Nonisothermal model

Latent heat associated with phase change in two-phase transport has a large impact on the temperature distribution and hence must be included in a nonisothermal model in the two-phase regime. The temperature nonuniformity will in turn affect the saturation pressure, condensation/evaporation rate, and hence the liquid water distribution. Under the local interfacial equilibrium between the two phases, which is an excellent approximation in a PEFG, the mass rate of phase change, ihfg, is readily calculated from the liquid continuity equation, namely... 

Still, sophisticated, exact, numerical, non-Newtonian and nonisothermal models are essential in order to reach the goal of accurately predicting final product properties from the total thermomechanical and deformation history of each fluid element passing through the extruder. A great deal more research remains to be done in order to accomplish this goal. 

Example 14.1 A Semiempirical, Simplified, One-Dimensional, Nonisothermal Model [C. D. Han, Rheology in Polymer Processing, Academic Press, New York, 1976, Section 12.3.1.] Assuming steady state and further assuming that there is only one nonvanishing velocity component v(z), which is a function of only ", and that temperature varies only in the z direction, the equation of motion reduces to... 

The inherently nonisothermal models that require temperature variations for oscillatory behavior fall into two groups. In both cases, the reaction is blocked and reactivated at different temperatures. The blockage is caused either by a surface blocking or by a bulk-phase transition of the catalyst. 

The models discussed thus far were essentially isothermal. Nonisothermal models as described below contain an additional degree of complexity that is always related to the characteristics of a particular reactor and the form of a particular catalyst. On the other hand, it is usually easier to construct a nonisothermal model that oscillates, because the exponential term in the Arrhenius law provides a very strong nonlinearity. Nonisothermal models can be classified into two categories surface blocking/reactivation models and models with additional bulk effects. 

The PSA process steps again followed those of the Poly-bed process except that the order of steps (c) and (d) were interchanged. The solid line represents the results of the nonisothermal model simulations and the points are experimental data from a bench-scale unit. Both figures show that the model simulations are in fair to good agreement with experimental data but the accuracy demanded by industrial designs may still be lacking. 

The use of process simulation software for process design is discussed by Seider, Seader, and Lewin [Product and Process Design Principles Synthesis, Analysis, and Evaluation, 2d ed. (Wiley, 2004)] and by Turton et al. [Analysis, Synthesis, and Design of Chemical Processes, 2d ed. (Prentice-Hall, 2002)]. Various computational procedures for extraction simulation are discussed by Steiner [Chap. 6 in Liquid-Liquid Extraction Equipment, Godfrey and Slater, eds. (Wiley, 1994)]. In addition, a number of authors have developed specialized methods of analysis. For example, Sanpui, Singh, and Khanna [AlChE J., 50(2), pp. 368-381 (2004)] outline a computer-based approach to rate-based, nonisothermal modeling of extraction processes. Harjo,... 

Substitution of equation (7-53a) into equation (iii) then completes the model for radial dispersion and isothermal first-order reaction. A corresponding nonisothermal model may be built up in the same way, using the approach of McGreavy and Cresswell shown in equation (7-63). 

FIGURE 5.9. Variation of diffusional time constant with sorbate pressure for (a) /7-butane in 55- m (X) and 27.5-/im (O) crystals of 5A zeolite (i) CO2 in 34- im (o), 2I.5-/im (A), and 7,3- m ( ) crystals of 4A zeolite. Values for CO2 in the 73-fim crystals derived from the nonisothermal model are shown by filled squares (see Figure 6.13). For the other systems diffusion is slow enough for heat effects to be neglected. (From refs. 2 and 49, with permission.)... 

The influence of CO poisoning at the anode of an HT-PEFC was investigated by Bergmann et ul. [28]. The dynamic, nonisothermal model takes the catalyst layer as a two-dimensional plane between the membrane and gas diffusion layer into account. The effects of CO and hydrogen adsorption with respect to temperature and time are discussed in detail. The CO poisoning is analyzed with polarization curves for different CO concentrations and dynamic CO pulses. The analysis of fuel-cell performance under the influence of CO shows a nonlinear behavior. The presence of water at the anode is explicitly considered to take part in the electrooxidation of CO. The investigation of the current response to a CO pulse of 1.31% at the anode inlet showed a reversible recovery time of 20 min. 

The authors of [104] attempted a qualitative and even semiquantitative analysis of the thermokinetic interactions and the nonlinear nature of this highly exothermic system. The results obtained from nonisothermal modeling of the process are qualitatively consistent with the above experimental results. A detailed mathematical description of the kinetics and processes of heat and heat transfer in a CSTR made it possible to reproduce the appearance of temperature hysteresis and to demonstrate its dependence on the oxygen concentration, reaction time, and temperature of the reactor walls. Figure 8.6 shows the calculated self-heating... 

D. Coker, Nonisothermal model for gas separation hollow-fiber membranes, AIChE J., 1999, 45, 1451-1468. 

Based on the experimental data of the C02-selective facUitated transport membranes described earlier in this chapter, we proposed the concept of C02-selective WGS membrane reactor and developed a one-dimensional nonisothermal model to simulate the reaction and transport process (Huang et al., 2005a). The modeling results have shown that H2 enhancement and CO reduction to 10 ppm or lower are achievable for autothermal reforming synthesis gas via CO2 removal. With this model, we have elucidated the effects of system parameters on the membrane reactor performance. Using the membrane synthesized and the commercial WGS catalyst, we have obtained a CO concentration of less than 10 ppm in the H2 product in WGS membrane reactor experiments and verified the model developed (Huang et al., 2005b Zou et al., 2007). 

Stream, that is, the H2 product, was <10 ppm (on the dry basis) for the various feed rates of the syngas at 20, 30, 40, 50, 60, and 70 cm /min (with 20% steam in the syngas). The nonisothermal model was modified for the flat-sheet membrane configuration of the reactor. As shown in this figure, the data agreed reasonably with the prediction by the model. 

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