Isothermal reactors series

These equations hold if an Ignition Curve test consists of measuring conversion (X) as the unique function of temperature (T). This is done by a series of short, steady-state experiments at various temperature levels. Since this is done in a tubular, isothermal reactor at very low concentration of pollutant, the first order kinetic applies. In this case, results should be listed as pairs of corresponding X and T values. (The first order approximation was not needed in the previous ethylene oxide example, because reaction rates were measured directly as the total function of temperature, whereas all other concentrations changed with the temperature.) The example is from Appendix A, in Berty (1997). In the Ignition Curve measurement a graph is made to plot the temperature needed for the conversion achieved. 

The second reaction type involves reactants forming products, but then the products undergo further reaction in series with the main reaction. We want to show here the implications of series reactions, so we consider a simple batch isothermal reactor at constant volume ... 

Equations (4-147) and (4-148) describe the conversion and coke profiles in an isothermal reactor subject to deactivation by coke formation via a parallel mechanism. Derive the corresponding equations for deactivation via a series mechanism. 

For a basic understanding of chemical reactor design, start with Sections 4.10.1 and 4.10.2, where different ideal and isothermal reactor types are introduced and the respective performance equations are derived. You should then study the behavior of real reactors (non-ideal flow and residence time distribution, Section 4.10.4) and the simplest model to account for deviations of real systems from ideal reactors, the tanks-in-series model (Section 4.10.5). 

Calculation of the conversion in a real isothermal reactor by means of the tanks-in-series model is straightforward. Based on a step or pulse input experiment, we get directly either the F or the E function of a real reactor. We just have to compare the measured function with the solutions given in Figures 4.10.49-4.10.52, and determine the hypothetical number N of CSTRs of our real system by the best fit of... 

Because the characteristic of tubular reactors approximates plug-flow, they are used if careful control of residence time is important, as in the case where there are multiple reactions in series. High surface area to volume ratios are possible, which is an advantage if high rates of heat transfer are required. It is sometimes possible to approach isothermal conditions or a predetermined temperature profile by careful design of the heat transfer arrangements. 

The OLEFLEX process uses multiple side-by-side, radial flow, moving-bed reactors connected in series. The heat of reaction is suppHed by preheated feed and interstage heaters. The gas-phase reaction is carried out over a catalyst, platinum supported over alumina, under very near isothermal conditions. The first commercial installation of this technology, having an annual capacity of 100,000 t, was made in 1990 by the National Petrochemical Corporation in Thailand. A second unit, at 245,000 t capacity, has been built in South Korea by the ISU Chemical Company (70). 

Continuous-flow stirred-tank reactors ia series are simpler and easier to design for isothermal operation than are tubular reactors. Reactions with narrow operating temperature ranges or those requiring close control of reactant concentrations for optimum selectivity benefit from series arrangements. 

Show that the Equation (3.34) is valid if the large and small reactors have the same value for /2 and that this will be true for an isothermal or adiabatic PER being scaled up in series. 

This section indicates a few useful generalizations that are pertinent in considerations of isothermal series and parallel combinations of ideal plug flow and stirred tank reactors. 

For the case where all of the series reactions obey first-order irreversible kinetics, equations 5.3.4, 5.3.6, 5.3.9, and 5.3.10 describe the variations of the species concentrations with time in an isothermal well-mixed batch reactor. For series reactions where the kinetics do not obey simple first-order or pseudo first-order kinetics, the rate expressions can seldom be solved in closed form, and it is necessary to resort to numerical methods to determine the time dependence of various species concentrations. Irrespective of the particular reaction rate expressions involved, there will be a specific time... 

In a series of laboratory scale experiments, streams of oxygen and sulfur dioxide were fed at different rates to a differential reactor containing 2.372 g of catalyst. The data below were recorded under essentially isothermal conditions... 

Consider a reactor system made up to two vessels in series a PFR of volume Vpp and a CSTR of volume EST, as shown in Figure 17.5. In Figure 17.5(a), the PFR is followed by the CSTR, and in Figure 17.5(b), the sequence is reversed. Derive E(d) for case (a) and for case (b). Assume constant-density isothermal behavior. 

A series of four well-mixed reactors operate isothermally in the steady state. Examine the figure. All the tanks do not have the same volume, but the sum of V, — 20 m3. The component whose concentration is designated by C reacts according to the following mechanism r = —kC1 in each tank. 

Example 15.13. The irreversible chemical reaction A B takes place in two perfectly mixed reactors connected in series as shown in Fig. 15.3. The reaction rate is proportional to the concentration of reactant. Let Xj be the concentration of reactant A in the first tank and X2 the concentration in the second tank. The concentration of reactant in the feed is Xg. The feed flow rate is F. Both Xo and F can be manipulated. Assume the specific reaction rates ki and >n Mch tank are constant (isothermal operation). Assume constant volumes Vi and 1. ... 

In conclusion, the maximum adsorption capacity should be measured in fixed-bed experiments under dynamic conditions, and if models are applicable, diffusion coefficients should be also determined in fixed-bed apparatus. Due to the fact that the equilibrium isotherms require extended data series and thus are time-consuming experiments, the latter are quite difficult to be conducted in fixed-bed reactors and from this point of view, it is more practical to evaluated equilibrium isotherms in batch reactor systems. Then, it is known that when applying fixed-bed models using an equilibrium isotherm obtained in batch-type experiments, the equilibrium discrepancy (if it exists) can be compensated by a different estimate for the solid diffusion coefficient (Inglezakis and Grigoropoulu, 2003 Weber and Wang, 1987). 

Styrene butadiene rubber (SBR) latex 25 000 tonnes Continuous isothermal reaction (5°C) in a series of reactors (33ni3 capacity each). 

The near completely random motion of the catalyst bed virtually ensures an isothermal operation, but the efficiency of the hydrodesulfurization reaction tends to suffer because of the back mixing of the product and feedstock. Hence, to effect sulfur removal at over 75% efficiency, it may be necessary to operate with two or more reactors in series. The need for two or more of these units to effectively desulfurize a feedstock may be cited as a disadvantage of the reactor, but the ability of the reactor to operate under isothermal conditions as well as the onstream catalyst addition-withdrawal system and the fact that the reactor size required for an expanded catalyst bed is often smaller than that required for a fixed bed can be cited in support of such a unit. 

The most common continuous emulsion polymerization systems require isothermal reaction conditions and provide for conversion control through manipulation of initiator feed rates. Typically, as shown in Figure 1, flow rates of monomer, water, and emulsifier solutions into the first reactor of the series are controlled at levels prescribed by the particular recipe being made and reaction temperature is controlled by changing the temperature of the coolant in the reactor jacket. Manipulation of the initiator feed rate to the reactor is then used to control reaction rate and, subsequently, exit conversion. An aspect of this control strategy which has not been considered in the literature is the complication presented by the apparent dead-time which exists between the point of addition of initiator and the point where conversion is measured. In many systems this dead-time is of the order of several hours, presenting a problem which conventional control systems are incapable of solving. This apparent dead-time often encountered in initiation of polymerization. 

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