sizing calculations for the higher
inlet concentrations. Analysis of breakthrough data has been com~licated
by the use of multiple types of carbons for which detailed isotherm data
were not available. Data examined were of two types:
1.
Respirator cartridge or air filter element breakthrough.
2.
Sovent recovery application breakthrough.
~:-
Examination of data in the first category generally did not permit an

appropriate comparison, because cartridges were apparently tested directly

without calming sections prior to the ~arbon. A_This may have resulted in
(u~~ \~4 ~ ~ ~~~~ 0.. c:J. IW},.") s~~.
Because a linear isotherm is assumed, BED_SIZE predicts that the con-
centration profile in the bed flattens out as it progresses through the
1

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/
~ ~'
~ 4'{f
) ~ol) ~~ () if \)~ I
-/ f' Y Z ~ I d
"0 vff ~ ~,oJb -,->~~~' 10'
~/ ~ ~ . ~t' I ~ L, ~
if {>l~ ~ //~ ~) (,;
.7 J V> yY.;; ~,jt( rf v--
l f/;'/ f I ~~ ~ .;'"(
J / r! Y ""~ ../ vi of",#,
/!;f f' .!:-) /- 'i-
~ Jj ;f r-
~ ~ /:} ~

~
-...r
c/

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~j:t fu 
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1.0
INTRODUCTION
The purpose of this report is to describe work performed for the USEPA
OAQPS Economics Analysis Branch under MAIN's project no. 4268-1,
"Modification of Computer Algorithm "BED_SIZE", with demonstration of va1-
idation data.
The scope of the project requires the following activities:
1. Compare the bed thickness, overall removal efficiency, working
capacity, and other outputs of the BED_SIZE model with experimental ad-
sorption data for 5 adsorbates to verify breakthrough curve prediction.
2. Establish the specifications of a well-regenerated carbon bed in
terms of "heel" and input the estimates for BED SIZE.
3. Send copies of BED SIZE to 3 vendors and solicit comments.
4. Send a draft letter report by February, 1988.
Data are reviewed in this report for the following six compounds:
o acetaldehyde7
o acetone17
o benzene9-13,18
o 1-bromobutane6
o carbon tetrach10ride2
o trichloroethylene16,19
Additional data of very inclusive nature have also been found for
ethyl acetate and butyl acetate4. G. O. Nelson et al. obtained break-
through curve data for over 121 compounds. Section 2 of this report
describes breakthrough curve data analysis. Breakthrough curve data for
3

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four of the six compounds selected have been taken for carbons other than
BPL carbon, so that computational procedures have been reviewed and
developed to either use isotherm data for the carbon to characterize it
with respect to BPL carbon for model calculation~, or to utilize the
breakthrough data themselves for this purpose. A single breakthrough
curve determines one isotherm data point, and this may be all that is
required for correlation of carbons.
Extensive steam regeneration data are available for trichloroethylene
and benzene, and the MSA npackage Adsorber Studyn16 provides a computa-
tional procedure for steam load vs. regeneration level that can be applied
to the remaining three compounds selected. This approach is described in
Section 3 of this report. Thermal effects in steam regeneration are in-
corporated in BED_SIZE based on the Calgon isotherm equation for BPL car-
bon. Also, review of Calgon's model for isotherm prediction has been con-
sidered for incorporation in predicting bed depth in the BED_SIZE code.
The Calgon model apppears to offer advantages to the D-R equation, al-
though it is more complex mathematically and so requires greater amounts
of experimental data for correlation.
Copies of BED SIZE have been mailed to vendors to solicit their
comments.
Follow-up contacts have been made to incorporate their comments
in this report in its, final version and the BED_SIZE code.
Vendors
contacted are Calgon Carbon, Westvaco, Envirotrol, and Charcoal Service
Corp. Vendor responses appear to also indicate the overestimation of bed
depth by BED_SIZE by roughly a factor of two.
Vapor degreaser
manufacturers, solvent recovery operations, and carbon filter
manufacturers have been contacted. Charcoal Service Corporation has
intiated a testing program, and may be a source of future data. Vendor
contacts are described in Section 4, and results and conclusions are given
in Section 5 of this report.
4

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2.0
BREAKTHROUGH PREDICTION
Table 1 contains a summary of the data analysis for the breakthrough
curve data referenced as below:
o acetaldehyde7
o acetone17
o benzene9-13,18
o l-bromobutime6
o carbon tetrachloride2
, -

o trichloroethylene16,19
Analyses of these data is complicated by the fact that the D-R equation is
a two parameter equation, requiring a structural constant k and a volumet-
ric capacity Yo to characterize the carbon. No information on the struc-
tural constant k was available for carbons other than BPL with the excep-
tion of data taken by G. O. Nelson et al.lO-~~. These data were taken
for respirator studies and U~d ecise ~hetisotherm descri~tion
We ~ ......~ 0vV ~"-~
approach taken for BED_SIZE. Ove 21 compounds were tested in these
studies9-l3,18. Urano et al.20 have developed a procedure to estimate
adsorption capacity for a variety of carbons based on knowledge of the per
cent micropore volume (pores less than 32 A in cross section). Micropore
volume is readily available from the vendor.
~~
most,~commercial c::ululIIlIS can be approximated as 2.8 x 10-9 mo12jJ2.
M1I.. iW\ S; o..e do. ~ Ui-("~~
Q, the capacity of the carbon in kgjkg, is given by:
Urano indicates that k for
Then
(~~~
log Q - log (v32 + 0.055)(do - at) - [(4.6 x 10-7)(273 + t)2jp2] x
[a - bj(c + t) - log 0.062(273 + t)CjM]2
"
w
(1)
where v32 - volumetric capacity of micropores < 32 A
do - adsorbate liquid density
5

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a - coefficient of thermal expansion of adsorbate liquid
p - affinity coefficient from D-R equation
a, b, c - coefficients in Antoine equation for adsorbate
C - adsorbate gas phase concentration
MW - adsorbate molecular weight,
all in consistent units.
This approach of Urano has not been evaluated
here, but could be used for any carbons encountered, based on Urano's

conclusions, to a high degree of accuracy. ~ ~~ ~'JL. \.Ui) o.J:) ~ t,.>V\.e. ~~lo..~,
v ~
To adjust the prdiction of BED SIZE for isotherm~iationP, the D-R
, - o...~ \~ ~"le.- .
equation has been treated as essentially a one parameter equation to give
'"
the results shown in Table 1 by two approaches. In the first approach, Wo ~
-~ok'<..~ \...~~,~
was adjusted to give the correct saturation capacity~at the inlet

concentration in the calculated results. This is shown in Table 1 as the

adjusted calc. value. In the second approach, the bed size itself was --~~
e.v-(\'v'c..iJ
adjusted to reflect the proportion of observed and predicted saturation l.Mdk~\Jl\U)

capacity. The second approach gave better agreement in predicted bed ~~or-

size.
Calculated isotherms for these adsorbates are attached in
appendix A
for both the D-R equation and the Calgon isotherm. Acetaldehyde was
tested at low inlet concentration and the predicted isotherm was roughly
linear. The acetaldehyde data are included to show isotherm conditions
under which BED_SIZE should give an accurate prediction. The D-R and
Calgon isotherm shapes are qualitatively similar, but the Calgon method
should be more accurate for BPL carbon. References for acetone and
trichloroethylene discuss the design procedure involved as well as the bed
parameters.
Data for benzene, l-bromobutane, and carbon tetrachloride are essen-
tially respirator studies, involving short packed beds and small mesh
carbons. The benzene data, and in fact all of Nelson's data, may have
suffered from the deficiency that calming sections were not used prior to
the bed, so that end effects could have been significant. Data for
l-bromobutane were taken at low inlet concentrations, and appear to
confirm the validity of BED_SIZE at these concentrations.
6

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    TABLE 1. BREAKTHROUGH CURVE DATA ANALYSIS      
     Cf~')~\1"" ~<-   ~uJ.)   ~~~1.4  
     Tb OR ~. Cb   ~C..~   Wsat. Co.etN.. ~  
 COMPOUND CARBON T VOID Dp Vo BED  Wcap BED BED
    DEG C CYCLE PPMV PPMV SPACE (MESH) FPM DENSITY   ~..sIZB SI.ZE
     TIME     IN.   LB/CU.FT. (LB/LB) (%)  (IN) ADJ.
     (HR)          . ~   (IN)
               Wy$ 
  J4;i                ~~
 1. ACETONE A 20 6.92 1500 15 0.3 (4X6) 75  28 0.2.6  17 . 211.5-
          0.157        
        ~-~~. FOR-BPL CARBON-- Q --11. 6 48.6 56 
           ADJUSTED~CALC.-- '0~~6 35.3 '. (":i~ '
             ''IJ- Q      
 2. ACETALDEHYDE PCB 30 17.3 28 0.28 0.3 (12) 32.3  28 0.00839   18 7.1
          0.0661        
          CALC. FOR BPL CARBON-- 0.000016   3741 
           ADJUSTED CALC.-- NA MUST CHANGE k 
I                AS WELL AS Wo 
-..J                
I 3. BENZENE TYPE 1 22 1.22 1000 10 0.3  54.4  23.4 0.327 21.4 1.79 2.7
               " 
          0.065        
          CALC. FOR BPL CARBON-- 0.1745 52.4 5.1 
           ADJUSTED CALC.-- 0.327 41.1 3..5 
 4. 1-BROMOBUTANE BPL 35 0.275 4335 43.35 0.3  29.5  32.4 0.363   0.858 2.32
          0.0548        
          CALC. FOR BPL CARBON-- 0.473 34.8 1.78 
           ADJUSTED CALC.-- 0.363 39.2 2..05 
 5. CARBON TETRA- BPL 37.7 1.1 1370 13.7 0.3 (8X10) 18.6  32.2 0.37   1.06 2.34
  CHLORIDE        0.0855        
          CALC. FOR BPL CARBON-- 0.424 30.4 2.04 
           ADJUSTED CALC.-- 0.37 32.2 2.2 
 6. TRICHLORO- BPL V 22 6.99 3000 30 0.3 (4X10) 110  31 0.363 92.2 21.3 74.4
  ETHYLENE        0.111        
          CALC. FOR BPL CARBON-- 0.486 61.4 55.6 
           ADJUSTED CALC.-- 0.363 66.2 69..1 

