Optimization triangle method

Operating point S is the theoretical optimal operating condition derived from triangle method [S]. The purity of the extract and the raf te at this experimental point is... 

Optimization of the SMB Process with a Linear Isotherm Using the Triangle Method... 

The formation of colloidal sulfur occurring in the aqueous, either alkaline or acidic, solutions comprises a serious drawback for the deposits quality. Saloniemi et al. [206] attempted to circumvent this problem and to avoid also the use of a lead substrate needed in the case of anodic formation, by devising a cyclic electrochemical technique including alternate cathodic and anodic reactions. Their method was based on fast cycling of the substrate (TO/glass) potential in an alkaline (pH 8.5) solution of sodium sulfide, Pb(II), and EDTA, between two values with a symmetric triangle wave shape. At cathodic potentials, Pb(EDTA)2 reduced to Pb, and at anodic potentials Pb reoxidized and reacted with sulfide instead of EDTA or hydroxide ions. Films electrodeposited in the optimized potential region were stoichiometric and with a random polycrystalline RS structure. The authors noticed that cyclic deposition also occurs from an acidic solution, but the problem of colloidal sulfur formation remains. 

However, not withstanding the above objections, further discussion of the Snyder solvent triangle classification method is justified by its common use in many solvent optimization schemes in liquid chromatography. The polarity index, P, is given by the sum of the logarithms of the polar distribution constants for ethanol, dioxane and nltromethane and the selectivity parameters, X, as the ratio of the polar distribution constant for solute i to... 

There are several systems which can be used to select the solvents of the mobile phase. The number of selected solvents and the solvents which are selected not only depend on the chromatographic problem but also on the method which will be used to optimize the system. With response surface methodology it is appropriate to use a minimum number of solvents. For reasons stated below this minimum number of solvents was four. The second question is, which solvents will be selected, is more difficult to answer when a small number of solvents is used because the consequences of a wrong selection are large. Several approaches are possible to select the solvents. The most simple method is comparison with common solvent systems for the solutes under investigation. A more general approach is to use the selectivity triangle of Snyder [4] in the selection of the solvents. 

We adopt the input/output data-based prediction model using the subspace identification technique. To find the correlation between the inputs and outputs, we need to obtain the input and output data. On the basis of the triangle Aeoiy[6], the optimal feed flow rate ratios at steady state are calculated. Then, the pseudo random binary input signal is generated on the basis of this optimal value. Figure 1 compares the output from the identified model (dot) with that from the first principles model (solid curve). Clearly, we observe that the identified model based on the subspace identification method shows an excellent prediction performance. The variance accounted for (VAF) indices for both outputs are higher than 99%. The detailed identification procedure can be founded in the literature [3,5,9,10]. 

Normal-phase, bonded-phase columns are likely underutilized for separations where they should be the method of choice. This is due both to the ease of use of reversed-phase, bonded-phase columns, discussed next, and also to the many problems inherent in the use of bare silica and alumina. Very straightforward method development in normal-phase chromatography can be performed by combining the solvent and stationary-phase selectivity triangles. The three columns, each used with the three recommended modifiers, should provide the maximum difference in selectivity available. These nine experiments, used in conjunction with chemometric optimization schemes, should then provide a ratio-... 

The simplex which lends its name to this optimization method is a convex geometric figure of k+l non-planar vertices in k dimensional space. For 2 dimensions it is a triangle, for 3 dimensions it is a tetrahedron,... 

Before Varicol, PowerFeed, or Modicon is taken into account for process design make sure that appropriate optimization tools are at your disposal. In contrast to SMB, no shortcut methods such as triangle theory are available for these processes. 

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