appendix a matlab code for predicting breakthrough...

105

APPENDIX A

MATLAB CODE FOR PREDICTING BREAKTHROUGH CURVES

clear all

clc

format long e;

global concarray concexp texparray

param =[0.11789467382528 35.57467768874226];

LB=[0.05 30];

UB=[0.3 40]

options=optimset('LargeScale','on','Display','iter','Diagnostics','on','FunValCheck','on','Ma

xiter', 1000,'Tolx',1e-3,'Tolfun',1e-3);

[para,CONCNORM,CONC,EXITFLAG]=lsqnonlin(@objective_knp1,param, LB,

UB,options)

figure(1)

plot(texparray,concarray,'b*')

% Plot residual solvent for optimized values

hold on

plot(texparray,concexp,'ko')

% To Plot residual solvent from experiments

hold on

function func =objective_knp1(para)

global A B A1 B1 P Q K R cg qm al r rho tres T n

global concarray concexp texparray

106

qm=para(1); % qm

K=para(2); % K

format long

% To calculate A, B matrix for the bulk phase

x=[0 0.00921968 0.0479413 0.115048 0.206341 0.316084 0.43738 0.56261 0.683915

0.793658 0.884951 0.95205 0.9907803 1]; % Collocation points along the axial length

of the column

for i=1:14

for j=1:14

Q2(i,j)=x(i)^(j-1);

end

end

for i=1:14

C2(i,1)=0;

end

for i=1:14

C2(i,2)=1;

end

for i=1:14

for j=3:14

C2(i,j)=(j-1)*(x(i))^(j-2);

end

end

for i=1:14

D2(i,1)=0;

end

for i=1:14

D2(i,2)=0;

end

for i=1:14

D2(i,3)=2;

end

for i=1:14

for j=4:14

107

D2(i,j)=(j-1)*(j-2)*(x(i))^(j-3);

end

end

Qin=inv(Q2);

A=C2*Qin;

B=D2*Qin;

% To calculate A1 and B1 matrix inside the pores of the adsorbent

x1=[0.21535 0.42063 0.60625 0.76351 0.88508 0.96524 1]; % collocation points along

the radial position of the adsorbent

for i=1:7

Q1(i,1)=1;

end

for j=2:7

for i=1:7

Q1(i,j)=x1(i)^(2*j-2);

end

end

for i=1:7

C1(i,1)=0;

end

for j=2:7

for i=1:7

C1(i,j)=2*(j-1)*(x1(i)^(2*j-3));

end

end

for i=1:7

D1(i,1)=0;

end

for i=1:7

D1(i,2)=2;

end

for j=3:7

for i=1:7

D1(i,j)=2*(j-1)*(2*j-3)*x1(i)^(2*j-4);

108

end

end

Qin1=inv(Q1);

A1=C1*Qin1;

B1=D1*Qin1;

% Parameters

c=zeros(84,1);

vel=5.9448E-4; % velocity in m/s

dis=6.062E-8; % axial dispersion coefficient in m2/s

le=0.015; % length of the column in m

P=(dis)/(le^2);

km=0.00149; % external mass transfer coeff. in m/s

bp=0.66; % bed porosity

rp=7.5e-4; % radius of the particle in m

Q1=3*km*(1-bp);

Q2=rp*bp;

Q=Q1/Q2;

De=2.2E-8; % Effective diffusivity in m2/s

al=0.45; % particle porosity

R=(km*rp)/(De);

tres=le/vel;

T=(De)/(rp^2);

r=[0.21535 0.42063 0.60625 0.76351 0.88508 0.96524]; % collocation points along

the radial position of the adsorbent

cg=0.025; % inlet adsorbate concentration in kg/m3

rho=400; % particle density in kg/m3

n=1;

[t,c]=ode15s(@knd1,[0:1:19000],c);

t=0:1:19000;

for k=1:1:19001

v1=0;

for j=1:12

v11=v1+(A(14,j+1)*c(k,j));

v1=v11;

109

end

v13=1/(A(14,14));

v15(1,k)=v13*(-A(14,1)-v1);

end

figure(2)

plot(t,v15)

hold on

% Various times in seconds

TIME=[3000 3300 3600 3900 4200 4800 5100 5400 6000 6300 6600 7200 8100 9000

9900 10500 11700 12900 13500 14400];

% Experimental values of

exptal_conc=[0.01271 0.011425 0.01457 0.014725 0.01524 0.01545 0.02132 0.02735

0.043 0.0542 0.065 0.08643 0.132 0.1879 0.241 0.2794 0.3742 0.4523 0.5223 0.5725 ];

count = 1;

texparray=TIME;

concexp=exptal_conc;

for itx = 1:length(texparray)

texp = texparray(itx);

concmodel=v15(texp);

texparray(count) = texp;

concarray(count,1) = concmodel;

count = count +1;

end

% For least square nonlinear fit for concentration

for i=1:length(texparray)

cfop(i)=((concarray(i)-concexp(i)));

end

func=cfop;

%for concentration at the surface of the pores vs time at different x(along the length of

%the column)

t=0:1:30000;

for k = 1:1:30001

v2=0;

110

for j=1:6

v22=v2+(A1(7,j)*c(k,12*j+12));

v2=v22;

end

v30=(A1(7,7)+R);

v31=1/v30;

v32=R*c(k,12);

v33(1,k)=v31*(v32-v2);

end

plot(t,v33)

hold on

%for concentration in the pores vs R at a given time and at different x(along the length of

