Modelling of two phase flow in packed bed (continued)

[casualguitar]

Apologies I didn't get the notification! Response below

Please try more, say at least 10

Will do

If you are talking about spatial position, increasing U should bring the bed and gas temperatures much closer together and make the temperature wave travel more slowly through the bed.

Agreed yes. Actually I retested it with much more values (rather than just extreme values) and I did find something. So the gas and bed temperature plots are unchanging (or unchanging to my eye at least) at about Ug = Ub = 10 and above i.e. below this value the plot changes with changing U, and there is no difference between U = 10 and U = 1000

Yes. But please expand the scale so that we can see what is happening in more detail at short times.

Here is the analytical vs numerical time vs temperature plot for tank 1 at short times:

So they are not completely identical. The simulation takes 1 second to reach max temperature and the analytical solution takes 3 seconds (assuming heat transfer coefficients are almost zero and mass transfer coefficients are equal to zero). However they are technically not exactly the same. In that the analytic solution uses a constant mass holdup whereas the simulation mass holdup varies very slightly. Is this significant?

So in summary it seems that the gas and bed temperatures are limited by the heat transfer coefficients up to about U=10 (for the other simulation values), and after that increases in U ($U_g$ or $U_b$) do not affect gas or bed temperature. Is this reasonable?
Also this value of 10 is obviously affected by the other simulation values so this does not necessarily mean that U would be approx 10 in the final simulation

 

[casualguitar]

Just as a side note here's a plot of time vs gas temperature for n=10. The CO2 simulation has been much faster to run than the air liquefaction one. I guess the thermo library really slows it down. I'll look into shaving off thermo uses where possible in the other model

EDIT: And just one last (important) update. So when the heat transfer coefficients are brought down to below 100 (its not really 10 but somewhere below 50 I guess), then both the heat and mass transfer coefficients start affecting the output (gas/bed temperature etc). So what seems to have happened is that the previously high U values I had were dominating any other effects.

 

[Chestermiller]

You should be able to calculate the U value for the bed from the geometry of the particles and the volume fraction particles. Hold this constant, and vary the U of the gas. As you increase the U of the gas, does the bed temperature approach the gas temperature (no mass transfer)? At very high U of the gas, the heat transfer is dominated by the bed resistance. So the temperature profiles should stop changing with increased Ug.

 

[Chestermiller]

Apologies I didn't get the notification! Response below

Will do

Agreed yes. Actually I retested it with much more values (rather than just extreme values) and I did find something. So the gas and bed temperature plots are unchanging (or unchanging to my eye at least) at about Ug = Ub = 10 and above i.e. below this value the plot changes with changing U, and there is no difference between U = 10 and U = 1000

Here is the analytical vs numerical time vs temperature plot for tank 1 at short times:
View attachment 303214View attachment 303213
So they are not completely identical. The simulation takes 1 second to reach max temperature and the analytical solution takes 3 seconds (assuming heat transfer coefficients are almost zero and mass transfer coefficients are equal to zero). However they are technically not exactly the same. In that the analytic solution uses a constant mass holdup whereas the simulation mass holdup varies very slightly. Is this significant?

Do whatever it takes in the numerical model to make them exactly comparable.

 

[casualguitar]

You should be able to calculate the U value for the bed from the geometry of the particles and the volume fraction particles. Hold this constant, and vary the U of the gas.

What equation uses the volume fraction to calculate $U_b$?

As you increase the U of the gas, does the bed temperature approach the gas temperature (no mass transfer)? At very high U of the gas, the heat transfer is dominated by the bed resistance. So the temperature profiles should stop changing with increased Ug.

Yes exactly this happens. So the bed temperature approaches the gas temperature as $U_g$ increases. And then yes above a certain value of $U_g$ (seems to be $U_g$ = 50W/m2.k or so), the temperature profile stops changing with $U_g$.

Once I get the $U_b$ value I'll rerun the simulation and check the output with the now 'reasonable' values of $U$ and $k_i$ to get an update on the output we're dealing with

 

[casualguitar]

Do whatever it takes in the numerical model to make them exactly comparable.

