Tubular reactor first order reaction

Figure 3.16 Influence of RTD on the performance of tubular reactors. First order reaction, k = 0.1 min . ...

Fig. 1.22. Comparison of size and cost of continuous stirred-tank reactors with a batch or a tubular plug-flow reactor first-order reaction, conversion 0.9 ...

Suppose an inert material is transpired into a tubular reactor in an attempt to achieve isothermal operation. Suppose the transpiration rate q is independent of and that qL = Qtrms- Assume all fluid densities to be constant and equal. Find the fraction unreacted for a first-order reaction. Express your final answer as a function of the two dimensionless parameters, QtranslQin and kVIQm where k is the rate constant and... 

The importance of dilfusion in a tubular reactor is determined by a dimensionless parameter, SiAt/S = QIaLKuB ), which is the molecular diffusivity of component A scaled by the tube size and flow rate. If SiAtlB is small, then the elfects of dilfusion will be small, although the definition of small will depend on the specific reaction mechanism. Merrill and Hamrin studied the elfects of dilfusion on first-order reactions and concluded that molecular diffusion can be ignored in reactor design calculations if... 

FIGURE 8.3 First-order reaction with fet = 1 in a tubular reactor with a parabolic velocity prohle. 

Tanks-in-series reactor configurations provide a means of approaching the conversion of a tubular reactor. In modelling, they are employed for describing axial mixing in non-ideal tubular reactors. Residence time distributions, as measured by tracers, can be used to characterise reactors, to establish models and to calculate conversions for first-order reactions. 

This example models the dynamic behaviour of an non-ideal isothermal tubular reactor in order to predict the variation of concentration, with respect to both axial distance along the reactor and flow time. Non-ideal flow in the reactor is represented by the axial dispersion flow model. The analysis is based on a simple, isothermal first-order reaction. 

A first order reaction, A => 2B, is carried out in a battery of two equal CSTRs followed by a tubular flow reactor with a volume Vr3 = 20 cuft. The process is adiabatic. Input consists of 20 lbmols of A dissolved in 100 cuft of solvent and is at 100 F. As shown on the sketch, 25% of the fresh feed bypasses the first CSTR. Specific volumes are independent of temperature and are additive. Heat of reaction at 560 R is AHr = -70,000 Btu/lbmol and specific rate is... 

A first order reaction is to be conducted in a choice of tubular reactors of diameters 25, 50 or 75 mm that are heated through the wall with a heat transfer medium at T . Data are... 

A plug flow or tubular flow reactor is tubular in shape with a high length/diameter (1/d) ratio. In an ideal case (as in the case of an ideal gas, this only approached reality) flow is orderly with no axial diffusion and no difference in velocity of any members in the tube. Thus, the time a particular material remains within the tube is the same as that for any other material. We can derive relationships for such an ideal situation for a first-order reaction. One that relates extent of conversion with mean residence time, t, for free radical polymerizations is ... 

For some purposes it is adequate to assume that a battery of five or so CSTRs is a close enough approximation to a plug flow reactor. The tubular flow reactor is smaller and cheaper than any comparable tank battery, even a single shell arrangement. For a first order reaction the ratio of volumes of an n-stage CSTR and a PFR is represented by... 

Fig. 1.25. Reaction in series—batch or tubular plug-flow reactor. Concentration Cr of intermediate product P for consecutive first order reactions, A -> P -> Q...

Fig. 1.28. Reactions in series—comparison between batch or tubular plug-flow reactor and a single continuous stirred-tank reactor. Consecutive first-order reactions,...

The multi-mode model for a tubular reactor, even in its simplest form (steady state, Pet 1), is an index-infinity differential algebraic system. The local equation of the multi-mode model, which captures the reaction-diffusion phenomena at the local scale, is algebraic in nature, and produces multiple solutions in the presence of autocatalysis, which, in turn, generates multiplicity in the solution of the global evolution equation. We illustrate this feature of the multi-mode models by considering the example of an adiabatic (a = 0) tubular reactor under steady-state operation. We consider the simple case of a non-isothermal first order reaction... 

Safe Design of Cooled Tubular Reactors for Exothermic Multiple First Order Reactions... 

Bilous and Amundson [1] were the first to describe the phenomenon of parametric sensitivity in cooled tubular reactors. This parametric sensitivity was used by Barkelew [2] to develop design criteria for cooled tubular reactors in which first order, second order and product- inhibited reactions take place. He presented diagrams from which for a certain tube diameter dt the required combination of CAO and Tc can be derived to avoid runaway or vice versa. Later van Welsenaere and Froment [3] did the same for first order reactions, but they also used the inflexion points in the reactor temperature T versus relative conversion XA trajectories, which describe the course of the reaction in the tubular reactor. With these trajectories they derived a less conservative criterion. Morbidelli and Varma [4] recently devised a method for single order reactions based on the isoclines in a temperature conversion plot as proposed by Oroskar and Stern [5]. 

Emig, Hofmann, Hoffmann and Fiand [14] proved experimentally that the criteria of Earkelew, of Agnew and Potter and of McGreavy and Adderley all predict runaway remarkedly well for a single first order reaction in a cooled catalytic tubular reactor. 

This set of equations describes the behaviour of multiple, first order reactions in a tubular reactor using the relative conversion to desired product Xp and to undesired product Xx, the dimensionless temperature T and the dimensionless reactor length Z. The is characterized by the ratio of the reaction heats H in addition to kR, TR, y and p. The operating and design are determined by PC, the dimensionless cooling medium temperature Da, the dimensionless residence time in the reactor U, the dimensionless cooling capacity per unit of reactor volume and ATacp the dimensionless adiabatic temperature rise for the desired reaction, which, of course, depends on the initial concentration of the reactant A. 

Table I. Criteria for the safe design of cooled tubular reactors with multiple exothermic first order reactions...

In order to approach idea PFR behavior, the flow must be turbulent. For example, with an open tube, the Reynolds number must be greater than 2100 for turbulence to occur. This flow regime is attainable in many practical situations. However, for laboratory reactors conducting liquid-phase reactions, high flow rates may not be achievable. In this case, laminar flow will occur. Calculate the mean outlet concentration of a species A undergoing a first-order reaction in a tubular reactor with laminar flow and compare the value to that obtained in a PFR when kV)/u = 1 ( = average linear flow velocity). 

Write down in dimensionless form the material balance equation for a laminar flow tubular reactor accomplishing a first-order reaction and having both axial and radial diffusion. State the necessary conditions for solution. 

Conversion for a first-order reaction in a tubular or packed-bed reactor with dispersion... 

Tanks-in-Series Model Versus Dispersion Model. We have seen that we can apply both of these one-parameter models to tubular reactors using the variance of the RTD. For first-order reactions the two models can be applied with equal ease. However, the tanks-in-series model is mathematically easier to use to obtain the effluent concentration and conversion for reaction orders other than one and for multiple reactions. However, we need to ask what would be the accuracy of using the tanks-in-series model over the dispersion model. These two models are equivalent when the Peclet-Bodenstein number is related to the number of tanks in series, n, by the equation ... 

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