Fixed bed reactors, modeling

Here x is the conversion of SiH4. combines the effect of the molar expansion in the deposition process as well as the change in the volumetric flow and the dispersion coefficient, D, with temperature. At low pressures and small Re in LPCVD reactors the dispersion occurs mainly by molecular diffusion, therefore, we have used (D/D0) = (T/T0)l 65. e is the expansion coefficient and the stoichiometry implies that e = (xi)q, the entrance mole fraction of SiH4. The expansion coefficient, e is introduced as originally described by Levenspiel (33) The two reaction terms refer to the deposition on the reactor wall and wafer carrier and that on the wafers, respectively. The remaining quantities in these equations and the following ones are defined at the end of the paper. The boundary conditions are equivalent to the well known Danckwerts1 boundary conditions for fixed bed reactor models. 

An extensive analysis of the behaviour of different types of non-adiabatic fixed bed reactor models is carried out and the importance of the heterogeneous one and two-dimensional models III-0 and III-T is stressed. Although in these models the heat and mass transfer phenomena are correctly taken into account, they... 

Investigation 10 was a study of fixed-bed reactor models and their application to the data of Hettinger et al. (1955) on catalytic reforming of C7 hydrocarbons. The heuristic posterior density function p 6 Y) proposed by Stewart (1987) was used to estimate the rate and equilibrium parameters of various reaction schemes, two of which were reported in the article. The data were analyzed with and without models for the intraparticle and boundary-layer transport. The detailed transport model led to a two-dimensional differential-algebraic equation system, which was solved via finite-element discretization in the reactor radial coordinate and... 

Lindborg H, Eide V, Unger S, Henriksen ST, Jakobsen HA (2004) Parallelization and performance optimization of a dynamic PBE fixed bed reactor model for practical applications. Computers and Chemical Engineering 28 1585-1597... 

In the previous examples, we have exploited the idea of an effectiveness factor to reduce fixed-bed reactor models to the same form as plug-flow reactor models. This approach is useful and solves several important cases, but this approach is also limited and can take us only So far. In the general case, we must contend with multiple reactions that are not first order, nonconstant thermochemical properties, and nonisothermal behavior in the pellet and the fluid. For these cases, we have no alternative but to solve numerically for the temperature and species concentrations profiles in both the pellet and the bed. As a final example, we compute the numerical solution to a problem of this type. 

In previous publications [1-4], the vapor phase catalytic hydrodechlorination (HDC) of 1,1,1-trichloroethane (111 TCA) and its reaction intermediates was studied. Various catalysts were evaluated, including Pt/T)-alumina. The Pt/ri-alumina catalyst deactivated rapidly during the HDC of saturated chlorocarbons such as 111 TCA, but remained stable during the HDC of unsaturated chlorocarbons such as 1,1-dichloroethylene (11 DCE). At 523K and higher, large quantities of coke were deposited on the Pt/rj-alumina during the HDC of 111 TCA. However, very little coke was observed on the catalyst after the HDC of any other compound. In this paper, a mathematical model is developed for the deactivation of Pt/q-alumina catalyst for the HDC of 111 TCA in a fixed-bed reactor. Model predictions are compared to experimental data. 

Figure 4.3 Basic types of fixed-bed reactor models.

In the following section, a classification of fixed bed reactor models is proposed and a brief description of each model type is reported. 

The simplest fixed bed reactor model formulation is the pseudo-homogeneous ideal model, by which ... 

The catalyst effectiveness factor rji was calculated from the pore network model of Wood and Gladden [15] under the conditions on which capillary condensation was expected. The pore network model was solved over a range of temperatures from 553 to 580 K and for several pressures in the interval 20-40 bar to create a database of effectiveness factors for input to the macroscopic reactor model. The hydrodesulfurization of 1 mole % diethyl sulfide in an inert dodecane carrier was considered, with a molar gas oil ratio of 4. The catalyst was taken to have a connectivity of 6 and a normal distribution of pore sizes with a mean of 136 A and standard deviation of 28 A. By using the results of the pore network simulation as input to the macroscopic fixed bed reactor model, capillary condensation at the scale of the catalyst pellets was accounted for. 

Even though the model in Table 3.1 results from several assumptions (detailed in Section 3.2.1), it can be considered as quite comprehensive. In fact, what is commonly found in the fitera-ture is a simplified version of this model The well-known classification of fixed-bed reactor models by Froment [51] and Froment and Bischoff [62] clearly exemplifies how a more general model unfolds into a hierarchy of several others with decreasing complexity. The dimensionafity of the model (usually one- or two-dimensional) and the presence of interphase and intraparticular resistances to mass/heat transfer are the main basis for distinguishing between different categories. 

Hartig F, Keil FJ. Large-scale spherical fixed bed reactors Modeling and optimization. Industrial Engineering Chemistry Research 1993 32 424-437. 

A model that includes all the above terms is normally called the radial axial flow packed reactor (RAFPR) and represents the most sophisticated fixed-bed reactor model. The coupled differential equations for momentum balance, component balance, and for a nonisothermal reactor, the energy balance must be simultaneously solved (Li, 2007 Singh, 2005). 

Examination of the criteria for significant dispersion in fixed bed reactors shows that in practical cases of fixed bed reactor modeling, axial dispersion of mass and heat as well as radial dispersion of mass are negligible, which should be proven by the criteria summarized in Table 4.10.8. Then the mass and heat balance equations (4.10.125) and (4.10.126) simplify to ... 

In contrast to fixed bed reactor modeling, see Section 4.10.7.2, we can neglect the influence of heat transfer at the internal reactor wall, as this induces a temperature jump directly at the wall. If the reaction temperature is measured in the bed, usually by a thermocouple located at the axis of the reactor, we only have to consider radial gradients in the bed itself... 

As inspected in the following, we may model the cooled tubular reactor by the so-called one- or two-dimensional fixed bed reactor model. 

Two-Dimensional Fixed Bed Reactor Model If we neglect axial dispersion of heat, the heat balance according to the two-dimensional reactor model is as follows [Eq. (4.10.126), Section 4.10.7.1] ... 

One-Dimensional Fixed Bed Reactor Model It may be convenient to use a onedimensional model, where only axial gradients of temperature and concentration are considered. We now compare how accurate this approach is. Like the two-dimensional model, the one-dimensional model also takes into account X d. w,int, Xwaii, and a ex, but now we assume a constant bed temperature and an overall thermal transmittance L/ovenii that combines conduction in the bed, heat transfer at the wall, through the wall, and to the cooling medium by ... 

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