Kinetic data from tubular reactors

De Deken and his colleagues197 have studied the nature of the carbon deposited on a commercial CCE catalyst (12 wt% Ni on a-Al203) and have concluded that it has diffused into the bulk of the nickel and that some of it is present as carbide. A more applied article from the same group198 presents intrinsic kinetic data from a tubular reactor in the temperature range 823-953K. 

If the rate equation is to be employed in its integrated form, the problem of determining kinetic constants from experimental data from batch or tubular reactors is in many ways equivalent to taking the design equations and working backwards. Thus, for a batch reactor with constant volume of reaction mixture at constant temperature, the equations listed in Table 1.1 apply. For example, if a reaction is suspected of being second order overall, the experimental results are plotted in the form ... 

A simple model of lumped kinetics for supercritical water oxidation included in the partial differential equations for temperature and organic concentrations allows to qualitatively simulate the dynamic process behavior in a tubular reactor. Process parameters can be estimated from measured operational data. By using an integrated environment for data acquisition, simulation and parameter estimation it seems possible to perform an online update of the process parameters needed for prediction of process behavior. 

This last item is important because it leads to an easy way to accommodate the molar contraction of the gas as the reaction proceeds. The program calculates steady-state profiles of each of these down the length of the tubular reactor, given the reaction kinetics models, a description of the reactor and catalyst geometries, and suitable inlet gas flow-rate, pressure and composition information. Reactor performance is calculated from the flow-rate and composition data at the reactor outlet. Other data, such as the calculated pressure drop across the reactor and the heat of reaction recovered as steam, are used in economic calculations. The methods of Dixon and Cresswell (7) are recommended for heat-transfer calculations. 

It should be noted that Equations 1, 2, 3, 4, and 5 imply a homogeneous kinetic system. Coking in tubular reactors results from a combination of homogeneous and heterogeneous processes. As the kinetics of these processes are not well understood and as the quantitative yield of coke is several orders of magnitude smaller than other pyrolysis products, it is more convenient to model coke formation separately based on commercial operating data. 

The simplicity and general utility of the Madon-Boudart criterion make it one of the most important experimental tests to confirm that kinetic data are free from artifacts. It can be used for heterogeneous catalytic reactions carried out in batch, continuous stirred tank, and tubular plug flow reactors. 

One advantage of the second method is that the design need not be limited to the same type of reactor. Data taken in a stirred reactor and manipulated to get intrinsic kinetic parameters could be used to estimate the performance of a tubular reactor, a packed bed, or perhaps a new type of contactor for the same reaction. Fundamental kinetic parameters obtained from a small fixed-bed reactor might lead to consideration of a fluidized-bed reactor for the large unit. Of course, pilot-plant tests of the alternate reactor type would be advised. 

More tests are needed comparing measured conversions and temperature profiles with model predictions for tubular reactors. Comparisons will be easier for reactions with simple kinetics than for complex reactions such as partial oxidations. Tests should be made over a wide range of Reynolds numbers, which may require high velocities and long reactors. If kinetic data are uncertain or unavailable, the overall heat transfer coefficient for the 1-D model can be obtained from the axial temperature profile and the total heat removal [41] ... 

Equation I l.S.a-1 is obtained from a material balance on a reference component, say A, over an elementary cross section of the tubular reactor, containing an amount of catalyst dW. Indeed, as previously mentioned, rate equations for heterogeneously catalyzed reactions are generally referred to unit catalyst weight, rather than reactor volume, in order to eliminate the bed density. Obviously, different packing densities between the laboratory reactor in which kinetic data were determined and the industrial reactor, calculated on the basis of these data would lead to different results. 

Estimation of the kinetic parameters from experimental data obtained from the start-up of an industrial tubular reactor. This requires dynamic simulation of a tubular reactor, comprising a set of partial differential equations. 

Schultz and Linden Ind. Eng. Chem. Process Design and Development, 1 (111), 1962] have studied the hydrogenolysis of low molecular weight paraffins in a tubular flow reactor. The kinetics of the propane reaction may be assumed to be first-order in propane in the regime of interest. From the data below determine the reaction rate constants at the indicated temperatures and the activation energy of the reaction. 

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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