AiS Challenge Team Interim

Team Number: 080

School Name: Santa Fe High School

Area of Science: Earth Sciences

Project Title: Computation of Compounding Pressure in a Magma Dome

 

 

Problem Definition:
This project will model the increased pressure inside a magma dome to predict a potential volcanic eruption. Pressure buildup and its subsequent release mechanism are valuable in predicting the potential dangers to an environment. The variables will be temperature, flow patterns, strata configurations, and depth of flow, among others. We chose this project so that we can enter data for any volcano and determine the amount of pressure it takes for a volcano to explode.

Volcanic eruptions are of two basic types. One type is the effusive eruptions (gas poor) where magma pushes up and flows as lava over the surface of the earth in a more or less passive manner, typified by ongoing eruptions in Hawaii that visitors can safely observe. Type two is the explosive eruptions (gas rich) where volatile fluids (mostly water) in the magma rapidly vaporize and dynamically tear the magma apart into fragments, called pyroclasts (Pumice and Ash). This type of eruption is truly explosive, generally accompanied by shock waves and devastation around the vent. Such was the case for Mt. St. Helen's as well as for the Valles Caldera in the Jemez Mountains about a million years ago. We will first limit our program to a specific type of eruption.

Problem Solution:
We will solve this problem using these key calculations that involve user-determined values: (1) volume (or mass) of magma (saturated with water) and (2) a rise rate of the magma from a magma chamber deep in the earth (say ten km). Calculations would then quantify the amount of water exsolved as a function of magma depth, which is most simply expressed as a form of Henry=92s law of solubility:

c=n(p)^x

for which c is mass fraction of water that is soluble, n and x are constants related to magma composition, and p is pressure (in bars--old term where 1 bar equals about 1 atmosphere or 14.7 lbs / in^2). Rhyolitic magmas (high silica content) are typical of many explosive eruptions (such as the Valles) and the solubility constants are commonly n= 0.13, x=1/2. So for a rhyolitic magma at a depth of 10 km, at a temperature of 900 C where the pressure is

p=rho*g*h

where rho equal rock density ( say 2500 kg /m^3 ), g= gravitation acceleration (9.8 m/s^2), p would be 245 MPa or about 2450 times that of atmospheric pressure. Sticking that value into Henry's law gives a solubility of about 6.5 percent. This means that every kg of magma contains 65 g of water doing that same calculation at atmospheric pressure (at the earths surface) shows that the magma can only contain 0.13 percent water, the other 6.37 percent would be steam. Computers will be used for calculations and analysis as well as to model this build up of pressure

Progress to Date:
To this day we have managed to find two mentors that are helping us with our project. Our programmer is working on a program that will program the amount of pressure it takes for a volcano to explode. So far, our main difficulty has been finding information to help us with the mathematical aspects of the project. Luckily our mentors have been able to help us with that. We have not yet begun our C++ program functions.

Expected Results:
When we are finished our program will be able to tell us the amount of pressure it takes for a given volcano to reach the eruption stage. If time allows, we will model more types of volcanoes and allow for input of strata types. Our project will help other people to determine time (s) of eruptions for volcanoes and be able to properly repair for its results. Assumptions:

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