Mass-transfer-rate

The fifth and final adsorbent characteristic is zeolite type. The adsorbent used in the Molex process is a proprietary and is a particularly effective adsorbent for normal paraffin separation [4, 5] and has achieved purity and recovery targets for the Molex processes. A sampUng of various molecules (and their corresponding dimensions) that Molex can easily separate is listed in Table 8.1. As discussed in Chapter 6, a zeoUtes s pore structure is dependent on its silica aluminum ratio and the proprietary Molex adsorbent possess a uniform repeating three-dimensional porous structure with pores running perpendicular to each other in the x. 

Since the Sorbex process is a liquid-phase fixed-bed process, the selection of particle size is an important consideration for pressure drop and process hydraulics. The exact particle size is optimized for each particular Molex process to balance the liquid phase diffusion rates and adsorbent bed frictional pressure drop. The Sorbex process consists of a finite number of interconnected adsorbent beds. These beds are allocated between the following four Sorbex zones zone 1 is identified as the adsorption zone, zone 2 is identified as the purification zone, zone 3 is identified as the desorption and zone 4 is identified as the buffer zone. The total number of beds and their allocation between the different Sorbex zones is dependent on the desired performance of the particular Molex process. Molex process performance is defined by two parameters extract normal paraffin purity and degree of normal paraffin recovery from the corresponding feedstock. Details about the zone and the bed allocations for each Molex process are covered in subsequent discussions about each process. 

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However, a note of caution should be added. In many multiphase reaction systems, rates of mass transfer between different phases can be just as important or more important than reaction kinetics in determining the reactor volume. Mass transfer rates are generally higher in gas-phase than liquid-phase systems. In such situations, it is not so easy to judge whether gas or liquid phase is preferred. 

Mass transfer rates may also be expressed in terms of an overall gas-phase driving force by defining a hypothetical equiHbrium mole fractionjy as the concentration which would be in equiHbrium with the bulk Hquid concentration = rax ) ... 

Design Procedure. The packed height of the tower required to reduce the concentration of the solute in the gas stream from to acceptable residual level ofjy 2 may be calculated by combining point values of the mass transfer rate and a differential material balance for the absorbed component. Referring to a sHce dh of the absorber (Fig. 5),... 

The term dqljdt represents the overall rate of mass transfer for component / (at time t and distance averaged over a particle. This is governed by a mass transfer rate expression which may be thought of as a general functional relationship of the form... 

This rate equation must satisfy the boundary conditions imposed by the equiUbrium isotherm and it must be thermodynamically consistent so that the mass transfer rate falls to 2ero at equiUbrium. It maybe a linear driving force expression of the form... 

Adsorption Dynamics. An outline of approaches that have been taken to model mass-transfer rates in adsorbents has been given (see Adsorption). Detailed reviews of the extensive Hterature on the interrelated topics of modeling of mass-transfer rate processes in fixed-bed adsorbers, bed concentration profiles, and breakthrough curves include references 16 and 26. The related simple design concepts of WES, WUB, and LUB for constant-pattern adsorption are discussed later. 

Design Methods. Improvements ia the ability to predict multicomponent equilibrium and mass-transfer rate performance will allow significant improvements ia the design of new adsorption systems and ia the energy efficiency of existing systems. 

The search for a suitable adsorbent is generally the first step in the development of an adsorption process. A practical adsorbent has four primary requirements selectivity, capacity, mass transfer rate, and long-term stabiUty. The requirement for adequate adsorptive capacity restricts the choice of adsorbents to microporous soUds with pore diameters ranging from a few tenths to a few tens of nanometers. 

In addition to the fundamental parameters of selectivity, capacity, and mass-transfer rate, other more practical factors, namely, pressure drop characteristics and adsorbent life, play an important part in the commercial viabiUty of a practical adsorbent. 

Temperature and pressure are not considered as primary operating variables temperature is set sufficiendy high to achieve rapid mass-transfer rates, and pressure is sufficiendy high to avoid vaporization. In Hquid-phase operation, as contrasted to vapor-phase operation, the required bed temperature bears no relation to the boiling range of the feed, an advantage when heat-sensitive stocks are being treated. 

The equations of combiaed diffusion and reaction, and their solutions, are analogous to those for gas absorption (qv) (47). It has been shown how the concentration profiles and rate-controlling steps change as the rate constant iacreases (48). When the reaction is very slow and the B-rich phase is essentially saturated with C, the mass-transfer rate is governed by the kinetics within the bulk of the B-rich phase. This is defined as regime 1. 

In industrial equipment, however, it is usually necessary to create a dispersion of drops in order to achieve a large specific interfacial area, a, defined as the interfacial contact area per unit volume of two-phase dispersion. Thus the mass-transfer rate obtainable per unit volume is given as... 

