Isothermal plug flow reactor model

The results confirm that the adsorption of ammonia is very fast and that ammonia is strongly adsorbed on the catalyst surface. The data were analyzed by a dynamic isothermal plug flow reactor model and estimates of the relevant kinetic parameters were obtained by global nonlinear regression over the entire set of runs. The influences of both intra-particle and external mass transfer limitations were estimated to be negligible, on the basis of theoretical diagnostic criteria. 

Most commonly, distributed parameter models are applied to describe the performance of diesel particulate traps, which are a part of the diesel engine exhaust system. Those models are one- or two-dimensional, non-isothermal plug-flow reactor models with constant convection terms, but without diffusion/dispersion terms. 

To describe the reactor behavior, a simplified isothermal dispersed plug-flow reactor model was used. The well-known mass balance of this model for steady-state conditions can be formulated as [14, 15] ... 

In addition to these experiments, a simplified isothermal 1-D dispersed plug-flow reactor model of the membrane reactor was used to carry out theoretical studies [47]. The model used consisted of the following mass balance equations for the feed and sweep sides ... 

Again, the simple isothermal 1-D plug-flow reactor model provides a good basis for quantitative descriptions. This model allows to explore the potential of using series connections of several membrane reactor segments. The corresponding mass balance for a component i and a segment k can be formulated as follows ... 

A one-dimensional pseudohomogeneous plug flow reactor model assuming isothermality was used to simulate experimental results. The continuity and kinetic expressions used were as follows ... 

We have modelled the reacting system as an isothermal plug flow reactor, by neglecting both axial dispersion and internal and external mass transfer resistance. These assumptions are justified by experimental findings as well as by theoretical calculations. 

Dehydrogenation of ethylbenzene to styrene is normally accomplished in a fixed-bed reactor. A catalyst is packed in tubes to form the fixed bed. Steam is often fed with the styrene to moderate the temperature excursions that are characteristic of adiabatic operation. The steam also serves to prolong the life of the catalyst. Consider the situation in which we model the behavior of this reactor as an isothermal plug flow reactor in which the dehydrogenation reaction occurs homogeneously across each cross section of the reactor. The stoichiometry of the primary reaction is... 

The steady-state model equations for an isothermal plug flow reactor with the three variable reactions system are given by... 

The fixed-bed laboratory reactor is regarded as an ideal isothermal plug flow reactor. The reactor model consists of the continuity equations for (1) N2, CO, NO, O2, CO2, N2O and NO2 in the gas phase, (2) surface species adsorbed on the noble metal surface, (3a) surface species adsorbed on the ceria surface, (3b) species in the ceria sub-layer, (4) CO2 adsorbed on the y-AI2O3 support. A detailed description can be found in [28]. 

At this time, we are unsure as to whether a packed-bed reactor (shell-and-tube type, modeled as a plug flow reactor) or a fluidized-bed reactor (modeled as an isothermal plug flow reactor with 10% feed gas... 

A one-dimensional isothermal plug-flow model is used because the inner diameter of the reactor is 4 mm. Although the apparent gas flow rate is small, axial dispersion can be neglected because the catalj st is closely compacted and the concentration profile is placid. With the assumption of Langmuir adsorption, the reactor model can be formulated as. 

The solution procedure to this equation is the same as described for the temporal isothermal species equations described above. In addition, the associated temperature sensitivity equation can be simply obtained by taking the derivative of Eq. (2.87) with respect to each of the input parameters to the model. The governing equations for similar types of homogeneous reaction systems can be developed for constant volume systems, and stirred and plug flow reactors as described in Chapters 3 and 4 and elsewhere [31-37], The solution to homogeneous systems described by Eq. (2.81) and Eq. (2.87) are often used to study reaction mechanisms in the absence of mass diffusion. These equations (or very similar ones) can approximate the chemical kinetics in flow reactor and shock tube experiments, which are frequently used for developing hydrocarbon combustion reaction mechanisms. 

Knowledge of these types of reactors is important because some industrial reactors approach the idealized types or may be simulated by a number of ideal reactors. In this chapter, we will review the above reactors and their applications in the chemical process industries. Additionally, multiphase reactors such as the fixed and fluidized beds are reviewed. In Chapter 5, the numerical method of analysis will be used to model the concentration-time profiles of various reactions in a batch reactor, and provide sizing of the batch, semi-batch, continuous flow stirred tank, and plug flow reactors for both isothermal and adiabatic conditions. 