%the column)

for i=1:6

v45(1,i)=c(20001,12*i+1);

end

v46=0;

for j=1:6

v47=v46+(A1(7,j)*c(20001,12*j+1));

v46=v47;

end

v48=(A1(7,7)+R);

v49=1/v48;

v50=R*c(20001,1);

v45(1,7)=v49*(v50-v46);

r51=[0.21535 0.420638 0.60625 0.76351 0.88508 0.96524 1];

plot(r51,v45)

hold on

%for concentration in the pores vs x/L, at a given time and at different r

for i=1:12

v232(1,i)=c(20001,72+i);

end

111

x232=[ 0.00921968 0.0479413 0.115048 0.206341 0.316084 0.43738 0.56261 0.683915

0.793658 0.884951 0.95205 0.9907803 ];

plot(x232,v232)

hold on

%for concentration in the pores vs time at given r and at different x

t=0:1:30000;

for k=1:1:30001

v238(1,k)=c(k,24);

end

plot(t,v238)

hold on

%for concentration in the bulk phase vs time at differernt x

t=0:1:30000;

for k=1:1:30001

v248(1,k)=c(k,1);

end

plot(t,v248)

hold on

%for conc in the bulk phase vs x at different times

for i=1:12

v268(1,i)=c(1001,i);

end

x242=[ 0.00921968 0.0479413 0.115048 0.206341 0.316084 0.43738 0.56261 0.683915

0.793658 0.884951 0.95205 0.9907803 ];

plot(x242,v268)

hold on

Function for generating ODE’s

function dM=knd1(t,c)

global A B A1 B1 P Q K R cg qm al r rho tres T n

112

p1=0;

for j=1:12

p=p1+(A(14,j+1)*c(j,1));

p1=p;

end

w31=(-A(14,1)-p1);

t84=A1(7,7)+R;

t85=1/t84;

f400=(K)^1/n;

t100=((1/n)*rho*(1-al)*qm*f400);

% For generating 12 ODE’s in the bulk phase of the column

% i loop starts

for i=1:12

s1=0;

for j=1:12

s=s1+(A(i+1,j+1)*c(j,1));

s1=s;

end

t1=0;

for j=1:12

t=t1+(B(i+1,j+1)*c(j,1));

t1=t;

end

f20=(A(i+1,14))/(A(14,14));

f21=(f20)*(w31);

f221=-(A(i+1,1)+f21+s1);

f22=f221/tres;

f23=(B(i+1,14))/(A(14,14));

f24=(f23)*(w31);

f25=P*(B(i+1,1)+f24+t1);

t11=0;

for j=1:6

t12=t11+(A1(7,j)*c(12*j+i,1));

113

t11=t12;

end

t13=-t11+(R*c(i,1));

t90=t13*t85;

t91=-Q*(c(i,1)-t90);

dM(i,1)=(f22+f25+t91);

end

% For generating 72 ODE’s along the radial direction of the adsorbent particle

for k=1:6

for i=1:12

f300=(K*cg*c(12*k+i,1))^(1/n);

f200=(1+f300)^2;

f201=(al*f200);

f205=(T*f201);

%t100=(rho*(1-al)*qm*K);

f301=(cg*c(12*k+i,1))^(1-n)/n;

f302=t100*f301;

f203=f201+f302;

f2=f205/f203;

t40=0;

for j=1:6

t41=t40+(B1(k,j)*c(12*j+i,1));

t40=t41;

end

t42=0;

for j=1:6

t43=t42+(A1(k,j)*c(12*j+i,1));

t42=t43;

end

t45=0;

for j=1:6

t46=t45+(A1(7,j)*c(12*j+i));

t45=t46;

end

114

t47=-t45+(R*c(i,1));

t48=(t47*t85); %cp(1,t)

t49=t48*(B1(k,7)+(2*A1(k,7)/r(k)));

t50=t40+(2*t42/r(k));

t51=t49+t50;

dM(12*k+i,1)=t51*f2;

end

end

Calculation of Parameters for toluene

z =70E-6; % volumetric flow rate in m3/min

Q=z/60; % volumetric flow rate in m3/sec

A = 1.9625E-3; % Cross-sectional area of the column in m2

mu=1.45E-5; %viscosity of the gas in kg/m.s

Dm=8.9936E-6; % Molecular diffusivity in m2/s

vel = Q/A % velocity in m/s

dia=0.0015; % diameter of the particle in m

PMR=((101325)*(28))/(8314); %PM/R

den=PMR/313; % Density of the gas in kg/m3

Re= ((den)*(vel)*(dia))/(mu) % Reynolds number

Sc= (mu)/(den*Dm) % Schimdt number

% calculation for Peclet number starts

a= Re*Sc;

b=3.8/a;

c=0.3/a;

d=1+b;

e=0.5/d;

f=c+e;

Pe=1/f % Peclet number

% calculation of Peclet number ends

dis=((dia)*(mu))/((den)*(Pe)) % Dispersion coefficient in m2/s

%calculation for mass transfer coefficient stars

g=Sc^0.33

h=Re^0.49

115

sh=0.8281*g*h % Sherwood number

k=sh*Dm;

km=k/dia % mass transfer coefficient in m/s

% calculation of mass transfer coefficient ends

Calculation of effective diffusivity for toluene

% calculation of molecular diffusivity DAB starts

vA=(7*0.0148)+(8*0.0037);

a=(vA^(1/3));

rA=1.18*a; % rA

rB=0.3798; % rB

rAB=(rA+rB)/2; % rAB

z=rAB^2;

b=0.56; % f(kT/epsAB)

p=101325; % Pressure

T=313; % temperature

c=(1/92)+(1/28);

d=c^0.5;

e=0.0001*(1.084-(0.249*d))*d;

f=e*(T^1.5);

