Fixed-Bed Operation

Usually, the supply of the feed solution is stopped when the ratio of the adsorbate concentration in the effluent to that in the feed has reached a predetermined value (the break point ). Then, in the elution operation the adsorbate bound to the adsorbent particles is desorbed (i.e., eluted) by supplying a suitable fluid (eluent) that contains no adsorbates. In this way, adsorbent particles are regenerated to their initial conditions. However, in some cases the column may be repacked with new adsorbent particles. 

Under the constant pattern, the term dq/dc should be constant. The integration of dqA/dCA — constant with the boundary conditions 

The time required from the start of feeding to the break point can be estimated with the assumption of the constant pattern stated above. Thus, substitution of Equation 11.10 into Equation 11.6 gives the following equation for the rate of adsorption  

Integration of this equation between the break point and exhaustion point, where the ratio of the adsorbate concentration in the effluent to that in the feed becomes a value of (1 - the ratio at the break point), gives 

An adsorbate A is adsorbed in a fixed-bed adsorber that is 25 cm high and packed with active charcoal particles of 0.6 mm diameter. The concentration of A in a feed solution CA is 1.1 mol m-3, and the feed is supplied to the adsorber at an interstitial velocity of 1.6 mh-1. The adsorption equilibrium of A is given by the following Freundlich-type isotherm. 

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Nonregenerable aluminum chloride catalyst is employed with various carriers ia a fixed-bed or Hquid contactor. Platinum or other metal catalyst processes that utilize fixed-bed operation can be either regenerable or nonregenerable. The reaction conditions vary widely, between 40—480°C and 1035— 6900 kPa (150—1000 psi), depending on the particular process and feedstock. 

The term three-phase fluidization requires some explanation, as it can be used to describe a variety of rather different operations. The three phases are gas, liquid and particulate solids, although other variations such as two immiscible liquids and particulate solids may exist in special applications. As in the case of a fixed-bed operation, both co-current and counter- current gas-liquid flow are permissible and, for each of these, both bubble flow, in which the liquid is the continuous phase and the gas dispersed, and trickle flow, in which the gas forms a continuous phase and the liquid is more or less dispersed, takes place. A well established device for countercurrent trickle flow, in which low-density solid spheres are fluidized by an upward current of gas and irrigated by a downward flow of liquid, is variously known as the turbulent bed, mobile bed and fluidized packing contactor, or the turbulent contact absorber when it is specifically used for gas absorption and/or dust removal. Still another variation is a three-phase spouted bed contactor. 

If the new catalyst requires drastically different conditions, e.g. fluid bed operation instead of fixed bed operation, or if it needs substantial additions to the purification train, it is again possible to calculate the benefit in terms of the return (in reduced operating cost) on the new capital, but it is probably more informative to draw up a cumulative cash flow diagram. This is illustrated in Fig. 3. 

A gas-liquid-particle process termed cold hydrogenation has been developed for this purpose. The hydrogenation is carried out in fixed-bed operation, the liquefied hydrocarbon feed trickling downwards in a hydrogen atmosphere over the solid catalyst, which may be a noble metal catalyst on an inert carrier. Typical process conditions are a temperature of 10°-20°C and a pressure of 2.5-7 atm gauge. The hourly throughput is as high as 20-kg hydrocarbon feed per liter of catalyst volume. 

The operations considered in this paper may be classified under the headings of fixed-bed operations or suspended-bed operations, depending on the state of motion of the solid particles. 

Two types of fixed-bed operations, characterized by distinctly different flow patterns, are in current industrial use. These are usually described as trickle-flow operation and bubble-flow operation. In both cases, a lower limit exists for the particle size, usually about k in. 

Equation (15) is derived under the assumption that the amount of adsorbed component transferred by flow or diffusion of the solid phase may be neglected. This assumption is clearly justified in cases of fixed-bed operation, and it is believed to be permissible in many cases of slurries or fluidized beds, since the absolute amount of adsorbed component will probably be quite low due to its low diffusivity in the interior of the catalyst pellet. The assumption can, however, be waived by including in Eq. (15) the appropriate diffusive and convective terms. 

However, the models represent only crude approximate descriptions of the complex physical systems involved. Probably the most important phenomenon excluded is that of heat transfer. Suspended-bed operations are characterized by a high effective thermal conductivity, and thus represent a good approximation to isothermal behavior, and the above models should provide an adequate description of these systems. Fixed-bed operations will probably in many cases depart significantly from isothermal conditions, and in such cases models should be constructed that take heat transfer into... 

Information regarding mass transfer between liquid and solid in fixed beds operated under trickle-flow conditions has apparently not appeared in the literature. 

The packing itself may consist of spherical, cylindrical, or randomly shaped pellets, wire screens or gauzes, crushed particles, or a variety of other physical configurations. The particles usually are 0.25 to 1.0 cm in diameter. The structure of the catalyst pellets is such that the internal surface area far exceeds the superficial (external) surface area, so that the contact area is, in principle, independent of pellet size. To make effective use of the internal surface area, one must use a pellet size that minimizes diffusional resistance within the catalyst pellet but that also gives rise to an appropriate pressure drop across the catalyst bed. Some considerations which are important in the handling and use of catalysts for fixed bed operation in industrial situations are discussed in the Catalyst Handbook (1). 

