Textbook references
- F2011: Chapter 8
- F2006: Chapter 6
Suggested problems
Will be posted soon
Class materials
06 March 2013 (08B-2)
07 March 2013
Polymath code for example in class. Make sure you plot the instantaneous selectivity, overall selectivity and yield over time. Compare these 3 plots during the batch to understand what each of these 3 variables mean.
# ODEs
d(CA) / d(t) = -k1*CA
d(CB) / d(t) = k1*CA - k2*CB
d(CC) / d(t) = k2*CB
# Initial conditions
CA(0) = 2 # mol/L
CB(0) = 0 # mol/L
CC(0) = 0 # mol/L
# Algebraic equations
k1 = 0.5 # 1/hr
k2 = 0.2 # 1/hr
# The 3 important algebraic variables: plot these 3 against time and interpret them.
S_DU = if (t>0.001) then (k1*CA - k2*CB) / (k2*CB) else 0
Overall_SDU = if (t>0.001) then CB/CC else 0
Yield = if (t>0.001) then CB / (2 - CA) else 0
# Independent variable details
t(0) = 0
t(f) = 3.1 # hours
11 March 2013
13 March 2013
Code for the CSTR example:
tau = 0:0.05:10;
CA0 = 2; % mol/L
k1 = 0.5; % 1/hr
k2 = 0.2; % 1/hr
CA = CA0 ./ (1 + k1 .* tau);
CB = tau .* k1 .* CA ./ (1 + k2 .* tau);
CC = tau .* k2 .* CB;
instant_selectivity = (k1.*CA - k2.*CB) ./ (k2.*CB);
overall_selectivity = CB ./ CC;
overall_yield = CB ./ (CA0 - CA);
conversion = (CA0 - CA)./CA0;
plot(tau, CA, tau, CB, tau, CC)
grid on
xlabel('\tau')
ylabel('Concentrations [mol/L]')
figure
plot(tau, overall_selectivity)
xlabel('\tau')
ylabel('Overall Selectivity')
grid on
figure
plot(tau, overall_yield)
xlabel('\tau')
ylabel('Overall Yield')
grid on
figure
plot(tau, conversion)
xlabel('\tau')
ylabel('Conversion')
hold on
grid on
14 March 2013
| MATLAB
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Polymath
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k1 = 0.014 # L^{0.5} / mol^{0.5} / s
k2 = 0.007 # L/(mol.s)
k3 = 0.14 # 1/s
k4 = 0.45 # L/(mol.s)
alpha = 0.002 # 1/L
CT0 = 1.0 # mol/L
FA0 = 10 # mol/s
FB0 = 5.0 # mol/s
FT0 = FA0 + FB0
# Concentration functions (isothermal conditions)
CA = CT0 * FA/FT * y
CB = CT0 * FB/FT * y
CC = CT0 * FC/FT * y
CD = CT0 * FD/FT * y
CE = CT0 * FE/FT * y
CG = CT0 * FG/FT * y
CW = CT0 * FW/FT * y
FT = FA + FB + FC + FD + FE + FW + FG
# Reaction 1: A + 0.5B -> C
r1A = -k1*(CA)*(CB)^(0.5)
r1B = 0.5*r1A
r1C = -r1A
# Reaction 2: 2A -> D
r2A = -k2*(CA)^2
r2D = -r2A/2
# Reaction 3: C -> E + W
r3C = -k3*(CC)
r3E = -r3C
r3W = -r3C
# Reaction 4: D + W -> G + C
r4D = -k4*(CD)*(CW)
r4W = r4D
r4G = -r4D
r4C = -r4D
# ODE's
d(FA) / d(W) = r1A + r2A
FA(0) = 10
d(FB) / d(W) = r1B
FB(0) = 5
d(FC) / d(W) = r1C + r3C + r4C
FC(0) = 0
d(FD) / d(W) = r2D + r4D
FD(0) = 0
d(FE) / d(W) = r3E
FE(0) = 0
d(FW) / d(W) = r3W + r4W
FW(0) = 0
d(FG) / d(W) = r4G
FG(0) = 0
W(0) = 0 # kg
W(f) = 500 # kg
Yield_C = if (W>0.001) then (FC / (FA0 - FA)) else (0)
S_CE = if (W>0.001) then (FC/FE) else (0)
S_CD = if (W>0.001) then (FC/FD) else (0)
d(y) / d(W) = -alpha/(2*y) * (FT / FT0)
y(0) = 1.0
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