Chapter 13 : Diffusion Mass Transfer

Example 13.1 Page No : 544

In [1]:
# Variables
ro2 = 0.21;			#Ratio of O2 in the mixture  
rn2 = 0.79;			#Ratio of N2 in the mixture  
T = (25+273);			#Temperature of container in degree C
p = 1;			#Total pressure in atm

# Calculations
Co2 = (ro2*10**5)/(8314*T);			#Molar concentration of O2 in K.mol/m**3
Cn2 = (rn2*10**5)/(8314*T);			#Molar concentration of N2 in K.mol/m**3
po2 = (32*Co2);			#Mass density in kg/m**3
pn2 = (28*Cn2);			#Mass density in kg/m**3
p = (po2+pn2);			#Overall mass density in kg/m**3
mo2 = (po2/p);			#Mass fraction of O2
mn2 = (pn2/p);			#Mass fraction of N2
M = (ro2*32)+(rn2*28);			#Average molecular weight 

# Results
print 'Molar concentration of O2 is %3.4f K.mol/m**3  \n \
Molar concentration of N2 is %3.3f K.mol/m**3  \n \
Mass density of O2 is %3.3f kg/m**3  \n \
Mass density of N2 is %3.3f kg/m**3  \n \
Mole fraction of O2 is %3.2f  \n \
Mole fraction of N2 is %3.2f  \n \
Mass fraction of O2 is %3.3f  \n \
Mass fraction of N2 is %3.3f  \n \
Average molecular weight is %3.2f'%(Co2,Cn2,po2,pn2,ro2,rn2,mo2,mn2,M)
Molar concentration of O2 is 0.0085 K.mol/m**3  
 Molar concentration of N2 is 0.032 K.mol/m**3  
 Mass density of O2 is 0.271 kg/m**3  
 Mass density of N2 is 0.893 kg/m**3  
 Mole fraction of O2 is 0.21  
 Mole fraction of N2 is 0.79  
 Mass fraction of O2 is 0.233  
 Mass fraction of N2 is 0.767  
 Average molecular weight is 28.84

Example 13.2 Page No : 545

In [2]:
# Variables
yh2 = 0.4;			#Mole fraction og H2
yo2 = 0.6;			#Mole fraction of O2
vh2 = 1;			#velocity of H2 in m/s
vo2 = 0;			#velocity of O2 in m/s

# Calculations
V = (yh2*vh2)+(yo2*vo2);		#Molar average velocity in m/s
M = (yh2*2)+(yo2*32);			#Molecular weight of the mixture
mh2 = (yh2*2)/M;	    		#Mass fraction of H2 
mo2 = (yo2*32)/M;		    	#Mass fraction of O2
v = (mh2*vh2)+(mo2*vo2);		#Mass average velocity in m/s
x1 = (mh2*vh2);			        #Mass flux 
x2 = (mo2*vo2);			        #Mass flux
y1 = (v*vh2);		    	    #Molar flux
y2 = (yo2*vo2);	    		    #Molar flux
jh2 = (mh2*(vh2-v));			#Mass diffusion flux
jo2 = (mo2*(vo2-v));			#Mass diffusion flux
Jh2 = (yh2*(vh2-V));			#Molar diffusion flux
Jo2 = (yo2*(vo2-V));			#Molar diffusion flux