DAB = f/(p*z*b) % Molecular diffusivity in m2/s

% calculation of molecular diffusivity DAB ends

% calculation of knudsen diffusivity starts

rpore=0.9E-9; % pore radius in m

z=(T/92);

y=z^0.5;

DK=97*rpore*y; % Knudsen diffusivity in m2/s

% calculation of knudsen diffusivity ends

DK1=1/DK;

DAB1=1/DAB;

DTA=1/(DK1+DAB1); % Transition diffusivity

alpha=0.45; %Particle porosity

tor=4; % Tortuosity factor

De=(DTA*alpha)/(tor) % Effective diffusivity in m2/s

116

APPENDIX B

DATA FOR DRAWING CALIBRATION CURVE

Table B.1: Data for drawing calibration curve for toluene at 313 K and 1 atm Volume

of sample injected

in m3

Total no. of moles

injected at 1 atm and at

313 K

Mole fraction of toluene in saturated

gas at 313 K

No. of moles of

toluene in the sample

Area under

the Curve

obtained from GC

Log (no. of moles

of toluene)

Log(area under

the curve)

10-6 3.893 × 10-5 0.077276091 3.00 × 10-6 62759941 -5.521 7.797 9 × 10-7 3.504 × 10-5 0.077276091 2.70 × 10-6 59174149 -5.567 7.772 8 × 10-7 3.114 × 10-5 0.077276091 2.40 × 10-6 55781211 -5.618 7.746 7 × 10-7 2.725 × 10-5 0.077276091 2.10 × 10-6 51689496 -5.676 7.713 6 × 10-7 2.336 × 10-5 0.077276091 1.80 × 10-6 44539213 -5.743 7.648 4 × 10-7 1.557 × 10-5 0.077276091 1.20 × 10-6 36913304 -5.919 7.567

Table B.2: Data for drawing calibration curve for xylene at 313 K and 1 atm Volume

of sample injected

in m3

Total no. of moles

injected at 1 atm and at

313 K

Mole fraction of xylene in

saturated gas at 313 K

No. of moles of xylene in

the sample

Area under

the Curve

obtained from GC

Log (no. of moles

of xylene)

Log(area under the

curve)

10-6 3.8937 × 10-5 0.025925455 1.009 × 10-6 32722735 -5.995 7.514 8 × 10-7 3.114 × 10-5 0.025925455 8.07 × 10-7 28133731 -6.092 7.449 6 × 10-7 2.336 × 10-5 0.025925455 6.05 × 10-7 23106539 -6.217 7.363 4 × 10-7 1.557 × 10-5 0.025925455 4.03 × 10-7 17399806 -6.393 7.240 2 × 10-7 7.7874 × 10-6 0.025925455 2.01 × 10-7 12619888 -6.694 7.101

117

APPENDIX C

DATA FOR DRAWING BREAKTHROUGH CURVES FOR TOLUENE

Table C.1: Data for drawing breakthrough curve for toluene (Gas flow rate = 70 ml/min, Inlet concentration = 11500 ppm, Bed height = 0.015 m, Particle diameter = 0.0015 m)

Sr.No. Time

(in sec)

Area under the curve obtained from GC

Moles of toluene at the

exit

Mole fraction of toluene at

the exit

(Expt.)

(Model) 1 2220 262996 3.065 × 10-10 7.872 × 10-6 0.000685 0.00055 2 2520 367847 5.382 × 10-10 1.382 × 10-5 0.001202 0.001101 3 2700 423261 6.811 × 10-10 1.749 × 10-5 0.001521 0.001589 4 3000 529633 9.922 × 10-10 2.548× 10-5 0.002216 0.002745 5 3300 674353 1.488 × 10-9 3.821 × 10-5 0.003323 0.004437 6 3600 878315 2.31838 × 10-9 5.954 × 10-5 0.005177 0.006797 7 3900 1111755 3.44293 × 10-9 8.842 × 10-5 0.007688 0.009967 8 4200 1386239 4.98557 × 10-9 0.0001280 0.011133 0.014091 9 4500 1667089 6.79431 × 10-9 0.00017449 0.015172 0.019318 10 4800 2013216 9.32427 × 10-9 0.00023947 0.020821 0.025797 11 5220 2628231 1.45836 × 10-8 0.00037454 0.032565 0.037251 12 5700 3302708 2.13953 × 10-8 0.00054948 0.047775 0.054204 13 6000 3848284 2.76518 × 10-8 0.00071016 0.061746 0.067121 14 6360 4601414 3.7322 × 10-8 0.00095852 0.083339 0.085173 15 6900 5663316 5.28778 × 10-8 0.00135803 0.118075 0.117797 16 7500 6822989 7.228 × 10-8 0.00185633 0.161399 0.162175 17 8100 8277540 9.99619 × 10-8 0.00256727 0.223212 0.21504 18 8700 9456934 1.24996 × 10-7 0.00321021 0.279113 0.275689 19 9000 10159524 1.40967 × 10-7 0.003620378 0.314774 0.308533 20 9300 10757207 1.55157 × 10-7 0.00398481 0.346461 0.342765 21 9600 11399916 1.71024 × 10-7 0.00439232 0.381891 0.378131 22 9900 11934101 1.84682 × 10-7 0.00474311 0.412391 0.41435 23 10500 13177845 2.18105 × 10-7 0.00560147 0.487021 0.488193 24 10800 13687445 2.32441 × 10-7 0.00596966 0.519034 0.525225 25 12000 15934848 2.99981 × 10-7 0.00770426 0.669849 0.667588 26 12600 16673915 3.23691× 10-7 0.00831319 0.722792 0.73191 27 12900 17233365 3.4212 × 10-7 0.00878649 0.763943 0.761656

