Residence Time Distribution RTD

If a tour group were to be shepherded by their leader from airport check-in to departure gate, they would arrive at the same time and would not be mixed up with other travellers. On the other hand, left to themselves, a few would get there quickly, others would take longer, and a number would tour the shops and arrive just in time to catch their flight. As a result the group would be well mixed with the other travellers. 

In the first situation there is a very narrow time distribution (or RTD) with little or no mixing, and in the second, a wide RTD and good mixing. 

Plug flow if the walls of a channel were perfectly lubricated, we would get plug flow. All the viscous fluid would travel at the same rate with no shearing between layers. If an extruder could operate like this, there would be no mixing. Furthermore, if a second material was added for a fixed time, it would appear at the outlet over the same time period. There would be no increase in interfacial area, i.e., no mixing. 

A comparatively simple technique used by Bigg and Middleman was to introduce a dyed fluid into a nearly empty hopper and measure light transmission through the extrudate for samples taken at regular time intervals [7]. Wolf and White used radioactive tracers [8]. 

In Chapter 3, it was stated that the ideal PFR and CSTR are the theoretical limits of fluid mixing in that they have no mixing and complete mixing, respectively. Although these two flow behaviors can be easily described, flow fields that deviate from these limits are extremely complex and become impractical to completely model. However, it is often not necessary to know the details of the entire flow field but rather only how long fluid elements reside in the reactor (i.e., the distribution of residence times). This information can be used as a diagnostic tool to ascertain flow characteristics of a particular reactor. 

In order to analyze the residence time distribution of the fluid in a reactor the following relationships have been developed. Fluid elements may require differing lengths of time to travel through the reactor. The distribution of the exit times, defined as the E(t) curve, is the residence time distribution (RTD) of the fluid. The exit concentration of a tracer species C(t) can be used to define E(t). That is  

Concentrations of tracer species using an impulse input, (a) PFR (ti = t(, + t). (b) CSTR. (c) Nonideal reactor. 

With this definition, the fraction of the exit stream that has residence time (age) between t and t + dt is  

Calculate the RTD of a perfectly mixed reactor using an impulse of n moles of a tracer. 

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Residence Time Distribution (RTD) This is established by injecting a known amount of tracer into the feed stream and monitor-... 

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. 

Maximum mixedness Exists when any molecule that enters a vessel immediately becomes associated with those molecules with which it will eventually leave the vessel. This occurs with those molecules that have the same life expectation. A state of maximum mixedness is associated with every residence time distribution (RTD). 

Residence time distribution (RTD) The time that elapses from when the element enters the vessel to when it leaves. 

The term macromixing refers to the overall mixing performance in a reactor. It is usually described by the residence time distribution (RTD). Originally introduced by Danckwerts (1958), this concept is based on a macroscopic lumped population balance. A fluid element is followed from the time at which it enters the reactor (Lagrangian viewpoint - observer moves with the fluid). The probability that the fluid element will leave the reactor after a residence time t is expressed as the RTD function. This function characterises the scale of mixedness in a reactor. 

In the design of optimal catalytic gas-Hquid reactors, hydrodynamics deserves special attention. Different flow regimes have been observed in co- and countercurrent operation. Segmented flow (often referred to as Taylor flow) with the gas bubbles having a diameter close to the tube diameter appeared to be the most advantageous as far as mass transfer and residence time distribution (RTD) is concerned. Many reviews on three-phase monolithic processes have been pubhshed [37-40]. 

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. 

Recycling to monomers, fuel oils or other valuable chemicals from the waste polymers has been attractive and sometimes the system has been commercially operated [1-4]. It has been understood that, in the thermal decomposition of polymers, the residence time distribution (RTD) of the vapor phase in the reactor has been one of the major factors in determining the products distribution and yield, since the products are usually generated as a vapor phase at a high temperature. The RTD of the vapor phase becomes more important in fluidized bed reactors where the residence time of the vapor phase is usually very short. The residence time of the vapor or gas phase has been controlled by generating a swirling flow motion in the reactor [5-8]. 

