Example Optimization of Friedel-Crafts alkylation by the Basic simplex method

Example Optimization of a Friedel-Crafts alkylation by the Basic simplex method 

The alkylation of chlorobenzene with rerf-butylchloride was studied.[4] The new feature was that ferric chloride (FeClj) was used as a catalyst. The reaction was conducted at room temperature. 

The amount of chlorobenzene was 0.6 mol in all runs and the variables were adjusted according to this constraint. The variables considered are summarized in Table 11.3. It is seen that negative step-lengths were used. The objective was to develop a cheap and convenient procedure, and it was believed that both the reaction time and the relative amounts of reagents could be lowered. 

The simplex design for four variables shown in Table 11.4 was used to define the starting simplex. From Table 11.2 is seen that with four variables, the corresponding values of p and q are  

The design variables, Xj, are transformed into the natural variables by 

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