Pulsed experiments residence times

Glaser and Lichtenstein (G3) measured the liquid residence-time distribution for cocurrent downward flow of gas and liquid in columns of -in., 2-in., and 1-ft diameter packed with porous or nonporous -pg-in. or -in. cylindrical packings. The fluid media were an aqueous calcium chloride solution and air in one series of experiments and kerosene and hydrogen in another. Pulses of radioactive tracer (carbon-12, phosphorous-32, or rubi-dium-86) were injected outside the column, and the effluent concentration measured by Geiger counter. Axial dispersion was characterized by variability (defined as the standard deviation of residence time divided by the average residence time), and corrections for end effects were included in the analysis. The experiments indicate no effect of bed diameter upon variability. For a packed bed of porous particles, variability was found to consist of three components (1) Variability due to bulk flow through the bed... 

Ross (R2) measured liquid-phase holdup and residence-time distribution by a tracer-pulse technique. Experiments were carried out for cocurrent flow in model columns of 2- and 4-in. diameter with air and water as fluid media, as well as in pilot-scale and industrial-scale reactors of 2-in. and 6.5-ft diameters used for the catalytic hydrogenation of petroleum fractions. The columns were packed with commercial cylindrical catalyst pellets of -in. diameter and length. The liquid holdup was from 40 to 50% of total bed volume for nominal liquid velocities from 8 to 200 ft/hr in the model reactors, from 26 to 32% of volume for nominal liquid velocities from 6 to 10.5 ft/hr in the pilot unit, and from 20 to 27 % for nominal liquid velocities from 27.9 to 68.6 ft/hr in the industrial unit. In that work, a few sets of results of residence-time distribution experiments are reported in graphical form, as tracer-response curves. 

A system of N continuous stirred-tank reactors is used to carry out a first-order isothermal reaction. A simulated pulse tracer experiment can be made on the reactor system, and the results can be used to evaluate the steady state conversion from the residence time distribution function (E-curve). A comparison can be made between reactor performance and that calculated from the simulated tracer data. 

The F-curve can also be determined from the E-curve obtained by a pulse experiment according to Equation 8-3. For a plug flow reactor, the step is extremely sharp, and in the limit it would approach a Heaviside function at the mean residence time. The Heaviside unit function H(t - t0) is... 

The age of a fluid element is defined as the time it has resided within the reactor. The concept of a fluid element being a small volume relative to the size of the reactor yet sufficiently large to exhibit continuous properties such as density and concentration was first put forth by Danckwerts in 1953. Consider the following experiment a tracer (could be a particular chemical or radioactive species) is injected into a reactor, and the outlet stream is monitored as a function of time. The results of these experiments for an ideal PFR and CSTR are illustrated in Figure 8.2.1. If an impulse is injected into a PFR, an impulse will appear in the outlet because there is no fluid mixing. The pulse will appear at a time ti = to + t, where t is the space time (r = V/v). However, with the CSTR, the pulse emerges as an exponential decay in tracer concentration, since there is an exponential distribution in residence times [see Equation (3.3.11)]. For all nonideal reactors, the results must lie between these two limiting cases. 

Following the concept of Fig. 6.9, the parameters describing the fluid dynamic and residence time distribution of the plant peripherals are determined by means of pulse experiments. For this purpose, a small amount of tracer is injected into the plant without the column and the output concentration is measured. 

In the first place, it is clear that not all molecules entering a reactor of holding time 6 Vjq will reside there for exactly S. It is because of the vigorous mixing, which causes some molecules to pass out of the reactor almost immediately and contribute so little to production, that the volume requirements of this type of reactor are so much higher. To determine the residence time distribution, a suitable experiment would be to inject a sharp pulse of some nonreacting tracer material at time t = 0 and measure its... 

The dispersion coefficient can be detennined from a pulse tracer experiment. Here, we will use / and a to solve for the dispersion coefficient D, and then the Peclet number, Pe Here the effluent concentration of the reactor is measured as a function of time. From the effluent concentration data, the mean residence time. and variance, o, are calculated, and these values are then used to determine Dg. To show how this is accomplished, we will write... 

Kinetic Measurements. The results of the shale oil cracking experiments are summarized in Table I. Oil yields are reported as a percentage of the LLNL assay result on both a condensed-oil basis and a C5+ basis. To conduct the kinetic analysis, an effective residence time had to be determined. It was assumed for simplicity that the gas-and-oil evolution profile could be approximated by a square pulse. The average residence time was calculated by multiplying the void volume of the bottom reactor by the time interval over which three-fourths of the products were evolved and then dividing by the total volume of gases and vapors at the cracking temperatures (14). The void volume was... 

