Transport effects, estimation

Because rates of reduction by Fe° vary considerably over the range of treatable contaminants, it is possible that there is a continuum of kinetic regimes from purely reaction controlled, to intermediate, to purely mass transport controlled. Fig. 9 illustrates the overlap of estimated mass transport coefficients (kmt) and measured rate coefficients (kSA). The values of kSA are, in most cases, similar to or slower than the kmi values estimated for batch and column reactors. The slower kSA values suggest that krxu < kml, and therefore removal of most contaminants by Fe° should be reaction limited or only slightly influenced by mass transport effects (i.e., an intermediate kinetic regime). 

The contents of the present contribution may be outlined as follows. Section 6.2.2 introduces the basic principles of coupled heat and mass transfer and chemical reaction. Section 6.2.3 covers the classical mathematical treatment of the problem by example of simple reactions and some of the analytical solutions which can be derived for different experimental situations. Section 6.2.4 is devoted to the point that heat and mass transfer may alter the characteristic dependence of the overall reaction rate on the operating conditions. Section 6.2.S contains a collection of useful diagnostic criteria available to estimate the influence of transport effects on the apparent kinetics of single reactions. Section 6.2.6 deals with the effects of heat and mass transfer on the selectivity of basic types of multiple reactions. Finally, Section 6.2.7 focuses on a practical example, namely the control of selectivity by utilizing mass transfer effects in zeolite catalyzed reactions. 

Theoretical criteria normally contain an explicit expression of the intrinsic chemical rate, and optionally also a measured value of the observed reaction rate. Thus, these criteria are useful only when the intrinsic kinetics are available, and one is, for example, interested in whether or not transport effects are likely to influence the performance of the catalyst as the operating conditions are changed. If it is not possible to generate a numerical solution of the governing differential equations, either due to a lack of time or to other reasons, then the use of theoretical criteria will not only save experimental effort, but also provide a more reliable estimation of the net transport influence on the observable reaction rate than simple experimental criteria can give, which do not contain any explicit... 

A similar situation occurs when interphase transport effects are considered. Table 3 gives a survey of experimental criteria for the estimation of interphase transport effects. The most general relationship here is criterion 4. However, again it may be suggested that the separate isothermicity criterion 5 be used first, and... 

Table 4 summarizes a number of well-known theoretical diagnostic criteria for the estimation of intraparticle transport effects on the observable reaction rate. Tabic 5 gives a survey of the respective criteria for interphase transport effects. It is quite obvious that these are more difficult to use than the simple experimental criteria given in Tables 2 and 3. In general, the intrinsic rate expression has to be specified and, additionally, either the first derivative of the intrinsic rate with respect to concentration (and temperature) at surface... 

In contrast to the experimental criteria of Tables 2 and 3, which apply to power law kinetics only, the criteria of Tables 4 and 5 can be used for arbitrary forms of rate expressions, although normally not for systems with more than one reaction. It is interesting to note that, in a recent publication, Gonzo [40] reports on the use of general theoretical criteria for the estimation of transport effects in networks of multiple catalyzed reactions. 

Experimentally determined effective transport properties of porous bodies, e.g., effective diffusivity and permeability, can be compared with the respective effective transport properties of reconstructed porous media. Such a comparison was found to be satisfactory in the case of sandstones or other materials with relatively narrow pore size distribution (Bekri et al., 1995 Liang et al., 2000b Yeong and Torquato, 1998b). Critical verification studies of effective transport properties estimated by the concept of reconstructed porous media for porous catalysts with a broad pore size distribution and similar materials are scarce (Mourzenko et al., 2001). Let us employ the sample of the porous... 

The main problem in the determination of association rates at the gas-liquid interface is the interplay of the mass transport effects and the biospecific sorption process. The experimental studies show that both effects are involved in the binding of antigen to the antibody attached to a surface. The variations of the value of the apparent adsorption rate constant with various experimental conditions reveal the importance of the nonideal effects in such experiments. To determine the effective rate of interaction, it is important both to minimize the diffusion resistances and to estimate this contribution by increasing the amount of information. Studies with varying flow rates, particle sizes, ligand densities. 

Production-rate estimates may also be somewhat low. It is known that macrofaunal reworking of sediments can stimulate microbial activity (Hargrave, 1970,1976 Fenchel, 1970 Aller, 1978 Aller and Yingst, 1978 Yingst and Rhoads, 1980). The lack of macrofaunal grazing and transport effects in the decomposition experiments can be expected to make the rates obtained minima. Overall, however, the similarity between the values obtained by the various methods of flux estimation is evidence that the measurement techniques are reasonably accurate. 

Atmospheric methylmercury precipitated from the atmosphere is usually at less than the 1 pmol level and represents about 1-5% of total mercury. Concentration of methylmercury in the atmospheric gas phase is estimated at 5-25fmolm level. Estimates for a budget of transport fluxes of methylmercury to the oceans have recently been made. Despite these astoundingly small concentrations, amounts in fish and marine animal may be much higher, both absolutely and proportionately (Section 12.13.7.3) arising from transportation effects. 