One of the major disadvantages of fixed bed operation is that catalyst regeneration or replacement is relatively difficult to accomplish. If the catalyst deactivation rate is sufficiently... 

This section treats batch and fixed-bed operations and reviews process cycles and equipment. As the processes indicate, fixed-bed operation with the sorbent in granule, bead, or pellet form is the predominant way of conducting sorption separations and purifications. Although the fixed-bed mode is highly useful, its analysis is complex. Therefore, fixed beds including chromatographic separations are given primary attention here with respect to both interpretation and prediction. 

Analogous relationships are derived for SMB systems where each zone comprises a number of fixed beds operated in a merry-go-round sequence, as shown in Fig. 16-48. External flow velocities are calculated from Eqs. (16-209a) to (16-209d), replacing us with... 

Conversion rate of the investigated reactor fixed bed operated as a plug flow reactor... 

As an example of the chemical significance of the process technology, the products of the Fischer-Tropsch synthesis, in which a significant amount of gas phase polymerization occurs vary markedly from fixed bed operation to the fluidized bed. The fixed bed product contains a higher proportion of straight chain hydrocarbons, and the fluidized bed produces a larger proportion of branched chain compounds. 

An analytical solution of these mass-transfer equations for linear equilibrium was found by Thomas [36] for fixed bed operations. The Thomas solution can be further simplified if one assumes an infinitely small feed pulse (or feed arc in case of annular chromatography), and if the number of transfer units (n = k0azlu) is greater then five. The resulting approximate expression (Sherwood et al. [37]) is... 

If the catalyst has to be treated (regenerated) frequently because it deactivates rapidly, then the liquid-like fluidized state allows it to be pumped easily from unit to unit. This feature of fluidized contacting offers overwhelming advantages over fixed bed operations for such solids. 

Acrivos, A., On the combined effect of longitudinal diffusion and external mass transfer resistance in fixed bed operations. Chem. Eng. Sci. 13, 1 (1960). 

The fixed-bed operation is usually a semicontinuous process. When the medium gets spent, the fixed-bed operation is stopped and the material is replaced with a fresh batch. In fixed-bed operation, the determination of the medium being spent is usually based on the breakpoint, which is the point at which the exit concentration of the solutes being removed starts to increase sharply to some predetermined level (typically below 10%). If interruptions in the process to replace the adsorbent or the ion exchange media are not desirable, multiple fixed beds can be connected in parallel. While one set is in operation, the other is filled with a fresh medium or, after refilling, is on standby. 

This equation holds for adsorption, ion exchange as well as for catalytic systems, which are in a transient operating condition, e.g. during severe catalyst deactivation. For a steady state catalytic fixed-bed operation, eq. (3.287) becomes... 

The general balance equation for an unsteady-state fixed-bed operation is (Ruthven, 1984 Froment and Bischoff, 1990)... 

In general, large industrial fixed beds operate under near-adiabatic conditions, whereas small laboratory-scale fixed beds may approach isothermal operation (Ruthven, 1984). Especially, for most environmental applications, for catalytic, adsorption, and ion-exchange operations, the species to be removed are in such low concentrations that the operarion is nearly isothermal. Thus, the heat transfer to the external fixed-bed wall is often of minimal importance. 

In the following equations, the Reynolds number is based on the superficial velocity. Fu and Tan correlation has been derived from experiments conducted in three-phase fixed beds packed with spherical particles and for particle diameters between 0.5 and 1.9 mm. Fixed bed operated under downflow conditions and a liquid distributor was used. The correlation was derived for Rep between 0.1 and 10 (Fu and Tan, 1996) ... 

More general is the equation proposed by Otake and Okada, derived for several particle shapes and for Rep between 10 and 2000. The proposed equation has been derived in two-phase fixed beds, operating under downflow condition and utilizing a liquid distribution system at the top of the bed (Doraiswamy et al., 1984 Van Swaaij et al., 1969) ... 

The following equation was derived utilizing direct weighting methods, in two-phase fixed beds operating under downflow condition and utilizing a liquid distributor at the bed inlet. This equation holds for particles of several shapes, including irregular-shaped particles of activated carbon of 1 mm diameter and for 0.3 < Rep < 3000 (Specchia and Baldi, 1977 Colombo and Baldi, 1976) ... 

The mechanical strength of a catalyst is really important in its commercial applications, since broken pieces and losses can lead to a decrease in catalytic activity and a significant expense, especially when precious metals are used as the catalytic agents. Mechanical strength is equally important in adsorption and ion exchange, especially in fixed-bed operations. 

General As analyzed in Section 3.1.2, among the various steps that are part of a process, there is frequently one that is much slower than the others, thus controlling the rate of the whole mechanism. Hence, the slow step is called the rate-limiting step or the rate-controlling step. The principle of the rate-limiting step is often applied since it greatly simplifies the models used, but we should keep in mind that it is valid for processes in series. Most of the criteria that will be presented can be equally used in batch and fixed-bed operations. 

Miura and Hashimoto (1977) used the following dimensionless number for fixed-bed operation ... 

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