118


Sr.No. Time

(in sec)



exit


the exit

(Expt.)

(Model) 1 6060 55686 2.2661× 10-11 5.819 × 10-7 5 × 10-5 0.000115 2 6300 75983 3.81715 × 10-11 9.803 × 10-7 9 × 10-5 0.0002 3 6600 124136 8.69813 × 10-11 2.233× 10-6 0.000207 0.000415 4 6900 188892 1.75924 × 10-11 4.518 × 10-6 0.000420 0.0007 5 7200 260878 3.02413 × 10-10 7.766 × 10-6 0.000722 0.000821 6 7500 345736 4.8508 × 10-10 1.245 × 10-5 0.001159 0.001263 7 8520 723441 1.67429 × 10-9 4.3 × 10-5 0.004001 0.004529 8 8700 789917 1.94039 × 10-9 4.983 × 10-5 0.004637 0.005236 9 9000 938158 2.58949 × 10-9 6.650 × 10-5 0.006188 0.006619 10 9300 1058253 3.16949 × 10-9 8.140 × 10-5 0.007574 0.008293 11 9600 1222947 4.04007 × 10-9 0.00010375 0.009655 0.010308 12 9900 1379423 4.94451 × 10-9 0.00012698 0.011817 0.012718 13 10740 1924704 8.64674 × 10-9 0.00022207 0.020665 0.022125 14 11100 2191900 1.07542 × 10-8 0.00027619 0.025701 0.027662 15 11400 2476217 1.31963 × 10-8 0.00033891 0.031538 0.033129 16 11700 2716276 1.54126 × 10-8 0.00039583 0.036835 0.039479 17 12600 3698286 2.58674 × 10-8 0.00066433 0.061821 0.064951 18 12900 4063804 3.02992 × 10-8 0.00077815 0.072413 0.075978 19 13560 5011364 4.3068 × 10-8 0.00110609 0.102930 0.105581 20 14100 5854762 5.59112 × 10-8 0.00143594 0.133624 0.135911 21 14400 6359242 6.42284 × 10-8 0.00164954 0.153502 0.155341 22 14700 6886194 7.34069 × 10-8 0.00188527 0.175438 0.176669 23 15000 7595538 8.65324 × 10-8 0.00222237 0.206807 0.199924 24 15300 8039623 9.51883 × 10-8 0.00244467 0.227494 0.225073 25 15900 9224644 1.19888 × 10-7 0.00307901 0.286525 0.280799 26 17100 1135927 1.70002 × 10-7 0.00436608 0.406296 0.409864


Sr.No. Time

(in sec)



exit


the exit

(Expt.)

(Model) 1 3000 1115848 3.46422× 10-9 8.897 × 10-5 0.01271 0.002346 2 3300 1152846 3.6591 × 10-9 9.397 × 10-5 0.013425 0.003694 3 3600 1210477 3.9711 × 10-9 0.000102 0.01457 0.005517 4 3900 1218135 4.0134 × 10-9 0.0001031 0.014725 0.007889 5 4200 1243350 4.1538 × 10-9 0.0001067 0.01524 0.010882

119

6 4800 1253533 4.2110 × 10-9 0.0001082 0.01545 0.018985 7 5100 1518769 5.8109 × 10-9 0.0001492 0.02132 0.024208 8 5400 1761818 7.4544 × 10-9 0.0001915 0.02735 0.030277 9 6000 2307181 1.172 × 10-8 0.000301 0.043 0.045109

10 6300 2648488 1.4772 × 10-8 0.0003794 0.0542 0.053931 11 6600 2951419 1.7716 × 10-8 0.000455 0.065 0.06372 12 7200 3497732 2.3557 × 10-8 0.000605 0.08643 0.086249 13 8100 4501907 3.5977 × 10-8 0.000924 0.132 0.12744 14 9000 5556417 5.1213 × 10-8 0.0013153 0.1879 0.177219 15 9900 6444907 6.5686 × 10-8 0.001687 0.241 0.234806 16 10500 7038586 7.6153 × 10-8 0.0019558 0.2794 0.276936 17 11700 8377305 1.0199 × 10-7 0.0026194 0.3742 0.367974 18 12900 9379263 1.2327 × 10-7 0.0031661 0.4523 0.464112 19 13500 10219151 1.4235 × 10-7 0.0036561 0.5223 0.512489 20 14400 10793658 1.5604 × 10-7 0.0040075 0.5725 0.583661


Sr.No. Time

(in sec)


Moles of toluene at

the exit


the exit

(Expt.)

