Reactor Performance Measures

There are four common measures of reactor performance fraction unreacted, conversion, yield, and selectivity. The fraction unreacted is the simplest and is usually found directly when solving the component balance equations. It is a(t)lao for a batch reaction and a utlcim for a flow reactor. The conversion is just 1 minus the fraction unreacted. The terms conversion and fraction unreacted refer to a specific reactant, usually the stoichiometrically limiting reactant. See Equations 1.26 and 1.27 for the tirst-order case. 

Suppose it is desired to make l,4-dimethyl-2,3-dichlorobenzene by the direct chlorination of para-xylene. The desired reaction is 

there are many other reactions that can occur and it is implausible that the desired reaction will occur as a single, elementary step. A feed stream containing 40 mol % p-xylene and 60 mol % chlorine was fed to the reactor. The results of one experiment in a batch reactor gave the following results on a molar basis  

Component Moles Output per Mole of Mixed Feed 

SOLUTION Write the reaction as A + B D + 2E where D is the desired dichlorobenzene. Some measures of performance based on xylene as the limiting component are 

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Before we can explore how reactor conditions can be chosen, we require some measure of reactor performance. For polymerization reactors, the most important measure of performance is the distribution of molecular weights in the polymer product. The distribution of molecular weights dictates the mechanical properties of the polymer. For other types of reactors, three important parameters are used to describe their performance ... 

In Chapter 1, Figure 1.4.1 (Berty et al, 1969) shows the actual measurement results of the older 5 diameter recycle reactor performance, using two different types of equipment. 

Solution Example 4.5 was a reverse problem, where measured reactor performance was used to determine constants in the rate equation. We now treat the forward problem, where the kinetics are known and the reactor performance is desired. Obviously, the results of Run 1 should be closely duplicated. The solution uses the method of false transients for a variable-density system. The ideal gas law is used as the equation of state. The ODEs are... 

Before exploring how reactor conditions can be chosen, some measure of reactor performance is required. 

In Section 11.1.3.2 we considered a model of reactor performance in which the actual reactor is simulated by a cascade of equal-sized continuous stirred tank reactors operating in series. We indicated how the residence time distribution function can be used to determine the number of tanks that best model the tracer measurement data. Once this parameter has been determined, the techniques discussed in Section 8.3.2 can be used to determine the effluent conversion level. 

Conditions during start-up can have a dramatic impact on time required to reach reasonable performance levels and on the ultimate reactor performance. Dilution rate, loading rate as measured by chemical oxygen demand (COD), carrier choice, inoculum amount, inoculum strategy, and inoculum species distribution are critical parameters (Sreekrishnan et al., 1991 Araki and Harada, 1994 Austermann-Haun et al., 1994 Yongming et al., 1993). Pore characteristics have a strong influence on time required for start-up and on the ultimate biomass density in the... 

In this introductory chapter, we first consider what chemical kinetics and chemical reaction engineering (CRE) are about, and how they are interrelated. We then introduce some important aspects of kinetics and CRE, including the involvement of chemical stoichiometry, thermodynamics and equilibrium, and various other rate processes. Since the rate of reaction is of primary importance, we must pay attention to how it is defined, measured, and represented, and to the parameters that affect it. We also introduce some of the main considerations in reactor design, and parameters affecting reactor performance. These considerations lead to a plan of treatment for the following chapters. 

Space time (r) is usually applied only to flow situations, and is the time required to process one reactor volume of inlet material (feed) measured at inlet conditions. That is, t is the time required for a volume of feed equal to the volume of the vessel (V) to flow through the vessel. The volume V is the volume of the vessel accessible to the fluid, t can be used as a scaling quantity for reactor performance, but the reaction conditions must be the same, point-by-point, in the scaling. 

In the case where no correlations are available (i.e., the application involves an exotic fluid, a non-traditional stirrer or a very small reactor), experimental measurements of kLa must be performed to afford power law correlations valid for very similar reactor, turbines and fluids. Several techniques for kLa determination have been published [56]. 

In order to compare the different preheating operations, and thus evaluating this effect on the reactor performance, temperature values measured in the reactor are reported in Table 9.1 for the following operating conditions O2 CH4 = 0.71, H20 CH4 = 0.69, GHSV= 13000h ... 

Just as the reaction time t is the natural performance measure for a batch reactor, so are the space-time and space-velocity the proper performance measures of flow reactors. These terms are defined as follows ... 

This example shows that t and r are not, in general, identical. Now which is the natural performance measure for reactors For batch systems Chapter 3 shows that it is the time of reaction however, holding time does not appear anywhere in the performance equations for flow systems developed in this chapter, Eqs. 13 to 19, while it is seen that space-time or does naturally appear. Hence, r or V/F o is the proper performance measure for flow systems. 

Small bubbles and flow uniformity are important for gas-liquid and gas-liquid-solid multiphase reactors. A reactor internal was designed and installed in an external-loop airlift reactor (EL-ALR) to enhance bubble breakup and flow redistribution and improve reactor performance. Hydrodynamic parameters, including local gas holdup, bubble rise velocity, bubble Sauter diameter and liquid velocity were measured. A radial maldistribution index was introduced to describe radial non-uniformity in the hydrodynamic parameters. The influence of the internal on this index was studied. Experimental results show that The effect of the internal is to make the radial profiles of the gas holdup, bubble rise velocity and liquid velocity radially uniform. The bubble Sauter diameter decreases and the bubble size distribution is narrower. With increasing distance away from the internal, the radial profiles change back to be similar to those before contact with it. The internal improves the flow behavior up to a distance of 1.4 m. 

Optimization problems are by their nature mathematical in nature. The first and perhaps the most difficult step is to determine how to mathematically model the system to be optimized (for example, paint mixing, chemical reactor, national economy, environment). This model consists of an objective function, constraints, and decision variables. The objective function is often called the merit or cost function this is the expression to be optimized that is the performance measure. For example, in Fig. 3 the objective function would be the total cost. The constraints are equations that describe the model of the process (for example, mass balances) or inequality relationships (insulation thickness >0 in the above example) among the variables. The decision variables constitute the independent variables that can be changed to optimize the system. 

Lerou and Froment [10] found by calculations that a reactor may ignite under non constant flow conditions while it is still stable if constant flow is assumed. Kalthoff and Vortmeyer [11],(Figure 4) found an improved agreement between measured and calculated ranges of multiple solutions for non -uniform flow. From the previous work therefore can be concluded that non-uniform porosity and flow distributions effect the chemical reactor performance. The question however, whether real improvements are obtained has to be subject to a comparison of experimental results with calculations. 

Figure 3 was calculated from steady-state measurements. Curvature of the rate vs composition relation causes the quasi steady-state rate to be well below the steady-state reactor performance. This emphasizes the very large effect of cycling frequency on the time average synthesis rate. 

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