Stirred tank inlets/outlets

There are two important types of ideal, continuous-flow reactors the piston flow reactor or PFR, and the continuous-flow stirred tank reactor or CSTR. They behave very diflerently with respect to conversion and selectivity. The piston flow reactor behaves exactly like a batch reactor. It is usually visualized as a long tube as illustrated in Figure 1.3. Suppose a small clump of material enters the reactor at time t = 0 and flows from the inlet to the outlet. We suppose that there is no mixing between this particular clump and other clumps that entered at different times. The clump stays together and ages and reacts as it flows down the tube. After it has been in the piston flow reactor for t seconds, the clump will have the same composition as if it had been in a batch reactor for t seconds. The composition of a batch reactor varies with time. The composition of a small clump flowing through a piston flow reactor varies with time in the same way. It also varies with position down the tube. The relationship between time and position is... 

Chapter 2 treated multiple and complex reactions in an ideal batch reactor. The reactor was ideal in the sense that mixing was assumed to be instantaneous and complete throughout the vessel. Real batch reactors will approximate ideal behavior when the characteristic time for mixing is short compared with the reaction half-life. Industrial batch reactors have inlet and outlet ports and an agitation system. The same hardware can be converted to continuous operation. To do this, just feed and discharge continuously. If the reactor is well mixed in the batch mode, it is likely to remain so in the continuous mode, as least for the same reaction. The assumption of instantaneous and perfect mixing remains a reasonable approximation, but the batch reactor has become a continuous-flow stirred tank. 

Perfectly mixed stirred tank reactors have no spatial variations in composition or physical properties within the reactor or in the exit from it. Everything inside the system is uniform except at the very entrance. Molecules experience a step change in environment immediately upon entering. A perfectly mixed CSTR has only two environments one at the inlet and one inside the reactor and at the outlet. These environments are specifled by a set of compositions and operating conditions that have only two values either bi ,..., Ti or Uout, bout, , Pout, Tout- When the reactor is at a steady state, the inlet and outlet properties are related by algebraic equations. The piston flow reactors and real flow reactors show a more gradual change from inlet to outlet, and the inlet and outlet properties are related by differential equations. 

The fractional tubularity model has been used to fit residence time data in flui-dized-bed reactors. It is also appropriate for modeling real stirred tank reactors that have small amounts of dead time, as would perhaps be caused by the inlet and outlet piping. It is not well suited to modeling systems that are nearly in piston flow since such systems rarely have sharp first appearance times. 

One of the simplest models for convective mass transfer is the stirred tank model, also called the continuously stirred tank reactor (CSTR) or the mixing tank. The model is shown schematically in Figure 2. As shown in the figure, a fluid stream enters a filled vessel that is stirred with an impeller, then exits the vessel through an outlet port. The stirred tank represents an idealization of mixing behavior in convective systems, in which incoming fluid streams are instantly and completely mixed with the system contents. To illustrate this, consider the case in which the inlet stream contains a water-miscible blue dye and the tank is initially filled with pure water. At time zero, the inlet valve is opened, allowing the dye to enter the... 

Figure 2 The stirred tank, a simple model for convective mass transfer. The liquid in the tank is characterized by its volume (V), density (p), and the concentrations of the components (CA). Liquid enters through the inlet stream at a flow rate Qm and concentration CA0. Liquid exits through the outlet stream at volumetric flow rate Qml and concentration identical to that in the tank (CA). The concentration profile below the tank shows the step change in concentration encountered as the inlet stream is mixed with tank contents of lower concentration.

The responses of a single ideal stirred tank reactor to ideal step and pulse inputs are shown in Figure 11.4. Note that any change in the reactor inlet stream shows up immediately at the reactor outlet in these systems. This fact is used to advantage in the design of automatic control systems for stirred tank reactors. 

The classical CRE model for a perfectly macromixed reactor is the continuous stirred tank reactor (CSTR). Thus, to fix our ideas, let us consider a stirred tank with two inlet streams and one outlet stream. The CFD model for this system would compute the flow field inside of the stirred tank given the inlet flow velocities and concentrations, the geometry of the reactor (including baffles and impellers), and the angular velocity of the stirrer. For liquid-phase flow with uniform density, the CFD model for the flow field can be developed independently from the mixing model. For simplicity, we will consider this case. Nevertheless, the SGS models are easily extendable to flows with variable density. 

Fig. 45.4 Left Schematic diagram of a continuous stirred tank reactor with gas and liquid inlet and outlet. Right A Rushton-type turbine (adapted from [3]).

C02 is to be absorbed by 2 N K2C03 in a stirred tank. The pressure is 7r = 2 atm, inlet partial pressure is 0.7 atm and outlet is to be 0.07. The tank is charged with the solution, then the gas is charged at variable rate to maintain the desired outlet partial pressure. The residence time is to be found as a function of the fractional conversion, f. 

Figure 3-1 The continuous stirred tank reactor (CSTR) of volume V with inlet molar flow rate Fja and outlet molar flow rate F ...

Two dynamic alternatives to the static approach have been used in HO calibration and measurement. In the CSTR (continuously stirred tank reactor) approach, air containing the tracer or tracers flows into the reactor to balance the bulk flow out to the HO measuring devices, and the contents are stirred by a fan or other means. The HO chemical tracer is measured in the inlet flow to obtain [T]() and in the outlet flow to obtain [T], Mass balance requires... 

