Inlet residence time distribution

Nonreacdive substances that can be used in small concentrations and that can easily be detected by analysis are the most useful tracers. When making a test, tracer is injected at the inlet of the vessel along with the normal charge of process or carrier fluid, according to some definite time sequence. The progress of both the inlet and outlet concentrations with time is noted. Those data are converted to a residence time distribution (RTD) that tells how much time each fracdion of the charge spends in the vessel. 

Constant RTD control can be applied in reverse to startup a vessel while minimizing olf-specification materials. For this form of startup, a near steady state is first achieved with a minimum level of material and thus with minimum throughput. When the product is satisfactory, the operating level is gradually increased by lowering the discharge flow while applying Equation (14.8) to the inlet flow. The vessel Alls, the flow rate increases, but the residence time distribution is constant. 

The time that a molecule spends in a reactive system will affect its probability of reacting and the measurement, interpretation, and modeling of residence time distributions are important aspects of chemical reaction engineering. Part of the inspiration for residence time theory came from the black box analysis techniques used by electrical engineers to study circuits. These are stimulus-response or input-output methods where a system is disturbed and its response to the disturbance is measured. The measured response, when properly interpreted, is used to predict the response of the system to other inputs. For residence time measurements, an inert tracer is injected at the inlet to the reactor, and the tracer concentration is measured at the outlet. The injection is carried out in a standardized way to allow easy interpretation of the results, which can then be used to make predictions. Predictions include the dynamic response of the system to arbitrary tracer inputs. More important, however, are the predictions of the steady-state yield of reactions in continuous-flow systems. All this can be done without opening the black box. 

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. ... 

Positive Step Changes and the Cumulative Distribution. Residence time distributions can also be measured by applying a positive step change to the inlet of the reactor Cm = Cout = 0 for r<0 and C = Co for r>0. Then the outlet response, F i) = CouMICq, gives the cumulative distribution function. ... 

Chapter 14 and Section 15.2 used a unsteady-state model of a system to calculate the output response to an inlet disturbance. Equations (15.45) and (15.46) show that a dynamic model is unnecessary if the entering compound is inert or disappears according to first-order kinetics. The only needed information is the residence time distribution, and it can be determined experimentally. 

The characterization is performed by means of residence time distribution (RTD) investigation [23]. Typically, holdup is low, and therefore the mean residence time is expected to be relatively short Consequently, it is required to shorten the distance between the pulse injection and the reactor inlet. Besides, it is necessary to use specific experimental techniques with fast time response. Since it is rather difficult, in practice, to perfectly perform a Dirac pulse, a signal deconvolution between inlet and outlet signals is always required. 

One method of characterising the residence time distribution is by means of the E-curve or external-age distribution function. This defines the fraction of material in the reactor exit which has spent time between t and t -i- dt in the reactor. The response to a pulse input of tracer in the inlet flow to the reactor gives rise to an outlet response in the form of an E-curve. This is shown below in Fig. 3.20. 

In a laminar flow reactor (LFR), we assume that one-dimensional laminar flow (LF) prevails there is no mixing in the (axial) direction of flow (a characteristic of tubular flow) and also no mixing in the radial direction in a cylindrical vessel. We assume LF exists between the inlet and outlet of such a vessel, which is otherwise a closed vessel (Section 13.2.4). These and other features of LF are described in Section 2.5, and illustrated in Figure 2.5. The residence-time distribution functions E(B) and F(B) for LF are derived in Section 13.4.3, and the results are summarized in Table 13.2. 

A reactor has a residence time distribution like that of that of two equal completely mixed tanks in series. The rate equation is -dC/dt = 0.5C1-5. Inlet concentration is C0 = 1.2 lbmol/cuft and the feed rate is 10 Ibmol reactant/min. Conversion required is 95%. Find the reactor volume needed (a) assuming segregated flow (b) in a two stage CSTR. 

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. 

P 62] A Lagrangian particle tracking technique, i.e. the computation of trajectories of massless tracer particles, which allows the computation of interfacial stretching factors, was coupled to CFD simulation [47]. Some calculations concerning the residence time distribution were also performed. A constant, uniform velocity and pressure were applied at the inlet and outlet, respectively. The existence of a fully developed flow without any noticeable effect of the inlet and outlet boundaries was assured by inspection of the computed flow fields obtained in the third mixer segment for all Reynolds numbers under study. 

The influence of channels, i.e. flow-guiding internal structures, also accounts for the overall residence time distribution in the square. This will be demonstrated by the observation of particles emitted at the structure inlet. The path of such an... 

Example 7.6 Residence Time Distribution in a CST Kinetic Derivation Consider a CST of volume V and volumetric flow rate Q (depicted in the figure below). At time t — 0 we increase the inlet concentration, in volume fraction, from zero to X(0). Unlike in the previous Example, in a CST the concentration of the exiting stream at time t is identical to that in the tank and equals X(t). A simple mass balance gives... 

The following example examines the SDF in drag flow between parallel plates. In this particular flow geometry, although the shear rate is constant throughout the mixer, a rather broad SDF results because of the existence of a broad residence time distribution. Consequently, a minor component, even if distributed at the inlet over all the entering streamlines and placed in an optimal orientation, will not be uniformly mixed in the outlet stream. 

The definition of symbols is in the Table of Nomenclature. Basically SD is a number proportional to the reactor length, made dimensionless by a proper combination of thermal and reaction kinetic paramters. t is proportional to the temperature rise, made dimensionless by a combination of inlet temperature and activation energy, y and a2 are the mean and variance, respectively, of the residence-time distribution in the reactor. 

This common measure is the variance of the residence-time distribution. In the absence of reaction, a sudden change in inlet conditions will be followed by a spread-out change in outlet conditions. The spreading can be described by common statistical parameters, the mean, variance, skewness, and so on. 

The following treatment considers the effect of the residence time distribution on the size distribution of particles produced in a gas phase reactor. To do this we have to assume that the particles are produced by nucleation, either single point at the inlet of the reactor or multipoint through out the reactor, and particle growth is atom by atom with a growth rate G. Using the residence time distribution, the particle size distribution can be calculated for these two cases of nucleation [33]. 

A well-known traditional approach adopted in chemical engineering to circumvent the intrinsic difficulties in obtaining the complete velocity distribution map is the characterization of nonideal flow patterns by means of residence time distribution (RTD) experiments where typically the response of apiece of process equipment is measured due to a disturbance of the inlet concentration of a tracer. From the measured response of the system (i.e., the concentration of the tracer measured in the outlet stream of the relevant piece of process equipment) the differential residence time distribution E(t) can be obtained where E(t)dt represents... 

The space velocity in cocurrent upflow, e.g., in the froth reactor, can be controlled within large areas by the pumping rate. There is an upper velocity limit for formation of small bubbles in the glass frit, and the very high back-mixing in the monolith indicates that draining of the monolith down to the inlet area can be a problem at low velocities. The residence-time distribution in the monolith froth reactor has been studied by Patrick et al. [36] and Thulasidas et al. [37]. 

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