TS-CSTR

The interpretation of TS-CSTR data in integral form does not come into consideration since that reactor makes rates available directly, without the necessity of taking slopes from surfaces. Integral methods can be used too, since reaction is taking place at isothermal conditions. 

Although the TS mode of operation does not require isothermal or steady-state conditions, it is assumed that the reaction is at all times in steady state with respect to certain steps in the reaction. For example, in catalytic TS-PFR operation, it is taken that the adsorption/desorption steady state is achieved much mare rapidly than the time scale involved in the temperature scanning procedure. In the TS-CSTR we assume this, as well as the fact that complete mixing of reactor contents takes place on a time scale much shorter than the temperature ramping. Moreover, although there may be temperature differences and heat flows between various components of the reactor, of the catalyst, and of the reactants, these should not be flow-velocity-dependent, nor should there be any flow-velocity-dependent diffusion effects. 

The basic TS mode of operation involves experiments, each consisting of a number of runs. Each run consists of operating the reactor over a period of time while the temperature of the feed, and usually of the reactor surroundings, is varied in some way. During each run, frequent (continuous if possible) measurements of temperature and conversion are made at the outlet conditions, i.e. of product drawn off from a TS-BR, or of product exiting a TS-PFR or TS-CSTR. Rates will later be calculated from this raw data obtained at the exit conditions present at the moment of sampling. 

As it is with all TS techniques, rate data acquisition using a TS-PFR can be very fast and a vast amount of data can be obtained from a single experiment. Unfortunately, in the TS-PFR rates cannot be calculated in real time, as was the case with the TS-BR and will be the case with the TS-CSTR. Instead, rate data is obtained after all the readings from the several runs of a TS-PFR experiment are available. This post-experiment processing of the raw data will, however, produce the same X-r-T triplets as we discussed above. The triplets will be available over the whole range of X-T conditions covered by the experiment, just as they were for the TS-BR. 

The operation and description of a temperature scanning continuously stirred tank reactor (TS-CSTR) is, in principle, much simpler than for the TS-PFR. It turns out that rates can be calculated from each individual point in each run, and that flow rates and temperature ramping do not need the same careful control as the TS-PFR. Nevertheless, the operation of die reactor should approach the perfectly mixed condition very closely. Although in practice it may be difficult to make the necessary physical arrangements for complete and instantaneous mixing within the reactor, as with other TS reactor types there are verification procedures that will reveal if proper operating conditions are not being met. 

As in the TS-PFR, volume expansion plays an important role. It is related to inlet and outlet flow rates in a rather more complicated way than might be supposed If the reactor were in steady state then we would simply have f = byfb- However, in the nonsteady-state case of the TS-CSTR, 8y itself may be changing over time, and this causes an additional effect on the outlet flow rate. 

It is interesting, and at first perhaps surprising, to have both clock time t and space time t appear in equation 5.28 since they measure very different aspects of time. Each of the two terms in equation 5.28 does, however, have the same units (moles/(liter-sec)), and the interpretation of the two terms given above suggests why it is in fact quite reasonable to have a x -term and a t-term in this case. Unlike in the case of the TS-PFR, the clock time and space time cannot be uncoupled in the TS-CSTR. 

When we solve equation 5.28 for dX/dt we obtain the following rate equation for a TS-CSTR system ... 

So far we have been considering temperature ramping only, with flow rates held constant. In this section we consider the possibility of varying the flow rate during a run. The TS-CSTR turns out to be very simple to deal with, with marvelous possibilities for interactive control. The TS-PFR, as usual, requires much more careful consideration. In both the plug flow and CSTR reactors, flow scanning can be used alone or in combination with temperature scanning. 

Equations 5.13 to 5.18, used to calculate rates in the TS-CSTR, and equation 5.24, used to update the calculation of 5v, all hold instantaneously whatever the current values of x, X, 5v, and dX/dt happen to be. Thus rate calculations for the TS-CSTR can proceed exactly as before, regardless of any variation in flow rates. It follows that the operator has complete freedom to ramp both the temperature and the flow rate of the TS-CSTR in any way that seems desirable. 

