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Session 3213 .— ..

Using Statistical Experimental Design to Optimize GC Operation

Douglas K. Ludlow The University of North Dakota

Introduction Statistical experimental design is useful to determine the optimum operating conditions of real processes and has applications for quality control and improvement. A laboratory assignment has been developed which uses a gas chromatography experiment to give quantitative results which the students use to apply statistical skills without being impeded by complex equipment or experimental methods. The experiment has been used for several years in the undergraduate chemical engineering laboratories at the University of North Dakota f’). In a classroom setting typical “experimental results” can be analyzed without necessarily running the experiment. One of the unique aspects of the experiment is that there is a trade-off between the two most significant variables, forcing students to compromise in the selection of optimum conditions. Such compromises are typical in many real-world industrial situations.

Data Analysis Techniques The problem presented assumes that the students have been introduced to statistical experimental strategies (or designs) and response surface analysis. Experimental designs such as the Central Composite design@3~ (based on the 2“ factorial design) or the Box-Behnken desigff-4) are used to collect data in a systematic way so that a mathematical model to the response surface can be determined. The Box-Behnken design has the advantage over the Central Composite Design in that fewer total experimental runs are needed and that the independent variables or factors are varied between three equally spaced values. This design collects enough data so that a mathematical model of the response surface can be determined. A simple response surface model is the polynomial: = .f bo + b]xl + bJz + b$j+ b,&$* + b,~$, + b,JJ,+ b,, X; + b2J; + b3J; [1] Where X,, &, and ~ are the independent variables (or factors) varied in the experiments a~d @ , b , etc. are coefficients or effects determined by regression of the data. This simple polynomial model has been found to be quite adequate for the majority of practical problems. The use of an experimental design assures that enough data is collected to assess the statistical significance of each term in the model so that the “best” model of the data can be determined. By “best” we mean the simplest model that adequately describes the response surface. The final model (with only statistically significant effects) can then be used to draw whatever conclusions are warranted about the system under investigation. We encourage the use of spreadsheets for this analysis since the use of statistical packages often makes the analysis too “canned” and inhibits learning of all the steps involved.

Task Assignment The students are asked to optimize the operating conditions of a GC so that the analysis of a two-component liquid mixture can be performed in the minimum amount of time with the desired level of accuracy (resolution). A problem that occasionally occurs in GC analyses is that of peak resolution. Due to similarities of the physical properties of some substances, their GC peaks will overlap. This often leads to inaccurate or unusable results. ., ----- . . - $iiiii: 1996 ASEE Annual Conference Proceedings ‘.,plylp..$ .

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Ludlow, D. (1996, June), Using Statistical Experimental Design To Optimize Gc Operation Paper presented at 1996 Annual Conference, Washington, District of Columbia. 10.18260/1-2--6383