Make the CSTR porosity and liquid volume definition consistent with the notation of the other unit operations.

[AntoniaBerger]

For column models, the volume of each unit operation is given by its geometric parameters (i.e. diameter / length) and the liquid volume is automatically adjusted when changing the porosity.

Since the Cstr has a variable volume, we need to explicitly provide an initial value. We would expect that a porosity of e.g. 0.9 is defined, the liquid volume of the tank is then also reduced by 10 % to account for the solid material. However, different porosities (for models without isotherms or reactions) don't change the simulation solutions at all. (Figure 1) The expected result is produced when the volume is additionally adjusted: (Figure 2)

cstr = Cstr(component_system, 'cstr')
cstr.c = [0]
cstr.V = 1
cstr.porosity = 0.9

This led us to the question about how liquid / solid volumes of the CSTR are handled by CADET internally and if the current approach is consistent / usefull. E.g. Does the volume refer to the total volume or just the liquid volume? Does the CSTR take into account that porosity changes when the volume changes? etc.

To be discussed...

[jbreue16]

Why would the porosity change the simulation results for a CSTR when theres no binding? At first thought I dont expect that since we dont model any transport with the CSTR. IF it would change the results similarly to an actual transport model like the LRM, wouldnt you expect the difference in figure 2 to be the opposite, i.e. more porosity -> less dispersion?

[lieres]

Porosity indicates the percentage of bulk void space within the column or CSTR. It affects the residence time for given volumetric flow rate (under non-binding conditions). Shorter residence times cause less band broadening.

[schmoelder]

You could also look at the mean residence time (assuming constant in and outflow)

$$ \tau = V_{liquid} / Q $$

[jbreue16]

Does the CSTR take into account that porosity changes when the volume changes?

No and I dont see why it would. As usual Iam only familiar with the equations, not the device, so please excuse me. From how I understand the equations, we consider a theoretically infinite large vessel thats completely filled with beads such that when the volume changes, the rest of the vessel simply runs dry, ie the porosity does not change? Hows that in reality, does the interstitial volume collapse/expand, such that porosity decreases/increases?

Does the volume refer to the total volume or just the liquid volume

From my understanding, the volume refers to the volume of the solvent and the molecules of the components are technically neglected, ie molecules being adsorbed does not change the volume.

Porosity indicates the percentage of bulk void space within the column or CSTR. It affects the residence time for given volumetric flow rate (under non-binding conditions).

If theres no binding, ie $c^s=0$ at all times, then I dont see how porosity affects residence time in our CSTR model. In our LRM, that would be accounted for by the axial dispersion parameter, right? But theres no such dependence (ie $D_{ax}(\varepsilon$)) in the model equations, maybe thats a ParameterParameter dependence that we could add in #189 And the axial dispersion parameter should negatively correlate with the porosity, ie the opposite of what we see in figure 2?

Edit: Possibility of $D_{ax}(\varepsilon$) parameter dependence was actually aready added in d2b4c27e0100e77b135fbc59d3c0a810baf945db

[schmoelder]

Hey, I think there might be some misconceptions. I'm happy to explain more in a call.

[jbreue16]

We have decided to implement a new CSTR unit operation that has variable porosity which is computed from a fixed solid volume and variable liquid volume, see #235

So this issue here is about explicitly describing that we only refern to liquid volume for this CSTR in the documentation.