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TABLE 1 (CONT.).
BREAKTHROUGH CURVE DATA ANALYSIS
COMPOUND CARBON T Tb OR Co Cb VOID Dp Vo BED Wsat. Wcap BED BED
   DEG C CYCLE PPMV PPMV SPACE (MESH) FPM DENSITY   SIZE SIZE
    TIME    IN. LB/CU.FT. (LB/LB) (%) (IN) ADJ.
    (HR)           (IN)
7. 1-BROMOBUTANE BPL 35 0.033 364.8 3.65 0.3   29.5 32.9 0.245  0.449 0.79
        0.0548      
        CALC. FOR BPL CARBON-- 0.35 3.23 0.55 
         ADJUSTED CALC.-- 0.249 4.23 0.61 
8. CARBON TETRA- BPL 37.7 0.466 5660 56.6 0.3 (8X10) 13.7 32.2 0.416  1.06 2.36
 CHLORIDE       0.0855      
        CALC. FOR BPL CARBON-- 0.525 34.6 1.87 
         ADJUSTED CALC.-- 0.416 38.5 2.11 
I               
co               
I               

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3.0
STEAM REGENERATION HEEL PREDICTION
Regeneration of carbon is an economic necessity for inlet
concentrations above 10 ppmv. Unfortunately, vendors have investigated
steam regeneration requirements primarily for high profit return
applications involving either expensive solvents or solvents at high con-
centration (>1000 ppmv). Steam regeneration is the most prevalent method,
but hot air, hot inert gas, and high temperature oxidation processes are
also used. Steam is the method of choice when the enthalpy of adsorption
of air contaminant is not too high (less than about 15 kca1/mo1e) and the
adsorbate is relatively immiscible with water, reducing water pollution
and permitting economic recovery. Low temperature steam is generally
used, which is often available in considerable quantity from plant power
supplies. The advantage of using steam rather than a hot gas is that the
heat of condensation of the steam initially aids in removing an organic
from carbon. During the later cooling period, air may then be used to
remove the condensed steam and cool the bed. If the inlet concentration
of the organic was low 200 ppmv) the amount of steam required may be
very large. In this case, hot gas regeneration may be more economical.
In some cases, this hot gas regeneration results in a gas stream of
sufficicient1y high concentration, acting as a preconcentrator, that a
conventional carbon system with steam regeneration can then be used.
\\.\'
,jl.' ~~
v'\~'
~ ~~~j'
~~~~
~ Iv~
(
In this report, a calculational procedure for the steam load for re-
generation is described as adapted from the MSA Package Adsorber Study
("Package Sorption Device System Study", 1973)16. This procedure is an
equilibrium stage model which considers the heat of adsorption and the
condensation of the steam in the bed. Only low grade steam (close to at-
mospheric pressure) is considered here, and the following restrictions and
assumptions are made, similar to the MSA procedure:
.1.
Steam is the only regenerating agent considered in the procedure.
2.
There is no interaction between the adsorbate and the steam.
9

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3.
The latent heat of adsorption of water on carbon can be neglected.
4.
The heat capacity of steam and water is the same.
5.
The Polanyi potential determines the heat of desorption, so there
is no hysteresis.
6.
Mass transfer effects can be neglected.
7.
The quality of the steam is low enough that the heat load for
re-
moval of condensed steam can be neglected.
The MSA report provides a detailed flow diagram for steam regeneration in
which the bed is partitioned into 32 equilibrium stages. To reduce compu-
tation time, the number of seqments was reduced to 7 for the BED_SIZE re-
generation procedure, titled "REGEN". The basis of the computation is the
estimation of the heat of desorption from the Polanyi adsorption
potential. The MSA report derives this as:
A-
T J2
2. 3 '\7~ I In, I p
(2)
where T - temperature, K
Vm - molar volume of adsorbate, cm3/mole
Po - vapor pressure of liquid adsorbate at T
p - equilibrium vapor pressure of adsorbate
This definition is equivalent to that of BED SIZE.
is then:
The heat of adsorption
Q -
2.3 VmRC
M
J "'2
~~
"'1

Btu/lb mol-OF
(3)
where Q - Btu heat absorbed
R - gas constant, 3.42
Wc - lb carbon in bed
'" - lb organic/lb carbon
10

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~l, ~2 - Ib organic/lb carbon at beginning and end of stage
A - Polanyi adsorption potential
The integral above is evaluated as a definite integral as follows:
J ~2
A~

~l

where
- (Ca - C9)(~2 - ~l) + C9 (~21~1 - ~ll~l)
(4)
C9 -
A2-AI
In (~2/~1)
1~
~
Ca - Al - C9 In ~l
Other equations for the REGEN routine' were derived from the
requirements of constant pressure, mass balance, and heat balance as
follows:
Open System Constant Pressure
Total system pressure is 1 atm.
For an open system,
Porgl + Psteaml - 1 atm - 14.7 psia
Porg2 + Psteam2 - 1 atm - 14.7 psia
(5)
(6)
Equilibrium Assumption
For the case of counterflow regeneration, the universally practiced
approach, it may be assumed that the gas flow enters a new seqment of the
bed after equilibration with the previous segment and leaves this new
seqment in a state of equilibrium. The amount of organic removed is then
determined by the difference in the two equilibrium concentrations in the
gas phase and the gas flow rate and temperature. From this assumption,
Porg2 - Porg*(intial state of' segment)
(7)
11

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Mass Balance
Mass balances can be written for the organic desorbed and for the
steam condensed. If the temperature is higher than 373.15 K no steam is
condensed. These equations are as follows:
~
[ S V2
RT2
Porg2
S V1 Porg1 ]
RT1
(8)
MWl1t
where S - cross-sectional area (ft2)
loVap - amount of organic removed (lb)
T1,T2 - inlet and exit temperature, respectively (K)
V1,V2 - inlet and exit velocity (ft/min)
R - universal gas constant, 19.32 psi-ft3/1b. mo1.-K
and
Qc -
6(:.
[ S V2
RT2
Psteam2
- S V1 P steam1]
RT1
(9)
where Qc - amount of steam condensed (lb)
Energ;y Balance
The final equation required for solution of the counterflow regenera-
tion is obtained from an energy balance involving the steam, adsorbate,
and the carbon bed.
~
SCp
P1 MW
These equations are put in the following form:
(T2-T1) l1t -
loVap Mivap
- A Qc - WcCp (carbon) (T2-T1) l1t
(10)
C1 Xl
C4 X3
X2 + C7 X3
+ C2 X2 - C3
+ C5 X2 - C6
- Cs Xl - C9
(11)
(12)
(13)
12

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where Xl - c.>yap

X2 - V2/T2

X3 - Qc

~ - T2

C1 - R/S MY l1t

C2 - Porg2

C3 - V1 Porg1/T1

C4 - R/S MYsteam l1t

C5 - Psteam2

