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Derivation Of Differential Equation For A Trickle Bed Catalyst Sphere

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Herakles

Mechanical
Mar 23, 2023
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Hey, could someone please give me a little more detail on the steps. I drew in the volume (spherical shape, radius of the catalyst particle), drawn in mass flows. What am I supposed to do now. How must the diffusion processes in the pores and at the boundary layer be taken into account? Especially the partial wetting confuses me... Thank you so much in advance!

Make the following assumptions:

Reaction takes place within the liquid-filled pores at the active centers of the heterogeneous catalysts.
The catalyst is not completely wetted with liquid. the wetting is described with 'w' or not wetted with '1-w', so that two different ways for the mass transport of the educts and products must be taken into account
The pore in the catalyst grain (in spherical form) and thus also the liquid is one-dimensional to be accounted for along the radius 'r'. As process engineering boundary conditions are to take into account:
Some of the pores are wetted with a liquid film
part of the pores are in contact with the gas phase
Reaction A(g) + B(l) → P(l)
Component B is supplied with the liquid flow.
Component A is supplied with the gas flow (pA = pges), not on the gas side mass transfer limitation
B is over-stoichiometric → reaction runs pseudo-1st order with respect to the Component A off

Editing notes:

Make a meaningful sketch of a balance area and its positioning in the apparatus the volume element to be balanced.
Name all incoming and outgoing material flows as well as all source, sink and Accumulation dates (non-stationary balance) in the balance area.
Explain all symbols used.
Name any assumptions made.
Based on your own sketch, derive from a general differential balance of the Material flows the differential equation for the trickle bed catalyst sphere forth for the case a constant wetting. Specify initial and boundary conditions.

 
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I don't get involved in your type of science , however, have looked into the Darcy's equation as it is used in many liquids seeping through soils.
 
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