Residence time distribution experiments

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. 

Hoogendoorn and Lips (H10) carried out residence-time distribution experiments for countercurrent trickle flow in a column of 1.33-ft diameter and 5- and 10-ft height packed with -in. porcelain Raschig rings. The fluid media were air and water, and ammonium chloride was used as tracer. The total liquid holdup was calculated from the mean residence time as found... 

To run the residence time distribution experiments under conditions which would simulate the conditions occurring during chemical reaction, solutions of 15 weight percent and 30 percent polystyrene in benzene as well as pure benzene were used as the fluid medium. The polystyrene used in the RTD experiment was prepared in a batch reactor and had a number average degree of polymerization of 320 and a polydispersity index, DI, of 1.17. 

It has already been pointed out that the forms of solution to the adsorption wave problem are similar to those representing the elution of tracer in a residence-time distribution experiment. Closest to what we considered in Chapter 5 are solutions of Levenspiel and Bischolf [O. Levenspiel and K.B. Bischolf, Adv. Chem. Eng., 4, 95 (1963)] and Lapidus and Amundson [L. Lapidus and N.R. Amundson, J. Phys. Chem., 56, 984 (1952)]. With the rate equation written as in equation (9-8a), these are... 

Mireur and Bischoff [6] correlated data on k[ and versus easily accessible parameters like uju f and d,/Lf the results are shovra in Figs. 13.4-3 and 4. The curve RTD data was obtained from residence time distribution experiments. These are performed with a nonadsorbable tracer like helium. The reaction experiments leading to the curve conversion data obviously involves adsorbable species. This may explain the difference between the two curves. The correlation is not meant to be d nitive since it does not account for the effect of the particle-size distribution pointed out by de Groot [2], by van Swaay and Zuiderweg [23], and by de Vries et al. [24]. The particle-size distribution is known to affect the quality of fluidization. De Vries et al. found that = Lfki/u, varies linearly as a flinction of the percentage of fines firom 4 at 7 percent fines to about 1.S at 30 percent fines. Also, Ro = is markedly affected by this variable. Nevertheless... 

Residence time distribution experiments have shown that the reactor behaves almost like a plug flow tubular reactor with a small dispersion [6]. The RTD can be described using a tanks in series model with 35 ideal mixers. As the simulated reactor behaviour based on the kinetic model is only slightly influenced by the number of ideal mixers for more than 8 tanks, this value was used for all simulations in order to reduce the calculation time needed for parameter optimisation. 

Residence Time Distribution experiments has been performed by pumping the fluid through the mill from a tank that contained a salt solution of known concentration until it reaches a stationary regime. Then a step change in composition is made by suddenly passing to a water flow instead of the salt. The decrease of the outlet conductivity in a cell placed after the mill was followed as the dynamic response to this negative step. 

A practical method of predicting the molecular behavior within the flow system involves the RTD. A common experiment to test nonuniformities is the stimulus response experiment. A typical stimulus is a step-change in the concentration of some tracer material. The step-response is an instantaneous jump of a concentration to some new value, which is then maintained for an indefinite period. The tracer should be detectable and must not change or decompose as it passes through the mixer. Studies have shown that the flow characteristics of static mixers approach those of an ideal plug flow system. Figures 8-41 and 8-42, respectively, indicate the exit residence time distributions of the Kenics static mixer in comparison with other flow systems. 

As we have said, the key to the analysis of asystemlike this one is tohave a function that approximates to the actual residence time distribution. The tracer experiment is used to find that distribution function,butwewillworkfroman assumed function to the tracer concentration-timecurvetoseewhattheexperimentaloutcomemightlooklike. 

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... 

Example 14.6 derives a rather remarkable result. Here is a way of gradually shutting down a CSTR while keeping a constant outlet composition. The derivation applies to an arbitrary SI a and can be extended to include multiple reactions and adiabatic reactions. It is been experimentally verified for a polymerization. It can be generalized to shut down a train of CSTRs in series. The reason it works is that the material in the tank always experiences the same mean residence time and residence time distribution as existed during the original steady state. Hence, it is called constant RTD control. It will cease to work in a real vessel when the liquid level drops below the agitator. 

Transient experiments with inert tracers are used to determine residence time distributions. In real systems, they will be actual experiments. In theoretical studies, the experiments are mathematical and are applied to a d5mamic model of the system. 

Washout experiments can be used to measure the residence time distribution in continuous-flow systems. A good step change must be made at the reactor inlet. The concentration of tracer molecules leaving the system must be accurately measured at the outlet. If the tracer has a background concentration, it is subtracted from the experimental measurements. The flow properties of the tracer molecules must be similar to those of the reactant molecules. It is usually possible to meet these requirements in practice. The major theoretical requirement is that the inlet and outlet streams have unidirectional flows so that molecules that once enter the system stay in until they exit, never to return. Systems with unidirectional inlet and outlet streams are closed in the sense of the axial dispersion model i.e., Di = D ut = 0- See Sections 9.3.1 and 15.2.2. Most systems of chemical engineering importance are closed to a reasonable approximation. 