C6 - Psteam1 V1/T1

C7 - 359/MYsteam S 273.15 l1t

Cs - 359/MY S 273.15 l1t

C9 - V1/T1
These equations are solved sequentially as follows:
  C3-C2 X2    
 Xl = C1    (14)
  C6- C5 X2    
 Xj = C4    (15)
 C7 C5 ~ ) X2 - (C9 - ~ - CB C:~~ ) '.1\ 
(1 - C3 C1 C3 (16)
The inputs required for steam regeneration calculations (REGEN) are
the initial bed loading, initial bed temperature, and flow rate of steam.
The output is an average heel within the bed, condensed steam profile
within the bed, adsorbate concentration profile within the bed, and all of
these as a function of time.
Several "canned" mathematical algorithms were used within the program
REGEN. To solve the Ca1gon polynomial and find the equilibrium vapor
pressure for a given carbon loading, the Laguerre a1gorithm22 was used.
This method works well with polynomials. The Ca1gon polynomial is fifth
degree, and of the five roots, only one was real. Imaginary roots were
rejected by recognizing that they occured in conjugate ,pairs, rather than
13

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relying on the magnitude of the imaginary part of the root to distinguish
real from imaginary.
To solve the recursive non-linear equations for steam load, the Brent
method was used2l. This method requires a bracketed range for roots, and
is more robust than methods relying on Newton-Raphson algorithms.
A release has been requested from the source23 for these algorithms
~ and their public domain application. No difficulty is currently
- ~anticiPated in obtaining this release. " LA 0;::- &",,'U
'3.1 REGEN Predictions r- ~ (\. U
~~
Figures 1 through 3 show predictions of the program REGEN for the
trial case of acetone regeneration from BPL carbon. Figure 1 shows pounds
of steam per pound of solvent removed vs. the steaming time. It can be
seen that the "energy cost" of removing solvent increases as higher
removals are reached, nearly doubling in 25 hours time from onset of
steaming. Figure 2 shows that the organic load on the carbon dropped 60
per cent in this period.
Figure 3 shows the pounds of acetone removed per pound of carbon vs.
steaming time. The slope of the curve in this figure is decreasing with
time, again showing that it requires more energy to remove organic at the
lower residual amounts.
The MSA study16 describes steam regeneration calculations for
trichloroethylene, propanone, and 4-methyl,2-pentanone. For propanone, to
drop the loading from 0.12 to 0.06 1b/solvent per 1b carbon would require
0.35 lb steam/lb of carbon for a BPL type V carbon, which is equivalent to .-.-Jc.P-- J
0.35/(0.12-0.06) or~8 1b ~team/lb organic. From Figure 3 in this l. ~u.r1r
report, to remove 0.06 1b acetone pe~ 1b of carbon would require 200 min. -of~
From Figure 1, this is equivalent to ,19 lb steam/1b carbon. This steam ~
-...:-
requirement would appear to be high for acetone as compared to propanone. ;(.
The cause of this has not yet been determined.
A listing of the REGEN source code is provided in Appendix B. A list-
ing of BED_SIZE as used in the calculations for this report is given in
Appendix C.
14
(

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   LB. STEAM / LB. SOL VENT  
    YS. STEAMING TIME   
 29       
 28       
 27       
 26       
I-        
z 25       
w       
>        
..J        
0 24       
en       
cD        
..J 23       
... "       
V1 :E        
< 22       
w       
I-        
en        
cD 21       
..J        
 20       
 19       
 18       
 17       
 0 0.2 0.4 0.6 0.8 1 1.2 1.4
     (Thousandsl   
    STEAMING TIME (MINI   
FIGURE 1

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  0.9
 " 
 z 
 z 
  
 :E 0.8
 LI.I
 a: 
 Q 
 < 
 0 
 ..J 
 U 0.7
...... Z 
0\ 
 < 
 " 
 a: 
 0 
 LI.I 0.6
 >
 i= 
 < 
 ..J 
 LI.I 
 a: 
  0.5
0.4
RELA TIVE ORGANIC LOAD REMAINING
1
VS. STEAMING TIME
o
0.2
0.4
1.2
0.6 0.8
(Thousands)
STEAMING TIME (MINI
FIGURE 2
1
1.4

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    LB. ORGANIC REMOVED / LB. CARBON 
     VS. STEAMING TIME   
  0.32       
  0.3       
  0.28       
  0.26       
 z        
 0 0.24       
 m       
 a::        
  0.22       
 (.)       
 cD 0.2       
 ..J       
 "        
 c 0.18       
 UJ        
 > 0.16       
 0       
.... ~        
...,J        
 UJ 0.14       
 a::       
 (.) 0.12       
 Z       
         
 " 0.1       
 a::       
 0 0.08       
 cD       
 ..J        
  0.06       
  0.04       
  0.02       
  0       
  0 0.2 0.4 0.6 0.8 1 1.2 1.4
      IThousands) .   
     STEAMING TIME IMIN)   
FIGURE 3

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4.0
VENDOR CONTACTS
Vendors contacted include Ca1gon Carbon, Pittsburgh PA; Envirotro1,
Sewick1ey, PA; Westvaco, Covington, Va., and Charcoal Service Corp., Bath,
NC, who have all been supplied with copies of the program BED SIZE for
comments.
Additional vendors contacted include the Society for Manufacturing
Engineers, in connection with vapor degreasers; Baron Blakeslee and Dedert
in connection with solvent recovery; and numerous smaller vendors and
distributors.
Few of these smaller vendors have the data required for
model comparison, or are reluctant to release it, as it may have applied
to a specific client.
A specific test case has been run by Westvaco.
case were as follows:
The inputs for this
No. of terms for inversion series - 20
Include humidity effects - yes
Water soluble in organic - no
Temperature = 25 c
Breakthrough time - 2 hours
Challenge concentration - 150 ppm
Adsorbate - toluene
Bed void fraction - 0.35
Pellet size - 0.2 inches
Superficial velocity - 85 fpm
Bed density - 24 1b/ft3
Outputs from Bed Size were as follows:
Working Capacity is 19.06 per cent
Pressure Drop is 18.01 per cent
Estimated upper bound for error in working capacity is 71.3 per cent from
linear isotherm
18

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" "".,:. - .:~ ~l . '-'-'~',...'..,A. '..:-,; ~; ';"!.,.;.:.....JI ..... .~.:..J,~""_I._''''''~''''",,; ., ;>~.;.... ...., <" . ~ '::... u' . .
~ 1... i'
BPL carbon efficiencey is 99.7 per cent
The bed thickness for approx. 150.0 ppm breakthrough
2.00 hours: 9.205 feet.
concentration after
According to Westvaco, in practice, a two (2.0) foot bed should be
sufficient. The model has been examined to find the source of
discrepancy, and the following observations resulted:
1. A discrepancy existed in the souce code used by Westvaco and that used
for the calculations reported here, in the expression for H (labeled
