Space time reactor

Figure A3.14.16. Spatiotemporal complexity in a Couette reactor space-time plots showing the variation of...

Using Equation 8-154 for the same reactor space time and volume gives... 

Heat transfer problems become more severe as reaction rates are increased and water-to-monomer ratios are reduced. In addition, as reactor sizes are increased for improved process economics, the amount of wall heat transfer surface area per unit volume will drop and result in a lower reactor space-time yield. 

Figure 5.75. The reaction rate of the second reaction step exhibits a maximum, as a function of reactor space time.

Although the concept of mean residence time is easily visualized in terms of the average time necessary to cover the distance between reactor inlet and outlet, it is not the most fundamental characteristic time parameter for purposes of reactor design. A more useful concept is that of the reactor space time. For continuous flow reactors the space time (t) is defined as the ratio of the reactor volume (VR) to a characteristic volumetric flow rate of fluid (Y). 

This value is considerably less than the reactor space time and differs from it by 38%. 

Unlike the situation in the PFR, there is always a simple relationship between the mean residence time and the reactor space time for a CSTR. Since one normally associates a liquid feed stream with these reactors, volumetric expansion effects are usually negligible (SA = 0). 

In this situation the mean residence time and the reactor space time become identical. 

VR/% is just the reactor space time t. Hence, for this case,... 

If desired, the last equation can also be written in terms of the reactor space time for the ith reactor as... 

In this case equation 8.3.45 can be solved for the reactor space time directly. 

In this case there are two intermediate unspecified reactant concentrations instead of just the single intermediate concentration encountered in Case II. At least one of these concentrations must be determined if one is to be able to appropriately size the reactors. In principle one may follow the procedure used in Case II where the design equations for each CSTR are written and the reactor space times then equated. This procedure gives three equations and three unknowns (VRl9 fBl, and fB2). Thus, for the first reactor,... 

Table 8.1 summarizes the fundamental design relationships for the various types of ideal reactors in terms of equations for reactor space times and mean residence times. The equations are given in terms of both the general rate expression and nth-order kinetics. 

As we stressed earlier, the reactor space time is the independent variable at the control of the reactor designer. This parameter is more meaningful than the mean residence time in the reactor. 

If one is interested in designing a reactor for maleic anhydride (C4H203) production, determine the reactor space time for a PFR that maximizes the concentration of this species in the effluent. Start by deriving equations for PB, PM, and Pcq2 as functions of the space time. At 350 °C, the values of the rate constants are ... 

This value corresponds to a reactor space time given by... 

Nonetheless, this reaction is certainly not at the most profitable edge, as the reaction time even in the microreactor is ultimately not short, still on the order of 1 min, and the reactor load is further limited by dissolubility of the reactants. Both limit the reactor space-time yield and thus decrease the productivity so that the following conclusions do not at all comprise a best-case scenario. 

Note that, in a laminar-flow tubular reactor, the material on the reactor centre line has the highest velocity, this being exactly twice the average velocity, Q/A, for the whole reactor. This means that, following any tracer test, no response will be observed until the elapsed time exceeds one half of the reactor space time or mean residence time. The following values for 0 and F(0) emphasise the form of the cumulative RTD and the fact that, even up to 10 residence times after a tracer impulse test, 0.25% of the tracer will not have been eluted from the system. 

The Homogeneous Catalytic Reaction. Consider the elementary reaction A + B —= kCpjC with k = 0.4 liter/mol min For the following feed and reactor space time... 

Figure 2. Influence of temperature on reactor space time for 70% conversion of an aqueous solution of cobalt acetate (1% Co2+) activated carbon as promoter, 280 atm, CO H2...

In the design of upflow, three phase bubble column reactors, it is important that the catalyst remains well distributed throughout the bed, or reactor space time yields will suffer. The solid concentration profiles of 2.5, 50 and 100 ym silica and iron oxide particles in water and organic solutions were measured in a 12.7 cm ID bubble column to determine what conditions gave satisfactory solids suspension. These results were compared against the theoretical mean solid settling velocity and the sedimentation diffusion models. Discrepancies between the data and models are discussed. The implications for the design of the reactors for the slurry phase Fischer-Tropsch synthesis are reviewed. 

In these equations the Damkohler numbers Dai and Da2 represent the ratios of reactor space time to the characteristic time for deposition on the reactor wall and on the wafers, respectively. 

The last assumption is referred to as the quasi-steady-state assumption. The fraction of the bed which is poisoned is a function of time only and not of bed length, reactor space time, or the concentration of the reactant A external to the pellets. At any given time the bed activity will be constant, and only one concentration of the poison precursor species S will exist in the bed. Such a situation will be more likely to occur when deactivation rates are low compared to reaction rates. Under this condition S will spread evenly throughout the bed. Within particles, however, concentration gradients of S may still exist depending on the poisoning mechanism and the pore and pellet properties. 

At constant pressure and granted ideal plug flow, the behavior of a tubular reactor at steady state is mathematically analogous to that of a batch reactor A volume element of the reaction mixture has no means of knowing whether it is suspended tea bag-style in a batch reactor or rides elevator-style through a tubular reactor being exposed to the same conditions it behaves in the same way in both cases. As in a batch reactor, what is measured directly are concentrations—here in the effluent—and a finite-difference approximation is needed to obtain the rate from experiments with different reactor space times and otherwise identical conditions. For a reaction without fluid-density variation ... 

A guideline for choosing a suitable method is to avoid approximations as much as possible. Thus, plots of concentration, or a function of concentrations, versus time or reactor space time are preferred for evaluation of experiments with batch, tubular, and differential recycle reactors, in which concentrations are directly measured and rates can only be obtained by a finite-difference approximation (see eqns 3.1, 3.2, 3.5, 3.6, and 3.8). On the other hand, plots of the rate, or a function of the rate, versus concentration or a function of concentrations serve equally well for evaluation of results from CSTRs or differential reactors without recycle (gradientless reactors), where concentrations and rate are related to one another by algebraic equations that involve no approximations (see eqns 3.3, 3.4, or 3.7). 

For tubular reactors and reactions with no fluid-density variation, the reactor space time, t = VIV, takes the place of the actual time, t. 

If fluid density does not vary with conversion, use same plots as for constant-volume batch, with reactor space time t substituted for time t. 

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