A substantial number of a priori criteria for the estimation of transport effects on catalytic reaction rates has been reported by a number of workers. These criteria are generally derived on the premise that one does not desire the net transport effect to alter the true rate by more than some arbitrarily specified amount, normally 5%. Because of the uncertainty involved in knowing some of the parameters, the philosophy in applying these criteria should be conservative one does not look to marginal satisfaction of their requirements, but perhaps to be an order of magnitude better. 

For the catalyst development and optimization as well as for the correct reactor design, it is important to ascertain the influences of transport phenomena on the reaction kinetics. It is essential that criteria for estimating transport effects are based on what is measurable or observable [31,32]. 

Despite the small gap size, transverse temperature and concentration gradients may exist in microchannels. These gradients depend on the rates of heat and mass transfer versus the rate of reaction. Da, as discussed above, provides an estimate of transport effects but cannot be used for quantitative modeling. The Nusselt number (Nu) and Sherwood number (Sh) provide the heat and mass transfer coefficients, respectively, between a surface and the bulk gas, in the direction perpendicular to the flow. They are defined as ratios of heat or mass flux at the boundary to the net flux between the bulk and the surface ... 

The analysis described in this paper can be used to make judgements and estimates of the mechanical behavior of paper materials under transient humidity conditions. Changing moisture content results in altered physical and chemical properties of sheets. One example is the surface electrical resistivity of sheets which is known to be an exponential function of the local moisture content. An analysis of the type shown here allows us to predict the electrical property variation under transient humidity conditions. Another example of the applicability of this analysis is in the compressive strength of paper board. It is known that the compressive strength of paper board decreases sharply with changing moisture contents. An analysis based on the thermal and moisture transport effects can easily identify whether thermal and moisture transients are responsible for accelerated loss in compressive strengths of paper materials. 

It has been demonstrated that the DNS model captures the influence of the CL microstructure on the underlying transport. The estimation of the Braggeman factors representing the effective oxygen diffusivity and ionic transport in the CL... 

In this chapter, we revisit the subject of reaction/transport interactions in heterogeneous catalysts, this time from a quantitative standpoint. The topic must be examined from two perspectives. First, a researcher that is studying the kinetics of a heterogeneous catalytic reaction (or reactions) must ensure that his or her experiments are free of transport effects. In other words, the experiments must be conducted under conditions where intrinsic chemical kinetics determines the reaction rate(s). The researcher may have to make calculations to estimate the magnitude of heat and mass transport influence. He or she may also have to carry out diagnostic experiments in order to define a region of operation where transport does not affect the reaction rate and selectivity. 

Carbonic anhydrase is an enzyme that catalyzes the hydration of carbon dioxide to bicarbonate The uncatalyzed hydration of carbon dioxide is too slow to be effective m transporting carbon dioxide from the tissues to the lungs and so animals have devel oped catalysts to speed this process The activity of carbonic anhydrase is remarkable It has been estimated that one molecule of this enzyme can catalyze the hydration of 3 6 X 10 molecules of carbon dioxide per minute... 

The use and effective costs of various energy alternatives are shown in Table 2. Use or internal costs include production, transportation, and distribution. Effective costs take into account the use costs estimated external costs, which include costs associated with damage to the environment caused by utili2ation of various fossil fuels and fuel utili2ation efficiencies, ie, the efficiency of converting fuels into mechanical, electrical, or thermal energy. The effective costs are expressed as /GJ of fossil fuel equivalent (15). The overall equation for the effective cost is... 

Nonetheless, these methods only estimate organ-averaged radiation dose. Any process which results in high concentrations of radioactivity in organs outside the MIRD tables or in very small volumes within an organ can result in significant error. In addition, the kinetic behavior of materials in the body can have a dramatic effect on radiation dose and models of material transport are constandy refined. Thus radiation dosimetry remains an area of significant research activity. 

Phonon transport is the main conduction mechanism below 300°C. Compositional effects are significant because the mean free phonon path is limited by the random glass stmcture. Estimates of the mean free phonon path in vitreous siUca, made using elastic wave velocity, heat capacity, and thermal conductivity data, generate a value of 520 pm, which is on the order of the dimensions of the SiO tetrahedron (151). Radiative conduction mechanisms can be significant at higher temperatures. 

The mass transport influence is easy to diagnose experimentally. One measures the rate at various values of the Thiele modulus the modulus is easily changed by variation of R, the particle size. Cmshing and sieving the particles provide catalyst samples for the experiments. If the rate is independent of the particle size, the effectiveness factor is unity for all of them. If the rate is inversely proportional to particle size, the effectiveness factor is less than unity and

experimental points allow triangulation on the curve of Figure 10 and estimation of Tj and ( ). It is also possible to estimate the effective diffusion coefficient and thereby to estimate Tj and ( ) from a single measurement of the rate (48). 

---