statement number 130).
Apparently, an older version of BED SIZE was sent
inadvertently. After this correction, the following run was obtained with
the same inputs used by Westvaco:
Working Capacity is 14.77 per cent
Pressure Drop is 13.47 per cent
Estimated upper bound for error in working capacity is 75.1 per cent from
linear isotherm
BPL carbon efficiency is 99.7 per cent
The bed thickness for approx. 150.0 ppm breakthrough concentration after
2.00 hours:
6.882 feet.
Saturation capacity of carbon:
31.43 1b/1b
2. Westvaco had utilized humidity effects. The program was rerun without
these effects to see the sensitivity. In this case, with all other inputs
the same, the following run was obtained:
Working Capacity is 28.10 per cent
Pressure Drop is 7.08 in. water
Estimated upper bound for error in working capacity is 63.47 per cent from
linear isotherm
BPL Carbon efficiency is 99.6 per cent
The bed thickness for approx. 150.0 ppm breakthrough concentration after
19

-------
2.00 hours:
3.617 feet
Saturation capacity of carbon:
31.43 1b/1b
A roughly 100 per cent increase in bed length because of humidity effects
seems excessive. Apparently, these effects are overestimated. The last
run, which predicts a bed length of about 4 ft., is again a factor of 2
greater than that observed.
Yestvaco indicates that a model with the inputs of bed size, and
adsorption and steaming conditions, and the outputs of adsorption time
with steam cycling and breakthrough profiles, would be very useful. The
text of their response is shown in Appendix D.
20

-------
5.0
RESULTS AND CONCLUSIONS
Referring to Table 1, it can be seen that predicted working capacities
were either higher (acetone and benzene) or lower (trichloroethylene) than
that observed, where available. Predicted bed sizes were roughly twice
that observed, unless an adjustment factor for the true isotherm satura-
tion capacity were included, as shown in the right most column of Table ~
With this factor, close agreement is seen for acetone and acetaldehyde, ~~
while the respirator-type test results for benzene, 1-bromobutane, and
carbon tetrachloride remain high. The predicted result for
trichloroethylene, after adjustment, remains exceptionally high by a
factor of 3. The TCE data may in fact be more a description of an actual
design procedure than observed, results.
High values for the predicted bed size may be due to the flattening
out of the concentration wave for a linear isotherm as a result of axial 
dispersion. Because adsorption is proportional to the slope of the
isotherm, a concave downwards (favorable) isotherm results in a steepening
concentration profile that counteracts axial dispersion.
not considered in BED SIZE.
This effect is
Agreement of predicted results for acetone with those published
indicates that BED_SIZE may correctly include the factor of 2 commonly
used for working capacity in design calculations. The acetone data were
used in conjunction with an estimation of a mass transfer zone of 2 inches
and the factor of 2. BED_SIZE can predict the same bed length but
predicts a mass transfer zone of about 12 inches. The isotherm for ace-
tone is more linear than for some of the other solvents, because of shape
and the lower concentration.
21

-------
6.0 REFERENCES
1.
Basdekis, H. S. and C. S. Parmele, "Control Device Evaluation - Carbon
Adsorption", EPA-450/3-80-027, vol. 5, December, 1980.
2.
Brothers, Paul D., PhD Thesis, NCSU at Raleigh, 1981.
3.
EI-Rifai, M. A., M. A. Saleh, and H. A. Youssef, "Steam Regeneration
of a Solvents Adsorber", The Chemical Engineer, pp. 36-38 (1973).
4.
Fraust, C. L. and E. R. Hermann, "The Adsorption of Aliphatic Acetate
Vapors onto Activated Carbon", Amer. Ind. Hygiene Assoc. J., 494-499
(1969).
5. Hemenway, D. R., B. J. Fitzgerald, and T. Paret, "Effects of intermit-
tent contaminant loading on the bed capacity of activated carbon filters",
Am. Ind. Hyg. Assoc. J., 43(9): 686-691 (1982).
6.
Klotz, William L., PhD Thesis (in preparation), NCSU at Raleigh, 1988.
7. Kyle, B. G., and N. D. Eckhoff, "Odor Removal from Air by Adsorption
on Charcoal", NTIS PB 236 928, September, 1974.
8.
Mastroianni, M. L., and S. G. Rochelle, "Improvements in Acetone Ad-
sorption Efficiency", Environmental Progress, ~(1), 7-13 (1985).
9. Nelson, G. O. and C. A. Harder, "Respirator cartridge efficiency
studies: IV. Effects of steady-state and pulsating flow", Amer. Ind. Hyg.
Assoc. J., 33, 797 (1972).
10.
Nelson, G. o. and C. A. Harder, "Respirator cartridge efficiency
studies:
V. Effect of solvent concentration."
22

-------
11.
Nelson, G. O. and C. A. Harder, "Respirator cartridge efficiency
studies:
VI. Effect of concentration".
12. Nelson, G. 0., R. E. Johnson, C. L. Lindeken, and R. D. Taylor,
"Respirator cartridge efficiency studies: III. A Mechanical Breathing
Machine to Simulate Human Respiration", Amer. Ind. Hyg. Assoc. J., 33, 745
(1972).
13. Nelson, G. O. and D. H. Hodgkins, "Respirator Cartridge Efficiency
Studies: II. Preparation of Test Atmospheres", Amer. Ind. Hyg. Assoc.
J., 33, 110 (1972).
14.
Nelson, James H. and Y. H. Yoon, " Application of Gas Adsorption
Kinetics-I. A Theoretical Model for Respiration Cartridge Service Life",
Amer. Ind. Hyg. Assoc. Journal, 45(8), 509-516 (1984).
15. Nelson, James. H. and Y. H. Yoon, "Application of Gas Adsorption
Kinetics-II. A Theoretical Model for Respirator Cartridge Service Life and
Its Practical Applications", 45(8), 517-524 (1984).
16.
"Package Sorption Device System Study", NTIS PB-221 138, prepared by
MSA, Inc., 1973.
17. Parmele, C. S., Y. L. OConnell, and H. S. Basdekis, "Vapor phase Ad-
sorption Cuts Pollution, Recovers Solvents", Chemical Engineering, pp.
59-70, December, 1979.
18.
Ruch, Y. E., G. o. Nelson, C. L. Lindeken, R. E. Johnsen, and D. J.
Hodgkins, "Respirator Cartridge Efficiency Studies:
Design", Amer. Ind. Hyg. Assoc. J., 11, 105 (1972).
I.
Experimental
23

-------
19.
Werner, M. D., R. L. Gross, and E. C. Heyse, "Predictive Models for
Gaseous-Phase Carbon Adsorption and Humidity Effects on Trichloroethylene
Adsorption", AD A159 l67/ESL-TR-85-29, August 1985.
20.
Urano, K., .S. Omori, and E. Yamamoto, "Prediction Method for
Adsorption Capacities of Commercial Activated Carbons in Removal of Organ-
ic Vapors", Env. Sci. Technol., 16(1), 10 (1982).
21.
Brent, Richard P., 1973, "Algorithms for Minimization without
Derivatives," Prentice Hall, Englewood Cliffs, N. J., Chapters 3 and 4.