One simple operating mode would be to imitate the up-down ramping mode described above fix the TS-PFR i.e. ramp the temperature linearly upwards, then change the flow rate, then ramp linearly downwards, all the while collecting X-T information. Doing this for several runs with different combinations of flow rates would allow good coverage of the X-T plane in a TS-CSTR experiment. 

A set of conversion vs. clock time data obtained by changing both flow rate and temperature ramping in each of ten runs of a TS-CSTR. The temperature ramps used are those shown in Figure 5.23 while flow rate changes are shown in Figure 5.24... 

A set of arbitrary broken linear ramping schemes, one per run of a TS-CSTR whose output conversions are shown in Figure 5.22. A little thought will lead to the identification of specific temperature trajectories shown here with corresponding conversion trajectories in Figure 5.22. 

Various broken flow ramping rates for the several TS-CSTR runs reported in Figure 5.22. In each case the flow rate was varied continuously from time zero up to the break, at which point the ramping rate was changed... 

The situation in the TS-CSTR is similar, with the added concern that recirculation through the bed of solids and gas phase mixing must be adequate at all temperature ramping rates to maintain an instantaneous steady state with the catalyst surface. A similar requirement governs the TS-BR. 

Schematic of a three-way liquid phase reactor setup. The setup can be operated as a TS-PFR in the configuration shown or converted to a TS-CSTR or a TS-BR by replacing the reactor coil in the thermostat with a stirred vessel.

The relationship between conversion and conductivity developed above was used to interpret data from the CSTR As described in Chapter 5, in interpreting data from a CSTR we must take into account the unsteady-state reaction conditions that prevail as temperature is ramped. Even for the case of zero volume expansion, the design equation pertinent to TS-CSTR operation has to account for the constantly changing operating conditions ... 

Notice that, in the case of the TS-CSTR, the calculation of the derivative dX/dt cannot be done in real-time due to noise in the measurement of T, and consequently in the calculated values of X. This problem is evident in Figure 11.17 where the original T, data is shown as a function of time. Figure 11.18 shows the consequent noise in the conversion vs. time plot. Slopes taken point-by-point from such data amplify this uncertainty and are not acceptable for further calculations. To deal with this we need to filter all the data, after the experiment is completed, using a simple 1-dimensional filter. A moving window filter was used in this work. 

Instantaneous conductivity as measured at the outlet of the TS-CSTR during temperature ramping. 

Rate of change of conversion with clock time as afunction ofclock time. This calculated value is necessary to extract rate constants from TS-CSTR data, as described above. 

TS-CSTR conversion data from Figure 11.18 remapped in the reaction phase plane. 

Arrhenius plot of rate constants extracted from TS-CSTR data as temperature was ramped during a single run. The number of points available is such that the experimental data produces the almost-continuous line shown. The fitted Arrhenius line is shown as a solid line. 

The essential components of a TS-PFR and of a TS-CSTR are similar to those of the corresponding PFR and CSTR reactors in their traditional configuration. In fact, by applying a lot of manual operation one could, in principle, operate a traditional PFR or CSTR as a TSR. That would be missing a critical advantage of the TSR. 

Components of TS-PFR and TS-CSTR reactors requiring automation, control and data logging. 

The batch reactor (BR) is distinct from the PFR and CSTR, which are steady state reactors, in that it is a transient reactor and in both its conventional and its TSR configuration involves a different operating procedure for gathering data. The temperature scanning stream swept reactor (TS-SSR), mentioned in Chapter 5, also requires a modified procedure since it is both a flow and a batch reactor at die same time. Both the TS-SSR and the TS-BR will be discussed separately from the TS-PFR and TS-CSTR. 

The component modules of a TS-PFR or TS-CSTR flow reactor are shown in Figure 13.1. Their functions in the overall configuration are ... 

The required modules for both the TS-PFR and the TS-CSTR are identical in function if not in configuration. The major differences are introduced if the TS-CSTR is to be operated in the joystick mode, as described in Chapter 5. In that case the control of feed flows must be done using a device offering instant response to command inputs. This is generally not possible with standard flow-meters and additional thought must be given to the selection of flow-control devices. 

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