### Optimization of a Water Gas Shift Reaction

## by Evan Crall

Submitted : Spring 2012

In a Fischer-Tropsch reactor, the optimum flow rate of the reactant (H_{2}O) to the reactor must be determined for the purpose of profiting from the sale of the product (H_{2}). First, the profit function was determined by subtracting the cost of H_{2}O from the potential sales of H_{2}. Next, to determine the amount of reactants and products that would result from the reaction, stoichiometry was utilized, creating a value for each gas in the reaction in terms of two variables. By expressing one variable in terms of the other, the profit function in terms of one variable was created. This function was then optimized by taking its derivative, to find the value of “x” that would result in the highest value for the profit function. By optimizing the profit function through taking its derivative, the ideal amount of H_{2}O that should enter the reaction is determined in order to maximize profits.

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