Reaction rate from laboratory data

Equation 8.3.4 may also be used in the analysis of kinetic data taken in laboratory scale stirred tank reactors. One may directly determine the reaction rate from a knowledge of the reactor volume, flow rate through the reactor, and stream compositions. The fact that one may determine the rate directly and without integration makes stirred tank reactors particularly attractive for use in studies of reactions with complex rate expressions (e.g., enzymatic or heterogeneous catalytic reactions) or of systems in which multiple reactions take place. 

As intrinsic rate equations cannot yet be predicted, they must be evaluated from laboratory data. Such data are measurements of the global rate of reaction. The first part of the problem is to extract the equation for the intrinsic rate from the global rate data. Since laboratory reactors are small and relatively low in cost, there is great flexibility in designing them. In particular, construction and operating conditions can be chosen to reduce or eliminate the differences between the global and intrinsic rates, so that more accurate equations for the intrinsic rate can be extracted from the... 

Pilot-plant studies. The reactors used in these studies are significantly larger than those employed in bench-scale laboratory experiments. One uses essentially the reverse of the design procedures developed later in the chapter to determine the effective reaction rate from the pilot-plant data. In analysis of data of this type, one... 

The laboratory studies utilized small-scale (1-5-L) reactors. These are satisfactoiy because the reaction rates observed are independent of reac tor size. Several reac tors are operated in parallel on the waste, each at a different BSRT When steady state is reached after several weeks, data on the biomass level (X) in the system and the untreated waste level in the effluent (usually in terms of BOD or COD) are collected. These data can be plotted for equation forms that will yield linear plots on rec tangular coordinates. From the intercepts and the slope or the hnes, it is possible to determine values of the four pseudo constants. Table 25-42 presents some available data from the literature on these pseudo constants. Figure 25-53 illustrates the procedure for their determination from the laboratory studies discussed previously. 

This involves knowledge of chemistry, by the factors distinguishing the micro-kinetics of chemical reactions and macro-kinetics used to describe the physical transport phenomena. The complexity of the chemical system and insufficient knowledge of the details requires that reactions are lumped, and kinetics expressed with the aid of empirical rate constants. Physical effects in chemical reactors are difficult to eliminate from the chemical rate processes. Non-uniformities in the velocity, and temperature profiles, with interphase, intraparticle heat, and mass transfer tend to distort the kinetic data. These make the analyses and scale-up of a reactor more difficult. Reaction rate data obtained from laboratory studies without a proper account of the physical effects can produce erroneous rate expressions. Here, chemical reactor flow models using matliematical expressions show how physical... 

Collect together all the kinetic and thermodynamic data on the desired reaction and the side reactions. It is unlikely that much useful information will be gleaned from a literature search, as little is published in the open literature on commercially attractive processes. The kinetic data required for reactor design will normally be obtained from laboratory and pilot plant studies. Values will be needed for the rate of reaction over a range of operating conditions pressure, temperature, flow-rate and catalyst concentration. The design of experimental reactors and scale-up is discussed by Rase (1977). 

Experimental Materials. All the data to be presented for these illustrations was obtained from a series of polyurethane foam samples. It is not relevant for this presentation to go into too much detail regarding the exact nature of the samples. It is merely sufficient to state they were from six different formulations, prepared and physically tested for us at an industrial laboratory. After which, our laboratory compiled extensive morphological datu on these materials. The major variable in the composition of this series of foam saaqples is the aaK>unt of water added to the stoichiometric mixture. The reaction of the isocyanate with water is critical in determining the final physical properties of the bulk sample) properties that correlate with the characteristic cellular morphology. The concentration of the tin catalyst was an additional variable in the formulation, the effect of which was to influence the polymerization reaction rate. Representative data from portions of this study will illustrate our experiences of incorporating a computer with the operation of the optical microscope. 

Most of the data in this chapter was obtained from laboratory experiments in which the dissolution kinetics were followed by monitoring the change in the level of iron released into solution. The dissolution rate and mechanism are often established on the basis of data corresponding to the first few percent of the reaction, (e.g. Stumm et ak, 1985). To insure that the initial stages are in fact representative of the behaviour of the bulk oxide ( and not an impurity, for example), a complete dissolution curve should be obtained in any investigation. 

The CEB method can be extended to chemically reactive species by introducing decay factors into the mass balances for the chemical species. The decay factors can be evaluated from data for the composition of emissions and of the ambient aerosol. They can be related to first order reaction rate coefficients measured in the laboratory by means of an appropriate atmospheric model. 

Figure 14.10 Plots of the relative (a-d) reaction rate constants [ krcl = itR(NAC)/ r(4-C1-NB)] and (e, f) competition coefficients (log Qc, Eq. 14-39) of 10 monosubstituted nitrobenzenes versus their one-electron reduction potentials (divided by 0.059 V, see Eq. 14-36) for some laboratory batch and column systems. For abbreviations see Table 14.4 note that only the substituent is indicated. Data from Schwarzenbach et al. (1990) Dun-nivant et al. (1992) Heijman et al. (1995) Klausen et al. (1995) and Hofstetter et al. (1999).

The pure compound rate constants were measured with 20-28 mesh catalyst particles and reflect intrinsic rates (—i.e., rates free from diffusion effects). Estimated pore diffusion thresholds are shown for 1/8-inch and 1/16-inch catalyst sizes. These curves show the approximate reaction rate constants above which pore diffusion effects may be observed for these two catalyst sizes. These thresholds were calculated using pore diffusion theory for first-order reactions (18). Effective diffusivities were estimated using the Wilke-Chang correlation (19) and applying a tortuosity of 4.0. The pure compound data were obtained by G. E. Langlois and co-workers in our laboratories. Product yields and suggested reaction mechanisms for hydrocracking many of these compounds have been published elsewhere (20-25). 

Model Equations to Describe Component Balances. The design of PVD reacting systems requires a set of model equations describing the component balances for the reacting species and an overall mass balance within the control volume of the surface reaction zone. Constitutive equations that describe the rate processes can then be used to obtain solutions to the model equations. Material-specific parameters may be estimated or obtained from the literature, collateral experiments, or numerical fits to experimental data. In any event, design-oriented solutions to the model equations can be obtained without recourse to equipment-specific fitting parameters. Thus translation of scale from laboratory apparatus to production-scale equipment is possible. 

---