Fuels and Combustion

Example 2.1,Page 76

In [1]:
# Initialization of Variable
from math import pi
from math import atan
from numpy import *
x1=0.135 #moisture 
x2=0.056 #ash content
veca=array([32.5, 48.4, 5.6, 13.5]) #materials as received
B1=11788.0 #Btu/lb

#calculations
vecb=veca/(1-x1) #moisture free
vecc=veca/(1-x1-x2) #moisture and ash free
B2=B1/(1-x1)
B3=B1/(1-x1-x2)
vecb[3]=0
vecc[3]=0
vecc[2]=0

#results
print "In Moisture free case",vecb
print "In Moisture and Ash free case ",vecc
print "Energy in Moisture free case  Btu per lb",round(B2,3)
print "Energy in Moisture and ash free case Btu per lb",round(B3,2)

In Moisture free case [ 37.57225434  55.95375723   6.47398844   0.        ]
In Moisture and Ash free case  [ 40.17305315  59.82694685   0.           0.        ]
Energy in Moisture free case  Btu per lb 13627.746
Energy in Moisture and ash free case Btu per lb 14571.08

Example 2.2,Page 77

In [5]:
# Initialization of Variable
from math import pi
from math import atan
from numpy import *
y1=13.5
x1=0.135 #moisture 
x2=0.056 #ash 
veca=array([66.0, 1.5, 1.1, 5.6, 5.9, 19.9]) # fram table 2.3
vecb=array([66.0, 1.5, 1.1, 5.6, 5.9, 19.9,13.5]) #with moisture 

#calculations
vecb[4] = vecb[4] - 1.0/9*y1 ;
vecb[5] = vecb[5] - 8.0/9*y1 ;
vecc=vecb/(1-x1)
vecd=vecb/(1-x1-x2) # moisture and ash free
vecd[3]=0
vecd[6]=0
vecc[6]=0
s1=sum(vecc)
s2=sum(vecd)

#results
print "With moisture as a separate item",vecb
print "In Moisture free case, ",vecc
print "In Moisture and Ash free case",vecd
print "Total Mositure free content  percent",round(s1,3)
print " Total Mositure and ash free content  percent",round(s2,3)
print "slight error due to rounding off error"

With moisture as a separate item [ 66.    1.5   1.1   5.6   4.4   7.9  13.5]
In Moisture free case,  [ 76.30057803   1.73410405   1.2716763    6.47398844   5.0867052
   9.13294798   0.        ]
In Moisture and Ash free case [ 81.58220025   1.85414091   1.35970334   6.92212608   0.           9.76514215
   0.        ]
Total Mositure free content  percent 100.0
 Total Mositure and ash free content  percent 101.483

Example 2.3,Page 78

In [3]:
# Initialization of Variable
from math import pi
from math import atan
from numpy import *
H=5.9 
O=19.9 
H2=4.4 
O2=7.9  

#calculations
Ha1=H-O/8
Ha2=H2-O2/8

#results
print "Available hydrogen in case 1  percent by weight",round(Ha1,3)
print " Available hydrogen in case 2  percent by weight",round(Ha2,3)

Available hydrogen in case 1  percent by weight 3.413
 Available hydrogen in case 2  percent by weight 3.413

Example 2.4,Page 93

In [6]:
# Initialization of Variable
from math import pi
from math import atan
from numpy import *
H1=0.059
O1=0.199
H2=0.044
O2=0.079
C=0.66
S=0.011

#calculations
Qh1= 14600*C+62000*(H1-O1/8)+4050*S #heating value
Qh2=14600*C+62000*(H2-O2/8)+4050*S  #heating value

#results
print "Heating value in case 1  Btu/lb ",round(Qh1,3)
print " Heating value in case 2  Btu/lb ",round(Qh2,3)

Heating value in case 1  Btu/lb  11796.3
 Heating value in case 2  Btu/lb  11796.3

Example 2.5,Page 110

In [5]:
# Initialization of Variable
from math import pi
from math import atan
from numpy import *
H1=0.059
O1=0.199
C=0.66
S=0.011

#calculations
Qh1= 11.52*C+34.56*(H1-O1/8)+4.32*S

#results
print "Theoretical air required in lb of air per lb of coal ",round(Qh1,3)

Theoretical air required in lb of air per lb of coal  8.83

Example 2.6,Page 110

In [12]:
# Initialization of Variable
from math import pi
from math import atan
from numpy import *
mf=10000 #lb
mr=700 #lb
Cr=0.20
Cco2=14.1 #% CO2
Co2=5.1 #% O2
Cco=0.1 #% CO
Cf=0.66 

#calculations
Cn2=100-(Cco2+Co2+Cco) #% N2
Ci=mf*Cf #carbon input
Ca=mr*Cr #carbon in ashpit
Cb=(Ci-Ca)/mf
Cb2=((mf*Cf)-mr*Cr)/(mf)
Mco2=Cco2 *44 #mass of CO2
Mo2=Co2 *32   #mass of O2
Mco=Cco *28   #mass of CO
Mn2=Cn2 *28   #mass of N2
sumvec=Mo2+Mco2+Mco+Mn2;
Lbc=Cco2*12 + Cco*12
Gc=sumvec/Lbc
Gf=Gc*Cb

