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Topic 2: homework deriving L-H expression for gaseous reaction using first principles.

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Topic 2: homework deriving L-H expression for gaseous reaction using first principles.

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Hi Sheila,

I attempted the above question however my denominator expression for the reaction complex is slightly different to your given answer- I have 1/Kreaction.
I have included my expression for the reaction surface concentration.

Any guidance on this would be much appreciated!
Thanks

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Topic 2: L-H rate expression for a gaseous reaction assuming ideal gas

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Topic 2: L-H rate expression for a gaseous reaction assuming ideal gas

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Topic 2: 1. Derive the dual site rate expression for a reversible reaction step. 2. Sketch shape of initial rate vs partial pressure (of A) for a. Dual site mechanism b. Eley-Rideal mechanism

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Topic 2: 1. Derive the dual site rate expression for a reversible reaction step. 2. Sketch shape of initial rate vs partial pressure (of A) for a. Dual site mechanism b. Eley-Rideal mechanism

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Hello shelia,
The maths revision sheet you put on moodle is useful, however it would be a lot more useful if you could potentially post some relevant math questions that we would be expected to do - since its been a long time since Ive done ODEs and dont want to spend too much time on doing stuff that wont be directly relevant to your material. Thanks in advance :)

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for the 2 examples of the 3 phase catalytic process we sketched in the in person activity - what was the reaction mechanism in each of those cases (Langmuir-Hinshelwood or Eley Rideal )? thanks

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Hi Sheila,
Please can you explain why we see the respective plot shapes for rAO vs PA for dual site L-H and E-R mechanism?
Is this to do with the active site S being saturated with A so a plateau is reached?
Is there any interaction with B or BS* as the rate of reaction does depend on the second reactant aswell?

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for the rate of reaction for the dual site mechanism, after a certain partial pressure of A would the rate start to decrease ? (since A and AB compete for the active sites - or is this not relevant) thanks

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Hi Sheila,

For Topic 3, would you like us to learn the different derivations or just appreciate how the Thiele Modulus and Effectiveness Factor were found and be able to use these?

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I know the chain rule is used but I am struggling to understand why the equation in the attached image is true?

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Hello, would you want us to know the derivations you carried out for the theile modulus and effectiveness factor ? Also I am really struggling to understand how you used the chain rule. could you please go through how you applied the chain rule in your derivations again ? thanks

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Hello, for slide 27 you go from the differential equation straight to its solution. would us just knowning this is the solution to that differential be sufficent (for the exam) or would you want us to be able to solve it to get those solutions (if so could you please explain how to get them) thanks

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Is the fluid film surrounding the pellet always assumed to be liquid ? (Assuming a 3 phase reactor) and in the case of a 2 phase reactor or gas reactants and solid catalyst how does that work ?

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U explained surface diffusion briefly in topic 3 and the equations related to it. But then we don’t look at it again in topic 3 - is this because it is only relevant for external diffusion ? And we are ignoring it in topic 3 (I.e assuming that Cas is constant). Thanks

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In topic 3 for the MB you made the term for the generation / consumption positive (even though the reactant is being consumed but in problem sheet 3 the generation / consumption term is negative ? So I am confused about which one to follow for future problems. Also should we always just make the flow in term negative and flow out term positive. Or is there any case where we should not do this ? Thanks

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If we were given -ra’’ for a sphere what would be the surface area element we multiply by to get units of mol / second. Would it be 4 pi (delta_r)^2 ?

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Hello,
- I had initially thought that a second B.C. could be that at z=L ca=0.1Cas. As this is what I understood from the question is there a reason why this isn’t the BC you use ?

Also you mentioned that BC in exam would be given unless it’s obvious - would you consider the BC from this probsheet as obvious or would you have given us the BC were this qs on the exam. Thanks

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Is it always safe to assume steady state and constant diffusion coefficient ( such that we can take it out of the derivative) ?

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Hi,
I just want to make sure my understanding for why the generation (rate) term for the problem sheet does not include catalyst density versus the lecture notes model.
- The problem sheet assumes only one pore whereas the lecture model is a catalyst pellet (of many pores).
- Hence ra(clindrical pore) is per SA of pore whereas ra(pellet) includes Sa term and hence is m2 per mass of catalyst (so need to multiple by density to get the current units).

