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isenthalpic assimilation, conceptual additional info?

Started by bpeterson, January 10, 2013, 10:53:01 AM

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bpeterson

Hi Paula,

I went through the previous post on isenthalpic assimilation (http://magmasource.caltech.edu/forum/index.php/topic,137.0.html); for the most part, I was able to follow it using alphamelts 1.2. I also ran into the bug where the temperature shot up to ~5000 degrees, but was able to work around it by imposing the initial entropy using menu option 7. So far it looks like I am doing it more or less right.

I guess I  have some conceptual questions; I want to make sure I understand what is being calculated. I am assuming that the point of the first calculation is to set some initial reference of the assimilant(?) - e.g. if I do the bulk calculation or the option 4 calculation to, say, 700 degrees, that I am effectively setting that as a reference point. Then when I do the second calculation using the binary file (the actual AFC), the enthalpy associated with the assimilant is sensible heat required to get that assimilant from the reference T (700) to whatever the system temperature is + latent heat of melting that assimilant. This is balanced by the sensible heat of the cooling magma + latent heat of crystallization(?)

What I'm not quite sure I understand is what - if anything - aphamelts is doing with the assimilant. If the system temperature is below the liquidus of the assimilant, is it partially melted? In other words, my assimilant could be a mafic granulite in the lower crust with 50 wt% SiO2, but if it only partially melts, the liquid could have higher SiO2 concent, 60-70 wt%. Let's say I specify an addition of 1g of assimilant per iteration. If the system temperature is such that the assimilant is only 50% melted, is the liquid added to the magma and the solid residual added to the crystallized totals? I guess I'm not really sure of what is going on; any help would be appreciated!

Thanks very much,

Brook

Paula

Hi Brook,

Sorry for the delay in replying.

Yes, the point of the first calculation (with 'garnet.melts' input) is to set the reference enthalpy for the assimilant at the chosen assimilant temperature. For the actual AFC calculation, the reference enthalpy of the system is first calculated for the given starting temperature (e.g. the liquidus). When, say, 1 gram of assimilant is added to the system the enthalphy associated with that 1g is also added. alphaMELTS then solves for the new temperature by bringing the system to equilibrium at the new system reference enthalpy, which results in the balance of sensible and latent heats that you describe.

In practice, when liquid is present, it is easiest to add the assimilant material to that. This is for bookkeeping reasons: the liquid has all the components available in the system. If liquid is not present then the assimilant is added to the solids and the phase compositions and / or assemblage adjusted accordingly so that things add up. Until the isenthalpic calculation is performed, the resulting liquid or solid compositions will be metastable. However, the system will generally be closer to equilibrium (because a little bit of solid is retained even after fractional crystallisation) than a pure liquid of the same bulk composition. So the isenthalpic calculation will be quicker than if we only recalculated the bulk composition and reference enthalpy and then started adding solid phases to the assemblage from scratch.

Fractionation of any solid phases occurs after the isenthalpic step. So for your example the solids will be a combination of the assimilant residue and any newly crystallised phases but everything, solid and liquid, will have been chemically equilibrated before fractionation. Clearly this is an end-member case. Another end member, perhaps closer to what you envision here, is one where magma and assimilant are in thermal but not chemical equilibrium during the isenthalpic step. The solids would then be fractionated and the two liquids could, optionally, be combined between assimilation iterations. We hope to be able to offer such capabilities over the coming months as part of alphaMELTS 2.

Hope that helps but please let me know if you have further queries or would like more clarification.

Cheers,
Paula

bpeterson

Paula, thanks very much for your reply! If I understand this correctly, at each iteration the assimilant is added, enthalpy is balanced, and finally the system is equilibrated at its new T and composition and solids are fractionated. So this is kind of like saying that any incorporated assimilant is totally melted (as opposed to partially melted; e.g. the assimilant added to the system is not chemically fractionated) (?)

If I wanted to do assimilation involving the chemical composition of partially-melted country rock, I'd need to use an appropriate assimilant composition, something like the "metapelite partial melt" of the Reiners et al. 1995 Geology paper. I imagine that the enthalpy associated with bringing up a metapelite partial melt composition from a references state is going to be different than the enthalpy associated with bringing up a metapelite composition and partially melting it. I can see that maybe this wouldn't matter for modeling overall chemical and isotopic trends, but might matter if I wanted to back out the total mass of assimilant added.

Also, I imagine its possible to use alphamelts to generate the composition of a partially-melted assimilant. So if I wanted to my assimilant to be the product of 50% melting of a granulite, I could run the granulite composition to 50% liquid mass remaining, then output the liquid as .melts file with option 14. Then proceed as normal with the isenthalpic AFC, equilibrating that .melts file in the first step...

