Reactor Parameters

Experimental Thermal-Disadvantage Factors In Some Very Undermoderated, 3%-Enriched Water-Uranium Oxide Lattices, 

As a part of the High Conversion Critical Experiment (Hi-C) at Argonne National Laboratory, the thermal disadvantage factor (() has been measured in five lattices that had water-to-uranium oxide-volume ratios of from 

96 down to 0.16. The data obtained in these cores indicate that i does not decrease monotonically with decreasing water-to-uranium oxide volume ratio but possesses a minimum and increases as the lattice pitch decreases beyond a certain value. 

The fuel in these cores was 3.04 wt% enriched uranium in the form of 10.17 g/cm UOa pellets of 0.935-cm diameter loaded to 122-cm length in 1.057-cm OD cladding tubes of 0.0496-cm-thick stainless steel. Both square and triangular lattice pitches were used. 

The disadvantage factor was obtained by the so-called integral technique. Foils of a uranium-aluminum alloy of 17.5 wt% uranium that was enriched to 92.75 wt% U-235 were shaped to measure the U-235 fission rate in representative portions of the fuel and moderator volumes of a unit cell. Cadmium ratios in both fuel and moderator sections were determined with 0.051-cm cadmium covers. Various thicknesses (0.0051 to 0.066 cm) of foils were used. The foil activities were corrected for thermal self-shielding. Ih the cadmium-covered irradiations, various masses of cadmium were used and the cadmium ratios were corrected to zero cadmium mass. 

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As an alternative to deriving Eq. (8-2) from a dynamic mass balance, one could simply postulate a first-order differential equation to be valid (empirical modeling). Then it would be necessary to estimate values for T and K so that the postulated model described the reactor s dynamic response. The advantage of the physical model over the empirical model is that the physical model gives insight into how reactor parameters affec t the v ues of T, and which in turn affects the dynamic response of the reac tor. 

Figure 1. Typical reactor temperature profile for continuous addition polymerization a plug-flow tubular reactor. Kinetic parameters for the initiator 1 = 10 ppm Ea = 32.921 kcal/mol In = 26.492 In sec f = 0.5. Reactor parameter [(4hT r)/ (DpCp)] = 5148.2. [(Cp) = heat capacity of the reaction mixture (p) = density of the reaction mixture (h) = overall heat-transfer coefficient (Tf) = reactor jacket temperature (r) = reactor residence time (D) = reactor diameter].

The computer investigation can also yield a more definable relationship with fewer parameter excursions since the output will be free of scatter. In addition, excursions in reactor parameters can be taken which might be considered unsafe on or beyond the equipment limitations of an existing real reactor. 

REACTION AND REACTOR PARAMETERS USED IN THE COMPUTER SIMULATION... 

The initiator is the most important reactor parameter in the polymer process. The initiator type affects the molecular weight and conversion limits in a reactor of fixed size and the molecular weight distribution of the material at a given conversion level. The initiator type dictates the initiator amount for a given conversion, the operating temperature range and sensitivity of the reactor to an unstable condition. 

Reprogram this example in terms of the actual reactor parameters, as given in the Nomenclature and the model equations. Investigate the influence of these parameters individually. 

A plot of (m/VP2 )(TR —T0) versus TR reveals a multivalued graph that exhibits a maximum as shown in Fig. 4.51. The part of the curve in Fig. 4.51 that approaches the value Tx asymptotically cannot exist physically since the mixture could not be ignited at temperatures this low. In fact, the major part of the curve, which is to the left of Topt, has no physical meaning. At fixed volume and pressure it is not possible for both the mass flow rate and temperature of the reactor to rise. The only stable region exists between Topt to T. Since it is not possible to mix some unbumed gases with the product mixture and still obtain the adiabatic flame temperature, the reactor parameter must go to zero when TR = T. ... 

FIGURE 4.51 Stirred reactor parameter ( WP2)(rR - r0) as a function of reactor temperature TR. 

Example 3. A MIMO design of the CSTR will illustrate the many possibilities of these approaches. Assume again the same reactor parameters (number 4 in Table 2). The system equations (23) are ... 

Typical values of the reactor parameters, to be used in the following discussion, are shown in Table 1. These values are different respect to those used in [1] because they represent another first order reaction. 

