Rich and lean phases

For all the above studies, the cycle time used for rich and lean phase, 15 and 30 min, respectively, was long and far from being realistic. In addition to such long cycle studies, to get an estimate of the catalyst performance under realistic conditions, we have also done second type of studies known as short cycle studies. In these studies, the total cycle time was kept relatively short ( s) to simulate the actual exhaust conditions, and... 

The simplest possible model is to assume that the volume fractions of PS in the rich and lean phases are independent of the bulk concentration and that there is no energy migration between phases. [6] This allows one to calculate the individual contributions to the excimer and monomer fluorescence from PS chains in both the rich... 

The partition coefficient of the solute between the phases contacted in the mass-exchange devices (separators, probably absorbers, strippers, or liquid-liquid extractors) must be included. This is acconplished by plotting the mole fraction in the rich phase (denoted y) on the left side of the CID, and the mole fraction of the lean phase (denoted x) on the right side of the diagram In a TID, the tenperatures on opposite sides of the same horizontal line differ by the minimum approach temperature. In a CID, the rich- and lean-phase conpositions are related by... 

Morphological Model. We first assume that the blend can be described by binary equilibrium thermodynamics with two uniform phases in the blends, one rich in PS and, one lean in PS. The volume fractions of PS in the rich and lean phases, and ()>j, respectively,... 

If and are the probabilities of eventual monomer decay given that the photon is absorbed by the rich or lean phase, respectively, then the ratio of excimer to monomer fluorescence is given by a simple weighted average of fluorescence contributions from the rich and lean phases ... 

As a result, there are some challenges when deal process condensate reusing system with the synthesis methods for ordinary MEN directly. First, this is a non-ideal multi-component system, in which the interactions of the components could not be omitted second, the mass transfer loads between the rich and lean streams are relatively larger, which means that the inlet/outlet flow rates cannot be considered as constants as most ordinary MEN do third, the effects of operating temperature and pressure in each unit on phase equilibrium equations cannot be omitted either. In order to synthesize an optimal process with minimum cost for process condensate reusing system of the ammonia plant, a simultaneous synthesis method based on the superstructure is presented in this paper. 

Here, assume that in the range of compositions involved, the thermodynamically phase equilibrium relations between rich and lean streams are linear, and concern with the operating temperature T and pressure P, then we can obtain phase equilibrium equations as Eq. (1). 

Similar to the discussion of heat integration in Section 10.2, the terminology pinch is understood more clearly in coimection with a graphical display, as introduced by El-Halwagi and Manousiouthakis (1989) for mass integration, in which composite rich and lean curves are positioned no closer than the phase equilibrium departure plus Ax, in. As Ax in 0, the curves pinch together toward the compositions at phase equilibrium and the area for mass transfer approaches infinity. The use of these curves is illustrated next in the composite-curve method. 

This sort of richness and leanness can be demonstrated in cascade or stagewise operations, where both a permeate phase and reject phase are introduced or recycled (or refluxed) into successive membrane cells. In this respect, the use of constant molar or molal flow rates in Chapter 4 for stagewise operations may not be too far afield. 

The overhead vapor of compositionj/gj is totaHy condensed into two equiHbrium Hquid phases, an entrainer-rich phase of composition x and an entrainer-lean phase of composition The relative proportion of these two Hquid phases in the condenser, ( ), is given by the lever rule, where ( ) represents the molar ratio of the entrainer-rich phase to the entrainer-lean phase in the condensate. 

The two condensate Hquids must be used to provide reflux and distiUate streams. NormaHy, the reflux ratio, r, is chosen so that r = L jD > (j). This requires that the reflux rate be greater than the condensation rate of entrainer-rich phase and that the distiUate rate be correspondingly less than the condensation rate of entrainer-lean phase. This means that the distiUate stream consists of pure entrainer-lean phase, ie, Xj = x, and the reflux stream consists of aU the entrainer-rich phase plus the balance of the entrainer-lean phase. Thus, the overall composition of the reflux stream, Hes on the... 

Throughout this bocdt, several mass-exchange operations will be considered simultaneously. It is therefore necessary to use a unified terminology such that y is always the composition in die rich phase and x is the composition in the lean phase. The reader is cautioned here that tiiis terminology may be different ftom other literature, in which y is used for gas-phase composition and x is used for liquid-phase composition. 

Whenever die rich and the lean phases are not in equilibrium, an interphase concentration gradient and a mass-transfer driving force develop leading to a net transfer of the solute from the rich phase to the lean phase. A common method of describing the rates of interphase mass transfer involves the use of overall mass-transfer coefficients which are based on the difference between the bulk concentration of the solute in one phase and its equilibrium concentration in the other phase. Suppose that the bulk concentradons of a pollutant in the rich and the lean phases are yi and Xj, respectively. For die case of linear equilibrium, the pollutant concnetration in the lean phase which is in equilibrium with y is given by... 

Let us define two overall mass transfer coefficients one for the rich phase, Ky, and one for the lean phase, Kj,. Hence, the rate of interphase mass transfer for... 

This value is in good agreement with the experimental conslant reported by Machay and Shiu (1981) to be 0.673 kPa - m /gm mol. It is instructive to demonstrate the convetsion between dilTerent ways of reporting Hemy s coefficient. First, the repotted value is inverted to be in the units of composition in the rich phase divided by composition in the lean phase, i.e., 1.486 gm mol/(kPa - m ) which can be converted into units of mole fraction as follows ... 

Chapters Three, Five and Six have covered the synthesis of physical mass-exchange networks. In these systems, the targeted species were transferred from the rich phase to the lean phase in an intact molecular form. In some cases, it may be advantageous to convert the transferred species into other compounds using reactive MSAs. Typically, reactive MSAs have a greater capacity and selectivity to remove an undesirable component than physical MSAs. Furthermore, since they react with the undesirable species, it may be possible to convert pollutants into other species that may either be reused within the plant itself or sold. 

Figure 11.30 shows the NOr and 02 responses monitored in the cyclic lean-rich operation over two different catalysts. At the beginning of the lean phase, a significant decrease in NOx concentration at the reactor outlet is observed for both catalysts. The best candidate (catalyst B) shows, however, a better activity within time-on-stream in the lean period and enables a lower overall level within lean-rich cycles. 

Figure 18.7 Interfaces resulting from two types of continuous transformation, (a) Initial structure consisting of randomly mixed alloy, (b) After spinodal decomposition. Regions of B-rich and B-lean phases separated by diffuse interfaces formed as a result of long-range diffusion, (c) After an ordering transformation. Equivalent ordering variants (domains) separated by two antiphase boundaries (APBs). The APBs result from A and B atomic rearrangement onto different sublattices in each domain.

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