1973.
22.
Ralston, Anthony. and P. Rabinowitz, "A First Course in Numerical
Analysis." vol. 1, J. Wiley, N. Y., 1978.
23.
Numerical Recipes Software, P.O. Box 243, Cambridge Mass. 02238.
24

-------
APPENDIX A
BPL ISOTHERM DATA

-------
D-R ADSORPTION ISOTHERM FOR
  ACETAlDEHYDE AND BPl CARBON 
 0.00012  
 o.ooon  
 0.0001  
; 0.00009  
c(   
(.) 0.00008  
d  
5 0.00007  
~   
~ 0.00006  
~ 0.00005  
~ 0.00004  
IE  
8 0.00003  
:::I   
c(   
 0.00002  
 0.00001  
 0  
 0 20 40
  ADSORBA TE PRESSURE IPPMVI 
 0 CAlCULA TED POINTS 
 0.13  
 0.12  
 o.n  
z   
g 0.1  
~   
c( 0.09  
(.)  
ci 0.08  
~  
\  
CI 0.07  
~  
~ 0.06  
~ 0.05  
~  
IE 0.04  
8 0.03  
:::I  
.C(   
 0.02  
 0.01  
 0  
 0 0.2 0.4
 o
D-R ADSORPTION ISOTHERM FOR
ACETONE AND BPl CARBON
0.6
0.8
1.2
t4
t8
2
1
1TI~U8and8)
ADSORBA TE PRESSURE (PPMV)
CAlCULA TED POINTS
t6

-------
    D-R ADSORPTION ISOTHERM FOR  
       HROMOBUT ANE AND BPL CARBON    
 0.5            
 0.45            
~ 0.4            
G:             
c 0.35            
0            
d             
~ 0.3            
~             
~ 0.25            
~ 0.2            
~             
!z 0.15            
:;:)             
0             
::E 0.1            
C            
 0.05            
 0            
  0 0.2 0.4  0.6 0.8 1 12 t4 t6 t8 2
        (Thousands)     
       ADSORBA TE PRESSURE (PPMV)    
     0 CALCULA TED POINTS     
    D-R ADSORPTION ISOTHERM FOR  
       BENZENE AND BPL CARBON    
 0.3            
 Q.28            
 0.26            
2 0.24            
G: 0.22            
c             
0 0.2            
d            
~ 0.18            
d            
~ 0.16            
~ 0.14            
~ 0.12            
~ 0.1            
!z            
; 0.08            
C 0.06            
 0.04            
 0.02            
 0            
  0 0.2 0.4  0.6 0.8 1 12 t4 t6 t8 2
        (Thousands)     
       ADSORBA TE PRESSURE (PPMV)    
     0 CALCULA TED POINTS     
=
=
!i
~
...
,.

-------
 0.5
~ 
~ 
(,) 0.4
c;
5 
~ 
~ 0.3
~ 
~ 0.2
Ii 
8 
::i 
< 
 0.1
D-R ADSORPTION ISOTHERM FOR
CARBON TETRACHLORIDE AND BPl CARBON
0.6
 o            
  0 0.2 0.4  0.6 0.8 1 1.2 l4 l6 l8 2
        m)usanda)     
       ADSORBATE PRESSURE (PPMV)    
     0 CAlCULA TED POINTS     
    D-R ADSORPTION ISOTHERM FOR  
      TRICHLOROETHYLENE AND BPl CARBON   
 0.5            
 0.45            
i 0.4            
a:             
< 0.35            
(,)            
C;             
~ 0.3            
d            
~             
~ 0.25            
~ 0.2            
~             
~ 0.15            
0.1            
<            
 0.05            
 0            
  0 0.2 0.4  0.6 0.8 1 1.2 l4 l6 l8 2
        (Thousanda)     
       ADSORB A TE PRESSURE IPPMV)    
     0 CALCULATED POINTS     

-------
    D-R ADSORPTION ISOTHERM FOR 
    ACETALDEHYDE AND BPL CARBON 
 0.03      
 0.028      
 0.026      
 0.024      
 0.022      
 0.02      
~ 0.018      
~ 0.016      
0      
C; 0.014      
~      
" 0.012      
C;      
~       
 0.01      
 0.008      
 0.006      
 0.004      
 0.002      
 0      
  0   2 3 4
     !Thousands)  
    ADSORBA TE PRESSURE (PPMV) 
   0 CALCULATED POINTS   
    D-R ADSORPTION ISOTHERM FOR 
    ACETONE AND BPL CARBON 
 0.17      
 0.16      
 0.15      
 0.14      
 0.13      
 0.12      
~ o.n      
m 0.1      
~ 0.09      
0      
C; 0.08      
~       
" 0.07      
C;      
~ 0.06      
 0.05      
 0.04      
 0.03      
 0.02      
 0.01      
 0      
  0   2 3 4
     !Thousands)  
    ADSORBA TE PRESSURE IPPMVI 
   0 CALCULATED POINTS   

-------
!
a:I
~
(J
ci
~
"
ci
~
D-R ADSORPTION ISOTHERM FOR
1-8ROMOBUT ANE AND BPL CARBON
0.5
0.4
0.3
0.2
0.1
 o      
  0   2 3 4
     IThouaandal  
    ADSORBA TE PRESSURE IPPMV) 
   0 CALCULA TED POINTS   
    D-R ADSORPTION ISOTHERM FOR 
    BENZENE AND BPL CARBON  
 0.32      
 0.3      
 0.28      
 0.26      
 0.24      
 0.22      
! 0.2      
a:I 0.18      
~      
(J O.E      
ci      
~ 0.14      
"      
ci 0.12      
~      
 0.1      
 0.08      
 0.06      
 0.04      
 0.02      
 0      
  0   2 3 4
     ITtlOuaandal  
    ADSORBA TE PRESSURE (PPMVI 
   0 CALCULATED POINTS   

-------
 0.4
~ 
III 
~ 
0 0.3
d
~ 
d 
~ 
 0.2
 0.4
~ 
III 
~ 
0 0.3
d
~ 
d 
~ 
 0.2
D-R ADSORPTION ISOTHERM FOR
CARBON TETRACHlORIDE AND BPl CARBON
0.6
0.5
0.1
o
o
2
ITtlOusandsl
. ADSORBATE PRESSURE IPPMVI
o CAlCULA TED POINTS
3
D-R ADSORPTION ISOTHERM FOR
TRICHlOROETHYLENE AND BPl CARBON
0.6
0.5
0.1
o
o
3
2
(Thousands)
AOSORBA TE PRESSURE (PPMV)
o CAlCULA TED POINTS
4
4

-------
    CALGON ADSORPTION ISOTHERM FOR  
     ACETALDEHYDE AND BPL CARBON   
 0.0017          
 0.0016          
 0.0015          
~ 0.0014          
0.0013          
a:           
< 0.0012          
(J          
d o.oon          
5 0.001          
~ 0.0009          
~ 0.0008          
~ 0.0007          
~ 0.0006          
~ 0.0005          
::::I           
0 0.0004          
~          
c( 0.0003          
 0.0002          
 0.0001          
 0          
  0    20   40  
      ADSORBA TE PRESSURE (PPMV)    
   0 CALCULA TED POINTS     
    CALGON ADSORPTION ISOTHERM FOR  
      ACETONE AND BPL CARBON    
 0.01          
 0.009          
Z 0.008          
~          
a:           
< 0.007          
(J          
d           
~ 0.006          
\          
e"           
~           
.~ 0.005          
~ 0.004          
~           
~ 0.003          
8           
~ 0.002          
<          
 0.001          
 0          
  0 0.2 0.4 0.6 0.8 12 14 16 18 2
      ADSORBATE PRESSURE IPPMVI    
   0 CALCULATED POINTS     

-------
    CAlGON ADSORPTION ISOTHERM FOR  
     HROMOBUTANE AND BPL CARBON   
 0.2          
 0.19          
 0.18          
 0.17          
~ 0.16          
0.15          
a:          
C 0.14          
(,)          
C; 0.13          
~ 0.12          
" o.n          
~          
~ 0.1          
0.09          
~ 0.08          
c 0.07          
0(          
!z 0.06          
:) 0.05          
0          
::I 0.04          
C          
 0.03          
 0.02          
 0.01          
 0          
  0 0.2 0.4 0.6 0.8 12 t4 t6 t8 2
      ADSORBA TE PRESSURE (PPMV)    
   0 CALCULA TED POINTS     
    CAlGON ADSORPTION ISOTHERM FOR  
      BENZENE AND BPL CARBON    
 o.n          
 0.1          
z 0.09          
~           
a: 0.08          
c          
(J           
d 0.07          
~          
\           
" 0.06          
~          
~ 0.05          
~          