(Model) 1 8100 86359 4.73 × 10-11 1.22 × 10-6 4 × 10-5 0.000093 2 8580 153504 1.24 × 10-10 3.19 × 10-6 0.000129 0.000221 3 8880 257818 2.96 × 10-10 7.61 × 10-6 0.000307 0.00052 4 9480 481097 8.44 × 10-10 2.17 × 10-5 0.000875 0.001115 5 9780 727283 1.69 × 10-9 4.34 × 10-5 0.001751 0.002291 6 10080 1090257 3.33 × 10-9 8.56 × 10-5 0.003454 0.003370 7 10800 2179844 1.07 × 10-8 2.74 × 10-4 0.011045 0.008422 8 11280 3398184 2.24 × 10-8 5.76 × 10-4 0.023265 0.015316 9 11880 4186495 3.18 × 10-8 8.18 × 10-4 0.033016 0.031829

10 12480 5470810 4.99 × 10-8 1.28 × 10-3 0.051725 0.064320 11 13080 8514496 1.05 × 10-7 2.69 × 10-3 0.108649 0.123374 12 13740 13259302 2.20 × 10-7 5.66 × 10-3 0.228444 0.230497 13 14400 18305384 3.79 × 10-7 9.72 × 10-3 0.392443 0.379363 14 15180 23109275 5.60 × 10-7 1.44 × 10-2 0.580213 0.579486 15 18480 31048550 9.19 × 10-7 2.36 × 10-2 0.952315 0.994420 16 18780 31414771 9.37 × 10-7 2.41 × 10-2 0.971237 0.996064

120

APPENDIX D

DATA FOR DRAWING BREAKTHROUGH CURVES FOR XYLENE

Table D.1: Data for drawing breakthrough curve for xylene (Gas flow rate = 50 ml/min, Inlet concentration = 6200 ppm, Bed height = 0.025 m, Particle diameter = 0.0015 m)

Sr.No. Time

(in sec)


Moles of xylene at the exit

Mole fraction of xylene at

the exit

(Expt.)

(Model) 1 11100 21921 5.7 × 10-12 1.4874 × 10-7 2.4 × 10-5 2 × 10-5 2 12000 23484 6.4 × 10-12 1.6672 × 10-7 2.7 × 10-5 3.8 × 10-5 3 12300 24730 7.0 × 10-12 1.8163 × 10-7 2.9 × 10-5 4.7 × 10-5 4 13020 32624 1.1 × 10-11 2.8745 × 10-7 4.7 × 10-5 7.6 × 10-5 5 13500 37010 1.3 × 10-11 3.5427 × 10-7 5.8 × 10-5 0.000102 6 14400 62662 3.3 × 10-11 8.4776 × 10-7 0.000139 0.000172 7 15000 79443 4.8 × 10-11 1.2561 × 10-6 0.000206 0.000238 8 16200 137058 1.2 × 10-10 3.1009 × 10-6 0.000508 0.000435 9 16800 168847 1.7 × 10-10 4.3812 × 10-6 0.000718 0.000577 10 18600 292375 4.2× 10-10 1.0881 × 10-5 0.001783 0.001252 11 22080 596969 1.38 × 10-9 3.5513 × 10-5 0.005817 0.004545 12 22200 626622 1.49 × 10-9 3.8483 × 10-5 0.006304 0.004734 13 22500 656626 1.61 × 10-9 4.1584 × 10-5 0.006812 0.005235 14 22800 697543 1.78 × 10-9 4.5965 × 10-5 0.007529 0.005783 15 23400 773956 2.12 × 10-9 5.4606 × 10-5 0.008945 0.007029 16 24000 858276 2.52 × 10-9 6.4812 × 10-5 0.010617 0.008504 17 24300 897236 2.71 × 10-9 6.9759 × 10-5 0.011427 0.009338 18 24900 1002403 3.26 × 10-9 8.382 × 10-5 0.013731 0.011227 19 25200 1058413 3.57 × 10-9 9.172 × 10-5 0.015025 0.012292 20 25800 1173681 4.23× 10-9 0.000108863 0.017833 0.014693 21 26100 1232794 4.5 × 10-9 0.000118098 0.019345 0.016043 22 26700 1366622 5.45 × 10-9 0.00014009 0.022948 0.019076 23 27000 1430379 5.88 × 10-9 0.000151085 0.024749 0.020774 24 27600 1589681 7 × 10-9 0.000179973 0.029481 0.02458 25 27900 1656695 7.50 × 10-9 0.000192718 0.031568 0.026705 26 28800 1919347 9.57 × 10-9 0.000245936 0.040286 0.034091

121

27 29100 2004375 1.02 × 10-8 0.000264251 0.043286 0.036926 28 29400 2101287 1.11 × 10-8 0.000285756 0.046809 0.039968 29 29700 2207784 1.20 × 10-8 0.000310151 0.050805 0.043229 30 30000 2298120 1.29 × 10-8 0.000331461 0.054295 0.046721 31 31800 2918850 1.91 × 10-8 0.000492599 0.080691 0.073318 32 32100 3032944 2.04 × 10-8 0.000524912 0.085984 0.078827 33 32400 3133318 2.15 × 10-8 0.000554009 0.09075 0.084682 34 33000 3391334 2.45 × 10-8 0.000631628 0.103465 0.097495 35 33300 3503945 2.59 × 10-8 0.000666759 0.109219 0.104483 36 33900 3740018 2.89 × 10-8 0.00074283 0.12168 0.119681 37 34200 3847937 3.03 × 10-8 0.000778682 0.127553 0.127922 38 34800 4104364 3.37 × 10-8 0.000866535 0.141944 0.145743 39 35100 4209710 3.51 × 10-8 0.000903698 0.148031 0.155339 40 35700 4473404 3.89 × 10-8 0.000999413 0.16371 0.175956 41 36000 4589657 4.06 × 10-8 0.001042815 0.17082 0.186987


Sr.No. Time

(in sec)



Mole fraction of

xylene at the exit

(Expt.)

