Megan Elwood Madden

University of Oklahoma

This problem set was developed as a homework assignment for upper level undergraduates and graduate students participating in the Principles of Geochemistry course offered as part of the Geology and Geophysics curriculum. The course is a general overview of mainly inorganic geochemistry which focuses on the thermodynamics and kinetics of natural systems. Many of our students continue on to graduate school and/or careers in energy industries.

The relationship between thermal conductivity, heat flow and geothermal gradient, as well as density, lithostatic, and hydrostatic load is covered in lecture before the assignment is given.

Students must understand the general concept of phase diagrams in order to complete the assignment.

This homework exercise is assigned early on in the semester when we discuss geothermal, lithostatic, and hydrostatic gradients within the Earth. This is one of the first exercises where I ask students to create spreadsheets and graphs.

Students will apply geothermal and lithostatic gradients to phase diagrams to determine the depth of methane hydrates. Concepts covered include heat flow, density, geothermal gradients, lithostatic and hydrostatic load, pressure, density, spatial analysis, and energy equivalents.

1. Apply heat flow, thermal conductivity, and density data to develop P-T models of the near surface for different geologic regions
2. Combine and analyze different types of data sets (geothermal gradient, lithostatic load, phase diagrams) to answer relevant geologic questions.
3. Use spatial analysis skills to calculate a volume of hydrate based on several known variables and convert that volume to mass, moles of methane, and finally energy and greenhouse gas equivalents.

• Construction of spreadsheets
• Developing useful graphs
• Converting between various units of measurement

In this problem set students use thermal conductivity, heat flow, and density of sediment to calculate the P-T conditions at depth within the Gulf of Mexico and Alaska permafrost. They compare this P-T data with a phase diagram for methane hydrate to determine the range of depths at which methane hydrate would be expected to form. A spreadsheet and graphing program like Excel is needed for the calculations. This exercise would be appropriate for a geochemistry course or as a quantitative exercise within a physical geology course. Students gain experience using spreadsheets and graphs, including phase diagrams to solve geologic problems related to environmental change and energy production.

The project is graded as a homework set, with partial to full credit assigned for each question and/or step in the calculations. Students are evaluated based on their accurate calculation of P-T conditions at depth within the different environments, as well as formulating graphs and text that communicate their results. Critical thinking skills are evaluated based on how they used their graphs and spreadsheets to answer the questions regarding the depth of the hydrate stability field in different regions. In the final question, the student's ability to apply density and molecular mass to geologic materials and successfully complete a series of conversions is also evaluated.

Sloan, 1998: Colorado School or Mines Center for Hydrate Research software
Dickens, G.R., Quinby-Hunt, M. 1994. Methane hydrate stability in seawater. Geophysical Research Letters 21, 2115-2118.

Elwood Madden, M.E., Ulrich, S.M., Onstott, T.C., Phelps, T.J., 2007. Salinity-induced hydrate dissociation: A mechanism for recent CH4 release on Mars. Geophysical Research Letters 34 CiteID L11202.