Batch system

Batch reactors are primarily used for the production of specialty chemicals and to obtain reaction rate data in order to determine reaction rate laws and rate law parameters such as k, the specific reaction rate. 

Species A is our basis of calculation, and is the number of moles of A initially present in the reactor. Of these. moles of A are consumed in the system as a result of the chemical reaction, leaving (Mao moles of A in the system. That is. the number of moles of A remaining in the reactor after a conversion X has been achieved is 

We now will use conversion in this fashion to express the number of moles of B, C and D in terms of conversion. 

To determine the number of moles of each species remaining after moles of A have reacted, we form the stoichiometric table (Table 3-3). This stoichiometric table presents the following information  

Column 2 the number of moles of each species initially present Column 3 the change in the number of moles brought about by reaction Column 4 the number of moles remaining in the system at time t 

As noted earlier, most applications of ultrasound-assisted leaching involve discrete systems using a bath or an ultrasonic probe. Although ultrasonic baths are more common, ultrasonic probes have the advantage that they focus their energy on a localized sample zone, thereby providing more efficient cavitation in the liquid. 

This section discusses various applications of discrete ultrasonic systems according to the organic or inorganic nature of the leached species, and to sample type. 

Ultrasonic extraction is an effective method for the extraction of a number of heavy metals from environmental and industrial hygiene samples. In many cases, it provides a means for quantitative recovery of metals and replacing drastic preparation procedures requiring the use of concentrated acids and the application of high heat and/or pressures (i.e. hot plate and/or microwave extraction). 

The potential of ultrasonic extraction for field-based extractions has been put into use in the industrial hygiene and environmental single-element analysis of, for example, lead from glass fibre filter ambient air samples [13,14] or from lead-based paint, urban dust and river sediment [15] hexavalent chromium from coal fly ash and paint chips [16] and strontium from river sediment [17]. Ultrasonic extraction has also proved effective as a prior step in multi-element determinations of heavy metals. 

Ultrasonic extraction is especially efficient with environmental and industrial hygiene samples however, in addition to the inapplicability to the extraction of some metals and the inability to quantitatively extract heavy metals from very large bulk environmental samples [14,15], ultrasounds occasionally produce ionic species that were absent from the original sample. The new species give unidentified signals that yield spurious analytical results such is the case with the extraction of ionic species from airborne particulate matter [23], where the new ions formed prevent accurate determination of those initially present in the sample. 

Integration of Eq. (18) then yields for the time dependence of X as a function of t  

The concentrations of ion B in solution as a function of t are subsequently obtained with Eq. (20) and Eq. (21). The equilibrium ionic composition of the ion exchanger at t - oo becomes 

Conventionally, the rates of ion exchange are presented in terms of the fractional attainment U(t) of equilibrium. This quantity is defined for the ion-exchanger phase as 

Mixtures of ion-exchanger particles which differ in their kinetic properties are considered next to examine the consequences of such heterogeneity. Eqs. (18) and (19) show that for a given pair of counterions the 

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Under some conditions, it is observed that complex oscillatory sequences develop even in batch systems, typically towards the end of the oscillatory phase of the reaction. Transient chaos —see section A3.14.3.3— appears to be established [18]. 

The reaction involving chlorite and iodide ions in the presence of malonic acid, the CIMA reaction, is another that supports oscillatory behaviour in a batch system (the chlorite-iodide reaction being a classic clock system the CIMA system also shows reaction-diffusion wave behaviour similar to the BZ reaction, see section A3.14.4). The initial reactants, chlorite and iodide are rapidly consumed, producing CIO2 and I2 which subsequently play the role of reactants . If the system is assembled from these species initially, we have the CDIMA reaction. The chemistry of this oscillator is driven by the following overall processes, with the empirical rate laws as given ... 

Another approach to the control of batching systems is to use a relatively simple scale indicator which does nothing but supply weight data to a controUer such as a PLC, which in turn controls the fiH and discharge system. The communications between the scale and controUer can be serial such as RS-232, or it can be an analogue signal such as 4-20 m A. While this system minimises operator interaction with the scale, it sacrifices speed and accuracy because of the relatively slow communications. 

Sorption Rates in Batch Systems. Direct measurement of the uptake rate by gravimetric, volumetric, or pie2ometric methods is widely used as a means of measuring intraparticle diffusivities. Diffusive transport within a particle may be represented by the Fickian diffusion equation, which, in spherical coordinates, takes the form... 

Fig. 17. The two basic modes of operation for an adsorption process (a) cycHc batch system (b) continuous countercurrent system with adsorbent...

Although the purification techniques used with the semicontinuous system are similar to that for the batch system, much less wastewater is produced because much less acid is retained on the nitrocellulose that is discharged from the centrifuge (135—137). 

