Tube-wall reactor model

TI Carbon monoxide hydrogenation over cobalt catalyst in a tube-wall reactor Part II Modeling studies KW Fischer Tropsch synthesis modeling, carbon monoxide hydrogenation cobalt catalyst, tube wall reactor Fischer Tropsch reaction IT Hydrogenation catalysts... 

Equations 12.7.28 and 12.7.29 provide a two-dimensional pseudo homogeneous model of a fixed bed reactor. The one-dimensional model is obtained by omitting the radial dispersion terms in the mass balance equation and replacing the radial heat transfer term by one that accounts for thermal losses through the tube wall. Thus the material balance becomes... 

The equations describing the concentration and temperature within the catalyst particles and the reactor are usually non-linear coupled ordinary differential equations and have to be solved numerically. However, it is unusual for experimental data to be of sufficient precision and extent to justify the application of such sophisticated reactor models. Uncertainties in the knowledge of effective thermal conductivities and heat transfer between gas and solid make the calculation of temperature distribution in the catalyst bed susceptible to inaccuracies, particularly in view of the pronounced effect of temperature on reaction rate. A useful approach to the preliminary design of a non-isothermal fixed bed catalytic reactor is to assume that all the resistance to heat transfer is in a thin layer of gas near the tube wall. This is a fair approximation because radial temperature profiles in packed beds are parabolic with most of the resistance to heat transfer near the tube wall. With this assumption, a one-dimensional model, which becomes quite accurate for small diameter tubes, is satisfactory for the preliminary design of reactors. Provided the ratio of the catlayst particle radius to tube length is small, dispersion of mass in the longitudinal direction may also be neglected. Finally, if heat transfer between solid cmd gas phases is accounted for implicitly by the catalyst effectiveness factor, the mass and heat conservation equations for the reactor reduce to [eqn. (62)]... 

The solution of Eq. (173) poses a rather formidable task in general. Thus the dispersed plug-flow model has not been as extensively studied as the axial-dispersed plug-flow model. Actually, if there are no initial radial gradients in C, the radial terms will be identically zero, and Eq. (173) will reduce to the simpler Eq. (167). Thus for a simple isothermal reactor, the dispersed plug flow model is not useful. Its greatest use is for either nonisothermal reactions with radial temperature gradients or tube wall catalysed reactions. Of course, if the reactants were not introduced uniformly across a plane the model could be used, but this would not be a common practice. Paneth and Herzfeld (P2) have used this model for a first order wall catalysed reaction. The boundary conditions used were the same as those discussed for tracer measurements for radial dispersion coefficients in Section II,C,3,b, except that at the wall. 

Non-isothermal and non-adiabatic conditions. A useful approach to the preliminary design of a non-isothermal fixed bed reactor is to assume that all the resistance to heat transfer is in a thin layer near the tube wall. This is a fair approximation because radial temperature profiles in packed beds are parabolic with most of the resistance to heat transfer near the tube wall. With this assumption a one-dimensional model, which becomes quite accurate for small diameter tubes, is satisfactory for the approximate design of reactors. Neglecting diffusion and conduction in the direction of flow, the mass and energy balances for a single component of the reacting mixture are ... 

The design of tubular fixed bed catalytic reactors has generally been based on a one dimensional model that assumes that species concentrations and fluid temperature vary only in the axial direction. Heat transfer between the reacting fluid and the reactor walls is considered by presuming that all of the resistance is contained within a very thin boundary layer next to the wall and by using a heat transfer coefficient based on the temperature difference between the bulk fluid and the wall. Per unit area of the tube wall, the heat flow rate from the reactor contents to the wall is then /t (r - T ). The correlations for presented in Section 12.7.1.3 may be used to estimate this parameter. 

Tosti et al. [22] compared a thin-walled dense tube Pd membrane and composite Pd-ceramic tube membranes. They developed a finite elemental model for membrane reactors. Table 6.1 shows the WGS reaction conversion values calculated for the dense and the composite membrane reactors both by taking into account the wall effects ( WE case) resistance and by neglecting such a resistance ( no WE case). The main result is that by increasing the temperature the reactiOTi conversion increases. Table 6.2 shows in co-current mode. Both the membranes show similar activities. 

Berger RJ, Kapteijn F. Coated-wall reactor modeling-criteria for neglecting radial concentration gradients. 2. Reactor tubes filled with inert particles. Industrial and Engineering Chemistry Research 2007 46 3871-3876. 

The view factor Fpj can be expressed by the ratio Ct/dt, but a correction for multiple radiation and in particular circumferential heat conductance in the tube wall must also be taken into consideration for a full -size tubular reformer [244]. For a mono-tube pilot plant, the tube spacing has no meaning, so a value fitted to proper measurements on the hot and cold sides must be used to evaluate the reactor models. 

Simulation of tubular steam reformers and a comparison with industrial data are shown in many references, such as [250], In most cases the simulations are based on measured outer tube-wall temperatures. In [181] a basic furnace model is used, whereas in [525] a radiation model similar to the one in Section 3.3.6 is used. In both cases catalyst effectiveness factor profiles are shown. Similar simulations using the combined two-dimensional fixed-bed reactor, and the furnace and catalyst particle models described in the previous chapters are shown below using the operating conditions and geometry for the simple steam reforming furnace in the hydrogen plant. Examples 1.3, 2.1 and 3.2. Similar to [181] and [525], the intrinsic kinetic expressions used are the Xu and Froment expressions [525] from Section 3.5.2, but with the parameters from [541]. 

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