Pseudo-integral reactor

Fig. 4.14. A special type of integral reactor (pseudo-integral reactor) is one constructed with taps at various distances along the length so that samples may be removed and the actual concentration profile measured. A disadvantage of integral reactors is that the balance equations are a system of coupled differential equations. The measured conversion often is due to a complex interaction of transport and reaction processes. For quick, empirical, and pragmatic process development, the integral reactor may be well suited, especially now that fast digital computers and effective integration algorithms facilitate parameterization.

Thus, with the usual experimental procedures, a comparison of conversion data as a function of space velocity (residence time) does not tell us whether the kinetics differ from first order in the region of conversion below 50% for the range of order tested (zeroth to second). On the contrary, first-order kinetics can be used to represent the conversion as a function of residence time for a wide range of situations. Some investigators have been aware of this approximate first-order behavior of integral reactors, as shown by the statement that even complex catalytic systems approximate a pseudo- first order relationship when only space velocity is varied. .. (10). 

The conversion per reaction cycle is a differential amount, but it is at the high level of conversion typical of an integral reactor. The loop reactor is therefore referred to as a pseudo-differential reactor or gradient-free reactor. The identity indicated in Equ. 4.16 can be more easily recognized when the two parts that result from the mass equivalence of a recycling reactor (left side) and set equal to that of an ideal stirred vessel (right side), and the resulting equation is then solved for ... 

Here the pseudo-homogeneous rate r is related to the surface reaction rate r" through the area of active catalyst per unit volume of reactor. Assuming further a plug-flow regime, the integration of the mass balance equation for this simple rate expression gives an expression for CO conversion ... 

Air and gaseous S02 in the required ratio enter Mixer 6 to mix fully with each other, and the resulting pseudo flue gas is divided into two equal streams to enter Absorber 7. The air flow rate is adjusted by a butterfly valve in the pipeline and measured with a Pitot tube-pressure difference meter and that of S02 by the rotameter 5. The total gas flow rate is also monitored by a wind velocity meter of DF-3 type at the gas outlet of the reactor. For each run, gas-samplings are made at both inlet and outlet of the reactor, and the S02 concentrations in the samples are measured with the Iodine-quantitative method, a standard and authentic method of determining the integral amount of S02 absorbed in the reactor. 

A chip-based integrated precolumn microreactor with 1 nl reaction volume has been explored by Jacobson et al. [67]. The reactor is operated in a continuous manner by electrokinetically mixing of sample (amino acids) and reagent (o-phthaldialdehyde) streams. The reaction time is adjusted via the respective flow velocities. By switching of potentials, small plugs of the reaction product were injected into a 15.4 mm separation channel in a gated injection scheme (< 1.8% RSD in peak area). The separation efficiency achieved was relatively poor, however, electrokinetic control of reaction time (and yield) permitted to monitor the kinetics of the derivatization under pseudo first-order conditions. A similar integrated precolumn reactor operated in a stopped flow mode has been described by Harrison et al. [68]. 

Inspecting Equation (5.29), we notice that three of the state variables (namely, Mr, My, and Ml) are material holdups, which act as integrators and render the system open-loop unstable. Our initial focus will therefore be a pseudo-open loop analysis consisting of simulating the model in Equation (5.29) after the holdup of the reactor, and the vapor and liquid holdup in the condenser, have been stabilized. This task is accomplished by defining the reactor effluent, recycle, and liquid-product flow rates as functions of Mr, My, and Ml via appropriate control laws (specifically, via the proportional controllers (5.42) and (5.48), as discussed later in this section). With this primary control structure in place, we carried out a simulation using initial conditions that were slightly perturbed from the steady-state values in Table 5.1. 

In this way, the diffusion/reaction equations are reduced to trial and error algebraic relationships which are solved at each integration step. The progress of conversion can therefore be predicted for a particular semi-batch experiment, and also the interfacial conditions of A,B and T are known along with the associated influence of the film/bulk reaction upon the overall stirred cell reactor behaviour. It is important to formulate the diffusion reaction equations incorporating depletion of B in the film, because although the reaction is close to pseudo first order initially, as B is consumed as conversion proceeds, consumption of B in the film becomes significant. 

The activity was tested in the simultaneous HDS/HDN of thiophene (TH) and pyridine (PY) in an integral flow reactor at 320°C and 20 bar. The feed contained 240 ppm of TH and 220 ppm of PY in H2 (overall flow rate 0.4 mol/h). The catalyst amoimt was 0.01-0.12 g. The steady state was achieved after 4 h on stream. The activities were expressed by pseudo-first-order rate constants kni, kpy and kcs for thiophene HDS, PY hydrogenation and C-N bond hydrogenolysis, respectively [2,4]. 

The effectiveness factor E is expressed in terms of the intrapellet Damkohler number, and the chemical reaction time constant co is the inverse of the best pseudo-first-order kinetic rate constant. The reactor design engineer employs an integral form of the design equation to predict the length of a packed catalytic tubular reactor Lpfr that will achieve a final conversion of CO specified by /final. The approximate analytical solution, vahd at high mass transfer Peclet numbers, is... 

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