Computational techniques conversion

Application of the computational techniques to predict conversions on pads of industrial gauzes give results which are rather lower than practical experience suggests, due probably to interruptions of the boundary layer and the larger surface area associated with the roughness of the active commercial gauzes. 

In theory, by feeding the MWD and experimental rate data into a mathematical model containing a variety of polymerization mechanisms, it should be possible to find the mechanism which explains all the experimental phenomena and to evaluate any unknown rate constants. As pointed out by Zeman (58), as long as there are more independent experimental observations than rate parameters, the solution should, in principle, be unique. This approach involves critical problems in choice of experiments and in experimental as well as computational techniques. We are not aware of its having yet been successfully employed. The converse— namely, predicting MWD from different reactor types on the basis of mathematical models and kinetic data—has been successfully demonstrated, however, as discussed above. The recent series of interesting papers by Hamielec et al. is a case in point. 

In complex reaction systems consisting of combinations of parallel and series reactions the availability of software packages (ODE solvers) makes it much easier to solve problems using moles Nj or molar flow rates Fj rather than conversion. For liquid systems, concentration may be the preferred variable used in, the mole balance equations. The resulting coupled differential equations can be easily solved using an ODE solver. In fact, tltis section has been developed to take advantage of the vast number of computational techniques now available on mainframe (e.g., Simulsolv) and personal computers (POLYMATH). 

An estimate of ri and r2 can be obtained from the slope of the experimental F versus f plot by comparison with curves based on Eq. (7.17) to choose, by trial and error, the values of ri and r2 for which the theoretical curve best fits the data. A limitation of this method is the relative insensitivity of the curves to small changes in r and r2. Another limitation is the assumption implied in using the differential form of the copolymerization equation [Eq. (7.11) or (7.17)] that the feed composition does not change during the experiment, which is obviously not true. To minimize the error, the polymerization is usually carried out to as low a conversion as possible at which a sufficient amount of the copolymer can still be obtained for direct analysis. The aforesaid limitations can be overcome, however, by the use of an integrated form of the copolymer composition equation, such as Eq. (7.23). In one method, for example, one determines by computational techniques the best values of r and V2 that fit Eq. (7.23) to the experimental curve of /i or /2 versus (1 - N/Nq). 

A non-linear regression analysis is employed using die Solver in Microsoft Excel spreadsheet to determine die values of and in die following examples. Example 1-5 (Chapter 1) involves the enzymatic reaction in the conversion of urea to ammonia and carbon dioxide and Example 11-1 deals with the interconversion of D-glyceraldehyde 3-Phosphate and dihydroxyacetone phosphate. The Solver (EXAMPLEll-l.xls and EXAMPLEll-3.xls) uses the Michaehs-Menten (MM) formula to compute v i- The residual sums of squares between Vg(,j, and v j is then calculated. Using guessed values of and the Solver uses a search optimization technique to determine MM parameters. The values of and in Example 11-1 are ... 

The availability of large and fast computers, in combination with numerical techniques to compute transient, turbulent flow, has made it possible to simulate the process of turbulent, premixed combustion in a gas explosion in more detail. Hjertager (1982) was the first to develop a code for the computation of transient, compressible, turbulent, reactive flow. Its basic concept can be described as follows A gas explosion is a reactive fluid which expands under the influence of energy addition. Energy is supplied by combustion, which is modeled as a one-step conversion process of reactants into combustion products. The conversion (combustion)... 

Single-event microkinetics describe the hydrocarbon conversion at molecular level. Present day analytical techniques do not allow an identification of industrial feedstocks in such detail. In addition current computational resources are not sufficient to perform simulations at molecular level for industrial feedstock conversion. These issues are addressed using the relumping methodology. 

Obviously this approach is not easily extended to cascades containing more than three reactors and, in those cases, an alternative trial and error procedure is preferable. One chooses a reactor volume and then determines the overall fraction conversion that would be obtained in a cascade of N reactors. When one s choice of individual reactor size meets the specified overall degree of conversion, the choice may be regarded as the desired solution. This latter approach is readily amenable to iterative programming techniques using a digital computer. 

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