Chemical Reaction in Porous Domain
I'm trying to model a packed bed reactor. I'm interested in getting the temperature distribution/development, species concentrations etc.
The packed bed consists of little Zn Particles (Solid Domain). The incoming gas mix (H2O, CO2) is reduced by the Zn particles when flowing through the bed and the out-coming gas mix now contains H2 and CO (Syngas). It’s a transient model.
I made a little sketch of the model to help understand what I want to do.
I'm quite new in the world of CFD and I'm having a lot of problems with another model (to find the BC for this one) and running out of time (master thesis). Therefore I urgently need help now for this model to start with the best and a convenient approach!
How should I model the chemistry within the porous domain (packed bed)?
1) Variable Composition Mixture (H2O, CO2, H2, CO) and then using source terms for the specific components and energy? Problem: Oxygen Sink (Mass Sink) is then not included in the continuity equation and therefore I will get wrong composition for the out-coming gas.
2) Defining a “Reaction” in CFX where atomic oxygen O is produced and then adding sources for energy…?
3) Variable Composition Mixture (H2O, CO2, H2, CO and Atomic O) then using a Continuity Source to model the Oxygen Sink and Sources for Energy, H2, H2O etc. I think this is the best way to do it. But what should I then use for the parameters required in the Continuity source Tab:
- Mass fractions are clear: All Y_i = 0 except Y_O = 1
- But Temperature = 0 K? and Velocity = 0? (to avoid secondary sources within the momentum and energy equations)
How can I model the consumption of Zn within the bed?
- The porosity is held constant (not true in reality) and the packed bed consists of Zn and ZnO particles. During the reaction going on, Zn is reduced to ZnO until Zn is consumed. Can I model this using an Additional Variable and then in the Porous Domain -> Solid Models Tab -> Add. Variables Models -> Zn Concentration -> Diffusive Transport Equation -> Kinematic Diffusivity = 0!
This way I think CFX will solve the Diffusive Transport Equation but neglecting the diffusive term, so I will have on the LHS the transient term alone and on the RHS the source describing the consumption of Zn, right?
I will be grateful for any comments!!!
Sounds like you should be modelling the reaction directly rather than just the species and heat sources/sinks. But I have no experience in reaction modelling in CFX so cannot help you much.
Can you inlude more details on:
1. What reaction kinetics you assume.
2. The phase of Zn when it reacts with CO2/H2O.
My first attempt would be to model species conservation of the incoming gas flow with a (mass) source term for the sublimation (?) of Zn. Whether or not you need 2-way coupling back to the gas flow for momentum should follow from reaction scheme. Energy conservation should be covered once you include your recation kinetics. The consumption of Zn will be linked through the same source term you include in the eularian phase. What is the rate limiting mechanism: sublimation, (turbulent) mixing or reaction kinetics?
Thanks for your reply. I had a meeting today and could clarify some of the questions you made:
1. The rate limiting mechanism is reaction kinetics. The reaction rate depends on T and the mass fractions of H2O and CO2.
The reaction rate is described by Langmuir-Hinshelwood kinetics.
r = k3*(k1*Y_CO2 + k2*Y_H2O)/(k3+k1*Y_CO2 + k2*Y_H2O) in [mol m-3 s-1]
The rate constants were assumed to follow an Arrhenius law dependency on temperature.
k_i = k_0i*exp(-E_i/(RT))
2. Phase of zinc when it reacts is 'solid'. The reactions are assumed to
occur at Zn/ZnO interface, which can be reasonably described by a shrinking
core model for spherical particles. (the particles react and a ZnO layer
developes, which then holdes the 'molten' Zn in it, diffusion is neglected,
as the kinetics are the rate limiting mechanism)
I hope this information is what you meant?
a. What do you exactly mean with 'Whether or not you need 2-way coupling back to the gas flow for momentum should follow from
b. eularian phase = solid phase? I thought to use the full porous model in CFX, not a multiphase model...(anyway it should be the same, right?)
c. Whats exactly the difference between implementing a chemical reaction by sources and using the Reaction menu in CFX (there it's possible to select multiphase...)?
d. Would this idea work?:
- Continuity source for atomic oxigen sink (incl. sources/sinks for the species mass fractions, which can be implemented after activating mass source)
- Energy Source depending on Temp., Gas composition (mass fractions), and Zinc Area
- An additional variable to model the consumption of Zn - > Zinc Area decreases with time (Diffusive Transport Equation -> Kinematic Diffusivity = 0)
e. Do you think its a 'possible' model, in sense of simulation time and convergence?
Some people I talk to at ETH say that a transient, 3D modeling of a porous bed would result in a too big simulation.
Thanks again for your interest!
This seems a tricky simulation to do. Im curious to find how it progresses. Anyways, my two cents:
a) The reaction kinetics will dictate the mass added to the gas flow. If the mass flux of added reactants is small compared to the overall flow, you wont need to model momentum transfer to the main flow.
b) by eularian phase I mean the phase(s) you use an Euler reference frame for, this was assuming you use a lagrangian approach for the particles.
c) Im not sure about the details, refer to manual.
d) You will need to model the consumption of Zn and the reducing interfacial area yourself, this should create a time and spatial dependent variable "Zn available for reaction". The idea being: amount of Zn links to interfacial area, determines local reaction, Zn consumption and finally back to amount of Zn available. The local porosity also follows from this. I dont think you will need to add any source terms if you use the CFX chemistry for the reaction. Edit: apart from a Zn source term in species conservation ofcourse.
e) This will depend on your hardware, but it does sound challenging.
Thanks for your reply!
I'm now again working on that. But I think I will try to model a moving energy source without modeling the chemistry... before.
I will give more details here, when I proceed.
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