Will do. Its just the mass holdup being temperature dependent so this is an easy change

 

[casualguitar]

Will do. Its just the mass holdup being temperature dependent so this is an easy change

Hi Chet, just letting you know I'm slightly sidetracked currently. Will be back on this tomorrow evening

 

[casualguitar]

Hold this constant, and vary the U of the gas. As you increase the U of the gas, does the bed temperature approach the gas temperature (no mass transfer)? At very high U of the gas, the heat transfer is dominated by the bed resistance. So the temperature profiles should stop changing with increased Ug.

All of the above now occurs as expected for normal mass transfer and zero mass transfer. I'll do another sweep to check that everything is as expected before adding any further correlations in.

Just two questions:
1) Is there any suitable correlation to add in next (maybe leaving the mass transfer coefficients vary rather than be held constant?)
2) You said this
"You should be able to calculate the U value for the bed from the geometry of the particles and the volume fraction particles"
What equation would be used to calculate U for the bed?

Edit: Just as a note, as far as I can see the main two correlations left out of the current model are the mass transfer and heat capacity correlations. I have both of these written up so I can add them in if this is suitable

 

[casualguitar]

One other note - the simulation running properly is dependent on the mass transfer coefficient (which is currently constant) being below a certain threshold. The current simulation uses a constant 8 x 10^-8 which is small enough, however the mass transfer coefficient calculator function does not return values in this range but rather in the 10^1 range. Is there anything wrong with this that you can see:

Where the following approximate ranges/values apply:
Reynolds number: 10<Re<10000
Schmidt Number: 0.5 < Sc < 0.7
Particle Diameter (dp) = 0.005
D CO2-N2 = 0.14 x 10^-4
D H2O-N2 = 0.259 x 10^-4

These values give a number in the 10^1 range, which causes the simulation to break, however the 10^-8 values produce expected results. Have I missed something?

 

[Chestermiller]

All of the above now occurs as expected for normal mass transfer and zero mass transfer. I'll do another sweep to check that everything is as expected before adding any further correlations in.

Just two questions:
1) Is there any suitable correlation to add in next (maybe leaving the mass transfer coefficients vary rather than be held constant?)

I can't think of any. Release the mass transfer coefficient correlation next.

2) You said this
"You should be able to calculate the U value for the bed from the geometry of the particles and the volume fraction particles"
What equation would be used to calculate U for the bed?

It's just what they gave in the other papers.

Edit: Just as a note, as far as I can see the main two correlations left out of the current model are the mass transfer and heat capacity correlations. I have both of these written up so I can add them in if this is suitable

Did you mean "heat capacity correlation" or did you mean "heat transfer correlation?"

 

[Chestermiller]

One other note - the simulation running properly is dependent on the mass transfer coefficient (which is currently constant) being below a certain threshold. The current simulation uses a constant 8 x 10^-8 which is small enough, however the mass transfer coefficient calculator function does not return values in this range but rather in the 10^1 range. Is there anything wrong with this that you can see:
View attachment 304339

Where the following approximate ranges/values apply:
Reynolds number: 10<Re<10000
Schmidt Number: 0.5 < Sc < 0.7
Particle Diameter (dp) = 0.005
D CO2-N2 = 0.14 x 10^-4
D H2O-N2 = 0.259 x 10^-4

These values give a number in the 10^1 range, which causes the simulation to break, however the 10^-8 values produce expected results. Have I missed something?

How do the mass transfer coefficients compare with the values in the paper? Any value of the mass transfer coefficient should not cause the calculation to crash. What values of the heat transfer coefficient does the correlation give?

 

[casualguitar]

Release the mass transfer coefficient correlation next.

Will do

It's just what they gave in the other papers.

$U_b = \frac{k_p}{d_p/\beta}$?

Did you mean "heat capacity correlation" or did you mean "heat transfer correlation?"