The use of inert tracer experiments to measure residence time distributions can be extended to systems with multiple inlets and outlets, multiple phases within the reactor, and species-dependent residence times. This discussion ignores these complications, but see Suggestions for Further Reading. ... 

This program is designed to simulate tracer experiments for residence time distributions based on a cascade of 1 to 8 tanks-in-series. An nth-order reaction can be run, and the steady-state conversion can be obtained. The important parameters to change are as follows for the tracer experiments k, CAINIT, and CAO ( = 0 for E curve, = 1 for F curve). For reaction studies, the parameters to change are n, k, CAO, and CAINIT. 

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. 

For isothermal, first-order chemical reactions, the mole balances form a system of linear equations. A non-ideal reactor can then be modeled as a collection of Lagrangian fluid elements moving independe n tly through the system. When parameterized by the amount of time it has spent in the system (i.e., its residence time), each fluid element behaves as abatch reactor. The species concentrations for such a system can be completely characterized by the inlet concentrations, the chemical rate constants, and the residence time distribution (RTD) of the reactor. The latter can be found from simple tracer experiments carried out under identical flow conditions. A brief overview of RTD theory is given below. 

In a batch sedimentation experiment, the sediment builds up gradually and the solids which are deposited in the early stages are those which are subjected to the compressive forces for the longest period of time. In the continuous thickener, on the other hand, all of the particles are retained for the same length of time with fresh particles continuously being deposited at the top of the sediment and others being removed at the same rate in the underflow, with the inventory thus remaining constant. Residence time distributions are therefore not the same in batch and continuous systems. Therefore, the value of tR calculated from equation 5.59 will be subject to some inaccuracy because of the mismatch between the models for batch and continuous operation. 

In a final RTD experiment, a sheet of dye was frozen as before and positioned in the feed channel perpendicular to the flight tip. The sheet positioned the dye evenly across the entire cross section. After the dye thawed, the extruder was operated at five rpm in extrusion mode. The experimental and numerical RTDs for this experiment are shown in Fig. 8.12, and they show the characteristic residence-time distribution for a single-screw extruder. The long peak indicates that most of the dye exits at one time. The shallow decay function indicates wall effects pulling the fluid back up the channel of the extruder, while the extended tail describes dye trapped in the Moffat eddies that greatly impede the down-channel movement of the dye at the flight corners. Moffat eddies will be discussed more next. Due to the physical limitations of the process, sampling was stopped before the tail had completely decreased to zero concentration. 

The purpose of tracer experiments is to extract information about the system in a chemical reaction engineering context, it is the mixing within the system which is of interest, as represented by the system residence time distribution. Because flow mixing is an inherently linear process, the exact form of the RTD which is recovered from a tracer response experiment should be independent both of the amount of tracer used in the test and also of the particular functional form in which the tracer was... 

The actual residence time of a reactor is measured by employing residence time distribution (RTD) experiments utilizing tracing techniques. Furthermore, several correlation forms estimating the fluid holdup can be found in the related literature. 

The study of nonideal flow and liquid holdup can be done by residence time distribution (RTD) experiments (tracing techniques) or by use of correlations derived from literature. Dining this step, physical mechanisms that are sensitive to size are investigated separately from chemical (kinetic or equilibrium) studies (Trambouze, 1990). Here, the fixed bed is... 

As predicted from the model, the residence time distribution curve shown in Fig. 3.11 exhibits the feature of perfect mixing with a certain lag time, that is, the feature of plug flow-perfect mixing flow in series. All the experiments yield the results of RTD exhibiting the same feature. 

In continuous operation, the residence time distribution in a rotating drum depends on the degree of both radial and axial dispersion. In previous work (des Boses et al., 1997), it was proposed that a particle in a distribution will have a preferred radial position, about which its actual position will be distributed, and will then experience an axial... 

If we accept the premise that the total strain is a key variable in the quality of laminar mixing, we are immediately faced with the problem that in most industrial mixers, and in processing equipment in general, different fluid particles experience different strains. This is true for both batch and continuous mixers. In the former, the different strain histories are due to the different paths the fluid particles follow in the mixer, whereas in a continuous mixer, superimposed on the different paths there is also a different residence time for every fluid particle in the mixer. To quantitatively describe the various strain histories, strain distribution functions (SDF) were defined (56), which are similar in concept to the residence time distribution functions discussed earlier. 

Continuous Mixers In continuous mixers, exiting fluid particles experience both different shear rate histories and residence times therefore they have acquired different strains. Following the considerations outlined previously and parallel to the definition of residence-time distribution function, the SDF for a continuous mixer/(y) dy is defined as the fraction of exiting flow rate that experienced a strain between y and y I dy, or it is the probability of an entering fluid particle to acquire strain y. The cumulative SDF, F(y), defined by... 

Fig. 9.12 Experimental verification of the RTD function in extruder by radioactive tracer techniques with a 44.2-mm-diameter, 24 1 L/D extruder, liquid polyester resin, and a radioactive manganese dioxide tracer Asterisk, Experiment 1 , Experiment 2 smooth curve indicates theoretical prediction. [Reprinted by permission from D. Wolf and D. H. White, Experimental Study of the Residence Time Distribution in Plasticating Screw Extruders, AIChE J., 22, 122-131 (1976).]...

---