In a variable-density reactor the residence time depends on the conversion (and on the selectivity in a multiple-reaction system). Also, in ary reactor involving gases, the density is also a function of reactor pressure and temperature, even if there is no change in number of moles in the reaction. Therefore, we frequently base reactor performance on the number of moles or mass of reactants processed per unit time, based on the molar or mass flow rates of the feed into the reactor. These feed variables can be kept constant as reactor parameters such as conversion, T, and P are varied. 

We need to examine the nature of these solutions X(T) for given inlet and reactor parameters. These are algebraic equations so after elimination of X from the mass-balance... 

This seems to be a simpler set of equations than the differential equations of the PFTR, but since the PFTR equations are first-order differential equations, their solutions must be unique for specified flow, reaction, and reactor parameters, as we discussed in the previous chapter. This is not necessarily tme for the CSTR. 

We have to write Cai terms of Cao in order to express the conversion in terms of the feed conditions and reactor parameters, and the preceding expression for Ca[ in terms of Cxo> Ca, and R allows us to do this. 

When we use a tracer study to develop reactor parameters for an environmental system, we are inherently assuming that the details of the transport processes are not essential to us. All that we have is an input and an output, and any sets of reactors that will simulate the output for a given input are acceptable. What you can learn about the system from a reactor model depends on your understanding of the transport processes and how they are simulated by reactor models. 

Although a variety of synthesis, compositions and reactor parameters were studied, the P-V-0 catalysts in the temperature series were synthesized in the up flow HTAD reactor using a 0.12 M solution of anunonium vanadate in water which contained the required amount of 85% phosphoric acid to result in a 1.2/1.0 P/V atom ratio. This atom ratio is normally preferred for the most selective oxidation of butane to maleic anhydride. Table I shows that the P/V atom ratios obtained for the analyzed, finished (green colored) catalysts were approximately the same as the feed composition when a series of preparations were studied between 350 C and 800°C. This was typical for all of the catalysts synthesized under a variety of conditions. 

FCC Gasoline. The produced light FCC gasoline typically contains a mixture of paraffins, olefins, and aromatic compounds in a ratio of around 5 3 2. This ratio will often vary depending upon feedstock, catalyst quality, and reactor parameters. The research octane number of FCC gasoline will typically be much higher than the motor octane number. 

Finally, note that in the solution (5.151) all the involved reactor parameters should be based on the reactor volume. 

The same assumptions in Chap. 5 on the experimental setup have been done. The reactor parameters and the initial conditions for the reactant concentrations and the temperatures of the vessel and the jacket are reported in Table 5.1. The model-based temperature controller proposed in Chap. 5 is adopted. Finally, both in the reactor vessel and in the jacket, duplicated temperature sensors have been considered. 

The review of the performance equations for the ideal system has been for the steady state situation. This occurs when the process has begun and all transient conditions have died out (that is, no parameters vary with time). In all flow reactors, parameters such as the flowrate, temperature, and feed composition can vary with time at the beginning of the process. It is important for designers to review this situation with respect to fluctuating conditions and the overall control and... 

For scale-up operations, the selection of the reactor is considered to be the key element in designing SCWO systems. Environmental regulations set the requirement for the destruction efficiency, which in turn sets requirements on the temperature and residence time in the reactor (as an example, the required DRE is 99.99% for principal hazardous components and 99.9999% for polychlorinated biphenyls, PCBs). The reactor parameters for the scale-up designs can be extrapolated from the available bench-scale data. A detailed discussion on available reactor types is given below. 

Figure 4.9 shows the results of a dynamic simulation we performed featuring the open-loop behavior of a backmixed reactor that satisfies the slope condition for steady-state stability but has dynamically unstable roots. Table 4.1 contains the reactor parameters and operating conditions used in the model, as listed by Vleeschhouwer et al. (1992). 

The NucMA code developed in the RSC Kurchatov Institute, is meant to calculate SNF residual energy release both for separate SFA s and for the whole inventory of accumulated SFA s or its any sampling. The code can be used to calculate SRP s bumup, radionuclide composition and residual energy release. Radionuclide composition is determined as a function of bumup (or power generation) at the averaged reactor parameters, i.e. power, coolant density and temperatme. Besides, the code uses... 

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