I meant heat capacity correlation but yes actually $U_g$ is constant in the current model also, so I'll need to add the heat transfer correlation in also. This seems more straightforward though so maybe I can leave that until the mass transfer correlation works

How do the mass transfer coefficients compare with the values in the paper?

The ones produced by my code are much larger than both the random constant value we have been using and the Tuinier et al values. Both of those are around 10^-7, whereas the calculation I'm doing produces a value around 10^1

Any value of the mass transfer coefficient should not cause the calculation to crash.

Yes it technically doesn't crash (it does run to completion), however the gas/bed temperatures level out at 180C rather than the inlet temperature of 300C. This does not happen when I use 'normal' values. It could be a tolerance issue for the larger mass transfer coefficients so I'll try that now. But either way, the Tuinier paper has mass transfer coefficients that are 10^7 times smaller so I'm likely doing something wrong in the mass transfer coefficient calculation

EDIT: I've checked all the terms in the mass transfer coefficient correlation and the only possible term that could be wrong is the diffusion coefficient (for both CO2 and H2O in N2). It is my guess that my units/magnitude is off for this. I need a term in the 10^-8 to 10^-9 range. The term I'm currently using is 10^-4
The terms seem to vary quite a bit across gas and liquid species. Am I right to say I'm looking for gaseous diffusion terms for both CO2 and H2O in air?

 

[Chestermiller]

Will do

$U_b = \frac{k_p}{d_p/\beta}$?

Correct.

I meant heat capacity correlation but yes actually $U_g$ is constant in the current model also, so I'll need to add the heat transfer correlation in also. This seems more straightforward though so maybe I can leave that until the mass transfer correlation works

The ones produced by my code are much larger than both the random constant value we have been using and the Tuinier et al values. Both of those are around 10^-7, whereas the calculation I'm doing produces a value around 10^1

Yes it technically doesn't crash (it does run to completion), however the gas/bed temperatures level out at 180C rather than the inlet temperature of 300C.

This indicates that there is something wrong. Maybe something like evaporation or sublimation is occurring without shutting off when liquid/solid is depleted. I don't know. But it can't be 180 C at long times.

This does not happen when I use 'normal' values. It could be a tolerance issue for the larger mass transfer coefficients so I'll try that now. But either way, the Tuinier paper has mass transfer coefficients that are 10^7 times smaller so I'm likely doing something wrong in the mass transfer coefficient calculation

Let's see the detailed hand calculation for a typical case. Also, the range of Reynolds numbers that you show for your bed seems very large to me. Please plot the Re vs tank number at a selection of times for a typical case. The only things that should affect the Re are the mass flow rate and the viscosity.

Also, please plot the heat transfer coefficient vs tank number at a selection of times. Also the mass transfer coefficient vs tank number at a selection of times.

EDIT: I've checked all the terms in the mass transfer coefficient correlation and the only possible term that could be wrong is the diffusion coefficient (for both CO2 and H2O in N2). It is my guess that my units/magnitude is off for this. I need a term in the 10^-8 to 10^-9 range. The term I'm currently using is 10^-4

The values you gave are in the right ballpark for m^2/s units.

The terms seem to vary quite a bit across gas and liquid species. Am I right to say I'm looking for gaseous diffusion terms for both CO2 and H2O in air?

In nitrogen.

 

[casualguitar]

The values you gave are in the right ballpark for m^2/s units.

Just one question before I do the above - is the right ballpark the 10^-4 one or the 10^-7 one?

 

[Chestermiller]

Just one question before I do the above - is the right ballpark the 10^-4 one or the 10^-7 one?

-4

 

[casualguitar]

-4

I attempted to find the point that the simulation deviates from what should happen (when I change from 10^-8 to 10^-4) however I couldn't.

I'll start on the plots above first thing tomorrow

 

[casualguitar]

I attempted to find the point that the simulation deviates from what should happen (when I change from 10^-8 to 10^-4) however I couldn't.

I'll start on the plots above first thing tomorrow

Will add these in as I do them.

