SRP Investigation of a Liquid-Solid Extraction in Batch

This example concerns a discontinuous (batch) liquid-solid extraction process. Here, the quantity of extracted species (y, - y - = kgA/kg liq, A = type of species) depends on the following factors the ratio of mixing phases (mi/mg-associated to Zj - mj/mg -= kg liq /kg solid), the contact time (t associated to Zj, T -= min) the mixing rate (w = Tind -associated to Z3, - w -= m/s, n-rotation speed, d - mixer diameter) the mean concentration of one species carrier, which is placed in the liquid phase (Cg -associated to Z4, CgA -= kg carrier/kg liq) the diameter of the solid particles (d-associated to Z5, d -= m). The temperature can be another important factor in the process, but initially we can consider that it is constant. Nevertheless, it will be considered as an additional factor in a second step of this analysis. The experiments are carried out with a solid containing 0.08 kg A/kg solid. 

The fundamental levels of the factors and the variation intervals are shown in Table 5.32. 

The objective of the problem is to obtain the values of the factors that correspond to a maximum concentration of the species (A) in the liquid phase. 

To solve this problem we use the simplex regular method. For k= 5, the dimensionless matrix of experiments is obtained with relation (5.138). Thus, the matrix of the dimensionless factors is transformed into dimensional values with relations (5.96) and (5.97). Table 5.33 corresponds to this matrix, the last column of which contains the values of the process response. According to this table, the point placed in position 4 was found to be the least favourable for the process. However, before rejecting it, we have to build the coordinates of the new point by means of the image reflection of point number 4 (this point will be calculated to be number 7 from k-i-l-i-1). For this purpose, we use relations (5.145) and (5.146). 

Now we show the results of these calculations, which began with the computation of the coordinate of the opposite face of the remaining simplex  

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