Loss-in- Weight Feeders. The loss-in-weight (LIW) gravimetric feeder is used when feed accuracy is essential. It measures the loss in weight of material discharged from the system. As such, it can be used both in continuous and batching systems, and may be used for Hquids by replacing the... 

The intrinsic rejection and maximum obtainable water flux of different membranes can be easily evaluated in a stirred batch system. A typical batch unit (42) is shown in Figure 5. A continuous system is needed for full-scale system design and to determine the effects of hydrodynamic variables and fouling in different module configurations. A typical laboratory/pilot-scale continuous unit using computer control and on-line data acquisition is shown in Figure 6. 

In sohd—sohd separation, the soHds are separated iato fractions according to size, density, shape, or other particle property (see Size reduction). Sedimentation is also used for size separation, ie, classification of soHds (see Separation, size separation). One of the simplest ways to remove the coarse or dense soHds from a feed suspension is by sedimentation. Successive decantation ia a batch system produces closely controUed size fractions of the product. Generally, however, particle classification by sedimentation does not give sharp separation (see Size MEASUREMENT OF PARTICLES). 

Flux is maximized when the upstream concentration is minimized. For any specific task, therefore, the most efficient (minimum membrane area) configuration is an open-loop system where retentate is returned to the feed tank (Fig. 8). When the objective is concentration (eg, enzyme), a batch system is employed. If the object is to produce a constant stream of uniform-quahty permeate, the system may be operated continuously (eg, electrocoating). 

Brandies are distiked using batch or continuous systems. Variations of the pot stik are used in France. Elsewhere, both systems are used. The batch system yields a more flavorful product, whereas the continuous stik yields a lighter flavor. The first distikate using a pot stik is taken off at 60° proof. It is then redistiked to 148—160° proof. Brandy is matured in charred-oak barrels for two to eight years and bottled at 80° proof or higher. 

Batch Crystallization. Crystal size distributions obtained from batch crystallizers are affected by the mode used to generate supersaturation and the rate at which supersaturation is generated. For example, in a cooling mode there are several avenues that can be followed in reducing the temperature of the batch system, and the same can be said for the generation of supersaturation by evaporation or by addition of a nonsolvent or precipitant. The complexity of a batch operation can be ihustrated by considering the summaries of seeded and unseeded operations shown in Figure 19. 

Nonagitated Batches Cases in which vessel contents are vertically stratified, rather than uniform in temperature, have been treated by Kern (op. cit.). These are of httle practical importance except for t, slender vessels heated or cooled with external exchangers. The result is that a smaller exchanger is required than for an equivalent agitated batch system that is uniform. 

Rate equations are used to describe interphase mass transfer in batch systems, packed beds, and other contacting devices for sorptive processes and are formulated in terms of fundamental transport properties of adsorbent and adsorbate. 

In this section, we consider the transient adsorption of a solute from a dilute solution in a constant-volume, well-mixed batch system or, equivalently, adsorption of a pure gas. The solutions provided can approximate the response of a stirred vessel containing suspended adsorbent particles, or that of a very short adsorption bed. Uniform, spherical particles of radius are assumed. These particles, initially of uniform adsorbate concentration, are assumed to be exposed to a step change in concentration of the external fluid. 

In general, solutions are obtained by couphng the basic conservation equation for the batch system, Eq. (16-49) with the appropriate rate equation. Rate equations are summarized in Table 16-11 and 16-12 for different controlhng mechanisms. 

Because of the differences in primary and secondaiy metabolism, a reactor may have a dual-stage fed-batch system. In other words, fed-batch operation optimizes growth with little or no product formation. When sufficient biomass has accumulated, a different fed-batch protocol comes into play. 

Process vents and drains, including emission control devices, are often overlooked but are important elements in the safety of batch systems. Inadequate attention to these items can result in incompatible chemical mixtures within the... 

Proper design of equipment, procedures and the work environment can greatly reduce the probability of human error. Designing and maintaining operating procedures is a challenge for batch systems because of the multiplicity of procedures for each piece of equipment, and the variety of operations within... 

Nutsche filters are usually operated as part of a batch system, and hence the vessel s volume is designed to accept an entire charge of slurry from the upstream equipment. Therefore, so that the idle time of the filter is kept to a minimum. 

The rate equation for a constant volume batch system is ... 

The oxidation of Fe(CN)g to Fe(CN)g by peroxidisulfate, SjOg", can be monitored spectrophotometrically by observing die increase in absorbance at 420 nm, D 2o well-mixed batch system. Assume dial die kinetic scheme is ... 

Since the reaction is carried out in a batch system of constant volume, the rate expression for a second order rate law is... 

The following details establish reactor performance, considers the overall fractional yield, and predicts the concentration profiles with time of complex reactions in batch systems using the Runge-Kutta numerical method of analysis. 

Consider a well-mixed batch reactor with a key reactant A, during time t to time t -i- 6t, where 6t is very small. For a well-mixed batch system, assume the following ... 

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