Design equations comparison

This chapter describes the different types of batch and continuous bioreactors. The basic reactor concepts are described as well as the respective basic bioreactors design equations. The comparison of enzyme reactors is performed taking into account the enzyme kinetics. The modelhng and design of real reactors is discussed based on the several factors which influence their performance the immobilized biocatalyst kinetics, the external and internal mass transfer effects, the axial dispersion effects, and the operational stabihty of the immobilized biocatalyst. 

A comparison of actual perf ormance with performance predicted by reaction kinetics equations shows that, for the most part, overall performance approached or exceeded predicted performance Although some flow characteristics failed to meet the modeled performance, we conclude that the design equations developed are valid for design of a high-water-cut, high-rale oihwatcr separator. 

Four hundred adults presenting with acute watery diarrhea were entered into a randomized, placebo controlled, double blind clinical trial of berberine, tetracycline, and tetracycline + berberine to study the antisecretory and vibriostatic effects of the alkaloid. Of 18S patients with cholera, those given tetracycline or tetracycline + berberine had considerably reduced volume and frequency of diarrheal stools, duration of diarrhea, and volumes of required intravenous and oral rehydration fluid. Berberine did not produce an antisecretory effect, but analysis by factorial design equations showed a reduction in diarrheal stools by one liter and a reduction in cyclic AMP concentrations in stools by 77% in the groups given berberine. Many fewer patients given tetracycline or tetracycline + berberine excreted vibrios in their stools after 24 hours in comparison with those given berberine alone. Neither tetracycline nor berberine had any benefit over placebo in 215 patients with noncholera diarrhea [219]. 

The design equations for ideal tubular-flow reactors involve no new concepts but simply substitute a rate of reaction for a heat-transfer rate or mass-transfer-rate function. The increased complexity of reactor design in comparison with the design of equipment for the purely physical processes lies in the difficulty in evaluating the rate of reaction. This rate is dependent on more, and less clearly defined, variables than a heat- or mass-transfer coefficient. Accordingly, it has been more difficult to develop correlations of experimental rates, as well as theoretical means of predicting them. 

Comparison of Eqs. (4-2) and (4-5) shows that the form of the design equations for ideal batch and tubular-flow reactors are identical if the realtime variable in the batch reactor is considered as the residence time in the flow case. The important point is that the integral c/C/r is the same in both reactors. If this integral is evaluated for a given rate equation for an ideal batch reactor, the result is applicable for an ideal tubular-flow reactor this... 

Equation 8.39 involves the use of the cloud point temperature. Its value depends on the standard method adopted for its determination principally designed for comparison purposes. The conditions at the interface are unlikely to match those used in the empirical standard method so that may not be the true temeprature at the assumed liquid/solid interface. 

Activity. A comparison of the global rates of CO conversion on a per gram of catalyst or on a per gram of cobalt in the catalyst at 500 K shows that the activities of the chromium- and zirconium-doped catalysts were substantially higher than any of the other catalysts studied. (Specific rates on a per active catalyst site basis (13,21) are not available for these catalysts. Such measurements will be undertaken for the more promising catalysts in the near future (22). Justification for this use of the continuous stirred-tank reactor (CSTR) design equation was provided by pulse tracer experiments (20).) These are followed by the activated carbon-... 

Appendix E Comparisons between experimental data and design equation predictions... 

In other words, as R goes to infinity, that is, when the amount of effluent stream 2 leaving the reactor is too small in comparison to the amount recycled RQp the design equation converges to that for an MFR ... 

The present chapter highlights recent developments in photocatalysis that are pertinent to its potential process applicability in water treatment for organic contaminants specifically, (i) mechanism understanding, intermediates and stoichiometry of the overall process (ii) its generality for complete contaminant destruction (mineralization) (iii) some specific contaminant classes of interest (chlorinated aromatics, surfactants, herbicides and pesticides) (iv) kinetics (equations, surface vs. bulk reactions) (v) influence of additional oxidants (vi) use of solar vs. artificial illumination (vii) different catalysts and catalyst s forms (suspended vs. immobilized) (viii) photoreactor design (ix) comparison with other techniques using oxidants and light, with care to the evaluation of efficiency and economics. 

Figure 4-7 Graphical representation of the design equations for three ideal CSTRs in series, and comparison with a single PFR (shaded area).

In many process-design calculations it is not necessary to fit the data to within the experimental uncertainty. Here, economics dictates that a minimum number of adjustable parameters be fitted to scarce data with the best accuracy possible. This compromise between "goodness of fit" and number of parameters requires some method of discriminating between models. One way is to compare the uncertainties in the calculated parameters. An alternative method consists of examination of the residuals for trends and excessive errors when plotted versus other system variables (Draper and Smith, 1966). A more useful quantity for comparison is obtained from the sum of the weighted squared residuals given by Equation (1). 

To design an air recirculation system it is necessary to know the performances of fans, air cleaners, and exhaust hoods included in the current system. The equations described here include the source generation rate and the total airflow rate through the room, which could be difficult to measure. The ratio between source rate and flow rate has the unit of concentration and should in fact be equal to the concentration without recirculation. The equations could thus be transformed to include the contaminant concentration without recirculation instead of this ratio. In this way a direct comparison between concentration without and with recirculation is possible. By using the described equations it is then possible to design an air recirculation system to result in the demanded concentration in a workroom. 

Comparison of results between the various empirical steam flow formulas suggests the Babcock equation as a good average for most design purposes at pressure 500 psia and below. For lines smaller than 4 inches, this relation may be 0-40 percent high [56]. 

Lateral flow (L) within the soil layer containing plant roots is small for most landfill cover situations and is zero for lysimeters with sidewalls. During the course of a hydrologic year, ASW is usually small in comparison to the other terms, but it may be large on a daily basis. A primary focus for the design is PRK below the ET landfill cover as represented by the rearranged equation ... 

As stated previously, the source of capital is often not known, and hence it is not known whether Equation 2.7 is appropriate to represent the cost of capital. Equation 2.7 is, strictly speaking, only appropriate if the money for capital expenditure is to be borrowed over a fixed period at a fixed rate of interest. Moreover, if Equation 2.7 is accepted, then the number of years over which the capital is to be annualized is known, as is the rate of interest. However, the most important thing is that, even if the source of capital is not known, and uncertain assumptions are necessary, Equation 2.7 provides a common basis for the comparison of competing projects and design alternatives within a project. 

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