# Results
print 'Molar average velocity is %3.1f m/s \n \
Mass average velocity is %3.2f m/s  \n \
Mass flux of H2 when it is stationary is %3.2fp kg/m2.s3 \n \
Mass flux of O2 when it is stationary is %3.0f kg/m**2.s \n \
Molar flux of H2 when it is stationary is %3.2fC k.mol/m**2.s \n \
Molar flux of O2 when it is stationary is %3.0f k.mol/m**2.s \n \
Mass diffusion flux of H2 across a surface moving with mass average velocity is %3.4fp kg/m**2.s \n \
Mass diffusion flux of O2 across a surface moving with mass average velocity is %3.4fp kg/m**2.s  \n \
Molar diffusion flux across a surface moving with molar average velociy for H2 is %3.2fC k.mol/m**2.s \n \
Molar diffusion flux across a surface moving with molar average velociy for O2\
 is %3.2fC k.mol/m**2.s'%(V,v,x1,x2,y1,y2,jh2,jo2,Jh2,Jo2)
Molar average velocity is 0.4 m/s 
 Mass average velocity is 0.04 m/s  
 Mass flux of H2 when it is stationary is 0.04p kg/m2.s3 
 Mass flux of O2 when it is stationary is   0 kg/m**2.s 
 Molar flux of H2 when it is stationary is 0.04C k.mol/m**2.s 
 Molar flux of O2 when it is stationary is   0 k.mol/m**2.s 
 Mass diffusion flux of H2 across a surface moving with mass average velocity is 0.0384p kg/m**2.s 
 Mass diffusion flux of O2 across a surface moving with mass average velocity is -0.0384p kg/m**2.s  
 Molar diffusion flux across a surface moving with molar average velociy for H2 is 0.24C k.mol/m**2.s 
 Molar diffusion flux across a surface moving with molar average velociy for O2 is -0.24C k.mol/m**2.s

Example 13.3 Page No : 557

In [3]:
# Variables
t = 0.001;			#Thickness of the membrane in m
CA1 = 0.02;			#Concentration of helium in the membrane at inner surface in k.mol/m**3
CA2 = 0.005;			#Concentration of helium in the membrane at outer surface in k.mol/m**3
DAB = 10**-9;			#Binary diffusion coefficient in m**2/s

# Calculations
NAx = ((DAB*(CA1-CA2))/t)/10**-9;			#Diffusion flux of helium through the plastic in k.mol/sm**2 *10**-9

# Results
print 'Diffusion flux of helium through the plastic is %3.0f*10**-9 k.mol/sm**2'%(NAx)
Diffusion flux of helium through the plastic is  15*10**-9 k.mol/sm**2

Example 13.4 Page No : 557

In [4]:
# Variables
T = 273+25;			#Temperature of Helium gas in K
p = 4;			#Pressure of helium gas in bar
Di = 0.1;			#Inner diamter of wall in m
Do = 0.003;			#Outer diamter of wall in m
DAB = (0.4*10**-13);			#Binary diffusion coefficient in m**2/s
S = (0.45*10**-3);			#S value for differentiation

# Calculations
A = (3.14*Di**2);			#Area in m**2
V = (3.14*Di**3)/6;			#Volume in m**3
R = 0.08316			#Gas consmath.tant in m**3 bar/kmol.K
d = ((-6*R*T*DAB*S*p)/(Do*Di))/10**-11;			#Decrease of pressure with time in bar/s*10**-11

# Results
print 'Initial rate of leakage for the system is provided by the decrease of pressure \
 with time which is %3.2f*10**-11 bar/s'%(d)
Initial rate of leakage for the system is provided by the decrease of pressure  with time which is -3.57*10**-11 bar/s

Example 13.5 Page No : 558

In [6]:
import math

# Variables
po2 = 2;			#Pressure of O2 in bar
Di = 0.025;			#inside diamter of the pipe in m
L = 0.0025;			#Wall thickness in m
a = (0.21*10**-2);			#Diffusivity of O2 in m**2/s
S = (3.12*10**-3);			#Solubility of O2 in k.mol/m**3.bar
DAB = (0.21*10**-9);			#Binary diffusion coefficient in m**2/s

# Calculations
CAi = (S*po2);			#Concentration of O2 on inside surface in kmol/m**3
RmA = ((math.log((Di+(2*L))/Di))/(2*3.14*DAB));			#Diffusion resismath.tance in sm**2
Loss = (CAi/RmA)/10**-11;			#Loss of O2 by diffusion per meter length of pipe *10**-11

