During a routine sample control inspection, a quality control engineer notices a significant discrepancy between the expected and actual concentration of paint produced in a reactor. An investigation into potential sources of error raises doubt in the validity of the original model. A comparison between the experimental and theoretical data leads to the source of the error: an inaccurate prediction of the rate constant for one of the reactants.
The challenge: to validate production concentration by assessing the quality of paint produced in a chemical process.
The quality control engineer uses Maple to:
- Derive and solve the system of six non-linear differential algebraic equations that define the reaction.
- Import experimental data sets and plot the concentrations of the compounds over time to determine the concentration at steady state
- Perform a comparative analysis between the predicted concentrations and test data using Maple's Statistics package. A discrepancy between the theoretical results and the experimental data is noted and traced back to an inaccurate reaction-rate constant for one of the reactants.
- Find a more accurate value for the rate constant using Maple's Optimization package.
With the corrected rate constant, the model now accurately predicts the actual concentration of the product as measured by the quality control engineer. Unlike traditional solution methods that require writing hundreds of lines of code, the resulting Maple document is quickly created using intuitive notation, saving days in production analysis. Since the document is an executable, modifiable description of the problem and its solution, the engineer can easily reuse it to create prototypes and optimize other reaction schemes.