(Model)

1 1500 29126 9.2 × 10-12 2.382 × 10-7 3.862 × 10-5 9.8 × 10-6 2 1800 33220 1.1 × 10-11 2.9620× 10-7 4.802 × 10-5 1.2 × 10-5 3 2100 41521 1.6 × 10-11 4.286 × 10-7 6.949 × 10-5 4.5 × 10-5 4 2400 57950 2.8 × 10-11 7.447 × 10-7 0.00012075 9.7 × 10-5 5 2700 73759 4.3 × 10-11 1.1107× 10-6 0.00018008 1.0 × 10-4 6 3000 96672 6.7 × 10-11 1.7389 × 10-6 0.00028193 2.4 × 10-4 7 3300 120860 9.8 × 10-11 2.5175 × 10-6 0.00040817 3.8 × 10-4 8 3600 156484 1.5 × 10-10 3.8625 × 10-6 0.00062624 5.8 × 10-4 9 3900 172480 1.7× 10-10 4.5385 × 10-6 0.00073583 6.8 × 10-4 10 4200 184048 1.9 × 10-10 5.0539 × 10-6 0.00081940 7.8 × 10-4 11 4500 216902 2.5 × 10-10 6.6347 × 10-6 0.00107570 0.000912 12 4800 230412 2.8 × 10-10 7.3334 × 10-6 0.00118898 0.001011 13 5100 250016 3.2 × 10-10 8.3959 × 10-6 0.00136125 0.001123 14 5400 259918 3.4 × 10-10 8.9540 × 10-6 0.00145174 0.001369 15 5700 290152 4.1 × 10-10 1.0745 × 10-5 0.00174211 0.001546 16 6000 327683 5.1 × 10-10 1.3144 × 10-5 0.00213114 0.001879 17 6300 360022 5.9 × 10-10 1.5363 × 10-5 0.00249082 0.002136 18 6600 403796 7.2 × 10-10 1.8580 × 10-5 0.00301242 0.002564 19 6900 440910 8.3 × 10-10 2.1494 × 10-5 0.00348492 0.003254 20 7200 481693 9.6 × 10-10 2.4887 × 10-5 0.00403511 0.003489 21 7500 516050 1 × 10-9 2.7897 × 10-5 0.00452309 0.003789

122

22 7800 549107 1.2 × 10-9 3.0920 × 10-5 0.00501322 0.003989 23 8100 591098 1.3 × 10-9 3.4936 × 10-5 0.00566429 0.004123 24 8400 633003 1.5 × 10-9 3.9135 × 10-5 0.00634505 0.004896 25 8700 678167 1.7 × 10-9 4.3869 × 10-5 0.00711263 0.005001 26 9000 721064 1.8 × 10-9 4.8562 × 10-5 0.00787351 0.005632 27 9300 767450 2.0 × 10-9 5.3847 × 10-5 0.00873039 0.00698 28 9600 818923 2.3 × 10-9 5.9962 × 10-5 0.00972186 0.00789 29 9900 868803 2.5 × 10-9 6.6134 × 10-5 0.01072255 0.00892 30 10200 924062 2.8 × 10-9 7.3249 × 10-5 0.01187606 0.009023 31 10500 970903 3.09× 10-9 7.9503 × 10-5 0.01289009 0.009162 32 10800 1034249 3.4 × 10-9 8.8281 × 10-5 0.01431329 0.010466 33 11100 1101079 3.8 × 10-9 9.7933 × 10-5 0.0158781 0.011904 34 11700 1225117 4.5 × 10-9 0.000116882 0.01895029 0.015213 35 12300 1367927 5.4 × 10-9 0.000140312 0.02274898 0.019161 36 12900 1521575 6.5 × 10-9 0.000167378 0.02713725 0.023821 37 13200 1607753 7.1 × 10-9 0.000183376 0.02973111 0.026443 38 13800 1779978 8.4 × 10-9 0.000217057 0.03519191 0.03232 39 14400 1977753 1 × 10-8 0.000258461 0.04190471 0.039111 40 15000 2211045 1.2 × 10-8 0.000310911 0.05040852 0.046902 41 15600 2410011 1.3 × 10-8 0.000358627 0.05814486 0.055779 42 16200 2657401 1.6 × 10-8 0.00042166 0.06836459 0.06583 43 17100 3038621 2.0 × 10-8 0.000526541 0.08536912 0.083293 44 17400 3168667 2.1 × 10-8 0.000564404 0.09150785 0.08979 45 18000 3470931 2.5 × 10-8 0.000656382 0.10642038 0.103857 46 18600 3748012 2.9 × 10-8 0.000745462 0.12086318 0.119409 47 19500 4271381 3.6 × 10-8 0.00092574 0.15009198 0.145639 48 20100 4519052 3.9× 10-8 0.001016368 0.16478560 0.165114 49 20700 4835239 4.4 × 10-8 0.001136889 0.18432589 0.186197 50 21300 5144090 4.9 × 10-8 0.001259725 0.20424155 0.208882 51 21600 5276024 5.1 × 10-8 0.001313711 0.21299437 0.220817


Sr.No. Time

(in sec)

Area under the

curve obtained from GC


Mole fraction of xylene at the exit

(Expt.)