The $U_b$ calculation:
$U_b$ = $\frac{k_p}{d_p/\beta}$
$k_p$ = 15 W/m.K
$d_p$ = 0.01 m
$\beta$ = 10 for spheres

$U_b$ = 15,000 W/m2.K

Seems very high?

Doing the plots now

 

[casualguitar]

As for the Reynolds Number vs Tank number plot (for inlet flow = 0.5 mol/s), the trend seems to be that initially there is a high Re (t=0), which levels off almost immediately:

This does correspond to the molar flow which jumps up to about 1 mol/s initially and then gradually levels off to about 0.56 mol/s. This flow should surely level off to 0.5 not 0.56 though?

Notes:
As for the mass transfer coefficient and heat transfer coefficient plots - the heat/mass transfer coefficients have been constant in all simulations so far, so all I'm doing is generating the mass and heat transfer coefficients from the Reynolds number etc, which aren't actually used in the simulation as constant values are used

Also one further note, after I changed the $U_b$ value to the new calculated value of 15,000 I also had to change $U_g$ to be a high number (in the thousands) to get the simulation to converge

Doing the mass/heat transfer coefficient plots now

 

[Chestermiller]

As for the Reynolds Number vs Tank number plot (for inlet flow = 0.5 mol/s), the trend seems to be that initially there is a high Re (t=0), which levels off almost immediately:
View attachment 304476
This does correspond to the molar flow which jumps up to about 1 mol/s initially and then gradually levels off to about 0.56 mol/s. This flow should surely level off to 0.5 not 0.56 though?

Yes.

Notes:
As for the mass transfer coefficient and heat transfer coefficient plots - the heat/mass transfer coefficients have been constant in all simulations so far, so all I'm doing is generating the mass and heat transfer coefficients from the Reynolds number etc, which aren't actually used in the simulation as constant values are used

That's OK. We're just checking to see what they would come out to be and to compare them with the constant values that you have used. So please provide these plots. Also, please specify the units.

 

[casualguitar]

Yes.

Will provide details on the mass flow calculation

That's OK. We're just checking to see what they would come out to be and to compare them with the constant values that you have used. So please provide these plots. Also, please specify the units.

Doing this currently

 

[casualguitar]

Will provide details on the mass flow calculation

Doing this currently

One further question. Just looking at my $U_g$ calculation. Will we still have the contribution from the bed in the $U_g$ calculation i.e. 1/$U_b$ as we had in the previous model where we lumped them, or will $U_g$ just be a function of re, pr, mu, etc? i.e. no bed properties involved

 

[Chestermiller]

One further question. Just looking at my $U_g$ calculation. Will we still have the contribution from the bed in the $U_g$ calculation i.e. 1/$U_b$ as we had in the previous model where we lumped them, or will $U_g$ just be a function of re, pr, mu, etc? i.e. no bed properties involved

Ug does not involve any bed properties. Ub does. The overall U combines both. This is the same for both models.

 

[casualguitar]

Ug does not involve any bed properties. Ub does. The overall U combines both. This is the same for both models.

Plots of the CO2 and H2O mass transfer coefficients versus position:

And $U_g$ versus position:

The $U_g$ plot seems to return values in a reasonable range. The mass transfer coefficient seems to be too high by a factor of about 1000. I'll confirm if all of the nested values in the ki function are in the right range

EDIT: for some reason the times didnt show up on the ki graphs. The legend is the same as for the $U_g$ plot

 

[casualguitar]

These are the values, ranges and equation used by the simulation to recalculate the mass transfer coefficient values (for both CO2 and H2O):
Reynolds Number: 3500 - 7000
Schmidt Number: Approx 0.7 average
$D_{CO2,N2}$ = 0.144 * 10^-4
$D_{H2O,N2}$ = 0.259 * 10^-4

The equation I'm using:
$k_i$ $=$ $(2.19Re^{1/3} + 0.78Re^{0.619})Sc^{1/3}D_i(1-\epsilon)/d_p$

and it produces values (as in the graph above) of approx 10^-1

Anything obviously wrong with this?

