Tubular reactor tracers

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. 

In Section 11.1.3.1 we considered the longitudinal dispersion model for flow in tubular reactors and indicated how one may employ tracer measurements to determine the magnitude of the dispersion parameter used in the model. In this section we will consider the problem of determining the conversion that will be attained when the model reactor operates at steady state. We will proceed by writing a material balance on a reactant species A using a tubular reactor. The mass balance over a reactor element of length AZ becomes ... 

Note that, in a laminar-flow tubular reactor, the material on the reactor centre line has the highest velocity, this being exactly twice the average velocity, Q/A, for the whole reactor. This means that, following any tracer test, no response will be observed until the elapsed time exceeds one half of the reactor space time or mean residence time. The following values for 0 and F(0) emphasise the form of the cumulative RTD and the fact that, even up to 10 residence times after a tracer impulse test, 0.25% of the tracer will not have been eluted from the system. 

As i the term in brackets above tends to exp (vit/V) for t < V/v), and F becomes zero(7>. Thus, for an infinite number of tanks the fraction of tracer that has escaped is zero for all times less than the residence time V/v. This is exactly the same as for the case of an ideal tubular reactor with plug flow. 

Previously, the RTD functions for flow systems were described. In practice, the RTD is determined experimentally by injecting a tracer at the inlet of the system and monitoring the response at the outlet information about the system is derived from these results. In a tubular reactor, the RTD measurements are used to determine how closely the plug flow assumption is obeyed. 

Multistage CSTR Since tubular reactor performance can be simulated by a series of CSTRs, multistage CSTR tracer models are useful in analyzing data from empty tubular and packed-bed reactors. The solution for a tracer through n CSTRs in series is found by induction from the solution of one stage, two stages, and so on. 

Here we use a single parameter to account for the nonideality of our reactor. This parameter is most always evaluated by analyzing the RTD determined from a tracer test. Examples of one-parameter models for a nonideal CSTR include the reactor dead volume V, where no reaction takes place, or the fraction / of fluid bypassing the reactor, thereby exiting unreacted. Examples of one-parameter models for tubular reactors include the tanks-in-series model and the dispersion model. For the tanks-in-series model, the parameter is the number of tanks, n, and for the dispersion model, it is the dispersion coefficient D,. Knowing the parameter values, we then proceed to determine the conversion and/or effluent concentrations for the reactor. 

To illustrate how dispersion affects the concentration profile in a tubular reactor we consider the injection of a perfect tracer pulse. Figure 14-3 shows how dispersion causes the pulse to broaden as it moves down the reactor and becomes less concentrated. 

P14-7j A tubular reactor has been sized to obtain 98% conversion and to process 0.03 mV s. The reaction is a first-order irreversible isomerization. The reactor is 3 m long, with a cross-sectional area of 25 cm. After being built, a pulse tracer test on the reactor gave the following (data t = 10 s and = 65 s. What conversion can be expected in the real reactor ... 

P14-18b The following E(t) curve was obtained from a tracer test on a tubular reactor in which dispersion is believed to occur. 

For tp t < 2tp (< tpi), there is a transfer of the tracer from reactor 1 to 2 only through the tubular reactor. As a result of this situation Qi = 0 and there are only... 

Co unsteady tubular reactor Initial value for tracer concentration mol m 15.1... 

Figure 8.12. Tracer experiments in a three phase tubular reactor with knitted silica catalyst layers (E. Toukoniitty, J. Warn , T. Salmi, P. Maki-Arvela, D.Yu. Murzin, Application of transient methods in three-phase catalysis hydrogenation of a dione in a catalytic plate column, Catalysis Today, 79-80 (2003) 383).

In order to improve the flow characteristics through the tubular reactor, 10 lengths (each 50 cm) of static mixer elements were inserted at 100 cm internals along the tube. Residence-time distribution studies using a pulse of potasiun chloride as tracer shewed that this tubular reactor had the flow characteristics equivalent to a cascade of 35 stirred tanks in series. Thus for practical purposes, this tube can be considered to have flow characteristics equivalent to those of a plug flow reactor. 

Figure 8.9 Residence time distribution (RTD) for a pulsed tubular reactor. Average residence time = 60 min, with a pulsation rate of 99 spm. C is a dimensionless concentration of a non-reactive tracer solid line is experimental data dashed line is theoretical laminar-flow RTD. [23]...

The response of the axial dispersion model to step or pulse tracer stimuli can be determined by writing a material balance over a short segment of the tubular reactor and then solving the resulting differential equations. A transient material balance on a nonreactive tracer for a cyhndrical element of length AZ gives... 

The initial and boundary conditions that apply to this equation depend on whether one is dealing with a pulse or a step stimulus and the characteristics of the system at the tracer injection and monitoring stations. At each of these points the tubular reactor is characterized as closed or open, depending on whether or not plug flow into or out of the test section is assumed. A closed boundary is one at which there is plug flow outside the test section an open boundary is one at which the same dispersion parameter characterizes the flow conditions within and adjacent to the test section. There are then four different possible sets of boundary conditions on equation (11.1.29), depending on whether a completely open or completely closed vessel, a closed-open vessel, or an open-closed vessel is assumed. Different solutions will be obtained for different boundary conditions. Fortunately, for small values of the dispersion parameter, the numerical differences between the various solutions will be small. 

To predict the response curve to an ideal pulse tracer injection at the entrance of the tubular reactor, the boundary conditions at both ends have to be known. Suppose the flow is undisturbed as it passes the inlet and the outlet boundaries of the reactor. This situation is depicted in Figure 3.11a and called an open/open system to dispersion. In contrary to this situation, ideal plug flow D = 0) is considered outside of the boundaries as illustrated in Figure 3.11b. A sudden change of the axial dispersion occurs at the inlet and the outlet of the reactor. This situation corresponds to a closed/closed system. In addition to these situations, vessels open for dispersion at only one site can be discussed. 

The RTD in the tubular reactor was determined experimentally with water as fluid and Brilliant Blue dye as tracer. The tracer was introduced at the reactor inlet in the form of a step function. The concentration of the dye was measured with an UV-vis spectrometer and the response curve is given as f-curve. As the experimental f-curve shown in Figure 3.29 is very steep, a low axial dispersion can be expected. Therefore, RTD will be described with the dispersion model supposing small deviation from plug flow (Equation 3.50). The f-curve valid for small dispersion Bo > 100) can be obtained by integrating the RTD given by (0) (Equation 3.50). 

Considering the mass flux entering and leaving an infinitesimally small element in a tubular reactor and integrating with the open boundary conditions, the response to a tracer pulse at the reactor inlet can be predicted at the reactor outlet from the following equation [6]) ... 

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