Hi all,
I am working on computing the melt fraction and total melt production for no-melt material models like the Steinberger model. Specifically, I aim to compute the melt fraction at each time step at each evaluation point based on P and T, and then integrate the melt volume over time. My model assumes that melts are not extracted and do not affect the model’s behavior, similar to the approach described inLi et al. (2016)
My current thought is to creat an additional generic compositional field called “melt_fractions” that could be updated at each time step by the material model. This way, I could use the existing melt statistic post-processor to compute the total melt volume.
Does this approach sound reasonable? If so, I would appreciate any guidance on which source files I should modify or add to implement this. Any thoughts or suggestions would be greatly appreciated!
Best,
Lucy
Hi Lucy,
Sorry for the late reply.
Just to make sure I understand this correctly:
When you say you want to integrate the melt volume over time, what you want is to compute–at each point in time–is the maximum melt fraction each parcel of rock has experienced at any point in time before, and then integrate that over the domain? In other words, if a part of the model is partially molten in one step, and then it’s still molten in the next, you do not want to count it twice? It’s like we pretend the melt is being extracted (we just do not let that affect the model) and then want to know the integrated “depletion” in each step? So in the end, we get the total amount of melt that has been produced in the model?
In this case, I think the melt statistics postprocessor is not useful, because it gives you the melt fraction at each point in time, so you can not track if any point in the model has experienced melting before. Instead, I think what you suggested with the additional compositional field makes sense. Let’s say we call the field “depletion”. You can implement a reaction term that compares the current melt fraction to whatever is stored in the depletion field, and if the current melt fraction is larger, add the difference to the depletion field. That is basically what the melt material models already do, so you can have a look at them. You can get the melt fraction from the “katz2003_model” reaction plugin as in melt_simple (see here), or compute your own melt fraction.
This means you only need to modify the material model you are using. You can then simply use the composition statistics postprocessor to get the total depletion (= total melt production).
Does that help?
-Juliane
Hi Juliane,
Thank you so much for your advice! I have implement melting calculation in my own material model and it works! I have a little follow-up question and would love to hear some of your insights on it.
After reading Katz et al. (2003) again carefully, I find that the Katz’s model is computing melt mass fraction but not volume fraction. From my understanding, since the compositional field value in aspect should represent mass fraction, it makes sense to record the maximum melt mass fraction as the “depletion” compositional field. However, when using the composition statics post-processor, it will return the total mass of the depletion field, while the common way to document the amount of melt is by volume. I am wondering what would be the appropriate way convert the total melt mass to total melt volume.
Thanks again for all your time and helpful suggestions!
Lucy
Hi Lucy,
That’s challenging, and I don’t see how this can be done accurately, for several reasons. For once, the Katz model does not provide the density of the melt (it does not even provide the composition of the melt). If you just want to get an approximation, you could just assume some reasonable average density for the melt and use that to convert mass to volume. Alternatively, you could make some assumptions, like, all the melt is in equilibrium and it’s batch melting. Then, the average depletion theoretically tells you what the average melt composition should be (the melt that is in equilibrium with the solid you have left). So you could, in principle, try and find a thermodynamic model that then gives you the density of the melt in dependence of its composition. But since you’re not tracking where the melt goes, you also do not know the pressure or temperature it’s at. So you can’t know the exact density (unless you assume melt stays where it is – but usually, one wants to know how much melt reaches the surface).
Therefore, I would just use the total mass unless there’s a really good reason for using the volume. If it’s just to compare to volumes of melt from observations, I would try to figure out if the observations say something about the melt density, or use some reasonable value for the melt density to make an estimate.
Cheers,
Juliane