ST-589: Climate Change and Carbon Sequestration

Final ProjectEarl Reynolds

Goal

• A flexible project that can be adapted to multiple problems and levels of mathematics, ranging from Pre-Algebra to Algebra II, which applies mathematics standards to the problems of CO2 sequestration.

Basic PremiseA coal power plant produces ____ Gt of CO2 each year. This CO2 must be sequestered. Figure out how this can be done at minimum cost.

Pre-Algebra

• CO2 transported by pipeline, constructed at fixed cost per mile

• Only one site is used• Sites have volumes easily expressed by formulas (e.g. cube,

prism, half sphere)• All but one site is too small; one site is more than large

enough.• Main question: How much will it cost to sequester the CO2 in

the appropriate reservoir?• Extra credit: cheaper to sequester in one site or multiple

sites?

Algebra I

• Two sequestration sites of adequate size can be used, of variable investment costs (possibly land rights, difficult terrain, etc.).

• These costs sum to a total initial cost. The cost of a pipeline varies with each site (e.g., $1000 per mile for site one, $5000 per mile for site two).

• Main question: Students must figure out which site to use for a given time period (e.g. 10 years, 50 years). Solutions are found by solving a system of equations.

• Decide if one site is always cheaper than the other, if it is worthwhile to build pipelines to both sites, etc.

Algebra II

• Students will solve a basic linear programming problem, with the following constraints:– Cost of pipeline construction– Capacity of each reservoir (fixed volume

calculated from porosity)– Permeability of each reservoir (if applicable)– Total CO2 to be sequestered

• The project must meet all constraints, and must include the optimal solution.

Resources for project expansion• “Carbon Dioxide Capture and Storage: summary for policy makers

– http://www.ipcc.ch/pdf/special-reports/srccs/srccs_summaryforpolicymakers.pdf• Provides general information and useful data tables that can be incorporated into the

assignments for the sake of authenticity. Numbers include: Coal Plant emission stats, cost of CO2 capture

• “Carbon in Underland”– http://www.youtube.com/watch?v=gr9cznZFuIc

• Short, cheesy animation explaining the basic processes of geologic CO2 sequestration

• “Geologic Sequestration”– http://www.southwestcarbonpartnership.org/GeoSeq.html

• SWP’s website illustrating geologic sequestration, including an animated applet demonstrating the sequestration of CO2 from a coal plant over time at varying percentages.

• “Simulation and Risk Assessment Focus Area”– http://www.netl.doe.gov/technologies/carbon_seq/corerd/simulation.html

• The DOE’s collection of simulation information, useful for student research in more open-ended adaptations of the project

Standards Correlation

• All levels: 9-12.A.3.1 Model real-world phenomena using linear equations and linear inequalities interpret resulting solutions, and use estimation to detect errors.

• Algebra I: 9-12.A.3.4 Solve systems of linear equations in two variables algebraically and graphically

• Algebra II: 9-12.A.1.17 Solve linear equations and inequalities in one variable including those involving the absolute value of a linear function.