The Reynolds numbers seem reasonable. Also the Schmidt number does seem to line up with BSL. And you say the D values are reasonable. Possibly suggesting that my $k_i$ equation is being used incorrectly? Or that my recalculation of $k_i$ is wrong somewhere (checking this now)

 

[Chestermiller]

Plots of the CO2 and H2O mass transfer coefficients versus position:
View attachment 304485View attachment 304486
And $U_g$ versus position:
View attachment 304487

The $U_g$ plot seems to return values in a reasonable range. The mass transfer coefficient seems to be too high by a factor of about 1000. I'll confirm if all of the nested values in the ki function are in the right range

EDIT: for some reason the times didnt show up on the ki graphs. The legend is the same as for the $U_g$ plot

Please show a hand calculation of k for a Reynolds number of 4000.

 

[casualguitar]

Please show a hand calculation of k for a Reynolds number of 4000.

Is the above (just posted) suitable?

 

[Chestermiller]

Is the above (just posted) suitable?

The k values calculated for these graphs with the equation you used seem correct to me. Also, the Ug's seem reasonable to me.

In using the k values, you multiply by the molar density of the gas by the difference in mole fractions between gas bulk and interphase equilibrium at the gas-bed interface temperature to get the molar flux at the surface. Correct?

 

[Chestermiller]

Please send me a link to that Tuinier et al paper again. I have lost track of it in my files.

 

[casualguitar]

In using the k values, you multiply by the molar density of the gas by the difference in mole fractions between gas bulk and interphase equilibrium at the gas-bed interface temperature to get the molar flux at the surface. Correct?

Not fully following the above, but I think so yes. To use the k values I'm using the molar deposition rate equation which is:
$$\dot{M}_i^"=k_i\left(\frac{Py_i-p_i(T_I)}{RT_I}\right)$$

Where P is pressure, $y_i$ is the gas phase mole fraction of species i, $p_i(T_I)$ is the saturation pressure of species i evaluated at the interface temperature, R is the gas constant and T is the gas temperature. Is this an equivalent to what you said above (if I factor out the molar density from the equation above)?

 

[casualguitar]

Please send me a link to that Tuinier et al paper again. I have lost track of it in my files.

https://www.sciencedirect.com/scien...jNb8NEK3mdGAivU7_KCet9gdzeQ2PUKUvtRz0izC8Wyrg

 

[Chestermiller]

https://www.sciencedirect.com/scien...jNb8NEK3mdGAivU7_KCet9gdzeQ2PUKUvtRz0izC8Wyrg

What is the value of g that they use?

 

[casualguitar]

What is the value of g that they use?

It seems they use these three values (using g as a tuning parameter I think). 1x10^-5 and 1x10-6 fit the data better than 1x10^-7 so I suppose 1x1-^-5 and 1x10^-6 are the g values here

 

[Chestermiller]

It seems they use these three values (using g as a tuning parameter I think). 1x10^-5 and 1x10-6 fit the data better than 1x10^-7 so I suppose 1x1-^-5 and 1x10^-6 are the g values here
View attachment 304579

What value did they use in their main calculations? I’ve derived a relationship between their g and our k:
$$k=\frac{1000RT}{M}g$$where T is the temperature and M is the molecular weight of the diffusing species. R is in J/mole-K, k is in m/s, and g is in s/m. What values of k do you calculate at 250 K using M=18 for water and M = 44 for CO2? How do they compare with the values from our correlation?

 

[casualguitar]

What value did they use in their main calculations? I’ve derived a relationship between their g and our k:
$$k=\frac{1000RT}{M}g$$where T is the temperature and M is the molecular weight of the diffusing species. R is in J/mole-K, k is in m/s, and g is in s/m. What values of k do you calculate at 250 K using M=18 for water and M = 44 for CO2? How do they compare with the values from our correlation?

It looks like they don't really have a 'main calculation' but they do use a range of g values and then conclude that g = 1x10^-6 is the value that best fits the experimental data.

