How Does Magma Injection Rate and Sill Height Affect Crustal Heating?

[PinkGeologist]

Imagine you inject a 16km high stack of magma in the Earth's crust continuously over X years and then analyze the size and shape of the final "hot zone" as your "result" ... let's say you want to quantify the volume of crust at a temperature (T) greater than 1000 Kelvin (K). In case 1, that volime is (X1 m^-3)

Not, imagine you insert the same amount of magma over the same amount of time but not continuously - you insert 40 sills of magma, each 400m in height. The fial volume you get for that is ... (X2 m^-3)

Then you insert 160 sills in the crust, each 100m tall and get a final V = X3 m^-3

Then you insert 320 sills in the crust, each 50m tall and get a final V = X4 m^-3

Then you insert 640 sills in the crust, each 25m tall and get a final V = X5 m^-3

I did this with a numerical model (COMSOL multi-physics) where the cooling is by conduction with some latent heat added to the system as minerals in the magma crystallize out and freeze while it cools.

What is weird is that the final V does not just get larger or smaller as the sills gets shorter (and the time between their injection obviously gets shorter).

You can SEE the results here (a picture is worth 1000 words and all that):
https://www.dropbox.com/s/irzgjkoj78czb78/Screen Shot 2015-04-29 at 9.30.13 PM.png?dl=0
https://www.dropbox.com/s/9wdpd3hlg3x80iu/Screen Shot 2015-04-29 at 9.30.03 PM.png?dl=0
https://www.dropbox.com/s/q2mrfkilkgme5p1/Screen Shot 2015-04-29 at 9.29.52 PM.png?dl=0
https://www.dropbox.com/s/ruemoh8wc4mr043/Screen Shot 2015-04-29 at 9.29.40 PM.png?dl=0

At each total rate I choose, somewhere in the 100m to 50m sills height range I get the highest final volume.

I need to describe this quantitatively rather than just qualitatively and was hoping for the insight of someone who works with thermodynamic problems to actually elucidate the finer points of what is happening.

I know there must be a "sweet spot" where the retained heat between injections and the added heat of the injections combined and amplify, but I'm not sure how to make a finer discussion.

 

[eljose79]

I would like to first commend you for conducting this experiment using a numerical model. It is always important to validate our hypotheses and theories through experimentation.

Based on the results you have presented, it is clear that there is a non-linear relationship between the number of sills and the final volume of crust at a temperature greater than 1000 K. This is not surprising, as there are many variables at play in this scenario, such as the rate of injection, the height of the sills, and the cooling mechanism.

One possible explanation for the observed trend is that as the sills get shorter, the time between injections decreases, leading to a more rapid cooling of the magma. This could result in a smaller hot zone and a smaller final volume of crust at a temperature greater than 1000 K. However, as the sills get even shorter, the time between injections may become too short for the heat to dissipate, leading to a build-up of heat and an increase in the final volume.

Another factor to consider is the heat transfer between the sills and the surrounding crust. As the sills get shorter, there is less surface area for heat transfer to occur, which could also contribute to the observed trend.

To make a more quantitative analysis, you could try varying the rate of injection while keeping the height of the sills constant. This would allow you to isolate the effect of the time between injections on the final volume. Additionally, you could also vary the composition of the magma and the properties of the surrounding crust to see how they affect the final volume.

Overall, this is a very interesting and complex problem, and further experimentation and analysis will be necessary to fully understand the underlying mechanisms. I hope my insights have been helpful to you in your research. Good luck!