Batch precedence

The previous general continuous-time formulations are mostly oriented towards arbitrary network processes. On the other hand, different continuous-time formulations focused their attention on particular features of a wide variety of sequential processes. One of the first contributions following this direction is based on the concept of time slots, which stand for a set of predefined time intervals with unknown durations. The main idea is to postulate an appropriate number of time slots for each processing unit in order to allocate them to the batches to be processed. The definition of the number of time slots required is not a trivial decision and represents an important trade-offbetween optimality and computational performance. Other alternative approaches for sequential processes were developed based on the concept of batch precedence. Model variables defining the processing sequence of batch tasks are explicitly embedded into these formulations and, consequently,... 

With the main purpose of developing more efficient optimization models for batch sequential processes, especially those involving sequence-dependent changeovers, different approaches were proposed based on the concept of batch precedence. 

An alternative formulation is based on the concept of immediate batch precedence. In contrast to the previous model, allocation and sequencing decisions are divided into two different sets of binary variables. This idea is described in the work presented by Mendez et al. [30], where a single-stage batch plant with multiple equipment in parallel is assumed. Relevant work following this direction can also be found in Gupta and Karimi [31]. Key variables are defined as follows ... 

To minimize the effects of this difficulty, an initiator is frequentiy employed. Among the numerous suggestions in the Hterature, the most satisfactory industrial procedure is to retain a portion of the Grignard from the preceding batch and to add this portion to the initial ether charge. The purpose of this procedure is to eliminate residual water and to clean the magnesium surface. Once this initiator has been added, the hahde is added at a rate deterrnined by the temperature and the pressure in the reaction vessel. 

Preceded by a blending operatiou and pasteurization, the iugredients are mixed iu a freezer that whips the mix to iucorporate air and freezes a portion of the water. Freezers may be of a batch or contiuuous type. Commercial ice cream is produced mosdy iu coutiuuous operatiou. 

Equivalent-Area Concept The preceding equations for batch operations, particularly Eq. 11-35 can be appliedforthe calculation of heat loss from tanks which are allowed to cool over an extended period of time. However, different surfaces of a tank, snch as the top (which would not be in contact with the tank contents) and the bottom, may have coefficients of heat transfer which are different from those of the vertical tank walls. The simplest way to resolve this difficulty is to nse an equivalent area A in the appropriate equations where... 

For a fixed molar ratio (ns/riAh equal to 0.05887, the temperature as applied in experiment E4, and a batch time of 347.8 dimensionless units, the feed rate of B (and thus the feed time) was optimized by computation to find tj = 323.19 dimensionless units. A run was carried out at these conditions. The data collected from this experiment were then used for re-estimation of the kinetic parameters. The new kinetic model was used to evaluate the new optimum feed rate for the same total amount of B. The optimum batch time reduced to 275.36 and the feed time to 242.75 units. Table 5.4-19 summarizes the results for three successive optimizations and re-estimations. Evidently, even a very simplified kinetic model can be successfully used in search for an optimum provided that kinetic parameters are updated based on every subsequent run carried out at the optimum conditions evaluated from the preceding set of kinetic parameters. 

Casual constraints the precedence or required sequence of tasks and resource requirements. There are unexpected events, failures, and/or events that have not been included in the scheduling program. Off-specification batches occasionally disturb the schedule. 

Figure 4.14 stipulates that three batches of process 1 and six batches of process 2 have to be completed over the chosen time horizon. Only recycle rather than reuse opportunities are exploited in both processes, since each batch either utilises freshwater or recycled water from the preceding batch of the same process. The quantities of recycled water are shown in the diagram. 

Figure 4.15 shows the exploitation of water reuse and recycle opportunities to achieve the target of 185 t of freshwater. Water from the second and fourth batches of process 2 is reused in the second and third batches of process 1, respectively. Water from storage is reused in the fourth and fifth batches of process 2. The rest of the batches either utilize freshwater or recycled water from preceding batches of the same process. 