We have seen that this model of the bubbling bed is essentially the same as a stirred tank when the two sources of the feed are recognized. These are the fraction (1 - /3) that comes with the gas feed at the bottom of the bed and the fraction /3 in the bubbles which feeds the reactor at all levels and from a diminishing concentration difference. The latter, when referred to the inlet difference c0 - cp, delivers a fraction 1 - exp(- Tr). Thus the total feed minus outlet is (1 - j8) + >3(1 - exp(- Tr)) (c0 — cp) = 1 - /3 exp(-7r) (c0 — cp) and this is what is equated to the reaction rate, (kH0IU)cp. 

On the basis of the considered macroscopic flow pattern, the dominant circulation flows (/ c and Fc/2) subdivide the reactor into three parallel levels, where each level is then divided into Nc/3 equally sized compartments of equal volume Vc = Vr/Nc. Every compartment is modeled as a nonstationary ideal continuous stirred tank reactor, with a main inlet and outlet flow, which connects the given compartment with adjacent compartments on the same level, and secondary exchange flow rates accounting for the turbulent mixing with adjacent compartments laying on the upper and/or lower level (Fig. 7.3). 

Physically, the semibatch reactor looks similar to a batch reactor or a CSTR. Reaction occurs in a stirred tank, with the following assumptions (1) the contents of the tank are well mixed, and (2) there are no inlet or outlet effects caused by the continuous stream. 

The discontinuous stirred tank reactor represents one of the most traditional reactor configurations for enzymatic reactions. It consists of a stirred tank where the enzyme, substrates, and cofactors are added at the beginning of the operation with no inlet and/or outlet stream during the reaction time. This type of reactor is usually considered to present an ideal hydrodynamic behavior therefore, the reactor is supposed to be completely mixed and the concentration of all... 

Various laboratory reactors have been described in the literature [3, 11-13]. The most simple one is the packed bed tubular reactor where an amount of catalyst is held between plugs of quartz wool or wire mesh screens which the reactants pass through, preferably in plug flow . For low conversions this reactor is operated in the differential mode, for high conversions over the catalyst bed in the integral mode. By recirculation of the reactor exit flow one can approach a well mixed reactor system, the continuous flow stirred tank reactor (CSTR). This can be done either externally or internally [11, 12]. Without inlet and outlet feed, this reactor becomes a batch reactor, where the composition changes as a function of time (transient operation), in contrast with the steady state operation of the continuous flow reactors. 

FIGURE 22 Cell (Kampers et al., 1989) that functions as a continuously stirred tank reactor (a) sample holder (b) heater/cooler cylinder (c) hollow tubes for coolant and electrical wires (d) reservoir for coolant liquid (e) thermocouple (f) flange enclosing in situ chamber (g) O-ring (h) X-ray transparent window (i) gas inlet/outlet. Reprinted with permission from J.A. van Bokhoven, T. Ressler, F.M.F. de Groot, and G. Knopp-Gericke, in In situ Spectroscopy of Catalysts , B.M. Weckhuysen, Ed., published by American Scientific Publishers (2004). Copyright American Scientific Publishers. 

Consider an isothermal stirred-tank adsorber under equilibrium-controlled conditions, r is the bulk porosity (volumetric fraction of the adsorber filled with fluid phase), r)p is the porosity of the adsorbent. Ft > 0 is the amount of component i added to the adsorber in the inlet stream, and Wi > 0 is the corresponding amount removed in the outlet stream both Fi and IF, represent amounts scaled with respect to the adsorber volume. 

A liquid-phase chemical reaction A B takes place in a well-stirred tank. The concentration of A in the feed is Cao (mol/m ), and that in the tank and outlet stream is Ca (mol/m ). Neither concentration varies with time. The volume of the tank contents is K(m ) and the volumetric flow rate of the inlet and outlet streams is v (m /s). The reaction rate (the rate at which A is consumed by reaction in the tank) is given by the expression... 

Interpretation of reaction rates using stirred flow-through reactors is more straightforward than for batch reactors because solution chemistry remains constant during dissolution. In a continuously stirred tank reactor (CSTR) or a mixed flow reactor (Rimstidt and Dove, 1986) a mineral sample is placed in a reactor of volume Rq and fluid is pumped through at flow rate Q (L T ). Fluid is stirred by a propeller or by agitation. The rate of reaction, r (molm s i), is calculated from the inlet (q) and outlet concentrations (cq) of a component released during dissolution of the mineral ... 

We turn now to consider the principal types of reactors and derive a set of equations for each that will describe the transformation 5 of the state of the feed into the state of the product. The continuous flow stirred tank reactor is one of the simplest in basic design and is widely used in chemical industry. Basically it consists in a vessel of volume V furnished with one or more inlets, an outlet, a means of cooling and a stirrer which keeps its composition and temperature essentially uniform. We shall assume that there is complete mixing on the molecular scale. It would be possible to treat of other cases following the work of Danckwerts (1958) and Zweitering (1959), but the corresponding transformation is much less wieldy. If the reactants flow in and out at a constant rate q, the mean residence time T/g is known as the holding time of the reactor. 

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