Spatial discretization Error PDE solver- Shouldn't the following PDE work?

I am currently trying to solve a Mass Transfer modeling problem that models a system of two PDE's:

Here are the PDE's: (1) (du1/dt)+(du1/dx)-(1/Pe)*(d^2u1/dx^2)=c_1*(u2-u1)

and (2) (du2/dt)=c_2*(u1-u2)

Where u1 and u2 are my variables. Pe, c_1, and c_2 are all constants.

The initial conditions are as follows: (@t=0, u1=0) and (@t=0, u2=qo) - Where qo is initial concentration at a value of .263

The boundary conditions are as follows (there are no boundary conditions for the second PDE equation as it is only related to time: (x=0; Pe*u1=du1/dx) and (x=1; du1/dx=0)

My code below is throwing me this error: "Spatial discretization has failed. Discretization supports only parabolic and elliptic equations, with flux term involving spatial derivative."

From my understanding, my PDE should be suited for this problem. Are there something wrong with my boundary conditions?

I would greatly appreciate any help on this. New to MATLAB and the world of PDE's. Thanks in advance!

My code for this is below:* 

   function pdex11
    clc
    clear all
    m=1; %M=1 for cylindrical 
    x=[0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1]; %x is z direction (axial) 
    t=[0 100 200 300 400 500 600 700 800 900 1000 1100 1200]; %t is Dimensionless time Tau 
    sol=pdepe(m,@pdex11pde,@pdex11ic,@pdex11bc,x,t);
    u1=sol(:,:,1); %U1 is Cf
    u2=sol(:,:,2); %U2 is Cs 

    %plot(x,u1(:,end))

    function [c,f,s]=pdex11pde(x,t,u,DuDx)
    global Pe H L Rp voidfrac kf vs
    Pe=1097.51
    H=1
    L=3
    Rp=.0000315
    voidfrac=.75
    kf=5.097
    vs=.1313
    c_1=3*L*Pe/Rp *((1-voidfrac)/voidfrac)*(kf/vs)
    c_2=-3*L/(Rp^(kf/vs))

    c=[Pe;H];
    f=[1;0].*DuDx;
    s1=c_1*u(1)-c_1*u(2)-Pe*DuDx(1);
    s2=c_2*u(2)-c_2*u(1);
    s=[s1;s2];

    function u0=pdex11ic(x); 
    q0=.263; %solute concentration solid phase (kmol/m^3)
    u0=[0;q0];

    function [pl,ql,pr,qr]=pdex11bc(xl,ul,xr,ur,t)
    global Pe 
    pl=[Pe*ul(1);0];
    ql=[-1;0];
    pr=[0;0];
    qr=[1;0];

[Torsten]

The solid phase equation is a simple ODE - thus pdepe is not suited to solve your equations.

Best wishes

Torsten.

[Henry Fulmer]

Thanks Torsten, very good point. Do you think it is possible to couple pdepe and ode45, using pdepe for the first equation and ode45 for the second?

[Torsten]

I'd discretize the first equation in Z-direction and leave the time derivatives in their continuous form. This way you get a system of ordinary differential equations that can be solved by ODE15S.

Look up "method-of-lines" for more details.

Best wishes

Torsten.

[Bill Greene]

Your equation for the solid phase contains C_f and you don't specify a specific point where C_f is evaluated. If that is the case, then that equation is a function of both tau and x because C_f is a function of x.

[Haniyeh Mohammadi]

Hi Henry

I'm having this problem. Can you please share the solution with me?