Unsteady periodic

Feed concentrations are A0 = 0.9 and B0 = 0.3. The material balances over the unsteady period, ... 

Thus the effect of fluid motion is to reduce the unsteady period e.g., Tq.i is reduced by a factor of 3 on raising Pe from zero to 0.5. 

The duration of the unsteady period, denoted by C, the time required for Sh to come within 100x% of the steady value, is different for rigid and fluid spheres. For a rigid sphere at high Pe, T ocPe "/". From Stokes s law, Eq. (3-18), Uj oc a" hence C is independent of particle size for a given fluid. However, for a fluid sphere, oc (1 + K )/Pe thus Ujt /a is a constant, and a given fractional approach to steady state is achieved when the particle has moved a fixed number of radii, e.g.. 

Approximate values of Sh for intermediate Pe may be obtained by using Eq. (3-61) until Sh equals the steady-state value of Fig. 3.10. For larger t this steady-state value is used. Although this approximation underestimates the duration of the unsteady period, the error in Sh is not large. In terms of the time-averaged Sh or the total mass transferred, the error is less than 15% for all times. 

There are other possible unsteady (periodic) operation modes for a packed bed reactor that could lead to process intensification [57]. Indeed, there are several unsteady state strategies available to run a process unit such as a reactor. Pulses of different magnitude can be imposed on an input, or the input could be either changed progressively or varied according to an analytical function. However, not all unsteady state strategies are feasible in a commercial situation. Table 3.2 gives examples of the possibilities. 

Our previous study showed that the reaction zone in the interior of the catalyst was not the w hole resin during the course of reaction because two liquid phases were undisturbed and unmixed in the center of the catalyst (42J. The phospha/ene reaction mechanism is shown in Figure 5. How ever, the reaction zone varied according to the solvent properties of two liquid phases. The plot of consumption of reactant and productions of pr(xiucts with space time is shown in Figure 9. The unsteady period of this reaction was larger than 2 h. The turnover number for the first substitution reaction was around 1,2x10 s at 30"X and lOOOrpm. Assuming the efl ectiveness factor q, to be constant at the steady state condition, the relative reaction-rate constant was calculated and listed in Table 1. The apparent reaction-rate constants k opi, (- calculated varied proportionately with the amount of the... 

The plot of consumption of reactant and production of products according to space time is shown in Figure 10. The unsteady period of this reaction was longer than 1 h. The effectiveness factor q, was assumed to be constant at steady state condition, the relative reaction-rate constants were calculated and are listed in Table I. The pressure drop was controlled below 1 psia. Different amounts (1.2 and 1.8 g) of catalyst were housed in dilTerent bed heights (20. 30 cm ). The conversion of reactant and yields of products for various residence times (or liquid flow rates) were obtained from the same catalytic bed (i.e. the same amount of the catalyst) at the steady state condition. The curve shapes of products in the slurry reactor arc different from those in the fixed-bed reactor, as shown in Figure 11. 

Flux expressions (3.4.72), (3.4.76) and (3.4.81a) for a diffusing gas species i through a membrane of thickness dm describe the observed behavior at steady state achieved after an initial unsteady period. The initial unsteady behavior begins when the gas containing the permeating species i at concentration Cif (partial pressure p,y) is introduced at time t = 0 to the z = 0 surface of the membrane, the feed side. The rate of penetration of the membrane by species i is governed by the unsteady state diffusion equation (3.4.79), where is governed by Fick s flrst law... 

Unsteady-State Direct Oxidation Process. Periodic iatermption of the feeds can be used to reduce the sharp temperature gradients associated with the conventional oxidation of ethylene over a silver catalyst (209). Steady and periodic operation of a packed-bed reactor has been iavestigated for the production of ethylene oxide (210). By periodically varyiag the inlet feed concentration of ethylene or oxygen, or both, considerable improvements ia the selectivity to ethylene oxide were claimed. 

Unsteady material and energy balances are formulated with the conservation law, Eq. (7-68). The sink term of a material balance is and the accumulation term is the time derivative of the content of reactant in the vessel, or 3(V C )/3t, where both and depend on the time. An unsteady condition in the sense used in this section always has an accumulation term. This sense of unsteadiness excludes the batch reactor where conditions do change with time but are taken account of in the sink term. Startup and shutdown periods of batch reactors, however, are classified as unsteady their equations are developed in the Batch Reactors subsection. For a semibatch operation in which some of the reactants are preloaded and the others are fed in gradually, equations are developed in Example 11, following. 

Unsteady noise can be evaluated by a phonometer, which measures the sound pressure level for a time period of noise fluctuation and gives the time-weighted average value. 

Most gas lift, flash gas, and vapor recovery compressors require a recycle valve because of the unsteady and sometimes unpredictable nature of the flow rate. Indeed there may be periods of time when there is no flow at all to the compressor. 

The symptoms of hypothyroidism maybe confused with symptoms associated with aging, such as depression, cold intolerance, weight gain, confusion, or unsteady gait. The presence of these symptoms should be thoroughly evaluated and documented in the preadministration assessment and periodically throughout therapy. 

A deep pool of ethanol is suddenly exposed to an atmosphere of pure carbon dioxide and unsteady state mass transfer, governed by Fick s Law, takes place for 100 s. What proportion of the absorbed carbon dioxide will have accumulated in the 1 mm layer closest to the surface in this period ... 

A 5% CoOj/Ti02 catalyst is quite active for the wet TCE oxidation at very low reaction temperatures, such as 310 K, and our proposed model of different forms of CoO species existing with the fresh catalyst can reasonably explain the unsteady-state catalytic behavior at the initial period during the wet catalysis. 

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