Fixed-bed adsorption - PDEPE?
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Dear support team!
I am trying so solve a convection dispersion equation with pdepe and I am only getting constant outlet concentration which is not correct. I am having problem figuring it out where I am wrong?
I think the equation should get solved by pdepe according to matlab (https://se.mathworks.com/help/matlab/ref/pdepe.html). But i am not sure if I am correct in defining the "c" parameter?
Deeply appreciate any help.
The equations are:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/370018/image.jpeg)
And here is the code:
function DiffusionConvectionReaction
% Solving advection-reaction-dispersion equation for a packed bed reactor with
% pdepe matlab function
clc
clear
close all
global u D C0 x t rho eps
% define the reactor parameters
L = 0.2; % reactor length (m)
Pe = 10; % Peclet number
u = 0.06; % average upflow velocity (m/s)
D = u*L/Pe; % axial dispersion (m2/s)
C0 = 1e-1; % initial concentration (kg/m3)
rho = 840; % density (kg/m3)
eps = 0.3; % porosity
% solution of a single pde
m = 0; % assuming slab symmetry (-)
x = linspace(0,L,10); % reactor's length
t = linspace(0,20,100); % operation time (s)
sol = pdepe(m,@pdefun,@icfun,@bcfun,x,t);
c = sol;
figure;
plot(t,c(:,end));
%-------------------------------------------------------------------------
% define the flux and source term
function [g,f,s] = pdefun(x,t,c,DcDx)
qmax = 4.3e-3;
b = 0.84e3;
g = 1+ rho*qmax*b/(eps*(1+b*c));
f = D*DcDx;
s = -u*DcDx;
end
%------------------------------------------------------------------------
% define initial condition
function c0 = icfun(x)
c0 = C0;
end
%-------------------------------------------------------------------------
% define boundary conditions
function [pl,ql,pr,qr] = bcfun(xl,cl,xr,cr,t)
pl = u*(C0-cl);
ql = 1;
pr = 0;
qr = 1/D;
end
end
2 Kommentare
Bill Greene
am 5 Okt. 2020
Actually, your solution equals the inital value at all points for all time. This is expected from your equation and boundary conditions with a constant initial condition.
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