Model batch

Our treatment of Chemical Reaction Engineering begins in Chapters 1 and 2 and continues in Chapters 11-24. After an introduction (Chapter 11) surveying the field, the next five Chapters (12-16) are devoted to performance and design characteristics of four ideal reactor models (batch, CSTR, plug-flow, and laminar-flow), and to the characteristics of various types of ideal flow involved in continuous-flow reactors. Chapter 17 deals with comparisons and combinations of ideal reactors. Chapter 18 deals with ideal reactors for complex (multireaction) systems. Chapters 19 and 20 treat nonideal flow and reactor considerations taking this into account. Chapters 21-24 provide an introduction to reactors for multiphase systems, including fixed-bed catalytic reactors, fluidized-bed reactors, and reactors for gas-solid and gas-liquid reactions. 

TABLE 7.3 NPD Functions, Means, Variances, and Moment of Some Model Batch and Flow Systems with Recirculation... 

The importance of modeling batch processing systems forces a review of the mathematical analysis needed to set up and solve the models. The mathematical definition of physical problems involves (1) identification, (2) expression of the problem in mathematical language, (3) finding a solution, and (4) evaluating the solution. The completion of these steps in the order established determines whether a solution can be attained. The problem must be identified before one spends time setting up equations these and the initial and boundary conditions that define the problem must be well established before a solution is attempted then a solution can be obtained and evaluated. 

This approach is also used to model batch treatments (4.6) with a high value of recycle and in which the produced chemicals are not too active, so they can be considered to live for a sufficiently long time and their concentration results homogeneous in the whole solution. In this case, the initial condition is the concentration of species i at time t = 0 ([S,-](=0)... 

This approach is also used to model batch treatments in which the recycle has a low or medium value In this case, two balances has to be drawn to characterize the discontinuous system one for the cell (4.8) and the other for the reservoir (4.9)... 

This approach is also used to model batch treatments with high recycle rates in which the products generated electrochemically can react rapidly. Consequently, a three region model is required to separate the high reaction rates that occur close to the anodic and cathodic regions from the other slower reactions that occur on the whole volume of the solution (4.13)—(4.15). The initial conditions for these equations arc ([5 /]b)(,=0) = ([Si]b) t=0) = ([>V ]b)(/=0) = [Si],=0... 

In this section, the population balance will be used to model batch and CSTR precipitators where aggregation is a competing growth mechanism. Figure 6.30 is an example of the aggregate microstructure in... 

In groundwater, as in surface waters, biofilms can be very effective in transforming pollutant chemicals. Modeling the behavior of biofilms is more complex than modeling batch or continuous cultures (Section 2.6.3), although... 

Limited extrapolation of the real-time data from the long-term testing storage condition beyond the observed range to extend the re-test period at approval time may be undertaken, particularly if the accelerated data are supportive. However, this assumes that the same degradation relationship will continue to apply beyond the observed data. Hence the use of extrapolation should be minimized but can be justified in an application in terms of what is known about the mechanism of degradation, the goodness of fit of any mathematical model, batch size, and existence of supportive data. 

Hand, D.W., J.C. Crittenden, and W.E. Thacker. 1981. User oriented solutions to the homogeneous surface diffusion model Batch reactor solutions. Proc. 54th Annual Conf, Water Pollution Control Federation, Detroit, ML 4-9 Oct. 1981. Water Pollution Control Federation, Alexandria, VA. 

The analysis above shows how three-way models can be used to model batch processes and serve as a basis for control charts. As of yet, there is no clear indication of what three-way models are best for modeling batch data. From the example above it is clear that both a... 

Parallel reactions, isothermal, segregation model batch globules... 

The suitability of the different operating modes can be determined with the aid of programs for modeling batch distillations. The treatment of batch distillations is much more laborious than that for continuous distillations. However, the decision can be simplified by using Equations (2.3.2-29) and (2.3.2-30), which were determined for the different operating modes with the aid of differential equations. The minimum vapor quantity G is used for comparison ... 

To evaluate the performance of the model, batch experiments were carried out in a lab-scale fluidized bed equipped with a two-fluid nozzle in top-spray configuration. The liquid solution was HPMC in water. Compact glass beads and porous alumina (Y-AI2O3) particles were used as the solids, with an initial average diameter do (primary particle diameter) equal to 0.4 and 0.36 mm, respectively. 

Zaldfvar C, Iglesias G, Del Sol O, Pinto JC. On the preparation of acrylic acid/vinyl acetate copolymers with constant composition. 4. Modeling batch and continuous free-radical AAJYA copolymerization. Polymer 1997 38 5823-5833. 

Saraceno A.,Curcio S.,Calabr6 V.,Iorio G., A hybrid neural approach to model batch fermentation of ricotta cheese whey to ethanol. Computers and Chemical Engineering, 2010,34(10), 1590-1596. 

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