Difference between revisions of "Isothermal reactor design  2013"
Kevin Dunn (talk  contribs) m 
Kevin Dunn (talk  contribs) 

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where :math:`F_T = F_A + F_B + F_C` and :math:`C_\text{T0} = \dfrac{P_0}{RT_0}`  where :math:`F_T = F_A + F_B + F_C` and :math:`C_\text{T0} = \dfrac{P_0}{RT_0}`  
Using all of the above derivations, we can set up our numerical integration.  Using all of the above derivations, we can set up our numerical integration as shown below.  
</rst>  </rst>  
Line 104:  Line 104:  
<syntaxhighlight lang="matlab">  <syntaxhighlight lang="matlab">  
sdfsdf  sdfsdf  
</syntaxhighlight>  
In a separate file (any name), for example: '''<tt>ode_driver.m</tt>''', which will "drive" the ODE solver:  
<syntaxhighlight lang="matlab">  
asdas  
</syntaxhighlight>  </syntaxhighlight>  
[[Image:PlotsMATLAB.png  550px]]  [[Image:PlotsMATLAB.png  550px]]  
Line 112:  Line 117:  
[[Image:PlotsPython.png550px]]  [[Image:PlotsPython.png550px]]  
}  }  
and in Polymath:  
<syntaxhighlight lang="text">  
d(FA)/d(V) = rA  
d(FB)/d(V) = rB  kDiff * CB  
d(FC)/d(V) = rC  
FA(0) = 0.25 # mol/s  
FB(0) = 0.0 # mol/s  
FC(0) = 0.0 # mol/s  
# Independent variable  
V(0) = 0  
V(f) = 0.4 #m^3  
# Algebraic equations  
rB = rA  
rC = rA  
rA = k * (CA  CB * CC / KC)  
CA = CT0 * FA / FT  
CB = CT0 * FB / FT  
CC = CT0 * FC / FT  
CT0 = P0 / (R * T0)  
FT = FA + FB + FC  
# Constants  
kDiff = 0.005 # s^{1}  
k = 0.01 # s^{1}  
KC = 50 # mol.m^{3}  
P0 = 830600 # Pa  
T0 = 500 # K  
R = 8.314 # J/(mol.K)  
</syntaxhighlight> 
Revision as of 00:13, 26 February 2013
Class date(s):  04 February to 14 February  
 
 
 
 
 
 F2011: Chapter 5 and 6
 F2006: Chapter 4
04 February 2013 (05A)
 General problem solving strategy for reactor engineering
 Audio and video recording of the class
06 February 2013 (05B)
 The Ergun equation derivation
 Audio and video recording of the class
07 February 2013 (05C)
 Notes used during the class
 The spreadsheet with the Ergun equation example. Use it to try
 different lengths of reactor
 different catalyst particle sizes
 different pipe diameters
 gas properties (e.g. density)
 to see the effect on pressure drop in the packed bed.
11 February 2013 (06A)
 Audio and video recording of the class
 Codes to solve the example in class are available on the page software for integrating ODEs.
14 February 2013 (06C): midterm review
25 February 2013 (07A)
The example covered in class is based on example 48 in F2006 and example 62 in F2011. <rst> The 3 ODE's are:
.. math::
\dfrac{dF_A}{dV} &= r_A\\ \dfrac{dF_B}{dV} &= r_B  R_B \\ \dfrac{dF_C}{dV} &= r_C
where :math:`r_A = r_B = r_C` and :math:`r_A = k\left(C_A  \dfrac{C_B C_C}{K_C} \right)`, and :math:`R_B = k_\text{diff}C_B`.
 :math:`k = 0.01\,\text{s}^{1}`
 :math:`k_\text{diff} = 0.005\,\text{s}^{1}`
 :math:`K_C = 50\,\text{mol.m}^{3}`
We derived earlier in the course that
.. math:: C_A = C_\text{TO}\left(\dfrac{F_A}{F_T}\right)\left(\dfrac{P}{P_0}\right)\left(\dfrac{T_0}{T}\right)
Assuming isothermal and isobaric conditions in the membrane:
.. math:: C_A = C_\text{T0}\left(\dfrac{F_A}{F_T}\right)
where :math:`F_T = F_A + F_B + F_C` and :math:`C_\text{T0} = \dfrac{P_0}{RT_0}`
Using all of the above derivations, we can set up our numerical integration as shown below. </rst>
MATLAB  Python 

In a file called membrane.m: sdfsdf
In a separate file (any name), for example: ode_driver.m, which will "drive" the ODE solver: asdas

asdasd

and in Polymath:
d(FA)/d(V) = rA
d(FB)/d(V) = rB  kDiff * CB
d(FC)/d(V) = rC
FA(0) = 0.25 # mol/s
FB(0) = 0.0 # mol/s
FC(0) = 0.0 # mol/s
# Independent variable
V(0) = 0
V(f) = 0.4 #m^3
# Algebraic equations
rB = rA
rC = rA
rA = k * (CA  CB * CC / KC)
CA = CT0 * FA / FT
CB = CT0 * FB / FT
CC = CT0 * FC / FT
CT0 = P0 / (R * T0)
FT = FA + FB + FC
# Constants
kDiff = 0.005 # s^{1}
k = 0.01 # s^{1}
KC = 50 # mol.m^{3}
P0 = 830600 # Pa
T0 = 500 # K
R = 8.314 # J/(mol.K)