(Model)

1 6000 55872 2.73 × 10-11 7.010 × 10-7 0.000292 0.000396 2 6600 72609 4.214 × 10-11 1.082 × 10-6 0.000451 0.000611 3 7200 95755 6.665 × 10-11 1.711 × 10-6 0.000713 0.000763 4 7800 141250 1.269 × 10-10 3.259 × 10-6 0.001358 0.001134 5 8100 136427 1.198 × 10-10 3.077 × 10-6 0.001282 0.001363 6 8400 158174 1.531 × 10-10 3.931 × 10-6 0.001638 0.001624

123

7 8700 163104 1.611 × 10-10 4.137 × 10-6 0.001724 0.001919 8 9000 189101 2.058 × 10-10 5.285 × 10-6 0.002202 0.002251 9 9600 231547 2.879 × 10-10 7.393 × 10-6 0.003081 0.003036

10 10200 282702 4.007 × 10-10 1.029 × 10-5 0.004288 0.003999 11 10800 329099 5.155 × 10-10 1.323 × 10-5 0.005516 0.005161 12 11400 380072 6.544 × 10-10 1.680 × 10-5 0.007003 0.006539 13 12000 436157 8.22 × 10-10 2.111 × 10-5 0.008797 0.008153 14 12600 498762 1.027 × 10-9 2.636 × 10-5 0.010986 0.010022 15 13200 565932 1.266 × 10-9 3.250 × 10-5 0.013544 0.012162 16 13800 626087 1.496 × 10-9 3.842 × 10-5 0.016012 0.01459 17 14400 706183 1.827 × 10-9 4.691 × 10-5 0.019547 0.017323 18 15000 743605 1.99 × 10-9 5.110 × 10-5 0.021293 0.020374 19 15600 798487 2.239 × 10-9 5.750 × 10-5 0.02396 0.023759 20 16200 866946 2.566 × 10-9 6.590 × 10-5 0.027459 0.02749 21 16800 945064 2.96 × 10-9 7.602 × 10-5 0.031679 0.031579 22 17400 1016530 3.34 × 10-9 8.578 × 10-5 0.035746 0.036038 23 18000 1098491 3.798 × 10-9 9.755 × 10-5 0.040647 0.040877 24 18600 1181714 4.287 × 10-9 0.0001101 0.045875 0.046106 25 19200 1267331 4.814 × 10-9 0.00012363 0.051513 0.051733 26 19800 1355708 5.383 × 10-9 0.00013824 0.0576 0.057766 27 20400 1447682 6.001 × 10-9 0.00015412 0.064219 0.064212 28 21000 1524356 6.537 × 10-9 0.00016788 0.069952 0.071077 29 21600 1612337 7.174 × 10-9 0.00018424 0.076768 0.078364

124

APPENDIX E

DATA FOR COMPARISON BETWEEN EXPERIMENTAL AND MODEL PREDICTED VALUES USING AVERAGE

PARAMETERS

Table E.1: Data for the comparison of experimental and model predicted values by using average parameters for toluene (Gas flow rate = 70 ml/min, Inlet concentration = 11500 ppm, Bed height = 0.015 m, Particle diameter = 0.0015 m)

Sr.No. Time

(in sec) Experimental

Values Model Predicted values using average

parameters 1 2220 0.000685 0.0005814 2 2520 0.001202 0.001161 3 2700 0.001521 0.001674 4 3000 0.002216 0.002888 5 3300 0.003323 0.004662 6 3600 0.005177 0.0048135 7 3900 0.007688 0.00936 8 4200 0.011133 0.01325 9 4500 0.015172 0.01789

10 4800 0.020821 0.024 11 5220 0.032565 0.03896 12 5700 0.047775 0.05664 13 6000 0.061746 0.07011 14 6360 0.083339 0.08891 15 6900 0.118075 0.1229 16 7500 0.161399 0.1689 17 8100 0.223212 0.2237 18 8700 0.279113 0.2862 19 9000 0.314774 0.32 20 9300 0.346461 0.3551 21 9600 0.381891 0.3913 22 9900 0.412391 0.4282 23 10500 0.487021 0.5029 24 10800 0.519034 0.5406 25 12000 0.669849 0.6828 26 12600 0.722792 0.7472 27 12900 0.763943 0.7759

125

Table E.2: Data for the comparison of experimental and model predicted values by using average parameters for xylene (Gas flow rate = 50 ml/min, Inlet concentration = 6200 ppm, Bed height = 0.025 m, Particle diameter = 0.0015 m)