#results
print "Carbon in the dry products combustion in lb per lb of fuel",round(Cb,3)
print " In case 2, Carbon in the dry products combustion in lb per lb of fuel",round(Cb2,3)
print " Dry gaseous products of combstion per lb of coal in lb ",round(Gf,3)

Carbon in the dry products combustion in lb per lb of fuel 0.646
 In case 2, Carbon in the dry products combustion in lb per lb of fuel 0.646
 Dry gaseous products of combstion per lb of coal in lb  11.548

Example 2.7,Page 111

In [8]:
# Initialization of Variable
from math import pi
from math import atan
from numpy import *
mf=10000.0 #lb
mr=700.0 #lb
Cr=0.20
Cco2=14.1
Co2=5.1
Cco=0.1
Cf=0.66

#calculations
Cn2=100-(Cco2+Co2+Cco)
Ci=mf*Cf
Ca=mr*Cr
Cb=(Ci-Ca)/mf
Cb2=((mf*Cf)-mr*Cr)/(mf)
Mco2=Cco2 *44 #mass of CO2
Mo2=Co2 *32   #mass of O2
Mco=Cco *28   #mass of CO
Mn2=Cn2 *28   #mass of N2
sumvec=Mn2+Mco2+Mco+Mn2;
Cbb1=Cb*Cco*12/(Cco2*12 + Cco*12)
Cbb2= Cb*(Cco /(Cco + Cco2))

#results
print "In case 1, Carbon burned per lb of fuel in lb per lb of fuel",round(Cbb1,6)
print " In case 2, Carbon burned per lb of fuel in lb per lb of fuel",round(Cbb2,6)

In case 1, Carbon burned per lb of fuel in lb per lb of fuel 0.004549
 In case 2, Carbon burned per lb of fuel in lb per lb of fuel 0.004549

Example 2.8,Page 111

In [7]:
# Initialization of Variable
from math import pi
from math import atan
from numpy import *
H=4.4/100 #hydrogen
M=13.5/100 #moisture
H2=0.059  #hydrogen

#calculations
pro=M+9*H
pro2=9*H2

#results
print "In case 1, watervapor present in products in lb",round(pro,3)
print  "In case 2, watervapor present in products in lb",round(pro2,3)

In case 1, watervapor present in products in lb 0.531
In case 2, watervapor present in products in lb 0.531

Example 2.9,Page 113

In [8]:
# Initialization of Variable
from math import pi
from math import atan
from numpy import *
Gf=11.57;#lb
f=11.57 #lb per lb of fuel
H=4.4/100
M=13.5/100
mr=700.0 #lb
mf=10000.0 #lb
mc=1 #lb

#calculations
pro=M+9*H
mrf=mr/mf
Aa=Gf+pro+mrf-mc

#results
print "Actual air supplied in lb of air supplied per lb of fuel",round(Aa,3)

Actual air supplied in lb of air supplied per lb of fuel 11.171

Example 2.10,Page 114

In [33]:
# Initialization of Variable
from math import pi
from math import atan
from numpy import *
Gf=11.57 #lb per lb of fuel
H=4.4/100
M=13.5/100
mr=700.0
mf=10000.0
mc=1.0 #lb

#calculations
pro=M+9*H
mrf=mr/mf
Aa=Gf+pro+mrf-mc
At=8.83
ea=(Aa-At)/At *100

#results
print "Excess air in percent",round(ea,3)

26.512 Excess air in percent

Example 2.11a,Page 114

In [1]:
# Initialization of Variable
from math import pi
from math import atan
from numpy import *
Gf=11.57 #lb per lb of fuel
tg=500 #F
ta=70 #F
#calculations

Q1=0.24*Gf*(tg-ta)

#results
print "Heat loss in Btu per lb of fuel",round(Q1,3)

Heat loss in Btu per lb of fuel 1194.024

Example 2.11b,Page 115

In [35]:
# Initialization of Variable
from math import pi
from math import atan
from numpy import *
Co=0.1
Co2=14.1
Cb=0.646

#calculations
Q2=Co/(Co+Co2) *Cb*10160

#results
print "Heat loss in Btu per lb of fuel",round(Q2,3)

46.221 Heat loss in Btu per lb of fuel

Example 2.11c ,Page 115

In [37]:
# Initialization of Variable
from math import pi
from math import atan
from numpy import *
mf=10000.0 #lb 
mr=700.0 #lb
Cr=0.2

#calculations
Q3=mr*Cr/mf *14600

#results
print "Heat loss in Btu per lb of fuel",round(Q3,2)

204.4 Heat loss in Btu per lb of fuel

Example 2.11d,Page 115

In [39]:
# Initialization of Variable
from math import pi
from math import atan
from numpy import *
M=0.135
tg=500.0 #F
ta=70.0 #F

#calculations
Q4=M*(1089+0.46*tg-ta) #heat loss

#results
print "Heat loss in Btu per lb of fuel",round(Q4,3)

168.615 Heat loss in Btu per lb of fuel

Example 2.11e,Page 115

In [2]:
# Initialization of Variable
from math import pi
from math import atan
from numpy import *
Per=0.044 #percentage
tg=500 #F
ta=70 #F

#calculations
Q5=9*Per*(1089+0.46*tg-ta) #heat loss

#results
print "Heat loss in Btu per lb of fuel",round(Q5,3)

Heat loss in Btu per lb of fuel 494.604