Laminar flow model

OS 41b] ]R 19] ]P 30] A Parity plot (Figure 4.65) for five different substrates (C4-Cg alcohols) was derived, showing a comparison of experimental data with a plug and laminar flow model [112]. In the plug-flow case, much higher conversions were theoretically expected than actually measured. Laminar-flow modeling describes the results much better and is in line with visual inspections of the liquid/liquid flow. 

Figure 4.65 Parity plot comparing the conversion of a batch and laminar flow model for five different substrates made by allyl alcohol isomerization. For calculation, the same rate law was used for all substrates. The increase in conversion is due to increased substrate solubility [112].

Yuasa H, Miyamoto Y, Iga T, Hanano M (1986) Determination of kinetic parameters of a carrier-mediated transport in the perfused intestine by two-dimensional laminar flow model Effects of the unstirred water layer. Biochim Biophys Acta 856 219-230... 

Under some laminar flow circumstances, the dispersion model (see Sect. 5.4) may be a better description of reality than the laminar-flow model discussed above. Ananthakrishnan et al. [48] discuss conditions under which one should opt for a particular model and their data are presented in modified form by Levenspiel [26]. If the tubular reactor aspect ratio, i.e. the length-to-diameter ratio, is less than 100 and the product of the reactor Reynolds, dup/p, and Schmidt, p/p S numbers is greater than approximately 10", then the laminar-flow model should give good predictions of reactor performance. 

It is important to know how mixing can influence the selectivity of chemical reactions, and computational fluid dynamics (CFD) simulations are quite helpful in providing a deeper insight into this issue. The calculations are based on a laminar flow model where mixing takes place only by molecular diffusion (Figure 6.9). Let us focus on the competitive... 

Similar plots are shown in Figure 6 for the 20" module. In this case, at lower values of X, one also finds that a portion of the results fit the laminar flow model, and the slope of log APq vs log Qp is unity. 

Annular. When the vapor velocity is high enough (j > 1.5), gravitational effects can be neglected, and the condensate collects as a thin annular film around the inside of the tube walls, with no stratification. A significant portion of most condensers operate in this flow regime. There are numerous predictive models described in the literature for annular flow. Laminar flow models predict heat transfer coefficients that are too low, and turbulent models must be used. The most commonly used models are listed in Table 14.1. All models have a form for the local Nusselt number... 

SEGREGATED FLOW MODEL ( LAMINAR FLOW MODEL ( n ) ... 

For power law fluids, Tomlta (1959) extended his laminar flow model (discussed in Section 5.2.1.3) to turbulent flows in smooth pipes by applying Prandtl s mixing length concept, and developed a different implicit equation ... 

FIGURE 4.38 Comparison of PFR, CSTR, and laminar flow models for a first-order reaction. 

For laminar conditions, the laminar flow model should be applied. The simplest one, laminar flow without radial diffusion, gives for first-order reactions... 

The result is readily calculated. See Figure 4.38 Section 4.6, which gives for ki = 2, ca/coa = 0.206, for the laminar flow model. The conversion becomes t a = 1 — ca/cqa = 0.794. The laminar flow model gives a lower conversion than the plug flow model. 

The methods listed in Sections 5.1.1-5.1.7 are illustrated by a tubular reactor with a first-order reaction and laminar flow. Models for species, heat, and momentum have been formulated and simplified. In addition to showing the methods, we discuss the assumptions in a traditional 1D lumped-parameter model for a tubular reactor with axial dispersion,... 

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