REDUCTION OF THE PARAMETER SPACE

In some cases, the results of the initial experiments can be used to reduce the number of parameters considered or to narrow down the limits defined for the selected parameters. In both cases this can result in great simplifications for the optimization process. This will be discussed in section 5.4. After the reduction of the parameter space additional experiments may have to be performed to complete the initial data set. 

At the same time we may wish to consider a slower contraction of the search region as the dimensionality of the parameter space increases. For example we could use a constant reduction of the volume (say 10%) of the search region rather than a constant reduction in the search region of each parameter. Namely we could use,... 

We now wish to test the above gel-reaction-diflfusion approach (Eqs 9.7-9.10) using the BZ reaction, which consists in the oxidation of malonic acid by bromate ions in acidic medium. The reaction proceeds only when catalyzed by a suitable metal ion. In the experiments, the chosen catalyst is the ruthenium tris(2,2 -bipyridine) that intervenes through its oxydo-reduction couple (Ru(bpy)3 /Ru(bpy)j ). In a batch reactor or a CSTR, this reaction exhibits well-documented periodic oscillations of concentrations in some region of the parameter space. 

Here, TUR = (thickness reduction)/BHi andPg = 2B in terms of the nomenclature used in Section 10.4 TUR and BUR are the takeup ratio and blowup ratio, respectively. The region marked U is unstable according to the linear theory. Only results for BUR > 1 are of practical interest. We see that both draw resonance and helical instabilities can occur, with the latter comprising a large part of the parameter space for dimensionless pressure B less than about 0.25 (pg < 0.50). This is consistent with what is seen experimentally, although the comparisons are qualitative. 

Many engineering problems involve several parameters, that impede the elaboration of the pi space. Fortunately, in some cases, a closer look at a problem (or previous experience) facilitates reduction of the number of physical quantities in the relevance list. This is the case when some relevant variables affect the process by way of a so-called intermediate quantity. Assuming that this intermediate variable can be measured experimentally, it should be included in the problem relevance list, if this facilitates the removal of more than one variable from the list. 

Additional care must be taken if the added solid has a porous structure. For instance, porous media add obstacles to the molecular movement as only the void space fraction, inside the pores and the between particles, is contributing to the transport. This is described typically by a parameter, the tortuosity factor, r,48 that illustrates the reduction of the space available with respect to the liquid phase as... 

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