0.04          
~          
!z 0.03          
:)          
j           
C 0.02          
 0.01          
 0          
  0 0.2 0.4 0.6 0.8 12 t4 t6 t8 2
      ADSORBATE PRESSURE IPPMV)    
   0 CALCULA TED POINTS     

-------
    CAlGON ADSORPTION ISOTHERM FOR  
     CARBON TETRACHLORIDE AND BPL CARBON   
 0.17          
 0.16          
 0.15          
~ 0.14          
0.13          
~ 0.12          
()          
C; 0.1          
5 0.1          
~ 0.09          
Q           
~ 0.08          
~ 0.07          
Q 0.06          
4(          
to- 0.05          
z          
;)           
0 0.04          
~          
4( 0.03          
 0.02          
 0.01          
 0          
  0 0.2 0.4 0.6 0.8 1.2 t4 t6 t8 2
     ADSORBA TE PRESSURE (PPMV)    
   0 CALCULATED POINTS     
    CAlGON ADSORPTION ISOTHERM FOR  
     TRICHLOROETHYLENE AND BPL CARBON   
 0.1          
 0.1          
Z 0.09          
g           
IX 0.08          
4(          
()           
C; 0.07          
~          
\           
CI 0.06          
~          
~ 0.05          
~ 0.04          
~          
~ 0.03          
;          
4( 0.02          
 0.01          
 0          
  0 0.2 0.4 0.6 0.8 1.2 t4 t6 t8 2
      ADSORBATE PRESSURE (PPMV)    
   0 CALCULA TED POINTS     

-------
 o       
  0    2 3 4
      1TI~U8anda)  
     ADSORB A TE PRESSURE (PPMV) 
   0 CALCULA TED POINTS   
    CAlGON ADSORPTION ISOTHERM FOR
     ACETONE AND BPL CARBON 
 0.21       
 0.2       
 0.19      ?
 0.18     
Z 0.11     
i1 0.16       
a: 0.15       
<       
0 0.14       
e,; 0.13     /  
~      
d 0.12       
~ o.n       
~ 0.1       
~ 0.09    /   
0.08       
~ 0.07   /    
IE 0.06   /    
~ 0.05      
< 0.04      
 0.03       
 0.02       
 0.01       
 0       
  0    2 3 4
      IThouaanda)  
     ADSORBATE PRESSURE (PPMV) 
   0 CALCULA TED POINTS   
 0.05
~ 
a: 
< 
(.) 0.04
d
5 
~ 
~ 0.03
~ 
~ 0.02
IE 
~ 
< 0.01
CAlGON ADSORPTION ISOTHERM FOR
ACETALDEHYDE AND BPL CARBON
0.06

-------
 o      
  0   2 3 4
     lTI~uaanda)  
    ADSORBATE PRESSURE IPPMVI 
   0 CALCULA TED POINTS   
    CALGON ADSORPTION ISOTHERM FOR 
    BENZENE AND BPL CARBON  
 0.4      
 0.35      
Z       
2 0.3      
A::      
4(       
0       
ci 0.25      
~      
d       
~       
~ 0.2      
~ 0.15      
!i      
IE       
8 0.1      
::I       
4(       
 0.05      
 0      
  0   2 3 4
     IThouaanda)  
    ADSORBATE PRESSURE (PPMVI 
   0 CALCULATED POINTS   
 0.5
i 
~ 
0 0.4
ci
~ 
\ 
e 
~ 
~ 0.3
~ 
c 
4( 0.2
I- 
z 
:;) 
0 
::I 
4( 
 0.1
CALGON ADSORPTION ISOTHERM FOR
HROMOBUTANE AND BPL CARBON
0.6

-------
  CALGON ADSORPTION ISOTHERM FOR 
  CARBON TETRACHlORIDE AND BPL CARBON 
 0.7    
 0.6    
~     
a: 0.5    
c(    
(J     
c;     
5 0.4    
~     
~     
~ 0.3    
~     
; 0.2    
;    
c(     
 0.1    
 0    
 0 2 3 4
   lTI~uaanda)  
  ADSORBATE PRESSURE (PPMV) 
 0 CALCULA TED POINTS   
  CALGON ADSORPTION ISOTHERM FOR 
  TRICHLOROETHYLENE AND BPL CARBON 
 0.6    
 0.5
Z 
~ 
a: 
c( 
(J 0.4
d
~ 
\ 
CI 
~ 
~ 0.3
~ 
~ 0.2
; 
; 
c( 
 0.1
o
o
2
(Thousandal
ADSORBA TE PRESSURE IPPMV)
o CALCULA TED POINTS
4
3

-------
APPENDIX B
LISTING FOR PROGRAM REGEN

-------
REGEN CODE LISTING
$DEBUG
PROGRAM MAIN
C SUBROUTINE REGEN(PO,T,V,OMEGA,W)
DIMENSION V(8), T(8), OMEGA(8),PSTEAM(8),PORG(8)
COMMON /SEGjVM,FMW,R,S,TINCR,QLAMBDA,CP,CPc,WC,PO,OMSAT
DATA V/8*6S./
DATA PSTEAM/8*14.7/
DATA PORG/8*0.0/
DATA T/8*S73.1S/
OPEN(20,FILE='REGEN.INP')
OPEN(2S,FILE='OMEGA.INP')
OPEN(3S,FILE='VELOCITY.INP')
OPEN(4S,FILE-'TEMP.INP')
OPEN(SO,FILE-'PRN')
5 FORMAT(1S(16X,F1S.6,41X,/
READ(20,S)CPc,VM,FMW,R,S ,TINCR,QLAMBDA,CP,WC, PO
6 FORMAT (10X,'INPUT DATA FOR CHECK')
WRITE(*,6)
WRITE(*,S)CPc,VM,FMW,R,S,TINCR,QLAMBDA,CP,WC,PO
OMEGA(1)-6.
OMEGA(2)-20.
OMEGA(3)=40.
OMEGA(4)-SO.
OMEGA(S)-SO.
OMEGA(6)-SO.
OMEGA(7)-SO.
OMEGA(8)-SO.
OMSAT-SO.
TMAX=24.
QC-O.O
TIME-O.
4 FORMAT(lX,'SEGMENT' " VELOCITY, FPM ' " TEMPERATURE, K ' " HEEL
1REMAINING, LB' ,I)
WRITE(SO,4)
DO 20 1-1,7
20 CALL SEGMENT(I,V,T,OMEGA,QC,PSTEAM,PORG)
10 FORMAT (lX,'TIME - ' ,F1S.6,' MINUTES'/)
WRITE(SO,10)TIME
TIME-TIME+TINCR
IF(TIME.EQ.TMAX)GO TO 40
GO TO 30
40 STOP
END
FUNCTION ENTHALPY(OMEGA1,OMEGA2)
COMMON /SEGjVM,FMW,R,S,TINCR,QLAMBDA,CP,CPc,WC,PO,OMSAT
30

-------
C
C THIS FUNCTION CALCULATES THE HEAT OF DESORPTION OF AN ADSORBATE TO
C CONDUCT A HEAT BALANCE FOR STEAM REGENERATION.
C
ENTHALPY-O.
IF(OMEGA1.EQ.OMEGA2) GO TO 20
A1-POLSTAR(OMEGA1)
A2-POLSTAR(OMEGA2)
C9-(A2-A1)/ALOG10(OMEGA2/0MEGA1)
C8-A1-C9*ALOG10(OMEGA1)
POLINT-(C8-C9)*(OMEGA2-0MEGA1)+C9*(OMEGA2*ALOG10(OMEGA2)-OMEGA1*
1 ALOG10(OMEGA1
ENTHALPY-2. 303*VM*WC*6. 156*POLINT/FMW
20 RETURN
END
C
SUBROUTINE SEGMENT(I,V,T,OMEGA,QC,PSTEAM,PORG)
COMMON /SEG/VM,FMW,R,S,TINCR,QLAMBDA,CP,CPc,WC,PO,OMSAT
DIMENSION V(8),T(8),OMEGA(8),PSTEAM(8),PORG(8)
EXTERNAL WET,DRY
C
C
C
C
C
X1-=QSVAP
X2-V2/T2
X3-QC
XTOTAL-O.
QCTOTAL-O.
WSAT--WC/100.*OMSAT
V1-V(I)
V2-V(I+1)
T1-T(I)
T2-T(I+1)
IF(I. EQ .1) THEN
OMEGA1-0.0
ELSE
OMEGA1-oMEGA(I-1)
ENDIF
OMEGA2-oMEGA(I)
C1-R/S/FMW/TINCR
C4-R/S/18/TINCR
10 FORMAT (lX,'I -' ,13,
1 - " F7 . 2)
v - " F6 . 1 , '
T - " F7 . 2 , '
HEEL
C
C THE FOLLOWING PROGRAM STEPS DETERMINE THE AMOUNT OF ORGANIC REMOVED
C WHILE THE CARBON IS DRY, AND THE RESULTING TEMPERATURE CHANGE.
C THE GAS ENTERS THE SEGMENT IN EQUILIBRIUM WITH OMEGA1, AND LEAVES IN
C EQUILIBRIUM WITH OMEGA2
C
IF (OMEGA1.NE.0.0) THEN

-------
PORGl-2.303*VM*POLSTAR(OMEGA1)/Tl
PORGI-EXP(PORG1)
PORGI-PO/PORGl
PORGI-AMIN1(PORG1,14.7)
ELSE
PORGI-O.O
ENDIF
PSTMl-14.7-PORGl
C3..Vl*PORG1/Tl
C6-PSTM1*Vl/Tl
IF(T2.EQ.373.15)GO TO 25
OM20LD-OMEGA2
RUP-T(l)
RLOW..50.
T2-ZBRENT(DRY,RLOW,RUP,2.,OMEGA2,Cl,C3,C4,C6,Tl)
IF (T2.LE.373.15) T2-373.15
PORG2-2.303*VM*POLSTAR(OM20LD)/T2
PORG2-EXP(PORG2)
PORG2-PO/PORG2
PORG2-AMIN1(PORG2,14.5)
PSTM2-14.7-PORG2
C2..PORG2
C5-PSTM2
X2-C6/C5
Xl-(C3-C2*X2)/Cl
XI-AMAX1(Xl,WSAT)
OMEGA2-oM20LD-ABS(Xl/WC*100.)
OMEGA2-AMAX1(OMEGA2,5.)
XTOTAL-XTOTAL-Xl
IF(T2.GT.373.15) GO TO 30
C
C
C
25 OM20LD-OMEGA2
RUP-WSAT*0.2
RLOW--RUP*2.0
XI-ZBRENT(WET,RLOW,RUP,O.l,OMEGA2,Cl,C3,C4,C6,Tl)
OMEGA2-oM20LD-ABS(Xl/WC*100.)
OMEGA2-AMAX1(OMEGA2,5.)
XTOTALmXTOTAL-Xl
QCTOTAL-QCTOTAL+QC
30 V(I)-Vl
T(I)-Tl
OMEGA(I)-oMEGA2
J-I+l
V2-X2*T2
DO 50 K-J,8
V(K)-V2
PSTEAM(K)-PSTM2
T2-373.15 WHEN CARBON BECOMES WET, FROM EQUILIBRIUM ASSUMPTION

-------
50 T(K)-T2
WRITE(50,lO)I,Vl,Tl,OMEGA2
RETURN
END
C
C
C
FUNCTION DRY(OM20LD,T2,Cl,C3,C4,C6,Tl)
COMMON /SEG/VM,FMW,R,S,TINCR,QLAMBDA,CP,CPc,WC,PO,OMSAT
EXTERNAL ENTHALPY
10 FORMAT(lX,5F15.6)
T...T2
