Steady-state removal

Compare the (steady-state) removal of species A from a gas stream by the absorption of A in... 

Figure 3 gives the results for the steady state removal of the three compounds using bubble fractionation on the small scale 5-cm diameter bubble column. The aqueous influent feed rate was 6 mL.min. The total aqueous height was 90 cm and the influent was fed at a height of 50 cm above the air sparger. The bottom effluent was maintained at 3 mL.min and hence the overflow rate was 3 mL.min ... 

The assumption of steady state removed the time dependence. 

I lic total energy release per fission in the LMFR is estimated to be 194 Mev. For a reactor having a heat rate of 500 Mw, this means that 542 g of U would be fissioned per day. Since the FPS represent about 44 ( of the total fission products by weight, 238 g of FPS s must be re-mo ed per day to maintain a steady concentration in the fuel. (See Table 22-10. j The Zr concentration is kept at about 250 ppm for purposes of corrosion inhibition, and the steady-state removal rate of this fission product will lie approximately 59 g/day. It is interesting to note that about 11% of the fission products end up as Zr. For a reactor with a heat rate of 500 Mw and a total fuel inventory of 150 tons, a fission-product Zr con-... 

Bromide ion acts as an inliibitor through step (9) which competes for HBr02 with the rate detennining step for the autocatalytic process described previously, step (4) and step (5). Step (8) and Step (9) constitute a pseudo-first-order removal of Br with HBr02 maintained in a low steady-state concentration. Only once [Br ] < [Br ] = /fo[Br07]//r2 does step (3) become effective, initiating the autocatalytic growth and oxidation. 

In this sequence the Cl also acts as a catalyst and two molecules are destroyed. It is estimated that before the Cl is finally removed from the atmosphere in 1—2 yr by precipitation, each Cl atom will have destroyed approximately 100,000 molecules (60). The estimated O -depletion potential of some common CFCs, hydrofluorocarbons, HFCs, and hydrochlorofluorocarbons, HCFCs, are presented in Table 10. The O -depletion potential is defined as the ratio of the emission rate of a compound required to produce a steady-state depletion of 1% to the amount of CFC-11 required to produce the 1% depletion. The halons, bromochlorofluorocarbons or bromofluorocarbons that are widely used in fire extinguishers, are also ozone-depleting compounds. Although halon emissions, and thus the atmospheric concentrations, are much lower than the most common CFCs, halons are of concern because they are from three to ten times more destmctive to O, than the CFCs. 

New radicals are introduced by thermolysis of the hydroperoxide by chain-branching decomposition (eq. 4). Radicals are removed from the system by chain-termination reaction(s) (eq. 5). Under steady-state conditions, the production of new radicals is in balance with the rate of radical removal by termination reactions and equation 8 appHes for the scheme of equations 1—5 where r. = rate of new radical introduction (eq. 4). 

Volumetric heat generation increases with temperature as a single or multiple S-shaped curves, whereas surface heat removal increases linearly. The shapes of these heat-generation curves and the slopes of the heat-removal lines depend on reaction kinetics, activation energies, reactant concentrations, flow rates, and the initial temperatures of reactants and coolants (70). The intersections of the heat-generation curves and heat-removal lines represent possible steady-state operations called stationary states (Fig. 15). Multiple stationary states are possible. Control is introduced to estabHsh the desired steady-state operation, produce products at targeted rates, and provide safe start-up and shutdown. Control methods can affect overall performance by their way of adjusting temperature and concentration variations and upsets, and by the closeness to which critical variables are operated near their limits. 

The other method is the ASTM cup method (34). In this method a desiccant is placed in a waterproof dish. The dish is covered with the experimental film and placed in an environmental chamber. The temperature and humidity ate set for the conditions of interest, typically 37.8 °C and 90% th. At regular intervals, the dish is removed and weighed. After a few days enough data have been gathered to describe a steady-state rate of weight gain, and the WVTR can be calculated. Typical experiments take about a week to complete. 