This value of g gives us k = 2.0785/M

which gives $k_{H2O}$ = 0.115 and $k_{CO2}$ = 0.047

Our correlation returns values of $k_{H2O}$ = 0.26 and $k_{CO2}$ = 0.14

They're not the same, but they are in an approximate ballpark range. Is this reasonable closeness? If so that would mean that the mass transfer coefficients are ok and it is something else that is causing the temperature to level out at an unusual temperature

 

[Chestermiller]

This is certainly reasonable closeness. I didn’t expect it to be this close.

 

[casualguitar]

This is certainly reasonable closeness. I didn’t expect it to be this close.

Interesting so the mass transfer coefficients check out, and the $U_g$ (and $U_b$) values are also ok. The gas temperatures level out at values lower than the inlet gas temperature though so there is still some bug present. Right now I have just 'recalculated' the $k_i$ and $U_g$ values. I could implement them in the actual simulation and see how the output looks? Or do you think it is worth checking for the bug elsewhere before doing this?

 

[Chestermiller]

Interesting so the mass transfer coefficients check out, and the $U_g$ (and $U_b$) values are also ok. The gas temperatures level out at values lower than the inlet gas temperature though so there is still some bug present. Right now I have just 'recalculated' the $k_i$ and $U_g$ values. I could implement them in the actual simulation and see how the output looks? Or do you think it is worth checking for the bug elsewhere before doing this?

You need to determine why the temperature doesn’t get to the inlet temperature first. It must have something to do with the evaporation coding logistics.

 

[casualguitar]

You need to determine why the temperature doesn’t get to the inlet temperature first. It must have something to do with the evaporation coding logistics.

The two 'clues':
- The simulation works as expected (gas temperature approaching the inlet gas temperature), when the $k_i$ value is sufficiently small
- The temperature at each point in the bed does not level off to the same value (shown below). This seems like a big hint as for where the simulation breaks. Will take a look

 

[Chestermiller]

The two 'clues':
- The simulation works as expected (gas temperature approaching the inlet gas temperature), when the $k_i$ value is sufficiently small
- The temperature at each point in the bed does not level off to the same value (shown below). This seems like a big hint as for where the simulation breaks. Will take a look
View attachment 304682

How does this compare with the results in the paper? What does it look like as a function of position at constant times?

 

[casualguitar]

How does this compare with the results in the paper? What does it look like as a function of position at constant times?

Well here is the gas temperature vs position (for a range of times):

The gas temperature profile seems to stop changing in any significant way after about 2000s. The final range of temperatures across the bed (210K to about 180K) does seem to be significant because as you said its this range that sublimation/desublimation occurs, suggesting that there is something not working with the sublimation/desublimation coding logistics

For reference, here's the time vs gas temperature plot for the 10 tank setup:

I'm now wondering why the evaporation bug would occur across a range of temperatures (210 to 180K), rather than at one specific temperature (as the pressure is constant). It seems slightly more intuitive that the temperature profile of the bed would level out at a single temperature (say 210K), rather than trend towards the profile it has trended towards

 

[Chestermiller]

Well here is the gas temperature vs position (for a range of times):
View attachment 304702
The gas temperature profile seems to stop changing in any significant way after about 2000s. The final range of temperatures across the bed (210K to about 180K) does seem to be significant because as you said its this range that sublimation/desublimation occurs, suggesting that there is something not working with the sublimation/desublimation coding logistics

For reference, here's the time vs gas temperature plot for the 10 tank setup:
View attachment 304703

I'm now wondering why the evaporation bug would occur across a range of temperatures (210 to 180K), rather than at one specific temperature (as the pressure is constant). It seems slightly more intuitive that the temperature profile of the bed would level out at a single temperature (say 210K), rather than trend towards the profile it has trended towards

The results don't look anything like the results in the paper. Try running a calculation for the same operating data as theirs and see how close you can come to matching them: column design, packing, initial temperature, inlet flow rate and mole fractions.

 

[Chestermiller]

The leveling off at 180 K could be consistent with CO2 desublimation. On their graphs, this leveling is at -95 C. Of course, the times are very different.