The behavior of drops in the centrifugal field has been studied (211) and the residence times and mass-transfer rates have been measured (212). PodbieHiiak extractors have been widely used in the pharmaceutical industry, eg, for the extraction of penicillin, and are increasingly used in other fields as weU. Commercial units having throughputs of up to 98 m /h (26,000 gal/h) have been reported. 

As velocity continues to rise, the thicknesses of the laminar sublayer and buffer layers decrease, almost in inverse proportion to the velocity. The shear stress becomes almost proportional to the momentum flux (pk ) and is only a modest function of fluid viscosity. Heat and mass transfer (qv) to the wall, which formerly were limited by diffusion throughout the pipe, now are limited mostly by the thin layers at the wall. Both the heat- and mass-transfer rates are increased by the onset of turbulence and continue to rise almost in proportion to the velocity. 

Below about 0.5 K, the interactions between He and He in the superfluid Hquid phase becomes very small, and in many ways the He component behaves as a mechanical vacuum to the diffusional motion of He atoms. If He is added to the normal phase or removed from the superfluid phase, equiHbrium is restored by the transfer of He from a concentrated phase to a dilute phase. The effective He density is thereby decreased producing a heat-absorbing expansion analogous to the evaporation of He. The He density in the superfluid phase, and hence its mass-transfer rate, is much greater than that in He vapor at these low temperatures. Thus, the pseudoevaporative cooling effect can be sustained at practical rates down to very low temperatures in heHum-dilution refrigerators (72). 

Stable operation of LPO reactors thus requires the presence of a mass-transfer rate-limited zone. It is usually desirable to limit this zone to minimize oxygen starvation problems. 

Pressure. Within limits, pressure may have Htfle effect in air-sparged LPO reactors. Consider the case where the pressure is high enough to supply oxygen to the Hquid at a reasonable rate and to maintain the gas holdup relatively low. If pressure is doubled, the concentration of oxygen in the bubbles is approximately doubled and the rate of oxygen deHvery from each bubble is also approximately doubled in the mass-transfer rate-limited zone. The total number of bubbles, however, is approximately halved. The overall effect, therefore, can be small. The optimum pressure is likely to be determined by the permissible maximum gas holdup and/or the desirable maximum vapor load in the vent gas. 

Reactor Configuration. The horizontal cross-sectional area of a reactor is a critical parameter with respect to oxygen mass-transfer effects in LPO since it influences the degree of interaction of the two types of zones. Reactions with high intrinsic rates, such as aldehyde oxidations, are largely mass-transfer rate-limited under common operating conditions. Such reactions can be conducted effectively in reactors with small horizontal cross sections. Slower reactions, however, may require larger horizontal cross sections for stable operation. 

Static mixing of immiscible Hquids can provide exceUent enhancement of the interphase area for increasing mass-transfer rate. The drop size distribution is relatively narrow compared to agitated tanks. Three forces are known to influence the formation of drops in a static mixer shear stress, surface tension, and viscous stress in the dispersed phase. Dimensional analysis shows that the drop size of the dispersed phase is controUed by the Weber number. The average drop size, in a Kenics mixer is a function of Weber number We = df /a, and the ratio of dispersed to continuous-phase viscosities (Eig. 32). 

The physical mass-transfer rate of o2one into water is affected by the gaseous o2one concentration, temperature, pressure, gas dispersion, turbulence, mixing, and composition of the solution, ie, pH, ionic strength, and the presence of reactive substances. Mass transfer of gaseous o2one into... 

The original hot carbonate process developed by the U.S. Bureau of Mines was found to be corrosive to carbon steel (55). Various additives have been used in order to improve the mass transfer rate as well as to inhibit corrosion. Vetrocoke, Carsol, Catacarb, Benfteld, and Lurgi processes are all activated carbonate processes. Improvements in additives and optimization of operation have made activated carbonate processes competitive with activated MDEA and nonaqueous solvent based systems. Typical energy requirements are given in Table 9. 

Combining equation 6 with the heat- and mass-transfer rate expressions gives... 

Eddy diffusion as a transport mechanism dominates turbulent flow at a planar electrode ia a duct. Close to the electrode, however, transport is by diffusion across a laminar sublayer. Because this sublayer is much thinner than the layer under laminar flow, higher mass-transfer rates under turbulent conditions result. Assuming an essentially constant reactant concentration, the limiting current under turbulent flow is expected to be iadependent of distance ia the direction of electrolyte flow. 

Wa Interpbase mass-transfer rate of solute A per interfacial area with respect to fixed coordinates kmoP(s-m ) (lbmol)/(h-fF)... 

FIG. 5-24 Flowchart iUnstrating problem solving approach using mass-transfer rate expressions in the context of mass conservation. 

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