As an aside: I also assume that using a smaller mass for the amount of assimilant added would make the equilibration calculations easier, insofar as the system is closer to the equilibrium of its last itereation(?)

Thanks again for all the info!

-Brook

Paula

Hi Brook,

Quote from: bpeterson on January 16, 2013, 10:38:29 AM
If I understand this correctly, at each iteration the assimilant is added, enthalpy is balanced, and finally the system is equilibrated at its new T and composition and solids are fractionated. So this is kind of like saying that any incorporated assimilant is totally melted (as opposed to partially melted; e.g. the assimilant added to the system is not chemically fractionated) (?)
Well it's never really totally melted as there isn't enough heat for that but the system is effectively homogenised before equilibration... or at least you can think of it that way, bookkeeping details aside. We might expect the solids crystallised to be more mafic, SiO2-poor etc. than for simple cooling of the liquid (without assimilation) or for addition of an assimilant partial melt. So, in a sense the end result is that the assimilant is chemically fractionated but, within the MELTS code, the fractionation occurs after mixing. A model in which fractionation of the assimilant occurs before or at the time of mixing would give a different result; how different is hard to say and probably depends on the exact chemical composition.
Quote
If I wanted to do assimilation involving the chemical composition of partially-melted country rock, I'd need to use an appropriate assimilant composition, something like the "metapelite partial melt" of the Reiners et al. 1995 Geology paper. I imagine that the enthalpy associated with bringing up a metapelite partial melt composition from a references state is going to be different than the enthalpy associated with bringing up a metapelite composition and partially melting it. I can see that maybe this wouldn't matter for modeling overall chemical and isotopic trends, but might matter if I wanted to back out the total mass of assimilant added.
Yes. It's true that using the partial melt composition, and ignoring the latent heat of melting of the metapelite, is going to affect the enthalpy balance and contribute to uncertainties in any estimate of the mass of assimilant added. I suspect that other uncertainties, such as in the temperature of assimilant, are at least as important. Hopefully it's somthing we'll be able to test with alphaMELTS 2, when it happens.
Quote
Also, I imagine its possible to use alphamelts to generate the composition of a partially-melted assimilant. So if I wanted to my assimilant to be the product of 50% melting of a granulite, I could run the granulite composition to 50% liquid mass remaining, then output the liquid as .melts file with option 14. Then proceed as normal with the isenthalpic AFC, equilibrating that .melts file in the first step...
Yes, that's how I would do it.
Quote
As an aside: I also assume that using a smaller mass for the amount of assimilant added would make the equilibration calculations easier, insofar as the system is closer to the equilibrium of its last itereation(?)
In principle, yes, and step size is always a good thing to play around with if alphaMELTS is struggling. The main benefit of the way the calculation is done in MELTS though is that a little bit of each solid that crystallises stays with the system after fractionation. This amount that is retained is determined by ALPHAMELTS_MASSIN so there will be play between that and the size of the assimilant increment.

Cheers,
Paula

bpeterson

Paula,

Thanks again for your help! I'm still playing with this but have had reasonably good success so far using the approaches above. I have noticed that in some areas of parameter space, alphamelts seems unable to perform the assimilation calculation. I get to the point where I tell it the mass of the assimilant to add, hit enter, and there is no output; the CPU load on my computer goes up and the fan cranks on, so I know it is attempting something, but there's no further output.

Its a bit peculiar. It only seems to happen with certain combinations in PT space, with certain assimilant files. For instance (all at 4000 bar), as an assimilant file, I took the F=0.2 liquid from a mafic granulite, ran it down to 780C to near-subsolidus, changed the T to 400C, and output a binary restart file. When I attempted to do the isenthalpic assimilation, I encountered the problem described above. When I did the same thing and changed the T to 100C or 700C, it worked.

Additionally, during equilibration when I took the same assimilant and ran it to 820, then stepped it sequentially to 790, 750, and 700 (using single calculations, option 3), then changed the T to 400C and output the binary restart file, it also worked. So I'm able to work around it generally, but there does seem to be parameter space where alphamelts seems to have difficulty in starting the assimilation. There's no output, so I'm not really sure what its doing. I can send you my files and shell scripts if you are interested, although as I mentioned, I think I can generally work around it, for the most part, so it. Of course, the problem seems to happen most often in exactly the part of PT space I'm interested in... Must be some variant of Murphy's Law there.

Paula

Hi Brook,

That kind of behaviour usually means it is trying to add a phase that has ordering e.g. pyroxene, spinel, feldspathoid...  Still, I'd be interested to check that that is indeed the case.  So if you do get a chance to send the files and scripts that would be great (e-mail address is on the MAGMA and alphaMELTS websites).  No hurry - it'll probably be next week before I get to alphaMELTS debugging as I'm still doing some website stuff right now.

Thanks!
Paula