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Hi Sheila,

Just wanted to check if my derivation for Cwp is correct?

Thanks!

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Hi Sheila,
For Q2 of the problem sheet, if MEK or H2 had not been weakly adsorbing, would you still be able to graph the reaction rate against partial pressure?
What would have to be done differently to consider them also?

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Hi Sheila,
Please can you upload your derivations for the heterogenous packed bed energy balances.
Thank you!

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Hi Sheila, will we be only asked for first order reaction in the exam? Thanks

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Hi Sheila,
When you have subbed in the expression for flux, you have taken the negative diffusion sign as a value rather then just a directional indicator. Then you have rewritten Ficks law as a positive value.
I don’t really understand why you can do that, since I always thought the negative diffusion constant was just to show the direction of diffusion versus the driving force?

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Hi Sheila, for the derivation of the Eley-Rideal Kinetics I am getting confused about what Kpa represents- is it the same as K'? Also, how did you come to the 3 expressions for Kpa, kr and Kd in terms of concentrations and partial pressures?

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Hi Sheila, for the example of diffusion and reaction in a spherical particle for a->B, where does the rate expression come from? It has no square on the denominator so am assuming it does not follow langmuir-hinshelwood and there is no 'PaPb' expression on the numerator so doesn't look from eley-rideal either?

Thanks

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Heterogeneous reaction: gas phase mass balance 

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Heterogeneous reaction: gas phase mass balance 

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Hi Sheila,

From topic two when drawing the transport of reactants in a three phase reactor, it had been said that the gas phase diffuses into the liquid phase and then diffuses to the surface catalyst.

I wanted to ask why the movement from the gas to liquid phase isn't included in the material balance for the gas phase of the heterogeneous reactor? the transport has been shown to go directly to the catalyst surface

Thank you

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The Biot number is defined as the ratio of internal diffusion resistance to external diffusion resistance.

From the equation, the resistance to internal diffusion seems to be d_p / D_e (particle diameter / effective diffusivity). Why is particle diameter the length scale for this internal diffusion instead of the particle radius?

If the particle is spherical and fully submerged in a well-mixed bulk, there would be equal diffusion from all angles toward the centre of the particle. In this case, the distance where internal diffusion occurs  should be the particle radius?

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Please can you provide diagrams of the control volumes for the rectangular slab and cylindrical pellet?

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Control volumes for practice problem 4 - by SS

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Control volumes for practice problem 4 - by SS

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Hi Sheila,
Why have you changed to dimensionless form when solving the differential equation?
I just worked out part a like your solution in PC3, getting n=tanh(oL)/ Lo.

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Hi Sheila, could you demonstrate how you obtained a_c for part a (rectangular slab) please? Thank you

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Problem sheet 4 - Overall effectiveness factor 

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Problem sheet 4 - Overall effectiveness factor 

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Hi Sheila,
I am confused as to where the minus sign has gone from the diffusion equation in the solutions. I have always though you write any diffusive flux as J=-D(dCa/dz) as the flux goes in the direction opposite to the concentration gradient. Then it is the sign of the differential part of the equation that will make the flux negative or positive, so that you know the direction that it is going in.

Any help explaining this would be appreciated!

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Balance at the interface for practice problem 4a - by SS

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Balance at the interface for practice problem 4a - by SS

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I think the unit of the overall material balance is in mol/s. However, from the last Generation term of the equation, it shows Vol. *(-ra'') which [m3]* [mol/m^(2)s] and I think the unit is inconsistent overall as you would got mol m/ s. Or do we consider the rho and Sa to cancel out the extra "m" ? Thanks.

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Is the reaction rate derived for Langmuir-Hinshelwood and Eley-Rideal in the lecture rA, rA' or rA''?

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Why is the flux at the centre of the slab zero?

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Hello Sheila,

Are there any more practise problems with solutions for any of the topics?

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Hi Sheila,

Can i leave my final answer as non-dimensionless form? Also in the exam would you want us to know how to predict the trendline when solving the equation with MATLAB?

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Hi Sheila,
The graph shown in (i) just has the axis of Rcr and dp. However, i thought for the correct slopes (as described in one of the answers) to be obtained we need to plot a ln-ln plot?
My answer for iii and iv therefore differ as i have used lnRcr as my value rather than just Rcr.