# Results
print 'Loss of O2 by diffusion per meter length of pipe is %3.2f*10**-11 kmol/s'%(Loss)
Loss of O2 by diffusion per meter length of pipe is 4.51*10**-11 kmol/s

Example 13.6 Page No : 560

In [7]:
# Variables
p = 1;			#Pressure of system in atm
T = 25+273;			#Temperature of system in K
pco2 = (190./760);			#Partial pressure of CO2 at one end in atm
pco2o = (95./760);			#Partial pressure of CO2 at other end in atm
DAB = (0.16*10**-4);			#Binary diffusion coefficient in m**2/s from Table 13.3
R = 0.08205			#Gas constant in m**3 atm/kmol.K

# Calculations
NAx = (DAB*(pco2-pco2o))/(R*T*p);			#Equimolar counter diffusion in kmol/m**2s
M = (NAx*3.14*(0.05**2/4)*3600);			#Mass transfer rate in kmol/h
MCO2 = (M*44)/10**-5;			#Mass flow rate of CO2 in kg/h *10**-5
Mair = (29*-M)/10**-5;			#Mass flow rate of air in kg/h *10**-5

# Results
print 'Mass transfer rate of CO2 is %3.2f*10**-5 kg/h Mass transfer rate of air is %3.2f*10**-5 kg/h'%(MCO2,Mair)
Mass transfer rate of CO2 is 2.54*10**-5 kg/h Mass transfer rate of air is -1.68*10**-5 kg/h

Example 13.7 Page No : 563

In [8]:
import math
# Variables
T = 27+273;			#Temperature of water in K
D = 0.02;			#Diameter of the tube in m
L = 0.4;			#Length of the tube in m
DAB = (0.26*10**-4);			#Diffusion coefficient in m**2/s

# Calculations
p = 1.0132;			#Atmospheric pressure in bar
pA1 = 0.03531;			#Vapour pressure in bar
m = ((p*10**5*3.14*(D/2)**2*18*DAB)/(8316*T*L))*(1000*3600)*math.log(p/(p-pA1));			#Diffusion rate of water in gram per hour

# Results
print 'Diffusion rate of water is %3.4f gram per hour'%(m)
Diffusion rate of water is 0.0019 gram per hour

Example 13.8 Page No : 564

In [9]:
import math
# Variables
T = 25+273;			#Temperature of water in K
D = 0.02;			#Diameter of the tube in m
L = 0.08;			#Length of the tube in m
m = (8.54*10**-4);			#Diffusion coefficient in kg/h

# Calculations
p = 1.0132;			#Atmospheric pressure in bar
pA1 = 0.03165;			#Vapour pressure in bar
DAB = (((m/3600)*8316*T*L)/(p*10**5*3.14*(D/2)**2*18*math.log(p/(p-pA1))*10**2))/10**-4;			#Diffusion coefficient of water in m**2/s *10**-4

# Calculations
print 'Diffusion coefficient of water is %3.3f*10**-4 m**2/s'%(DAB)
Diffusion coefficient of water is 0.259*10**-4 m**2/s

Example 13.9 Page No : 569

In [1]:
# Variables
CAs = 0.02;			#Carbon mole fraction
CAo = 0.004;		#Content of steel
CA = 0.012;			#Percet of depth
d = 0.001;			#Depth in m
H = (6*10**-10);	#Diffusivity of carbon in m**2/s

# Calculations
X = (CA-CAs)/(CAo-CAs);			#Calculation for erf function
n = 0.48;           			#erf(n) = 0.5; n = 0.48
t = ((d/(n*2.))**2/(3600.*H))*3600;			#Time required to elevate the carbon content of steel in s


# Results
print 'Time required to elevate the carbon content of steel is %3.2f s'%(t)


# note : rounding error.
Time required to elevate the carbon content of steel is 1808.45 s