Packed Bed Adsorber - PDE

Hello,

I have an equation that I would like to solve. It is the basic equation which models adsorption on a packed bed adsorber:

0 = u*(dci/dz) + dci/dt + ([1-e]/e)*rho*(dqi/dt)

Where:

u - velocity

ci - concentration of component i in time t

z - length of the bed

t - time

e - voidage of the bed

rho - density of the component i

dqi/dt = adsorption energy which is the concentration of component i in the solid (adsorbent) that is given by the given equation:

dqi/dt = k*(q*-qi)

I have attached a paper which I want to simulate. How can I import this into matlab?

[Harman jot Singh]

Ca youu help me with the same equation?

Answer 1

[Torsten]

Use the method of lines.

Discretize the partial differential equation

0 = u*(dci/dz) + dci/dt + ([1-e]/e)*rho*k*(q-qi)

in space.

Now solve the resulting system of ordinary differential equations (consisting of the discretized PDE and the ODE for the adsorbat concentration) using ODE15S, e.g..

Best wishes

Torsten.