Resident Time Distribution (RTD) is widely employed in the chemical engineering industry, as an analytical tool for characterizing flow dynamics within reactor vessels. RTD provides a quantitative measure of the back-mixing with in a reactor system [2]. However the cost and time involved in building and operating a pilot- or full scale reactor for RTD analysis can be economically prohibitive. As such we have implemented a numerical RTD technique through the FLUENT (ver. 6.1) commercial CFD package. 

It is desired to compare the residence time distributions (RTD) for these cases. 

Residence-time distribution (RTD) relative times taken by different elements of fluid to flow through a vessel a spread in residence times leads to a statistical treatment, in the form of a distribution whether or not there is a spread in residence times has important implications for reactor performance. 

Consider the steady flow of fluid at a volumetric rate q through a stirred tank as a closed vessel, containing a volume V of fluid, as illustrated in Figure 13.4. We assume the flow is ideal in the form of BMF at constant density, and that no chemical reaction occurs. We wish to derive an expression for E(t) describing the residence-time distribution (RTD) for this situation. 

The general features of a PFR are outlined in Section 2.4.1, and are illustrated schematically in Figure 2.4. Residence-time distribution (RTD) functions are described in Section 13.4.2. The essential features are recapitulated as follows ... 

We focus attention in this chapter on simple, isothermal reacting systems, and on the four types BR, CSTR, PFR, and LFR for single-vessel comparisons, and on CSTR and PFR models for multiple-vessel configurations in flow systems. We use residence-time-distribution (RTD) analysis in some of the multiple-vessel situations, to illustrate some aspects of both performance and mixing. 

Some multiple-vessel configurations and consequences for design and performance are discussed previously in Section 14.4 (CSTRs in series) and in Section 15.4 (PFRs in series and in parallel). Here, we consider some additional configurations, and the residence-time distribution (RTD) for multiple-vessel configurations. 

In this chapter, we consider nonideal flow, as distinct from ideal flow (Chapter 13), of which BMF, PF, and LF are examples. By its nature, nonideal flow cannot be described exactly, but the statistical methods introduced in Chapter 13, particularly for residence time distribution (RTD), provide useful approximations both to characterize the flow and ultimately to help assess the performance of a reactor. We focus on the former here, and defer the latter to Chapter 20. However, even at this stage, it is important to realize that ignorance of the details of nonideal flow and inability to predict accurately its effect on reactor performance are major reasons for having to do physical scale-up (bench —> pilot plant - semi-works -> commercial scale) in the design of a new reactor. This is in contrast to most other types of process equipment. 

The TIS and DPF models, introduced in Chapter 19 to describe the residence time distribution (RTD) for nonideal flow, can be adapted as reactor models, once the single parameters of the models, N and Pe, (or DL), respectively, are known. As such, these are macromixing models and are unable to account for nonideal mixing behavior at the microscopic level. For example, the TIS model is based on the assumption that complete backmixing occurs within each tank. If this is not the case, as, perhaps, in a polymerization reaction that produces a viscous product, the model is incomplete. 

Residential exposure, pesticide registration requirements for, 73 549-550 Resident time distribution (RTD), in reactors, 27 355-356 Residual property, 24 659... 

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. 

Figure 1.4. Sketch of the residence time distribution (RTD) in a non-ideal reactor. 

In the CRE literature, the residence time distribution (RTD) has been shown to be a powerful tool for handling isothermal first-order reactions in arbitrary reactor geometries. (See Nauman and Buffham (1983) for a detailed introduction to RTD theory.) The basic ideas behind RTD theory can be most easily understood in a Lagrangian framework. The residence time of a fluid element is defined to be its age a as it leaves the reactor. Thus, in a PFR, the RTD function E(a) has the simple form of a delta function ... 

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