Process Control. Some hot nickel and flash electroless copper solutions are plated to the point of exhaustion and then discarded. Most baths are formulated to give bath fives of >6 turnovers of the bath constituents some reach steady-state buildup of the by-products and can be used indefinitely. AU. regenerable solutions should be filtered to remove particulates that can cause deposit roughness and bath instability. 

The LHS (heat generation) and RHS (heat removal) of Eq. (7-110) are plotted against T after x has been eliminated between the two balances the intersections identify the same steady state temperatures as the plot in Fig. 7-7a. 

Under steady-state conditions the temperature of the evaporating surface increases until the rate of sensible heat transfer to the surface equals the rate of heat removed by evaporation from the surface. To calculate this temperature, it is convenient to modify Eq. (12-26) in terms of humidity rather than partial-pressure difference, as follows ... 

When this is substituted into the previous equation, both sides become functions of T and may be plotted against each other. As Fig. 23-17 of a typical case shows, as many as three steady states are possible. When generation is greater than removal (as at points A— and B-t-), the temperature will rise to the next higher steady state when generation is less than removal (as at points A-t- and B—), it will fall to the next steady state. Point B is an unsteady state, while A and C are steady. 

Although the continuous-countercurrent type of operation has found limited application in the removal of gaseous pollutants from process streams (Tor example, the removal of carbon dioxide and sulfur compounds such as hydrogen sulfide and carbonyl sulfide), by far the most common type of operation presently in use is the fixed-bed adsorber. The relatively high cost of continuously transporting solid particles as required in steady-state operations makes fixed-bed adsorption an attractive, economical alternative. If intermittent or batch operation is practical, a simple one-bed system, cycling alternately between the adsorption and regeneration phases, 1 suffice. 

Humidification of the gas stream is the preferred method of keeping the filter bed moist. Gas moisture is usually added to the incoming gas stream downstream of the particulate removal APC equipment by either water sprays or steam. Adding moisture directly to the top of the bed in order to maintain filter media moisture is not recommended since this can result in (I) locahzed drying of the substrate, and (2) cold water addition will reduce the ac tivity of the microorganisms until the water becomes warmed to the steady-state filter ed temperature. 

The next stage in the zone-refining process is to move the furnace slowly and steadily to the right. The left-hand end of the bar will then cool and refreeze but with the equilibrium composition /cCq (Fig. 4.4c). As the furnace continues to move to the right the freezing solid, because it contains much less impurity than the liquid, rejects the surplus impurity into the liquid zone. This has the effect of inereasing the impurity concentration in the zone, which in turn then increases the impurity concentration in the next layer of freshly frozen solid, and so on (Fig. 4.4d). Eventually the concentrations ramp themselves up to the situation shown in Fig. 4.4(e). Flere, the solid ahead of the zone has exactly the same composition as the newly frozen solid behind the zone. This means that we have a steady state where as much impurity is removed from the... 

Temperature gradient normal to flow. In exothermic reactions, the heat generation rate is q=(-AHr)r. This must be removed to maintain steady-state. For endothermic reactions this much heat must be added. Here the equations deal with exothermic reactions as examples. A criterion can be derived for the temperature difference needed for heat transfer from the catalyst particles to the reacting, flowing fluid. For this, inside heat balance can be measured (Berty 1974) directly, with Pt resistance thermometers. Since this is expensive and complicated, here again the heat generation rate is calculated from the rate of reaction that is derived from the outside material balance, and multiplied by the heat of reaction. 

The steady-state operation of any reactor requires that the heat removed should equal the heat generated ... 

It is important to emphasize that direet studies sueh as those earned out on the eyelopropylmethyl radieal ean be done with low steady-state eoneentrations of the radical. In the case of the study of the eyelopropylmethyl radical, removal of the source of irradiation leads to rapid disappearance of the EPR spectrum, because the radicals react rapidly and are not replaced by continuing radical formation. Under many conditions, the steady-state concentration of a radical intermediate may be too low to permit direct detection. Failure to observe an EPR signal, therefore, cannot be taken as conclusive evidence against a radical intermediate. 

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