-
Notifications
You must be signed in to change notification settings - Fork 0
/
get_CO_oxidation_jac.m
163 lines (145 loc) · 6.37 KB
/
get_CO_oxidation_jac.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
%% Jacobian for tanks-in-series model with surface kinetics
% t : Time (s), not used but required for ode solver
% y : Solution vector for surface coverage and pressure
% y_tanki = (yCO, yO2, yO, yox, pO2, pCO, pCO2)
% y = zeros(n * 7, 1);
% params : System parameters
% params = (T, pCO, pO2, pCO2, rhoCat, F, Vtank, A, ntanks,...
% Ea_oxide, deactivation)
% Reactions
% =========
% Overall: 2CO + O2 -> 2CO2
% 1) CO + * <-> CO*
% 2) O2 + * <-> O2*
% 3) O2* + * <-> 2O*
% 4) CO* + O* -> CO2 + 2*
% 5) O* -> Oox
% 6) CO* + Oox -> CO2 + *
function j = get_CO_oxidation_jac(~, y, params)
% Parameters
T = params(1);
pCOin = params(2);
pO2in = params(3);
pCO2in = params(4);
rhoCat = params(5);
F = params(6);
V = params(7);
A = params(8);
n = params(9);
Ea_oxide = params(10);
deactivation = params(11);
% Constants
atm = 101325; % Convert atm to Pa
kB = 1.38064852e-23; % Boltzmann constant
sigma = kB * T * rhoCat * A / V; % Convert rate to Pa/s
itau = F / V; % Inverse residence time (1/s)
% Initialise jacobian matrix
ny = length(y) / n;
j = zeros(n * ny, n * ny);
% Loop over tanks
for i = 1:n
% Variables for current tank
current = ny * (i - 1); % Offset to current tank indices
previous = ny * (i - 2); % Offset to previous tank indices
yCO = y(current + 1); % CO coverage
yO2 = y(current + 2); % O2 coverage
yO = y(current + 3); % O coverage
yox = y(current + 4); % ox coverage
pCO = y(current + (ny - 2)); % pCO (atm)
pO2 = y(current + (ny - 1)); % pO2 (atm)
pCO2 = y(current + ny); % pCO2 (atm)
% Free sites
yf = 1 - sum(y(current + 1 : current + (ny - 3)));
% Get process rate constants
rate_params = [T, A, Ea_oxide, deactivation];
rate_constants = get_CO_oxidation_rate_constants(rate_params);
k_ads_CO = rate_constants(1);
k_ads_O2 = rate_constants(2);
k_des_CO = rate_constants(3);
k_des_O2 = rate_constants(4);
k_fwd = rate_constants(5);
k_fwd_O = rate_constants(6);
k_rev_O = rate_constants(7);
k_oxd = rate_constants(8);
k_fwd_ox = rate_constants(9);
% Row/column indices for variables in each tank:
% 1-7, 8-14, 15-21, 22-28, 29-35, 36-42, 43-49, 50-56, 57-63, 64-70
% ddyCO/d...
j(1 + current, 1 + current) = -k_ads_CO * pCO * atm - k_des_CO -...
k_fwd * yO - k_fwd_ox * yox;
j(1 + current, 2 + current) = -k_ads_CO * pCO * atm;
j(1 + current, 3 + current) = -k_ads_CO * pCO * atm - k_fwd * yCO;
j(1 + current, 4 + current) = -k_ads_CO * pCO * atm -...
k_fwd_ox * yCO;
j(1 + current, 5 + current) = k_ads_CO * yf;
j(1 + current, 6 + current) = 0;
j(1 + current, 7 + current) = 0;
% ddyO2/d...
j(2 + current, 1 + current) = -k_ads_O2 * pO2 * atm +...
k_fwd_O * yO2;
j(2 + current, 2 + current) = -k_ads_O2 * pO2 * atm - k_des_O2 -...
k_fwd_O * yf + k_fwd_O * yO2;
j(2 + current, 3 + current) = -k_ads_O2 * pO2 * atm +...
k_fwd_O * yO2 + 2 * k_rev_O * yO;
j(2 + current, 4 + current) = -k_ads_O2 * pO2 * atm +...
k_fwd_O * yO2;
j(2 + current, 5 + current) = 0;
j(2 + current, 6 + current) = k_ads_O2 * yf;
j(2 + current, 7 + current) = 0;
% ddyO/d...
j(3 + current, 1 + current) = -2 * k_fwd_O * yO2 - k_fwd * yO;
j(3 + current, 2 + current) = -2 * k_fwd_O * yO2 +...
2 * k_fwd_O * yf;
j(3 + current, 3 + current) = -2 * k_fwd_O * yO2 -...
4 * k_rev_O * yO - k_fwd * yCO - k_oxd;
j(3 + current, 4 + current) = -2 * k_fwd_O * yO2;
j(3 + current, 5 + current) = 0;
j(3 + current, 6 + current) = 0;
j(3 + current, 7 + current) = 0;
% ddyox/d...
j(4 + current, 1 + current) = - k_fwd_ox * yox;
j(4 + current, 2 + current) = 0;
j(4 + current, 3 + current) = k_oxd;
j(4 + current, 4 + current) = - k_fwd_ox * yCO;
j(4 + current, 5 + current) = 0;
j(4 + current, 6 + current) = 0;
j(4 + current, 7 + current) = 0;
% ddpCO/d...
j(5 + current, 1 + current) = sigma * k_des_CO + sigma *...
k_ads_CO * pCO * atm;
j(5 + current, 2 + current) = sigma * k_ads_CO * pCO * atm;
j(5 + current, 3 + current) = sigma * k_ads_CO * pCO * atm;
j(5 + current, 4 + current) = sigma * k_ads_CO * pCO * atm;
j(5 + current, 5 + current) = -itau * atm - sigma * k_ads_CO * yf;
j(5 + current, 6 + current) = 0;
j(5 + current, 7 + current) = 0;
% ddpO2/d...
j(6 + current, 1 + current) = sigma * k_ads_O2 * pO2 * atm;
j(6 + current, 2 + current) = sigma * k_des_O2 + sigma *...
k_ads_O2 * pO2 * atm;
j(6 + current, 3 + current) = sigma * k_ads_O2 * pO2 * atm;
j(6 + current, 4 + current) = sigma * k_ads_O2 * pO2 * atm;
j(6 + current, 5 + current) = 0;
j(6 + current, 6 + current) = -itau * atm - sigma * k_ads_O2 * yf;
j(6 + current, 7 + current) = 0;
% ddpCO2/d...
j(7 + current, 1 + current) = sigma * k_fwd * yO + sigma *...
k_fwd_ox * yox;
j(7 + current, 2 + current) = 0;
j(7 + current, 3 + current) = sigma * k_fwd * yCO;
j(7 + current, 4 + current) = sigma * k_fwd_ox * yCO;
j(7 + current, 5 + current) = 0;
j(7 + current, 6 + current) = 0;
j(7 + current, 7 + current) = -itau * atm;
% Add terms for inlet pressure (outlet from previous tank)
if i > 1
j(5 + current : 7 + current, 5 + previous : 7 + previous) =...
diag(ones(3, 1) * itau);
end
% Scale to match odes for pressure in atm
j(5 + current : 7 + current, 1 + current : 7 + current) = ...
j(5 + current : 7 + current, 1 + current : 7 + current) / atm;
j(1 + current : 7 + current, 5 + current : 7 + current) = ...
j(1 + current : 7 + current, 5 + current : 7 + current) * atm;
end
end