 

[casualguitar]

The leveling off at 180 K could be consistent with CO2 desublimation. On their graphs, this leveling is at -95 C. Of course, the times are very different.

The times are different yes I suppose because the flow, dimensions, initial conditions etc are different, but yes the temperature could be consistent with CO2 desublimation.

Why a higher $k_i$ value would cause this levelling off, and not the lower value is not obvious to me. Theres a point at around $k_i$ = 10^-6 somewhere where the temperature no longer gets to inlet temperature but instead levels off at a temperature around the desublimation temperature. I can try find a more accurate value for this $k_i$ value

 

[Chestermiller]

The times are different yes I suppose because the flow, dimensions, initial conditions etc are different, but yes the temperature could be consistent with CO2 desublimation.

Why a higher $k_i$ value would cause this levelling off, and not the lower value is not obvious to me. Theres a point at around $k_i$ = 10^-6 somewhere where the temperature no longer gets to inlet temperature but instead levels off at a temperature around the desublimation temperature. I can try find a more accurate value for this $k_i$ value

Please don’t bother. Just use their input operating conditions please. This will tell us a lot.

 

[casualguitar]

Please don’t bother. Just use their input operating conditions please. This will tell us a lot.

So using their operating conditions as much as is possible (I can lay out the exact values used if necessary), this is the position vs gas temperature output:

And the Tuinier et al equivalent:

So they are not that similar in that our one stops at -90C (around the desublimation temperature), and that there is no clear constant temperature section.

One thing I noticed - here's the plot of CO2 solid buildup versus position:

This is in moles. Notice how the solid builds up at each position and then decreases, suggesting that sublimation is also occurring. But how can this happen if the temperature is below the sublimation temperature? I don't know the exact temperature of sublimation but even if the gas temperature is slightly above that it would still likely be slow desublimation, not like the above

The mechanics for the sublimation/liquefaction pressure are as follows:

and for water:

The above is just to show what I do outside the temperature bounds. I either set the sublimation/liquefaction pressure equal to 0 or a very large number

It seems odd that the solid buildup would take on a normal trend, while the gas temperature stays below (or on) the sublimation temperature?

EDIT: I mentioned above that there is no clear constant temperature section in the plot, when actually this is probably not true as the constant temperature section would occur at the maximum temperature on this plot. I guess if the temperature went higher (above sublimation temperature) we would see that constant section

 

[casualguitar]

In addition, one thing I have found is that the $Q_{IB}$ and $Q_{GI}$ values at the left boundary start at a few hundred and trend gradually to zero (as expected), however the internal node values of $Q_{IB}$ and $Q_{GI}$ start at a decimal value and trend to very small numbers (10^-10), suggesting that heat transfer in the inner nodes is much less. Looking into this

 

[Chestermiller]

So using their operating conditions as much as is possible (I can lay out the exact values used if necessary), this is the position vs gas temperature output:

View attachment 304767
And the Tuinier et al equivalent:

View attachment 304768
So they are not that similar in that our one stops at -90C (around the desublimation temperature), and that there is no clear constant temperature section.

One thing I noticed - here's the plot of CO2 solid buildup versus position:View attachment 304769
This is in moles. Notice how the solid builds up at each position and then decreases, suggesting that sublimation is also occurring. But how can this happen if the temperature is below the sublimation temperature? I don't know the exact temperature of sublimation but even if the gas temperature is slightly above that it would still likely be slow desublimation, not like the above

The mechanics for the sublimation/liquefaction pressure are as follows:
View attachment 304770
and for water:
View attachment 304771
The above is just to show what I do outside the temperature bounds. I either set the sublimation/liquefaction pressure equal to 0 or a very large number

It seems odd that the solid buildup would take on a normal trend, while the gas temperature stays below (or on) the sublimation temperature?