In this chapter the simulation examples are presented. They are preceded by a short description of simulation tools and the MADONNA program in particular. As seen from the Table of Contents, the examples are organised according to thirteen application areas Batch Reactors, Continuous Tank Reactors, Tubular Reactors, Semi-Continuous Reactors, Mixing Models, Tank Flow Examples, Process Control, Mass Transfer Processes, Distillation Processes, Heat Transfer, Biological Process Examples and Environmental Process Examples. There are aspects of some examples that make them relevant to more than one application area, and this is usually apparent from their titles. Within each section, the examples are listed in order of their degree of difficulty. 

Drying and milling the resulting wet pigment presscakes, possibly preceded by extrusion or granulation, finally affords the desired pigment powder. Drying may be carried out either by a continuous process on a conveyor belt or as a batch operation in a convection oven. 

Significant process conditions preceding the incident should be identified, especially if the process is a batch operation or if there was any known deviation from normal conditions of sequences, flows, pressures, concentrations, temperatures, pH, or other process parameters. Often it is helpful to separate the background conditions into several distinct periods. One category may be normal conditions, a second category may be the time period from 48 hours up to 1 hour before the occurrence, and a third section may address the background immediately (1-20 minutes) before the occurrence. 

We can therefore replace dt by dz/u in all of the preceding differential equations for the mass balance in the batch reactor and use these equations to describe reactions during flow through a pipe. This reactor is called the plug-flow tubular reactor, which is the most important continuous reactor encountered in the chemical industry. 

Thus we search for the approximate solution for the single nonelementary reaction A —> C, which proceeds through the reaction intermediate B in the two preceding reactions. We of course know the exact solution in batch, PFTR, and CSTR This will allow us to test... 

The composition in each drop now changes with the time that the drop has been in the CSTR in the same way as if the drop were in a batch reactor. However, since the drops are in a CSTR, the time each drop stays in the reactor is given by the previous expression for p(t), and the overall conversion for any reaction is given by solving the preceding equation. 

In the preceding decade, solid-state NMR spectroscopy has provided important and novel information about the nature and properties of surface sites on working solid catalysts and the mechanisms of these surface reactions. This spectroscopic method offers the advantages of operation close to the conditions of industrial catalysis. A number of new techniques have been introduced and applied that allow investigations of surface reactions by solid-state NMR spectroscopy under both batch and flow conditions. Depending on the problems to be solved, both of these experimental approaches are useful for the investigation of calcined solid catalysts and surface compounds formed on these materials under reaction conditions. Problems with the time scale of NMR spectroscopy in comparison with the time scale of the catalytic reactions can be overcome by sophisticated experimental... 

Chromatographic Techniques. These techniques have long been applied to the problems of separation and analysis of trace atmospheric species. For stable species, batch samples are usually collected as described in the preceding section and transported to the laboratory for subsequent analysis. However, some compounds are not sufficiently stable to survive transport intact. In situ chromatographic analyses have been used for these samples. Usually, chromatography is used on aircraft in a batch mode samples are collected, preconcentrated, and separated on a column, and the individual species are detected as they elute the process is then repeated for the next sample. Thus, as with other batch techniques, time resolution is limited. 

Care should be taken that the sulfonyl chloride is not added too rapidly, as the increased hydrolysis rate at this point will not permit adequate control of temperature and pH if a large amount of sulfonyl chloride is present. For repeat preparations a portion of the reaction mixture from a preceding batch may be introduced to achieve a more rapid hydrolysis rate sooner in the reaction. For the first preparation there are ways of increasing the initial rate of hydrolysis, or shortening the time interval before the transition from low to higher hydrolysis rate occurs. These are use of sodium sulfate solution instead of pure water, addition of a few tenths of a gram of potassium iodide, or addition of a small amount (1 ml.) of methylene chloride. However, these steps are not necessary if a reasonable amount of patience is exercised. 

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