ST-589: Climate Change and Carbon Sequestration Final Project Earl 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 CO 2 sequestration.

Basic Premise A coal power plant produces ____ Gt of CO 2 each year. This CO 2 must be sequestered. Figure out how this can be done at minimum cost.

Pre-Algebra CO 2 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 CO 2 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 CO 2 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 – reports/srccs/srccs_summaryforpolicymakers.pdf 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 CO 2 capture “Carbon in Underland” – Short, cheesy animation explaining the basic processes of geologic CO 2 sequestration “Geologic Sequestration” – SWP’s website illustrating geologic sequestration, including an animated applet demonstrating the sequestration of CO 2 from a coal plant over time at varying percentages. “Simulation and Risk Assessment Focus Area” – 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.1.17Solve linear equations and inequalities in one variable including those involving the absolute value of a linear function.