% 07 Nov 2005: Simulation + Computation of eigenvalues for multicomponent distillation
% Note: Need to change data (incl. feed composition) in multicomA_lv.m

[t,x]=ode15s('multicomA_lv',[0 20000],0.5*ones(1,NC*NT)');
lengthx=size(x); Xinit = x(lengthx(1),:)';

% later simulations starting from steady-state
[t,x]=ode15s('multicomA_lv',[0 20000],Xinit);
lengthx=size(x); Xss = x(lengthx(1),:)';

% Splitting the states
x1=x(:,(NC-4)*NT+1:(NC-3)*NT);    % liquid composition of component 1 
x2=x(:,(NC-3)*NT+1:(NC-2)*NT);    
x3=x(:,(NC-2)*NT+1:(NC-1)*NT);    
M =x(:,(NC-1)*NT+1:NC*NT);    % holdups 


% linearize
Ls=2.70629; Vs=3.20629; Ds=0.5; Bs=0.5; Fs=1.0; qFs=1; zFs=[0 0.5 0.5 0];   
%Ls=2.70629; Vs=3.20629; Ds=0.5; Bs=0.5; Fs=1.0; qFs=1; zFs=[0.05 0.45 0.45 0.05];   
%Ls=2.70629; Vs=3.20629; Ds=0.5; Bs=0.5; Fs=1.0; qFs=1; zFs=[0.25 0.25 0.25 0.25];   
[A,B,C,D]=cola_linearize('col4_lin',Xinit',[Ls Vs Ds Bs Fs qFs zFs]);

z=eig(A);
z(find(z>-0.5))

-----

RESULTS (07 Nov 2005):


Hello,

I did some calculations on eigenvalues for multicomponent mixtures.
The conclusion is that there for high-purity columns is a single slow mode even for multicomponent mixtures

Best regards,
Sigurd

-----------

Data: Relative volatility 1.5 between neighbouring components. 41 stages. Feed middle of column. F=1,. L=2.7, V=3,2, D=B=0.5
See
http://www.nt.ntnu.no/users/skoge/distillation/multicomp_skouras/
see eigenvalues.txt

1. I first did a binary 50/50 mixture with zf=[0 0.5 0.5  0]. Data (including flows) as for column A
Product purity: 1% impurity in each product
Found  two integrators (from the levels) + 194 min + 12.1 min + 3.5 min and smaller

z=eig(A)
z(find(z>-0.5))
-5.1555e-003
-8.2982e-002
-2.8512e-001
-3.2739e-001
-3.4443e-001
-3.8489e-001
-4.6280e-001
           0
           0

2. I then did multicomponent with zf=[0.05 0.45 0.45 0.05] and same flows.
Found integrators + 271 min + 10.7 min + two complex around 3.4 min

-3.6829e-003             
-9.3951e-002             
-2.9447e-001 +6.3571e-003i
-2.9447e-001 -6.3571e-003i
-3.1414e-001             
-4.0017e-001             
-4.7493e-001          
           0
           0            

3. I finally did multicomponent with zf=[0.25 0.25 0.25 0.25] and same flows. Product is now much purer, so linearized response is slower
Found: Two integrators +  1190 min + 6.9 min + 5.8 min + 5.2 min + 2.8 min + smaller

-8.4084e-004
-1.4622e-001
-1.7229e-001
-1.9132e-001
-3.3569e-001
-4.1971e-001
-4.8546e-001
           0
           0

-Sigurd