Tubular reactors space time

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 flow method that has been briefly discussed sometimes offers special advantages in kinetic studies. The basic equations for flow systems with no mixing may be derived as follows let us consider a tubular reactor space of constant cross-sectional area A as shown in Fig. 7.4 with a steady flow of u of a reaction mixture expressed as volume per unit time. Now we will select a small cylindrical volume unit dV such that the concentration of component i entering the unit is C(- and the concentration leaving the unit is C,- + dC-,. Within the volume unit, the component is changing in concentration due to chemical reaction with a rate equal to r(. This rate is of the form of the familiar chemical rate equation and is a function of the rate constants of all reactions involving the component i... 

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. 

For tubular reactors, the same procedure can be used with reactor space time t substituted for time t. 

The condition expressed by the Bodenstein approximation rx = 0 is often misleadingly called a steady state. It is not. It is not a time-independent state, only a state in which a specific variation with time (or reactor space time) is small compared with the others. In fact, some older textbooks applied what they called the steady-state approximation to batch reactions in order to derive the time dependence of the concentrations, unwittingly leading the incorrect presumption of a steady state ad absurdum. And a continuous stirred-tank or tubular reactor may, and usually does, come to a true steady state, even if the Bodenstein approximation is and remains inapplicable. [The approximation compares process rates r, it is irrelevant for its validity whether or not the reactor comes to a steady state, that is, whether the rates of change, dC /dr, become zero.]... 

Consider the problem of predicting how the concentrations of species A, B, and C in the effluent from a tubular reactor depend on the reactor space time when the values of fc, 2 and are 0.20,0.09, and 0.04 s , respectively. Prepare plots of the concentrations of each species for space times from 0 to 20 s. In addition, prepare a plot of the yield of species B per mole of A reacted [Cg/(C o — C )] as a function of the space time. 

Although fluidized sand or alumina can also be used in the jacket of these somewhat larger reactors, the size makes the jacket design a problem in itself, hence these reactors are seldom used. An advantage of the jacketed reactor is that several—usually four—parallel tubes can be placed in the same jacket. These must be operated at the same temperature, but otherwise all four tubes can have different conditions if needed. This type of arrangement saves time and space in long-lasting catalyst life studies. Jacketed tubular reactors come close, but still cannot reproduce industrial conditions as needed for reliable scale-up. Thermosiphon reactors can be used on all but the most exothermic and fast reactions. 

The terms space time and space velocity are antiques of petroleum refining, but have some utility in this example. The space time is defined as F/2, , which is what t would be if the fluid remained at its inlet density. The space time in a tubular reactor with constant cross section is [L/m, ]. The space velocity is the inverse of the space time. The mean residence time, F, is VpjiQp) where p is the average density and pQ is a constant (because the mass flow is constant) that can be evaluated at any point in the reactor. The mean residence time ranges from the space time to two-thirds the space time in a gas-phase tubular reactor when the gas obeys the ideal gas law. 

For a CSTR equal in volume to the tubular reactor, one moves along a line of constant kCB0T in Figure 8.16 in order to determine the conversions accomplished in cascades composed of different numbers of reactors but with the same overall space time. The intersection of the line/cCg0T = 19.6 and the curve for N = 1 gives fB = 0.80. 

At a given temperature the parameters k, KM, and Kx are constants. KM is known as a Mi-chaelis constant and K1 as an inhibition constant. S and Px are the concentrations of reactant S and product Pl9 respectively. What effective space time for a tubular reactor will be required to obtain 80% conversion of the lactose at 40 °C where KM = 0.0528M, Kx = 0.0054M and k = 5.53 moles/(liter-min). The initial lactose concentration may be taken as 0.149M. 

Quite new ideas for the reactor design of aqueous multiphase fluid/fluid reactions have been reported by researchers from Oxeno. In packed tubular reactors and under unconventional reaction conditions they observed very high space-time yields which increased the rate compared with conventional operation by a factor of 10 due to a combination of mass transfer area and kinetics [29]. Thus the old question of aqueous-biphase hydroformylation "Where does the reaction takes place " - i.e., at the interphase or the bulk of the liquid phase [23,56h] - is again questionable, at least under the conditions (packed tubular reactors, other hydrodynamic conditions, in mini plants, and in the unusual,and costly presence of ethylene glycol) and not in harsh industrial operation. The considerable reduction of the laminar boundary layer in highly loaded packed tubular reactors increases the mass transfer coefficients, thus Oxeno claim the successful hydroformylation of 1-octene [25a,26,29c,49a,49e,58d,58f], The search for a new reactor design may also include operation in microreactors [59]. 

Different approaches to overcome the discussed limitations have been published [152,153,177]. Wiese et al. reported that space-time yields increased by a factor of ten when using a packed tubular reactor and altered operating conditions compared to those in a conventional stirred tank reactor [ 176]. 

The space velocity for a given conversion is often used as a ready measure of the performance of a reactor. The use of equation 1.25 to calculate reaction time, as if for a batch reactor, is not to be recommended as normal practice it can be equated to VJv only if there is no change in volume. Further, the method of using reaction time is a blind alley in the sense that it has to be abandoned when the theory of tubular reactors is extended to take into account longitudinal and radial dispersion and other departures from the plug flow hypothesis which are important in the design of catalytic tubular reactors (Chapter 3, Section 3.6.1)... 

Different problems are modeled by two-point boundary value differential equations in which the values of the state variables are predetermined at both endpoints of the independent variable. These endpoints may involve a starting and ending time for a time-dependent process or for a space-dependent process, the boundary conditions may apply at the entrance and at the exit of a tubular reactor, or at the beginning and end of a counter-current process, or they may involve parameters of a distributed process with recycle, etc. Boundary value problems (BVPs) are treated in Chapter 5. 

The tubular reactor was divided into three sections of 54 ft, 54 ft and 22 ft to allow sampling at different space times or conversions. 

Figure 13. Conversion vs. space time for the tubular reactor...

Clearly, the space-time, t, in the ideal tubular reactor is the same as the residence time in the batch reactor only if volume changes are neglectable. This is easy to see from Equation (3.4.2) by substituting C,-v for F,- and recalling that for volume changes... 

The space time is the time necessary to process one reactor volume of fluid based on entrance conditions. For example, consider the tubular reactor shown in Figure 2-10, which is 20 m long and 0.2 in volume. The dashed line in Figure 2-10 represents 0.2 m of fluid directly upstream of the reactor. The time it takes for this fluid to enter the reactor completely is the space time. It is also called the holding time or mean residence time. 

An alternative to filling or coating with a catalyst layer the microcharmels, with the related problems of avoiding maldistribution, which leads to a broad residence time distribution (RTD), is to create the microchannels between the void space left from a close packing of parallel filaments or wires. This novel MSR concept has been applied for the oxidative steam reforming of methanol [173]. Thin linear metallic wires, with diameters in the millimeter range, were close packed and introduced into a macro tubular reactor. The catalyst layer was grown on the external surface of these wires by thermal treatment. 

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