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"derive the time required to completely regenerate a catalyst particle of diameter 𝐷𝑐𝑎𝑡 which has been covered with solid deposit of diameter 𝐷"
Please can you upload a solution so i can compare my answer? Thanks!

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very enjoyable sessions well explained although this module is very hard

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for the exam if we need to plot something would we be able to do this on excel or would it need to be by hand on graph paper. thanks

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Just to make sure I understand it correctly. for the Oxygen MB in the ash layer we are just left with In - Out = 0. Our flow is from the center of the pellet to outside (against conc gradient - cause this is the convention) so from r to r+dr in the direction of from the inside of the pellet to the outside direction. correct ? thanks

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Hi Sheila,
Would it be possible to release the solutions to the practise problems to help with further understanding of the topic ?
Thank you.

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Hi Sheila, would you please be able to provide the pdf version for the answer sheet that we used to complete Topic 2 (in week 4) practice problems so that we can use it for our revision? Thank you!

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Hi Sheila,
please can you release the solution for problem 7 as well so I can compare my solution?
Many thanks

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Hi Sheila, just going through the previous topics and wanted to ask in the equation -rA'' = k*CA/(1+KACA+KBCB), is k just a group of constants (= kfR*KA)? And just to confirm, was this derived assuming a LH mechanism?

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Can this be recorded please for those of us who can not attend. Thanks

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Hi Sheila,

If internal diffusion is rate limiting, why does changing the catalyst material change the reaction rate? Is this related to different materials having different pore structures (porosity, tortuosity, etc.) or something else?

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Question about the transformation in topic 3.

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Question about the transformation in topic 3.

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Hi Sheila,

when you went from line 4 to line 5 here. How did you get lambda^n-1? Surely it would be lambda^1-n and it moves to the numerator since lambda/lambda^n = lambda^1-n? Thanks!

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Hi Sheila,

In the lecture notes you equated the rate of external mass transfer to the total reaction rate within the catalyst pellet. So you equated external flux to -rAs'' * n * Sa * density and got the overall effectiveness factor from there by rearranging for CAs.

However, in PS4, you equated external mass transfer to the flux diffusing just inside the slab and not the total reaction rate in the pellet, can you explain why this is the case?

Thank you in advance!

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hi Sheila, regarding the generation term in this slide. Is it ok if we use replace catalyst density * rA' with catalyst density*Sa*rA'' instead since we still end up with the same solution? Or do we always have to start with rA'* catalyst density.

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Hello shelia to clarify, you mentioned when we did topic 4 that energy balances are not examinable. Just want to make sure that’s 100% the case. Thanks

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Could you please explain where the 1-eb comes from here and why it is necessary?

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Problems in Catalytic Processes and Reactor Design

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Problems in Catalytic Processes and Reactor Design

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For problem 2 part b)The answer suggests that "According to the form of the rate law, the mechanism must be second order. " Would it be possible for you to explain how you come down to this, please?

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Would it be possible for you to explain how the second and third conditions gives th two expressions , please?

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Could you elaborate part ii) on zone 3 &4 please?

"Zone 3: The next region of the curve is where the slope is 2 and the controlling step is external diffusion: 𝑅𝑟𝑐~1/(𝑘𝑐𝑎𝑐). This is for larger particles and where there is no shear between the particles and the fluid. The Sherwood number is independent of Reynolds number and Schmidt number, so 𝑅𝑟𝑐 ∝ 𝑑𝑝 2 and the slope is 2.

Zone 4: The last region of the curve is where the slope is between 1.5 and 1.7 and the controlling step is external diffusion, but this time there is shear between the particles and the fluid. In this regime 𝑅𝑟𝑐 ∝ 𝑑𝑝 1.5 or 𝑅𝑟𝑐 ∝ 𝑑𝑝 1.7 , hence the slope."

How did you find the value of the slope and why do you mention Sh, Re and Sc?

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For the exam, are we expected to use excel solver (and or other iterative methods) to determine a solution of a question as you did in your problem (part c)? Thanks

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For the rate expressions used in the material balances, why does it use the expression where mass transfer limits the dissolution instead of the general one?

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Hi Sheila…i am struggling with the integration of hyperbolic functions. How do you get from the penultimate line of working to the bottom line?