The differences between the TBR and the MR originate from the differences in catalyst geometry, which affect catalyst load, internal and external mass transfer resistance, contact areas, as well as pressure drop. These effects have been analyzed by Edvinsson and Cybulski [ 14,26] via computer simulations based on relatively simple mathematical models of the MR and TBR. They considered catalytic consecutive hydrogenation reactions carried out in a plug-flow reactor with cocurrent downflow of both phases, operated isothermally in a pseudo-steady state all fluctuations were modeled by a corresponding time average ... 

Numerical simulations and analyses were performed for both the continuous stirred-tank reactor (CSTR) and the plug-flow reactor (PER). A comparison between the microkinetic model predictions for an isothermal PFR and the experimental results [13], is presented in Fig. 2 for the following conditions commercial low temperature shift Cu catalyst loading of 0.14 g/cm total feed flow rate of 236 cm (STP) min residence time r = 1.8 s feed composition of H20(10%), CO(10%), C02(0%), H2(0%) and N2(balance). As can be seen, the model can satisfactorily reproduce the main features of the WGSR on Cu LTS catalyst without any further fine-tuning, e.g., coverage dependence of the activation energy, etc, which is remarkable and provides proof of the adequacy of the... 

J. M. Castro, S. D. Lipshitz, and C. W. Macosko [AIChE J., 28, 973 (1982)] modeled a thermosetting polymerization reaction in a laminar flow reactor under several different operating conditions. Demonstrate your ability to simulate the performance of a plug flow reactor for this reaction under both isothermal and adiabatic reaction conditions. In particular, determine the reactor space times necessary to achieve 73% conversion for both modes of operation and the following parameter values for a (3/2)-order reaction (r = kc - ). 

The model calculations were performed with CHEMKIN II [117]. A single run calculated the concentrations of all species in dependence of the reaction time for a radial homogeneous plug-flow reactor and for overall isothermal conditions. In addition, sensitivity calculations and flow analysis were performed in order to gain information about important reaction steps. (For details see [128].)... 

Thus, the zone model of a reactor implies a combination of sequentially connected adiabatic (autothermal) quasi-isothermal turbulent plug flow reactors and heat exchange elements with external heat removal. 

In this chapter the most important operation modes of reactors are considered. Models are developed by combining simple reaction kinetics for single-phase reactions with mass balances for five ideal model reactors the ideal batch reactor the semi-batch reactor the plug flow reactor the perfectly mixed continuous reactor and the cascade of perfectly mixed reactors. For isothermal conditions, conversions can be calculated on the basis of chemical kinetics only. 

There will be velocity gradients in the radial direction so all fluid elements will not have the same residence time in the reactor. Under turbulent flow conditions in reactors with large length to diameter ratios, any disparities between observed values and model predictions arising from this factor should be small. For short reactors and/or laminar flow conditions the disparities can be appreciable. Some of the techniques used in the analysis of isothermal tubular reactors that deviate from plug flow are treated in Chapter 11. 

The reactor model adopted for describing the lab-scale experimental setup is an isothermal homogeneous plug-flow model. It is composed of 2NP + 2 ordinary differential equations of the type of Equation 16.11 with the initial condition of Equation 16.12, NP + 3 algebraic equations of the type of Equation 16.13, and the catalytic sites balance (Equation 16.14) ... 

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. 

The axial dispersion plug flow model is used to determine the performance of a reactor with non-ideal flow. Consider a steady state reacting species A, under isothermal operation for a system at constant density Equation 8-121 reduces to a second order differential equation ... 

One of the simplest models used to describe the performance of tubular reactors is the well-known isothermal one-dimensional plug flow tubular reactor (PFTR) model. The mass balance of this model for steady-state conditions, the simultaneous occurrence of M reactions and a constant volumetric flow rate V is ... 

A summary of reactor models used by various authors to interpret trickle-bed reactor data mainly from liquid-limiting petroleum hydrodesulfurization reactions (19-21) is given in Table I of reference (37). These models are based upon i) plug-flow of the liquid-phase, ii) the apparent rate of reaction is controlled by either internal diffusion or intrinsic kinetics, iii) the reactor operates isothermally, and iv) the intrinsic reaction rate is first-order with respect to the nonvolatile liquid-limiting reactant. Model 4 in this table accounts for both incomplete external and internal catalyst wetting by introduction of the effectiveness factor r)Tg developed especially for this situation (37 ). 

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