Sr.No. Time

(in sec) Experimental

Values Model Predicted values using average

parameters 1 11100 2.40 × 10-5 1.87 × 10-5 2 12000 2.70 × 10-5 2.51 × 10-5 3 12300 2.90 × 10-5 4.87 × 10-5 4 13020 4.70 × 10-5 7.91 × 10-5 5 13500 5.80 × 10-5 9.61 × 10-5 6 14400 0.000139 0.000101164 7 15000 0.000206 0.000175408 8 16200 0.000508 0.000396053 9 16800 0.000718 0.000519955 10 18600 0.001783 0.001330719 11 22080 0.005817 0.004222672 12 22200 0.006304 0.005147787 13 22500 0.006812 0.006180255 14 22800 0.007529 0.006566589 15 23400 0.008945 0.007163978 16 24000 0.010617 0.009189639 17 24300 0.011427 0.010431157 18 24900 0.013731 0.011986209 19 25200 0.015025 0.012702475 20 25800 0.017833 0.01368289 21 26100 0.019345 0.0165636 22 26700 0.022948 0.019670383 23 27000 0.024749 0.020144988 24 27600 0.029481 0.025253301 25 27900 0.031568 0.028313261 26 28800 0.040286 0.032149347 27 29100 0.043286 0.036118044 28 29400 0.046809 0.039227441 29 29700 0.050805 0.040485959 30 30000 0.054295 0.04771233 31 31800 0.080691 0.065280061 32 32100 0.085984 0.069104953 33 32400 0.09075 0.078474497 34 33000 0.103465 0.088075242 35 33300 0.109219 0.093536972 36 33900 0.12168 0.099427582 37 34200 0.127553 0.116922173 38 34800 0.141944 0.125867619

126

39 35100 0.148031 0.134586214 40 35700 0.16371 0.151458934 41 36000 0.17082 0.162569844

127

APPENDIX F

SAMPLE CALCULATION FOR THE PARAMETERS

The following are the sample calculations for the parameters used in the model for

toluene. The calculations have been done corresponding to the experimental conditions

given in Table E.1:

Table F.1: Experimental conditions for the calculation of parameters Parameter Value Gas flow rate, ml/min 70 Bed height, m 0.015 Adsorbent particle size, m 0.0015 Pore radius, nm 1.1 Particle density, kg/m3 400 Amount of adsorbent, g 4 Temperature, K 313

A.1 Calculation of Diffusivity The effective diffusivity inside the pores is given by a combination of both Knudsen and

molecular diffusion.

Knudsen Diffusivity, Dk:

= 97.

where rp is the pore radius in m.

Ms is the molecular weight of solute in kg/kmole.

T is the temperature in K.

Dk is the Knudsen diffusivity in m2/s.

For micropore radius of 1.1 nm,

= 97(1.1 × 10 )31392

.

= 1.968× 10 /

128

Molecular Diffusivity, DAB (Treybal, 1980):

=10 1.084 0.249 1 + 1 .

. 1 + 1 .

( )

where, MA & MB are the molecular weights of two interacting species (A: Toluene, B: N2)

P is the pressure in Pa.

rAB is the molecular separation at collision, nm =

AB A B)0.5

k is the Boltzmann’s constant.

= collision function, a function of

rA = 0.6026 nm , = 463.43

rB = 0.3798 nm, = 71.4

= (463.34× 71.4) . = 181.903

= 0.56

=0.6026 + 0.3798

2 = 0.4912

1+

1 .

= 1

92 +1

28

.

= 0.2158

=10 1.084 (0.249)(0.2158) (313) . (0.2158)

(101325)(0.4912) (0.56) = 8.995 × 10

Combined Diffusivity, D:

1

=1

+1

1=

11.968× 10 +

18.995× 10

= 1.968 × 10 /

Effective Diffusivity inside the Pores, De:

=

129

=(0.45)(1.968 × 10 )

4 = 2.2 × 10 /

A.2 Calculation of Reynolds Number, Schmidt Number, Peclet Number,

Axial Dispersion Coefficient and External Mass Transfer Coefficient Superficial Gas Velocity, U:

=

4

where Q is the volumetric flow rate of gas in m3/s.

and Dc is the diameter of the column in m.

For Q = 70 ml/min = 1.16 × 10-6 m3/s and Dc = 0.05 m

= =1.16× 10

(0.05)4

= 5.91 × 10 /

g:

=..

M is the molecular weight of gas in kg/kmol.

R is the universal gas constant in J/kmol.K.

=(101325)(28)(8314)(313) = 1.09

Reynolds Number Based On Particle Diameter, Re:

=. .

where dp is the particle diameter in m.

=(1.09)(5.91× 10 )(0.0015)

(1.45× 10 ) = 0.066

130

Schimdt Number, Sc:

= .

=(1.45× 10 )

(1.09)(8.9936× 10 ) = 1.479

Peclet Number, Pe (Yang, 1997): 1

=0.3

( )( ) +0.5

1 + 3.8.

, 0.008 < < 400 0.28 < < 2.

=0.3

(0.066)(1.479) +0.5

1 + 3.8(0.066)(1.479)

Pe = 0.324

Axial Dispersion Coefficient, DL:

=.

.

=(0.0015)(1.45× 10 )

(1.09)(0.324) = 6.158× 10

External Film Mass Transfer Coefficient, km (Perry et al., 1997):

= 0.91 ( ) . ( ) . , 0.01 < < 50

where is the shape factor.

and Sh is the Sherwood number given by

=

= 0.91(0.91)(0.066) . (1.479) . = 0.248

=.

=(0.248)(8.9936× 10 )

(0.0015) = 0.00149 /

A.3 Calculation of Bed Porosity, b Amount of adsorbent, w = 4 g

D 3

131

Actual volume of the adsorbent = . = 10

Volume of the packed bed = ( ) ( )

= 4(0.05) (0.015) = 2.94 × 10

=(2.94 × 10 ) (10 )

(2.94 × 10 ) = 0.66

appendix a matlab code for predicting breakthrough...

Documents