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Hi Sheila, please can you explain how to linearise the rate equation?

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Please can you post your line of working for differentiating this?

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Hi Sheila,

You defined ac as the external surface area per unit reactor volume in the lectures. Just to confirm, is the 'reactor volume' term the volume of the bed, and not the volume of the entire reactor? Since you used the volume of the bed for the above question I believe this is the case.

Thank you.

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Hi Sheila, please can you explain how you integrated this?

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Hi Sheila,

For Q2(b) (iii) do we have to include the catalyst loading while calculating the reaction resistant? In lecture, Rc = 1/(n.k), so i wasn't sure what to do with the catalyst loading.

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Hi Sheila,

I attempted this past paper question but couldn't get the P_Q on the rate equation. Could you guide me roughly on how to obtain that term? Thanks in advance! :)

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2020-21 S1-CE40127 Exam Feedback Outline Solution ShS  SPP (v2).pdf - Adobe Acrobat Reader DC (64-bit) 1_8_2022 10_23_42 AM_LI

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Would we be expected to solve part c in an exam, or just know how to get to the coupled equations and explain the next steps?

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Hi Sheila, how would you answer this question, given no particle diameters but a plot CAi/ra vs. 1/m for both the catalyst sizes? Thanks!

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Hi Sheila, when and why is it acceptable to assume constant Diffusivity (effective or per species, i.e. De or DAb0) when you do the mass balances?

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Please could you have this online so that we can all attend and engage?

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Effectiveness factor - internal & overall

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Effectiveness factor - internal & overall

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Hi Sheila, would you have any literature/book recommendations to learn more about the effectiveness factor and the effect with temperature as I am still confused, thanks!

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Could you please explain how you transform from the top line to the bottom line? I cannot seem to get the R algebra to work

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If the volume fraction of carbon in porous catalyst the same as 1-e? Therefore, pc*vol.fra=pc(1-e)

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Hi Sheila,
I was just wondering if the K' and K can be used interchangeably for the overall reaction constant as I saw that in the problem sheet, lecture notes and exam solutions you used it for the same definition? Also, in past year exam 20/21, is K_A the same as K_PA and can we use them interchangeably too? Thank you!

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Hi Sheila,
For a question of this type, do we need to show the full derivation of how we obtained the equation for conversion,X?
Or is what was provided in the feedback for the exam paper the steps you expect to see?

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Hi sheila, when asked to derive for rate expression like we did in revision session today. Do we get the full marks for that part only if we re arrange rate expression to include overall equilibrim constant,K?

Thanks

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Hi Sheila,

In Past Paper 17/18 Q1 a ii), I tried to plot the graph to obtain the value of k using the first equation that I have derived (the not linear equation) but its not linearized when I plotted it. I tried plotting 1/(-rc0) vs 1/pco and obtained a linear plot.
Is there a specific linearized form of plot for each of the mechanism?

Thanks!

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Hi Sheila, I was wondering if you use the notes from both Topic 4 and 5 for this rather than just Topic 5 (slurry reactors)? Would you also be able to give the numerical answers too so I can compare? Thank you!

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Hi Sheila, could you please explain how to solve the question? I'm guessing that we would have to find out the 'ac' first in order to solve 1/kc*ac ? Thank you.

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Example problem and solution - Hydrogenation

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Example problem and solution - Hydrogenation

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Hi Sheila,
For this question do you work out -rar by using the dimensionless numbers and Frossling correlation for kc and substitute into -rar = kc x cab? Also, I'm confused as to how to calculate War, do you relate it to -rar?

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Hello Sheila I’m not sure how to solve this question
For I) I tried to use the formula Rc = 1/kcapM(Cab-Cas) but there are too many unknowns also for II) ans III)
Could you please help ?

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Hi Sheila,

If the rate equation derived using L-H mechanism gives:(k*Ka*Pa*Kb*Pb)/ (1+Ka*pa+Kb*Pb)^2
And it is mentioned B is weakly adsorbed. Other than removing the denominator term, can we remove the Kb*Pb in the numerator  as well?

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Hi Sheila,

Could you explain how you differentiate to get this dimensionless form, I understand chain rule is applied but I am unsure where the first order derivative comes from.

Thanks