Lean phase

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... 

Consider a lean phase, j, which is in intimate contact with a rich phase, i, in a closed vessel in order to transfer a certain solute. The solute diffuses from the rich phase to the lean phase. Meanwhile, a fraction of the diffused solute back-transfers to the rich phase. Initially, die rate of rich-to-lean solute transfer surpasses that of lean to rich leading to a net transfer of the solute from the rich phase to the lean phase. However, as the concentration of the solute in the rich phase increases. 

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... 

The stage efficiency may be defined based on the rich phase or the lean phase. For instance, when the stage efficiency is defined for the rich phase, r)y, Eq. (2.11) becomes... 

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 ... 

Cost estimation and screening external MSAs To determine which external MSA should be used to remove this load, it is necessary to determine the supply and target compositions as well as unit cost data for each MSA. Towards this end, one ought to consider the various processes undergone by each MSA. For instance, activated carbon, S3, has an equilibrium relation (adsorption isotherm) for adsorbing phenol that is linear up to a lean-phase mass fraction of 0.11, after which activated carbon is quickly saturated and the adsorption isotherm levels off. Hence, JC3 is taken as 0.11. It is also necessary to check the thermodynamic feasibility of this composition. Equation (3.5a) can be used to calculate the corresponding... 

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. 

In order to establish the conditions for thermodynamic feasibility of reactive mass exchange, it is necessary to invoke the basic principles of mass transfer with chemical reactions. Consider a lean phase j that contains a set Bj = z —... 

It is now useful to recall the concepts of molarity and fractional saturation (Astarita etal., 1983). The molarity, mj, of areactive MSA is the total equivalent concentration of species that may react with component A. On the other hand, the fractional saturation, uj, is a variable that represents the degree of saturation of chemically combined A in the jth lean phase. Therefore, ujmj is the total concentration of chemically combined A in the yth MSA. Hence, the total concentration of A in MSA j can be expressed as... 

As discussed earlier, the admissible compositions may be selected as the lean-phase composition at some particular instant of time, or any other situation which is compatible with stoichiometry and mass-balance bounds such as Eqs. (8.20) and (8.21). Let us aihitrarily select the admissible composition of to be zero. 

There are three basic modes of transport which are employed. The first, and most common, is termed dilute phase or lean phase transport in which the volume fraction of solids in this suspension does not exceed about 0.05 and a high proportion of the particles spend most of their time in suspension. The second is transport which takes place largely in the form of a moving bed in which the solids volume fraction may be as high as 0.6 this is relevant only for horizontal or slightly inclined pipelines. The third form is dense phase transport in which fairly close packed slugs of particles, with volume fractions of up to... 

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... 

Because of the inadequacies of the aforementioned models, a number of papers in the 1950s and 1960s developed alternative mathematical descriptions of fluidized beds that explicitly divided the reactor contents into two phases, a bubble phase and an emulsion or dense phase. The bubble or lean phase is presumed to be essentially free of solids so that little, if any, reaction occurs in this portion of the bed. Reaction takes place within the dense phase, where virtually all of the solid catalyst particles are found. This phase may also be referred to as a particulate phase, an interstitial phase, or an emulsion phase by various authors. Figure 12.19 is a schematic representation of two phase models of fluidized beds. Some models also define a cloud phase as the region of space surrounding the bubble that acts as a source and a sink for gas exchange with the bubble. 

The lean/gas phase convection contribution has received the least attention in the literature. Many models in fact assume it to be negligible in comparison to dense phase convection and set hl to be zero. Compared to experimental data, such an approach appears to be approximately valid for fast fluidized beds where average solid concentration is above 8% by volume. Measurements obtained by Ebert, Glicksman and Lints (1993) indicate that the lean phase convection can contribute up to 20% of total... 

Some researchers have noted that this approach tends to underestimate the lean phase convection since solid particles dispersed in the up-flowing gas would cause enhancement of the lean phase convective heat transfer coefficient. Lints (1992) suggest that this enhancement can be partially taken into account by increasing the gas thermal conductivity by a factor of 1.1. It should also be noted that in accordance with Eq. (3), the lean phase heat transfer coefficient (h,) should only be applied to that fraction of the wall surface, or fraction of time at a given spot on the wall, which is not submerged in the dense/particle phase. This approach, therefore, requires an additional determination of the parameter fh to be discussed below. 

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. 

SZEKELY, J. Third Congress of the European Federation of Chemical Engineering (1962). The Interaction between Fluids and Particles 197. Mass transfer between the dense phase and lean phase in a gas-solid fluidised system. 

---