Lumped tubular reactor model

The notable feature of the wall-cooled tubular reactor is that there can exist a hot spot near the center of the reactor and near the entrance. We saw this for the lumped model, which allowed only for variations in the direction, but when radial variations are allowed, the effect can become even more severe as both temperature and concentration vary radially. 

Effect Of Number Of Lumps If the number of plotting points in Aspen Plus is set at 10 (the default), the resulting exit temperature from the reactors under steady-state conditions in Aspen Dynamics is 578 K. Remember that it should be 583 K from the rigorous integration of the ordinary differential equations describing the steady-state tubular reactor that are used in Aspen Plus. Changing the number of points to 20 produces an exit temperature of 580 K. Changing the number of points to 50 produces an exit temperature of 582 K, which is very close to the correct value. Therefore a 50-lump model should be used. 

The reaction considered is the gas-phase, irreversible, exothermic reaction A + B — C occurring in a packed tubular reactor. The reactor and the heat exchanger are both distributed systems, which are rigorously modeled by partial differential equations. Lumped-model approximations are used in this study, which capture the important dynamics with a minimum of programming complexity. There are no sharp temperature or composition gradients in the reactor because of the low per-pass conversion and high recycle flowrate. 

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. 

Illustrate temperature and molecular weight changes in a tubular reactor by constructing a lumped-parameter model of styrene polymerization in a tube. 

The methods listed in Sections 5.1.1-5.1.7 are illustrated by a tubular reactor with a first-order reaction and laminar flow. Models for species, heat, and momentum have been formulated and simplified. In addition to showing the methods, we discuss the assumptions in a traditional 1D lumped-parameter model for a tubular reactor with axial dispersion,... 

The assumptions in a lumped-parameter model are not always transparent. For example, in the ID model for a tubular reactor with axial dispersion (Equations (5.36) and (5.37), repeated here for convenience)... 

While lumped parameter models are normally used to describe processes, many important process units are inherently distributed parameter, that is, the output variables are functions of both time and position. Hence, their process models contain one or more partial differential equations. Pertinent examples include shell-and-tube heat exchangers, packed-bed reactors, packed columns, and long pipelines carrying compressible gases. In each of these cases, the output variables are a function of distance down the tube (pipe), height in the bed (column), or some other measure of location. In some cases, two or even three spatial variables may be considered for example, concentration and temperature in a tubular reactor may depend on both axial and radial positions, as well as time. 

Distributed parameter systems such as tubular reactors and heat exchangers often can be modeled as a set of lumped parameter equations. In this case an alternative (approximate) physical interpretation of the process is used to obtain an ODE model directly rather than by converting... 

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