PIPECO experiments have provided direct estimates of kinetic shifts. The limit of the observation window has been varied and the changes in the measured appearance energies observed. The limit t2 is the source residence time and was known in these experiments, being determined by a delay prior to applying the drawout pulse. Changing from 0.7 to... 

The pulse residence time under vacuum conditions is much shorter than in conventional pulse experiments. Thus, a high time resolution is achievable. TAP pulse transients are capable of providing information about short-lived reaction intennediates, which are not detectable with a conventional step-transient technique. Therefore, transient experiments using TAP pulsing are valuable mostly for the detection and identification of reaction intermediates to formulate a reaction mechanism. 

Chemical engineers also use this kind of experiment. It can be utilized to great advantage in chemical reactors to find the "residence time distribution" of the reactor, a crucial piece of information which links microscopic flow behavior, that is, fluid dynamics, to measurables of the system, such as chemical conversion and selectivity. For vessels that are not used for reaction processes, but are used for other operations that are also critically dependent upon mixing, this tracer experiment provides a great deal of insight into how the system behaves. We can analyze how a pulse of injected tracer would behave in the well-stirred vessel we have been analyzing here. 

A second type of experiment often used in the determination of RTD is the response to a pulse input of tracer rather than a step function. Here a total quantity, Q, of the tracer is injected into the feed stream at a concentration of Q over a small time period At. Differing residence times of molecules in the system will lead to a dispersion of the pulse with typical response curves shown in the C-diagram of Figure 4.4, corresponding to those illustrated in Figure 4.3. The response of the C(t) curves of Figure 4.4 is just the derivative of the F t) curves in Figure 4.3. 

Thus, either pulse-response or step-function response experiments give sufficient information to permit evaluation of exit-age, internal-age, and residence-time distributions. The average age or mean residence time, which we have defined intuitively in equation (4-13), can be more precisely stated in terms of the time average of the exit-age distribution. 

Experimental data on exit-age or residence-time distributions most often take the form of discrete values of tracer concentration measured at successive time intervals after introduction of the tracer. Thus, the integrals involved can be replaced by summations in the analysis of actual data. We will illustrate the procedure for the analysis of a pulse-response experiment. Available are tracer concentrations in the effluent, C t) and corresponding times, and from these data we would like to determine the exit-age distribution, or E 0)d6, the distribution in terms of the residencetime variable 6. First determine E t) from C t) versus t by... 

The resonance absorption of an ion in an ICR cell can be treated as limited in either time or space. Therefore the duration of a pulsed rf field or the residence time in a continuous rf field must be known in order to calculate T. In pulsed ICDR experiments 55) the length of time the rf field is applied and the peak strength Ei together determine the kinetic energy 2 ). 

R. S. Peterson [Ph.D. thesis, University of Wisconsin -Madison (1987)] carried out a series of residence time measurements on a Damrace immobilized enzyme reactor used to effect the hydrolysis of lactose to glucose and galactose. The effluent composition data given below correspond to an experiment in which a pulse of sodium acetate was injected at the reactor entrance. The liquid flow rate was maintained constant at 6 cm / min. 

The models have been tested by one type of control experiment, which measures the magnitude of the rf pulse necessary to drive a particular ion to the cell wall. It has been clearly established that, unless considerable care and skill are exercised, the experimental magnitude may be significantly less than that predicted by the models, by a factor of up to one-third. Unless justified by appropriate control experiments, this challenges the ability of the models to describe the phenomena in the cell and their application to yield reliable values for ion energies and residence times. Once again, it underlines the need to measure these parameters directly. 

The main advance of the TAP reactor over the conventional puke reactor, by Gleaves and coworkers [2], is increased time resolution due to the pulse generation technique used. An electronically controlled solenoid valve was introduced which could produce pulses with widths shorter than the reaction times of most elementary steps of heterogeneous catalysis. Most TAP experiments are carried out with the mean residence time of the pulse in the reactor of ca. one hundred milliseconds. In contrast, pulse widths of the input pulse can be less than four hundred microseconds. The input pulses are much sharper. These numbers suggest that these very sharp pulses had not been fully utilized and that one can further increase the time resolution of TAP data by decreasing the mean residence time of the pulse in the reactor. 

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