# Calculating Fractional Yield as a function of temperature for a parallel reaction in a plug flow model

(This question comes from a Chemical Engineering background, I hope it still falls in the scope of engineering.stackexchange.com If not, please move.)

I am trying to calculate and plot fractional yield as a function of temperature for a parallel reaction of first-order reactions forming 3 products R, S and P from reactant A.

I know the highest possible reaction temperature is 500k. S is the desirable product and I am trying to find the reaction temperature to maximize its production and calculate reactor outlet concentration of S for XA = 100%. Thus far, I have tried to construct the respective rate equations and thus corresponding Arrhenius equations (which I have data for), what I'm not sure is if I am plotting this equation against temperature, is this a valid solution to evaluate the fractional yield?

Here is my MATLAB code and corresponding graph:

CA0 = 100; % Initial concentration of A (mol/m^3)

V_reactor = 1; % Reactor volume (for example, 1 m^3)

T_range = linspace(0, 1000, 10); % Temperature range from 0 K to 500 K

YieldS = zeros(size(T_range));

for i = 1:length(T_range)
T = T_range(i); % Temperature at this iteration
R = 8.314; % Universal gas constant (J/(mol*K))

k1 = 5*10^8 * exp(-65000 / (R * T)); % Adjust activation energy (kJ/mol) as needed
k2 = 10^9 * exp(-50000 / (R * T)); % Adjust activation energy (kJ/mol) as needed
k3 = 10^7 * exp(-45000 / (R * T)); % Adjust activation energy (kJ/mol) as needed

dC = @(V, C) [-k1 * C(1) - k2 * C(1) - k3 * C(1); % dCA/dV
k1 * C(1); % dCR/dV
k2 * C(1); % dCS/dV
k3 * C(1)]; % dCP/dV

% Initial conditions (at V = 0)
C0 = [CA0; 0; 0; 0]; % Initial concentrations of A, R, S, and P

[V, C] = ode45(dC, [0, V_reactor], C0);

CA_outlet = C(end, 1);
CS_outlet = C(end, 3);

YieldS(i) = (CS_outlet / CA0) * 100;
end


• Does a Chemistry Stack exist? Commented Oct 8, 2023 at 14:18