Continuous stirred tank reactor residence time distributions

FIGURE 17.1 Residence time distributions for plug flow and continuous stirred tank reactors residence time versus fiaction of the outlet stream having that residence time. This material is reproduced with permission of John Wiley Sons, Inc. from Levenspiel O. Chemical Reaction Engineering. 3rd ed. New York Wiley 1999. 

Figure 7.5 Residence time distribution function as a function of the dimensioniess reaction time for an ideai batch or continuous stirred tank reactor. CSTR, PSD, and dp represent continuous stirred tank reactor, particie size distribution function, and dimensioniess particie diameter, respectiveiy,...

Continuous stirred tank reactor Dispersion coefficient Effective diffusivity Knudsen diffusivity Residence time distribution Normalized residence time distribution... 

The particles in the latex stream leaving a continuous stirred-tank reactor (CSTR) would have a broad distribution of residence times in the reactor. This age distribution, given by Equation 5, comes about because of the rapid mixing of the feed stream with the contents of the stirred reactor. 

Mixing Models. The assumption of perfect or micro-mixing is frequently made for continuous stirred tank reactors and the ensuing reactor model used for design and optimization studies. For well-agitated reactors with moderate reaction rates and for reaction media which are not too viscous, this model is often justified. Micro-mixed reactors are characterized by uniform concentrations throughout the reactor and an exponential residence time distribution function. 

For a few highly idealized systems, the residence time distribution function can be determined a priori without the need for experimental work. These systems include our two idealized flow reactors—the plug flow reactor and the continuous stirred tank reactor—and the tubular laminar flow reactor. The F(t) and response curves for each of these three types of well-characterized flow patterns will be developed in turn. 

In Section 11.1.3.2 we considered a model of reactor performance in which the actual reactor is simulated by a cascade of equal-sized continuous stirred tank reactors operating in series. We indicated how the residence time distribution function can be used to determine the number of tanks that best model the tracer measurement data. Once this parameter has been determined, the techniques discussed in Section 8.3.2 can be used to determine the effluent conversion level. 

The residence time distribution for a continuous stirred tank reactor may be represented in terms of the F(t) curve as... 

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 mean residence time for a continuous stirred-tank reactor of volume Vc may be defined as Vc/v in just the same way as for a tubular reactor. However, in a homogeneous reaction mixture, it is not possible to identify particular elements of fluid as having any particular residence time, because there is complete mixing on a molecular scale. If the feed consists of a suspension of particles, it may be shown that, although there is a distribution of residence times among the individual particles, the mean residence time does correspond to Vc v if the system is ideally mixed. 

Continuous Stirred Tank Reactors. Biesenberger (8) solved for the MWD with condensation polymerization in a CSTR, analogous to the treatment Denbigh (14) provided for the other two mechanisms. In this case, the variable residence time distribution leads to an extremely broad MWD with even the maximum weight fraction at the lowest molecular weight (monomer). The dispersion index approaches infinity as the condensation is driven to completion in a stirred tank reactor. A sequential analytical solution of the algebraic equations was obtained with a numerical evaluation of the consecutive equations. 

The residence time distribution (RTD), also referred to as the distribution of ages, is based on the assumption that each element traveling through the column takes a different route and will therefore have a different residence time. Different methods are developed to determine the RTD in a module or in a reactor [190]. The RTD of a chromatographic column is defined by a function E (Figure 3.20), such that E dt is the fraction of material in the exit stream with an age between t and f - - dt. The -curve lies between the extremes of plug flow and continuously stirred tank reactor. The surface below the curve between f = 0 and t = oo has to be equal to unity E t) dt = 1, because all elements that enter the module must also exit the module. 

To complete the model of lime dissolution, a discretized particle size distribution is defined, with [x,] being the molar concentration of size fraction i with radius For an ideal continuous stirred tank reactor (CSTR) with residence time T the equation for updating the concentrations of the solid lime size fractions is... 

The reactor in which chemical reactions lake place is fhe mosl imporlanl piece of equipmenl in each chemical planl. A variety of reactors are used in induslry, bul all of Ihem can be assigned to cerlain basic types or a combination of fhese ideal reactors [53] (1) bafch slirred-lank reactor, (2) continuous slirred-lank reactor, and (3) lubular reactor. The ideal slirred-lank bafch reactor is characterized by complete mixing, while in the ideal tubular reactor, plug flow is assumed. In contrast to the stirred-tank batch reactor with well-defined residence time, the continuous stirred-tank reactor has a very broad residence-time distribution. In... 

In the third case, the residence time distribution (RTD) of the solid becomes an important factor. Though the liquid RTD will again approximate closely to the perfectly mixed condition required for a continuous stirred tank reactor model except on a very large scale, generally the solid will not. Therefore the actual solid RTD must be determined as set out in Chapter 16 for a satisfactory reactor design to be made. 

The simplest kinetic reactor model is the CSTR (continuous-stirred-tank reactor), in which the contents are assumed to be perfectly mixed. Thus, the composition and the temperature are assumed to be uniform throughout the reactor volume and equal to the composition and temperature of the reactor effluent However, the fluid elements do not all have the same residence time in the reactor. Rather, there is a residence-time distribution. It is not difficult to provide perfect mixing of the fluid contents of a vessel to approximate a CSTR model in a commercial reactor. A perfectly mixed reactor is used often for homogeneous liquid-phase reactions. The CSTR model is adequate for this case, provided that the reaction takes place under adiabatic or isothermal conditions. Although calculations only involve algebraic equations, they may be nonlinear. Accordingly, a possible complication that must be considered is the existence of multiple solutions, two or more of which may be stable, as shown in the next example. 

Continuous stirred-tank reactors (CSTRs) are used for large productions of a reduced number of polymer grades. Coordination catalysts are used in the production of LLDPE by solution polymerization (Dowlex, DSM Compact process [29]), of HDPE in slurry (Mitsui CX-process [30]) and of polypropylene in stirred bed gas phase reactors (BP process [22], Novolen process [31]). LDPE and ethylene-vinyl acetate copolymers (EVA) are produced by free-radical polymerization in bulk in a continuous autoclave reactor [30]. A substantial fraction of the SBR used for tires is produced by coagulating the SBR latex produced by emulsion polymerization in a battery of about 10 CSTRs in series [32]. The CSTRs are characterized by a broad residence time distribution, which affects to product properties. For example, latexes with narrow particle size distribution cannot be produced in CSTRs. 

There are two common types of continuous reactors continuous stirred tank reactors (CSTRs) (53), and plug flow reactors (PFRs). CSTRs are simply large tanks that are ideally well-mixed (such that the emulsion composition is uniform throughout the entire reactor volume) in which the polymerisation takes place. CSTRs are operated at a constant overall conversion. CSTRs are often used in series or trains to build up conversion incrementally. Styrene-butadiene rubber has been produced in this manner. Not all latex particles spend the same amount of time polymerising in a CSTR. Some particles exit sooner than others, producing a distribution of particle residence times, diameters and compositions. 

Details are given of a non-steady-state operation for controlling latex particle size distribution by using a continuous emulsion polymerisation of vinyl acetate. The experiment was conducted in a continuously stirred tank reactor under conditions below the critical micelle concentration of the emulsifier. The mean residence time was switched alternately between two values in the nonsteady-state operation to induce oscillations in monomer conversion in time. The effect of the switching operation on particle size distribution is discussed. 13 refs. 

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