One dimensional heterogeneous

An extension of this one-dimensional heterogeneous model is to consider intraparticle diffusion and temperature gradients, for which the lumped equations for the solid are replaced by second-order diffu-sion/conduction differential equations. Effectiveness factors can be used as applicable and discussed in previous parts of this section and in Sec. 7 of this Handbook (see also Froment and Bischoff, Chemical Reactor Analysis and Design, Wiley, 1990). 

The one dimensional heterogeneous model equations are as follows Continuity equations ... 

W. D. Rannie, Perturbation Analysis of One-Dimensional Heterogeneous Flow in Rocket Nozzles, in Detonation and Two-Phase Flow, vol. 6 of Progress in Astronautics and Rocketry, S. S. Penner and F. A. Williams, eds.. New York Academic Press, 1962, 117-144. 

FIGURE 3.11 Proliie of rate of methane disappearance dependence upon steam feed partial pressure and the corresponding exit methane conversion predicted by a one-dimensional heterogeneous model, operating conditions are given as follows tube length/O.D./LD. 11.95/ 0.102/0.0795 m feed composition for point a (mol%) 12.98,... 

Attempts have been made to develop two-dimensional heterogeneous models (McGreavy and Cresswell, 1968, 1969, Deasch and Froment, 1971). McGreavy and Cresswell proceded by adding to the one-dimensional heterogeneous model the terms accounting for radial heat and mass transfer in the bed. 

Figure 11.8.a-1 One-dimensional heterogeneous model with interfacial gradients. 

Figure I I.8.a-2 One-dimensional heterogeneous model with interfacial gradients. Nonmique steady-state case Pq = 0.15 atm. To = 393°C. Initial T, A 393°C, B = 560f°C (after Liu and Amundson 91], from Froment [9]).

Figure II.8.b-I One-dimensional heterogeneous model with interfacial gradients. Start up of reactor, transient temperature profiles. AT = temperature increase of gas phase above feed value AT = increase of solid temperature above initial value.

The mathematical model used by Capelli et al. to simulate the reactor may be classified as a one-dimensional heterogeneous model considering external and internal gradients, but not axial difiusion and conduction. The steady-state model equations are, in terms of the partial pressures... 

By using a one-dimensional heterogeneous model, in nonisothermal conditions (by solving the energy balances above mentioned), the effect of heat profiles can be studied in the reactor. 

A steady-state one-dimensional heterogeneous plug-flow model has been used to represent the behavior of the laboratory reactor. The internal and external mass transfer resistances are taken into account. For different operating conditions, very small Prater numbers were calculated. For this reason, the thermal gradients inside the washcoat were not included in the reactor model (Froment and Bischoff, 1990). The axial solid temperature profiles were measured for each experiment, therefore only the mass balances for gas and solid phases are needed to model the reactor. The equations that represent the system are the following ... 

From the work of De Deken et al. [1982] it was already clear that the reactions are strongly diffusion-controlled. This was confirmed by the present work, so that the reactor simulation required a one-dimensional heterogeneous model. It was also confirmed that interfacial gradients are negligible [De Deken... 

The experimental results were adequately represented by a one-dimensional heterogeneous non-isothermal model of the plate-type structured catalysts, accounting for heat generation by CO oxidation over the catalyst slabs, heat conduction along... 

The model developed to simulate a TBR for HDT of oil fractions at bench and commercial scales is a dynamic one-dimensional heterogeneous model, which is based on the three-phase steady-state reactor model reported in the literature (Korsten and Hoffmann, 1996 Rodriguez and Ancheyta, 2004). 

This chapter is devoted to illustrate the modeling and simulation of a heavy oil hydrotreating experimental bench-scale reactor. Hydrodesulfurization and hydrodemetallization of Maya crude oil was carried out at moderate reaction conditions. The parameters of the kinetic model were derived from experimental data at different reaction conditions of liquid hourly space velocity (LHSV) (0.33-1.5) and temperature (380°C-420°C) keeping constant the pressure and hydrogen-to-oil ratio (6.9 MPa and 5000 std fP/bbl oil, respectively). The bench-scale reactor is modeled as one-dimensional heterogeneous. The chapter gives details about the experiments, the development of the model, and its application to simulate the HDS and HDM of Maya crude oil. 

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