20 PORG2=2.303*VM*POLSTAR(OM20LD)/T
PORG2-EXP(PORG2)
PORG2-PO/PORG2
PORG2=AMIN1(PORG2,14.5)
PSTM2-l4.7-PORG2
C2-PORG2
C5-PSTM2
X2-C6/C5
Xl-(C3-C2*X2)/Cl
WSAT--WC/100.*OMSAT
Xl-AMAX1(Xl,WSAT)
OMEGA2-oM20LD+Xl/WC*lOO.
OMEGA2-AMAX1(OMEGA2, 5.)
DELH-ENTHALPY(OM20LD,OMEGA2)
T-Tl+DELH/(S*CP*Vl/RHO(400.)+WC*CPc)
DRY-T-T2
RETURN
END
C
C THE FUNCTION "WET" DETERMINES THE AMOUNT OF ORGANIC REMOVED FROM
C THE CARBON AFTER THE POINT AT WHICH STEAM CONDENSATION BEGINS
C
FUNCTION WET(OM20LD,Xl,Cl,C3,C4,C6,Tl)
COMMON /SEG/VM,FMW,R,S,TINCR,QLAMBDA,CP,CPc,WC,PO,OMSAT
EXTERNAL ENTHALPY
Xl OLD-Xl
PORG2-2.303*VM*POLSTAR(OM20LD)/373.15
PORG2-EXP(PORG2)
PORG2-PO/PORG2
PORG2-AMIN1(PORG2,14.5)
PSTM2-14.7-PORG2
C2-PORG2
C5-PSTM2
OMEGA3-oM20LD+Xl/WC*100.
OMEGA3-AMAX1(OMEGA3,5.)
DELH - ENTHALPY(OM20LD,OMEGA3)
X3-DEUI/QLAMBDA

-------
X2-(C6-C4*X3)/C5
X-(C3-C2*X2)/C1
10 FORMAT(lX,5F15.6)
WET-X-X10LD
RETURN
END
C
C THE FUNCTION RHO DETERMINES THE DENSITY OF THE GAS STREAM
C
FUNCTION RHO(T)
RHD-0.081*273.15/T
RETURN
END
C
C THE FUNCTION ZBRENT SOLVES MASS AND HEAT BALANCE EQUATIONS ITERA-
C TIVELY TO DETERMINE THE AMOUNT OF ORGANIC REMOVED AFTER STEAM BEGINS
C TO CONDENSE. IT USES THE FUNCTION "WET" AS AN EXTERNAL FUNCTION
C
FUNCTION ZBRENT(FUNC,X1 ,X2, TOL"OMEGA, CI ,C3, C4, C6, TI)
EXTERNAL FUNC
PARAMETER (ITMAX-100,EPS-3.E-3)
A-Xl
B-X2
FB-FUNC(OMEGA,B,CI,C3,C4,C6,TI)
FA-FUNC(OMEGA,A,C1,C3,C4,C6,T1)
IF(FB*FA.GT.O.) PAUSE 'Root must be bracketed for ZBRENT,
Iro1 break'
FC-FB
DO 11 ITER-1,ITMAX
IF(FB*FC.GT.O.) THEN
C-A
FC-FA
D-B-A
E-D
ENDIF
IF(ABS(FC).LT.ABS(FB THEN
A-B
B-C
C-A
FA-FB
FB-FC
FC-FA
ENDIF
TOLl-2.*EPS*ABS(B)+O.5*TOL
XM"'.5*(C-B)
IF(ABS(XM).LE.TOL1 .OR. ABS(FB).LT.TOL1)THEN
ZBRENT-B
RETURN
ENDIF
use cont

-------
11
IF(ABS(E).GE.TOL1 .AND. ABS(FA).GT.ABS(FB THEN
S-FB/FA
IF(A.EQ.C) THEN
P-2.*XM*S
Q-1. -S
ELSE
Q-FA/FC
R-FB/FC
P-S*(2.*XM*Q*(Q-R)-(B-A)*(R-1.
Q-(Q-1.)*(R-1.)*(S-1.)
ENDIF
IF(P.GT.O.) Q--Q
P-ABS(P)
IF(2.*P .LT. MIN(3.*XM*Q-ABS(TOL1*Q),ABS(E*Q) THEN
E-D
D=P/Q
ELSE
D-XM
E-D
ENDIF
ELSE
D-XM
E-D
ENDIF
A-B
FA-FB
IF(ABS(D) .GT. TOLl) THEN
B-B+D
ELSE
B-B+SIGN(TOL1,XM)
ENDIF
FB-FUNC(OMEGA,B,C1,C3,C4,C6,T1)
CONTINUE
PAUSE 'ZBRENT exceeding maximum iterations.'
ZBRENT-B
RETURN
END
C
C
FUNCTION POLSTAR(OMEGA)
Driver for routine ZROOTS
PARAMETER(M=5,M1-M+1)
COMPLEX A(M1),X,ROOTS(M)
LOGICAL POLISH
DATA ,A/(1.71,0.0),(-.0146,0.0),(-.00165,0.0),(-.000411,0.0)
1 (.0000314,0.0),(-.000000675,0.0)/
C
C OMEGA SHOULD NOT BE GREATER THAN 10(+1.71) OR ERRONEOUS ROOTS RESULT,
C BECAUSE THIS WOULD EXCEED THE CARBON VOLUMETRIC CAPACITY
C

-------
POLISH-.TRUE.
OMEGA2-ALOG10(OMEGA)
A10I..D-A(1)
A(1)-A(1)-CMPLX(OMEGA2,.0)
CALL ZROOTS(A,M,ROOTS,POLISH)
DO 11 I-1,M
ROOT-REAL(ROOTS(I
C
C ELIMINATE COMPLEX CONJUGATE ROOTS TO OBTAIN THE ONE REAL ROOT
C
DO 11 K-I+1,M
IF (ABS(ROOT-REAL(ROOTS(K).LT.0.0001.AND.ABS(1./ROOT-
1 1./REAL(ROOTS(K).LT.0.0001) THEN
ROOTS(I)-CMPLX(O.,O.)
ROOTS(K)-CMPLX(O.,O.)
ENDIF
11 CONTINUE
DO 12 I-1,M
IF(ROOTS(I).NE.CMPLX(O. ,O.POLSTAR-REAL(ROOTS(I
12 CONTINUE
A(1)-A10LD
RETURN
END
SUBROUTINE ZROOTS(A,M,ROOTS,POLISH)
PARAMETER (EPS-1.E-6,MAXM-101)
COMPLEX A(*) ,ROOTS(M) ,AD(MAXM),X,B,C
LOGICAL POLISH
DO 11 J-1,M+1
AD(J)-A(J)
CONTINUE
DO 13 J-M,1,-1
X-CMPLX(O. ,0.)
CALL LAGUER(AD,J,X,EPS,.FALSE.)
IF(ABS(AIMAG(X.LE.2.*EPS**2*ABS(REAL(X) X-CMPLX(REAL(X) ,0.)
ROOTS (J)-X
B-AD(J+1)
DO 12 JJ-J,1,-1
C-AD(JJ)
AD(JJ)-B
B-X*B+C
CONTINUE
CONTINUE
IF (POLISH) THEN
DO 14 J-1,M
CALL LAGUER(A,M,ROOTS(J),EPS,.TRUE.)
CONTINUE
ENDIF
t DO 16 J-2,M
X-ROOTS(J)
11
12
13
14

-------
15
10
16
11
DO 15 I-J-1,1,-1
IF(REAL(ROOTS(I.LE.REAL(XGO TO 10
ROOTS (I+1)-ROOTS (I)
CONTINUE
1-0
ROOTS (I+1)-X
CONTINUE
RETURN
END
SUBROUTINE LAGUER(A,M,X,EPS,POLISH)
COMPLEX A(*),X,DX,X1,B,D,F,G,H,SQ,GP,GM,G2,ZERO,XX,WW
LOGICAL POLISH
PARAMETER (ZERD-(0.,0.),TINY-1.E-15,MAXIT-100)
IF (POLISH) THEN
DXOLD-CABS (X)
NPOL-O
END IF
DO 12 ITER-1,MAXIT
B-A(M+l)
D-ZERO
F-ZERO
DO 11 J -M , 1 , -1
F-X*F+D
D-X*D+B
B-X*B+A(J)
CONTINUE
IF(CABS(B).LE.TINY) THEN
DX-ZERO
ELSE IF(CABS(D).LE.TINY.AND.CABS(F).LE.TINY)THEN
DX-CMPLX(CABS(B/A(M+1**(1./M) ,0.)
ELSE
G-D/B
G2-G*G
H-G2-2.*F/B
XX-(M-1)*(M*H-G2)
YY-ABS (REAL (XX) )
ZZ-ABS(AIMAG(XX
IF(YY.LT.TINY.AND.ZZ.LT.TINY) THEN
SQ-ZERO
ELSE IF (YY.GE.ZZ) THEN
WW-(1.0jYY)*XX
SQ-SQRT(YY)*CSQRT(WW)
ELSE
WW-(1.0/ZZ)*XX
SQ-SQRT(ZZ)*CSQRT(WW)
ENDIF
GP-G+SQ
GM-G - SQ
IF(CABS(GP).LT.CABS(GM GP-GM

-------
12
DX-M/GP
ENDIF
X1-X-DX
IF(X.EQ.X1)RETURN
X-Xl
IF (POLISH) THEN
NPOL-NPOL+1
CDX-CABS(DX)
IF(NPOL.GT.9.AND.CDX.GE.DXOLD)RETURN
DXOLD-CDX
ELSE
IF(CABS(DX).LE.EPS*CABS(XRETURN
END IF
CONTINUE
PAUSE 'too many iterations'
RETURN
END

-------
APPENDIX C
LISTING FOR PROGRAM BED SIZE

-------
MAIN PROGRAM CODE LISTING FOR BED SIZE
$DEBUG
COMPLEX PO
C
C REDlMENSION VARIABLES TO AUGMENT ADSORBATE DATA BASE
C
DIMENSION VAPOR(32 ,7) ,VAPNAME(32 ,10)
DOUBLE PRECISION TMAX,TMAXO,TMAX2,DELT
C
C VARIABLES LISTED IN COMMON BLOCKS ARE, IN ORDER, "BED THICKNESS (BL) ,
C SUPERFICIAL VELOCITY (V), SPECIFIC SURFACE AREA OF PELLET (Ag),
C SPECIFIC SURFACE AREA OF MICROPARTICLE WITHIN PELLET (Ap) ,
C EXTERNAL MASS TRANSFER COEFFICIENT (FKgd) , INTRAPARTICLE MASS
C TRANSFER COEFFICIENT (FKpd), PELLET VOID FRACTION (EPSg), VOID
C FRACTION OF MICROPARTICLE WITHIN PELLET (EPSp), SIZE OF MICRO-
C PARTICLE WITHIN PELLET (dm), MICROPORE DIFFUSIVITY (Dmm), PELLET
C SIZE (dp) , MACRO PORE DIFFUSIVITY (Dpp), ISOTHERM CONSTANT PROPOR-
C TIONAL TO SLOPE (H), AXIAL DIFFUSIVITY (Dg), TEMPERATURE (TEMP) AND
C PRESSURE (PRESS)
C
COMMON BL,V,Ag,Ap,Fkgd,Fkpd,EPSg,EPSp,dm,Dmm,dp,Dpp,H,Dg
COMMON /BLOCK2/TEMP,PRESS
DATA VAR,VAR2/'N' ,'Y'/
OPEN (2,FlLE-'CON')
OPEN (4,FlLE-'INVERT.DAT')
OPEN (8,FILE-'VAPNAME.FIL')
OPEN (10,FlLE-'VAPOR.FIL')
READ (10,71) VAPOR(I,J),J-1,7),I-1,32)
71 FORMAT (F5.0,F7.2,2F7.4,F8.5,F9.3,F8.3)
A-O.O
B-O.O
READ (4,24) TEMP,TMAX,Co,Cb
READ (4,18) MENU2
READ (4,24) EPSg,Dp,Vo,RHOB
READ (8,90)VAPNAME
90 FORMAT (10A4)
98 WRITE (*,28)
28 FORMAT(lX, ,
*00) ')
READ (2,40) NMAX
40 FORMAT(I4)
WRITE (*,96)
96 FORMAT (lX,'
*)
ENTER NUMBER OF TERMS FOR INVERSION SERIES (UP TO 1
DO YOU WANT TO INCLUDE HUMIDITY EFFECTS? (Y OR N)'
READ (2,21) TEST3
IF (TEST3.EQ.VAR) GO TO 120
WRITE (*,101)

-------
101 FORMAT (lX,' IS WATER SOLUBLE IN THE ORGANIC COMPOUND? (Y OR N)
* ') .
READ (2,21) TESTS
120 WRITE (*,20) .
20 FORMAT (lX,' DO YOU WANT TO USE PREVIOUS PARAMETER VALUES? (Y 0
*R N)')
READ (2,21) TEST
21 FORMAT (AI)
IF (TEST.EQ.VAR2) GO TO 36
22 WRITE (*,23)
23 FORMAT (//////10X,'SELECT VARIABLE TO CHANGE '/
