Recipe optimization

Today 80% of PVC is manufactured by the technique of batchwise suspension polymerization (S-PVC), the remaining part being shared between emulsion and bulk polymerization. A distinctive characteristic of the S-PVC processes is the large size of the reactors, 50 to 200m3, and operation at 10 to 12 bar pressure. The reaction time has been reduced from 18 h in the 1960s to only 3.5-5 h today by making use of fast initiation systems and recipe optimization. 

Unconstrained optimization methods [W. II. Press, et. ah, Numerical Recipes The An of Scieniific Compulime.. Cambridge University Press, 1 9H6. Chapter 101 can use values of only the objective function, or of first derivatives of the objective function. second derivatives of the objective function, etc. llyperChem uses first derivative information and, in the Block Diagonal Newton-Raphson case, second derivatives for one atom at a time. TlyperChem does not use optimizers that compute the full set of second derivatives (th e Hessian ) because it is im practical to store the Hessian for mac-romoleciiles with thousands of atoms. A future release may make explicit-Hessian meth oils available for smaller molecules but at this release only methods that store the first derivative information, or the second derivatives of a single atom, are used. 

Since the stereochemical course of a catalytic hydrogenation is dependent on several factors, " an understanding of the mechanism of the reaction can help in the selection of optimal reaction conditions more reliably than mere copying of a published recipe . In the first section the factors which can influence the product stereochemistry will be discussed from a mechanistic viewpoint. In subsequent sections the hydrogenation of various functional groups in the steroid ring system will be considered. In these sections both mechanistic and empirical correlations will be utilized with the primary emphasis being placed on selective and stereospecific reactions. 

Since quite a bit of difference exists between raw materials, the recipe, and the equipment, the processing procedure and conditions vary a lot. Also, the processing procedures of commercial products are usually not available to the public. Thus, much work needs to be done to find the best procedure and condition for each individual system. In general, a good procedure is a combination of optimal processing time, temperature, and rotating speed of the screw (in the case of extruder use) or the roll nip (in the case of calender use). 

The performance of a chemical plant depends upon an enormously high number of design and operating variables. This great number of process variables makes it impossible to find optimal conditions within the region of safe operation if no quantitative relationships (defined in terms of mathematics) between performance indices and process variables are known. In general, optima are complex functions of process variables, and therefore quantification of experimental ressults is needed. The methods for scale-up that were conventionally used at the time of Perkin chemistry resulted in successful commercialization of many laboratory recipes. This evolutionary, step-by-step method of scale-up is illustrated in Fig. 5.3-1 (after Moulijn et al. 2001). 

Loonkar and Robinson (1972) extended the design problem to the optimal selection of semi-continuous equipment for pre-selected batch equipment that was fixed by the recipe. 

It is hands-on-experience time let us tune the spectrometer for optimal performance, and then take a spectrum. The cooking recipe in Table 2.3 is spelled out for an old fashioned all-hardware X-band spectrometer with 200 mW maximal output power. 

Elaboration of the method for the identification of colour compounds by RPLC MS should comprise four steps (1) spectral characterization of reference materials (standards) and subsequent optimization of detection parameters, as well as those of their chromatographic separation (2) analysis of natural dyestuffs used as colouring materials in historical objects (3) analysis of model samples (dyed fibres, paintings) prepared according to old recipes (4) application of the acquired knowledge to identification of colourants present in historical objects. 

During normal operation of the copper plant, there are a number of regular maintenance jobs that need to be planned. They are included in the scheduling problem as additional jobs that have given release dates and due dates. These maintenance jobs can mostly be performed only when a unit is empty and not in use. The optimization approach finds the best location for each maintenance job with the least impact on production throughput and, furthermore, modifies the batch recipes such that there will be a suitable break in the operation for the equipment that must be maintained. 

The resulting optimization problem is solved using ILOG CPLEX [4], which generates a schedule for all major process steps, as well as the main material requirements for the production (optimal recipe definition for each batch). The schedule obtained is furthermore passed on to a crane movement simulation module, which... 

The presented solution approach is unique, since it performs a full schedule optimization, simultaneously taking into account equipment availability, process sequencing, material amounts (recipes) based on the underlying chemical reactions,... 

The end customer s main benefits after commissioning of the solution described can be summarized as follows optimal production schedules with optimal batch recipes are available on demand within seconds, better overall process coordination and visibility of the process and faster recovery from disturbances through efficient scheduling. This leads to a significant increase in plant throughput and revenues. 

In this section, the numerical solutions of the MINLP-model and of the MILP-model as presented in Sections 7.4 and 7.5 are compared with respect to their solution quality (measured by the objective values) and the required solution effort (measured by the computing time). In order to compare the MILP-solution with the MINLP-solution, the optimized values for the start times of polymerizations tn, the recipe assignments W, and the total holdups Mnr are inserted into the MINLP-model and the objective is calculated. To guarantee comparability of the results, the models were stated with identical initial conditions, namely t° = 0, = 2 Vk, pf = 0 Vs, and ra = 0.4 Vs (i.e., the variables defined at the beginning of the corresponding time axes are fixed to the indicated values). For the algorithmic solution procedure, all variables were initialized by 1 (i.e., the search for optimal values starts at values of 1 ), and none of the solvers was specifically customized. 

The SNP optimizer is based on (mixed-integer) linear programming (MILP) techniques. For a general introduction into MILP we refer to [11], An SAP APO user has no access to the mathematical MILP model. Instead, the modeling is done in notions of master data of example products, recipes, resources and transportation lanes. Each master data object corresponds to a set of constraints in the mathematical model used in the optimizer. For example, the definition of a location-product in combination with the bucket definition is translated into inventory balance constraints for describing the development of the stock level over time. Additional location-product properties have further influence on the mathematical model, e.g., whether there is a maximum stock-level for a product or whether it has a finite shelf-life. For further information on the master data expressiveness of SAP SCM we refer to [9],... 

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