EDIT: I mentioned above that there is no clear constant temperature section in the plot, when actually this is probably not true as the constant temperature section would occur at the maximum temperature on this plot. I guess if the temperature went higher (above sublimation temperature) we would see that constant section

You need to compare these on a more common basis. Remember that $\Delta x=L/n$, where n is the total number of tanks. The tank centers are therefore at $\Delta x/2, 3\Delta x/2, 5\Delta x/2,\ etc$. Plot the data at these distances, not tank numbers. There is also a data point at x = 0, of course, corresponding to the inlet conditions.

I'm guessing that you are using 10 tanks for the whole bed. They seem to be using a finer grid, with approximately 3x your resolution. So,, for comparison, please use 30 tanks.

You should also be comparing the mass buildup per unit area of bed, not the molar solid buildup within each tank. Please, for comparison, show the mass buildups per unit bed area within each tank.

I'm definitely not going to go through your coding. If you want to show a logic diagram for how the deposition is calculated, I'll consider it.

What is this all about: "I either set the sublimation/liquefaction pressure equal to 0 or a very large number". I thought we are assuming the total pressure is 1 bar.

 

[casualguitar]

I'm guessing that you are using 10 tanks for the whole bed. They seem to be using a finer grid, with approximately 3x your resolution. So,, for comparison, please use 30 tanks.

I'm currently using 10 tanks yes. Ah ok I did attempt to make the grids comparable, using the below statement from the paper (and knowing that the bed is 300m in length):

I thought that 300mm length divided into 3cm increments would be about 10 'tanks'. Is this incorrect? If so I can switch to 30 but I don't yet see how you got 30

You should also be comparing the mass buildup per unit area of bed, not the molar solid buildup within each tank. Please, for comparison, show the mass buildups per unit bed area within each tank.

I noticed this also yes that they use $kg.m^3$ not just $kg$. I guess multiplying my molar solid buildup value by a tank volume ($dz * A_c$) works here?

I'm definitely not going to go through your coding. If you want to show a logic diagram for how the deposition is calculated, I'll consider it.

Yes that was my intention to show the logic above. I'll make a logic diagram for how this currently works

What is this all about: "I either set the sublimation/liquefaction pressure equal to 0 or a very large number". I thought we are assuming the total pressure is 1 bar.

Yes the total pressure is 1 bar however the sublimation rate is dependent on the sublimation pressure at a given temperature. Above the critical temperature I set the sublimation/liquefaction pressure equal to a very large number to stop any desublimation happening

 

[Chestermiller]

I'm currently using 10 tanks yes. Ah ok I did attempt to make the grids comparable, using the below statement from the paper (and knowing that the bed is 300m in length):View attachment 304777
I thought that 300mm length divided into 3cm increments would be about 10 'tanks'. Is this incorrect? If so I can switch to 30 but I don't yet see how you got 30

OK. I was confused. I missed the point that their total length of bed was 30 cm. However, the locations of their thermocouples do not necessarily correspond to the grid spacing in their model. I would suggest using more tanks in your calculations. Their graphs seem to suggest that the used a finer resolution than $\Delta x = 3\ cm.$. I suggest 30 tanks, so that $\Delta x = 1 \ cm$ and so that the center of the first tank is at x = 0.5 cm and the center of the last tank is at 29.5 cm.

The locations where the temperatures are changing substantially in their model do not seem to correspond to where they are changing substantially in your model. All the variation seems to be happening closer to the inlet in your model. Is there a scaling problem on time?

I noticed this also yes that they use $kg.m^3$ not just $kg$. I guess multiplying my molar solid buildup value by a tank volume ($dz * A_c$) works here?

I'll let you work this geometric conversion out. But please provide the rationale and equations for the conversion that you develop. It is not simply Adz.

 

[Chestermiller]

On second thought, surface area to volume ratio of a particle is $$\frac{4\pi r_p^2}{\frac{4}{3}\pi r_p^3}=\frac{3}{r_p}=\frac{6}{d_p}$$The particle volume per bed column volume is $1-\epsilon$. The column volume per tank is $A_c\Delta z$. So, the available deposition area per tank is $$\frac{6}{d_p}(1-\epsilon)A_c\Delta z$$