*/15X,'1. TEMPERATURE'/15X,'2. BREAKTHROUGH TIME'
*/15X,'3. CHALLENGE CONCENTRATION'
*/15X,'4. BREAKTHROUGH CONCENTRATION'/15X,'5. ADSORBATE'/
*15X,'6. BED VOID FRACTION'/15X,'7. PELLET SIZE'/
*15X,'8. SUPERFICIAL VELOCITY '/15X,'9. BED DENSITY'/
*14X,'10. CONTINUE CALCULATION'////)
READ (2,25) MENU1
25 FORMAT (14)
GO TO (l,2,3,4,5,6,7,8,9,10),MENU1
1 WRITE (*,51)TEMP
51 FORMAT (lX,' ENTER TEMPERATURE (C) , ,FI5.6,4X)
READ (2,24) TEMP
GO TO 22
FORMAT (IFI5.6)
WRITE (*,52) TMAX
FORMAT (lX,' ENTER BREAKTHROUGH TIME (H)
READ (2,24) TMAX
GO TO 22
3 WRITE (*,53) Co
53 FORMAT (lX,' ENTER INLET CONCENTRATION (PPMV)' ,F15.6,4X)
READ (2,24) Co
GO TO 22
4 WRITE (*,54) Cb
54 FORMAT (lX,' ENTER BREAKTHROUGH CONCENTRATION (PPMV)' ,F15.6,4X)
READ (2,24) Cb
GO TO 22
5 WRITE (*,90) VAPNAME
WRITE (*,55) MENU2
55 FORMAT (lOX,' ADSORBATE SELECTION MENU ' ,IS, 2X)
READ (2,74) FMENU2
MENU2-INT(FMENU2)
74 FORMAT (F5.0)
GO TO 22
6 WRITE (*,56)EPSg
56 FORMAT(lX,' ENTER BED VOID FRACTION (CU.FT./CU.FT.) , ,F15.6,
*4X)
READ (2,24) EPSg
GO TO 22
24
2
52
, ,F15. 6 ,4X)

-------
 7
 57
 8
 58
 9
 59
 45
C 
C 
 10
 36
WRITE (*,57) Dp
FORMAT (lX,' ENTER PELLET SIZE (IN)
READ (2,24) Dp
GO TO 22
WRITE (*,58)Vo
FORMAT (lX,' ENTER SUPERFICIAL VELOCITY (FPM) , ,F15.6,4X)
READ (2,24) Vo
GO TO 22
WRITE (*,59) RHOB
FORMAT (lX,' ENTER BED DENSITY (LB/CU. FT)' ,F15.6,4X)
READ (2,24) RHOB
GO TO 22
FORMAT (E9. 2)
, ,F15.6,4X)
TEMP,TB,Co,Cb
MENU2
EPSg,Dp,Vo,RHOB
WRITE (4,24)
WRITE (4,18)
WRITE (4,24)
Dp-Dp/39.37
Vo-Vo*0.005080
RHOB-RHOB*16.02
C
C CONVERT INPUT VARIABLES TO MKS SYSTEM OF UNITS
C
C
C SET K VALUE, DRKVAL, FOR BPL CARBON TO PUBLISHED VALUE
C
DRKVAL-4.417E-08
WO-0.4204
WRITE (*,252) WO
252 FORMAT (lX,' WO
READ (2,24) WO
, ,F15.6,4X)
C
C ASSUME 2 PER CENT OF ORGANIC IS NOT REMOVED DURING REGENERATION
C CYCLE AND REMAINS AS RESIDUAL ORGANIC (RESIDORG)
C
RESIDORG-0.02
C
C CALCULATE PARTICLE VOID FRACTION FROM PUBLISHED VALUE FOR
C VOLUMETRIC CAPACITY
C
EPSp-WO*RHOB/(1.-EPSg)/1000.
EPSp-EPSp*(l.-RESIDORG)
C
C SET HUMFACT-1.0 IN EVENT WATER IS NOT SOLUBLE IN ADSORBATE
C
HUMFACT-1.0
IF (TEST3.EQ.VAR.OR.TEST5.EQ.VAR) GO TO 110
EPSp-(WO-0.09)*RHOB/(1.-EPSG)/1000.0

-------
C
C ADJUST VOLUMETRIC CAPACITY FOR RESIDUAL MOISTURE ON CARBON IF
C WATER IS SOLUBLE IN THE ORGANIC
C
HUMFACT-(WO-O.09)/W0
110 R-1.98622
C
C TMP IS THE ABSOLUTE TEMPERATURE (K)
C
TMP-TEMP+273.15
C
C SET PRESSURE EQUAL TO 760 MM HG
C
PRESS-760.0
TMAX-TMAX*3600.0
C
C CALCULATE THE VAPOR PRESSURE FROM THE ANTOINE COEFFICIENTS
C
148
149
*
Ps-10.0**(VAPOR(MENU2,5)-VAPOR(MENU2,6)/
(TMP-273. 15+VAPOR(MENU2 ,7)/760.
IF (Ps.LE.1.0) GO TO 149
WRITE (*,148)
FORMAT (lX,' CALCULATED VAPOR PRESSURE GREATER THAN 1 ATM.')
Ps-Ps*1.E06
C
C CALCULATE THE RELATIVE POLARIZABILITY,
C DUBININ-RADUSHKEVIC EQUATION
C
150
BETA, FOR THE
*
BETA-(VAPOR(MENU2,4)**2-1.)/(VAPOR(MENU2,4)**2+2.)*
VAPOR (MENU 2 ,2)jVAPOR(MENU2 ,3)/26.6
ACONST-R*R*TMP*TMP/BETA/BETA*DRKVAL
U-ALOG(Ps/Co)
XPFACT-ACONST*U*U
IF (XPFACT.LT.20.) GO TO 130
WRITE (*,150)
FORMAT (IX,' NO ADSORPTION OCCURS FOR THIS COMPOUND')
GO TO 140
C
C CALCULATE A CONSTANT, H, PROPORTIONAL TO SLOPE OF ISOTHERM
C FOR VAN DONGEN'S ADSORPTION MODEL
C
130
*
H-RHOB/IOOO.*VAPOR(MENU2,3)*EPSp/(1.-EPSg)/(1.-EPSp)/Co*
22.4*1.E09jVAPOR(MENU2,2)/EXP(XPFACT)*WO
C
C MICROPOROUS PARTICLE IS APPROX.
C FINE GRAINED CARBON
Dm-Dp/100.0
1/100 OF GRANULE SIZE FOR A
C
C CALCULATE SPECIFIC SURFACE AREAS

-------
C
Ag-(1-EPSg)*6.0/Dp
Ap-(1-EPSp)*6.0/Dm
C
C CALCULATE REAL, OR INTERSTITIAL, VELOCITY
C
V-Vo/EPSg
Fkgd-0.0105*SQRT(Vo/Dp)
C
C CALCULATE PORE DIFFUSION AND AXIAL DISPERSION COEFFICIENTS
C USING MOLECULAR DIFFUSIVITY, Do
C
*
*
Do=0.0039*TMP**1. 5*SQRT(1./VAPOR(MENU2 ,2)+0.034)/
VAPOR (MENU2 ,2)**0. 17/(VAPOR(MENU2 ,2)**0. 33/VAPOR(MENU2 ,3)/
2.5+1.81)**2.*1.E-04
Dg-0.73*Do+0.5*V*Dp/(1.+9.7*Do/V/Dp)
Dpp-EPSg/4./(18.4*(Co*VAPOR(MENU2,2)/TMP)**0.5+1./Do)
Dmm-EPSp/4./(920.*(Co*VAPOR(MENU2,2)/TMP)**0.5+1./Do)
IF (TEST3.EQ.VAR.OR.TEST5.EQ.VAR2) GO TO 97
C
C ASSUME PORE DIFFUSIVITIES ARE 25 PER CENT OF DRY VALUES IF RESIDUAL
C MOISTURE IS ON CARBON AND WATER IS NOT SOLUBLE IN THE ORGANIC
C
Dpp=Dpp*0.25
Dmm=Dmm*0.25
FKpd=Dpp*2.0/Dm
97
C
C
C CALCULATION OF APPROXIMATE BED THICKNESS
C
C
PHIPDP=0.5*Dp*SQRT(Ap*FKpd/EPSp/Dpp)
ETAP-3./PHIPDP*(1./TANH(PHIPDP)-1./PHIPDP)
FKG=l./FKgd+EPSp*Dm/Dp/(l.-EPSp)/FKpd/ETAP
FKG=l. /FKG
FK=0.5/FKG*(1.+SQRT(1.+24.*Dg/V*EPSg*FKG/V/Dp/(1.-EPSg)
FK-1. /FK
BL=-V/(1.-EPSg)*EPSg*(Dp/6./FK*ALOG(Cb/Co)-TMAX*EPSp/
(1. -EPSp)/H)
*
C
C
C
C
REFINE ESTIMATE OF BED THICKNESS FOR DEFINED BREAKTHROUGH
200 FUNCTEST-Cb/Co
IF (FUNCTEST.GT.0.00001) GO TO 152
WRITE (*,153)
153 FORMAT (lX,' EXIT CONCENTRATION MAY BE TOO LOW FOR PRACTICAL
*CALCULATION')
18 FORMAT (lX,I4)

-------
152
PO-CMPLX(A,B)
TMAX2-1.0*TMAX
FUNC-O.O
CALL LAPINV(TMAX,PO,TMAX2,NMAX,FUNC)

-------
APPENDIX D
VENDOR RESPONSE

-------
June 2, 1988
Westviico
William L. Klotz
Chas. T. Main, I,nc.
Two Fairview Plaza
POBox 240236
Charlotte, N.C. 28224
Dear Bill:
I apologize for taking so long to write to you, but I wanted to
go back and retry your program BED-SIZE after we talked. As we
had discussed, I believe the program is greatly over estimating
the length of the mass transfer zone'. I've attached a copy of
the output, with input listed below it for a toluene applica-
tion. This is similar to an application where we are using our
pelletized product. With steam cycling,a 2 foot bed depth is
capable of removing the inlet concentration of 3000 ppm to 150
ppm or less for 2 hours. Your program calculates a 9.2 foot bed
depth with virgin carbon.

We feel that a computer model that can simulate steam desorption
would be very useful to the industry. Through our own develop-
ment work and work with other consultants, we have models that
we use but are uncertain of their validity due to the complexity
of the solvent recovery systems being modeled.
For a model to be useful to us, we would need to be able to
insert isotherms from different types of carbon. The input
would be bed size, adsorption and steaming conditions. Output
would be adsorption time with steam cycling and breakthrough
profiles. Multicomponent adsorption would be very useful. The
effect of relative humidity would be useful, but of secondary
concern.
We are willing to give you feedback as you continue to develop
your model. Good luck.
Sincerely,

~:!~:Jr

Applications Specialist
PJL:ckh
Ch8mIc81 DIwIaIon
Carbon Department
Covington, V A 24426
T.lephone 703 882 1121

-------