= 4.33 x 10-5 weights H2/100 weights H2O = 0.43 parts per million weight
Pure-component vapor pressure can be used for predicting solubilities for systems in which Raoult's law is valid. For such systems pA = p0AxA, where p"A is the pure-component vaporpressure of the solute and pA is its partial pressure. Extreme care should be exercised when using pure-component vapor pressures to predict gas absorption behavior. Both vapor-phase and liquid-phase nonidealities can cause significant deviations from Raoult's law, and this is often the reason particular solvents are used, i.e., because they have special affinity for particular solutes. The book by Poling, Prausnitz, and O'Connell (op. cit.) provides an excellent discussion of the conditions where Raoult's law is valid. Vapor-pressure data are available in Sec. 3 for a variety of materials.
Whenever data are available for a given system under similar conditions of temperature, pressure, and composition, equilibrium distribution coefficients (K = y/x) provide a much more reliable tool for predicting vapor-liquid distributions. A detailed discussion of equilibrium K values is presented in Sec. 13.
Calculation of Liquid-to-Gas Ratio The minimum possible liquid rate is readily calculated from the composition of the entering gas and the solubility of the solute in the exit liquor, with equilibrium being assumed. It may be necessary to estimate the temperature of the exit liquid based upon the heat of solution of the solute gas. Values of latent heat and specific heat and values of heats of solution (at infinite dilution) are given in Sec. 2.
The actual liquid-to-gas ratio (solvent circulation rate) normally will be greater than the minimum by as much as 25 to 100 percent, and the estimated factor may be arrived at by economic considerations as well as judgment and experience. For example, in some packed-tower applications involving very soluble gases or vacuum operation, the minimum quantity of solvent needed to dissolve the solute may be insufficient to keep the packing surface thoroughly wet, leading to poor distribution of the liquid stream.
When the solvent concentration in the inlet gas is low and when a significant fraction of the solute is absorbed (this often the case), the approximation y1GM = xLm = (y°/m)LM
leads to the conclusion that the ratio mGM/LM represents the fractional approach of the exit liquid to saturation with the inlet gas, i.e., mGM/LM = yï/yx
Optimization of the liquid-to-gas ratio in terms of total annual costs often suggests that the molar liquid-to-gas ratio LM/GM should be about 1.2 to 1.5 times the theoretical minimum corresponding to equilibrium at the rich end of the tower (infinite height or number of trays), provided flooding is not a problem. This, for example, would be an alternative to assuming that LM/GM ~ m/0.7.
When the exit-liquor temperature rises because of the heat of absorption of the solute, the value of m changes through the tower, and the liquid-to-gas ratio must be chosen to give reasonable values of mGM/LM and m2GM/LM, where the subscripts 1 and 2 refer to the bottom and top of the absorber, respectively. For this case, the value of m2GM/LM will be taken to be somewhat less than 0.7, so that the value of miGM/LM will not approach unity too closely. This rule-of-thumb approach is useful only when the solute concentration is low and heat effects are negligible.
When the solute has a large heat of solution or when the feed gas contains high concentrations of the solute, one should consider the use of internal cooling coils or intermediate liquid withdrawal and cooling to remove the heat of absorption.
Selection of Equipment Trays and random packings have been extensively used for gas absorption; structured packings are less common. Compared to trays, random packings have the advantages of availability in low-cost, corrosion-resistant materials (such as plastics and ceramics), low pressure drop (which can be an advantage when the tower is in the suction of a fan or compressor), easy and economic adaptability to small-diameter (less than 0.6-m or 2-ft) columns, and excellent handling of foams. Trays are much better for handling solids and fouling applications, offer greater residence time for slow absorption reactions, can better handle high L/G ratios and intermediate cooling, give better liquid turndown, and are more robust and less prone to reliability issues such as those resulting from poor distribution. Details on the operating characteristics of tray and packed towers are given later in this section.
Column Diameter and Pressure Drop Flooding determines the minimum possible diameter of the absorber column, and the usual design is for 60 to 80 percent of the flooding velocity. In near-atmospheric applications, pressure drop usually needs to be minimized to reduce the cost of energy for compression of the feed gas. For systems having a significant tendency to foam, the maximum allowable velocity will be lower than the estimated flooding velocity. Methods for predicting flooding velocities and pressure drops are given later in this section.
Computation of Tower Height The required height of a gas absorption or stripping tower for physical solvents depends on (1) the phase equilibria involved; (2) the specified degree of removal of the solute from the gas; and (3) the mass-transfer efficiency of the device. These three considerations apply to both tray and packed towers. Items 1 and 2 dictate the required number of theoretical stages (tray tower) or transfer units (packed tower). Item 3 is derived from the tray efficiency and spacing (tray tower) or from the height of one transfer unit (packed tower). Solute removal specifications are usually derived from economic considerations.
For tray towers, the approximate design methods described below may be used in estimating the number of theoretical stages, and the tray efficiencies and spacings for the tower can be specified on the basis of the information given later. Considerations involved in the rigorous design of theoretical stages for tray towers are treated in Sec. 13.
For packed towers, the continuous differential nature of the contact between gas and liquid leads to a design procedure involving the solution of differential equations, as described in the next subsection. Note that the design procedures discussed in this section are not applicable to reboiled absorbers, which should be designed according to the procedures described in Sec. 13.
Caution is advised in distinguishing between systems involving pure physical absorption and those in which chemical reactions can significantly affect design procedures. Chemical systems require additional procedures, as described later in this section.
Selection of Stripper Operating Conditions Stripping involves the removal of one or more components from the solvent through the application of heat or contacting it with a gas such as steam, nitrogen, or air. The operating conditions chosen for stripping normally result in a low solubility of solute (i.e., high value of m), so that the ratio mGM/LM will be larger than unity. A value of 1.4 may be used for rule-of-thumb calculations involving pure physical absorption. For tray-tower calculations, the stripping factor S = Kgm/Lm, where K = y°/x usually is specified for each tray.
When the solvent from an absorption operation must be regenerated for recycling to the absorber, one may employ a "pressure-swing" or "temperature-swing" concept, or a combination of the two, in specifying the stripping operation. In pressure-swing operation, the temperature of the stripper is about the same as that of the absorber, but the stripping pressure is much lower. In temperature-swing operation, the pressures are about equal, but the stripping temperature is much higher than the absorption temperature.
In pressure-swing operation, a portion of the gas may be "sprung" from the liquid by the use of a flash drum upstream of the stripper feed point. This type of operation has been discussed by Burrows and Preece [Trans. Inst. Chem. Eng., 32, 99 (1954)] and by Langley and Haselden [Inst. Chem. Eng. Symp. Ser. (London), no. 28 (1968)]. If the flashing of the liquid takes place inside the stripping tower, this effect must be accounted for in the design of the upper section in order to avoid overloading and flooding near the top of the tower.
Often the rate at which residual absorbed gas can be driven from the liquid in a stripping tower is limited by the rate of a chemical reaction, in which case the liquid-phase residence time (and hence the tower liquid holdup) becomes the most important design factor. Thus, many stripper regenerators are designed on the basis of liquid holdup rather than on the basis of mass-transfer rate.
Approximate design equations applicable only to the case of pure physical desorption are developed later in this section for both packed and tray stripping towers. A more rigorous approach using distillation concepts may be found in Sec. 13. A brief discussion of desorption with chemical reaction is given in the subsection "Absorption with Chemical Reaction."
Design of Absorber-Stripper Systems The solute-rich liquor leaving a gas absorber normally is distilled or stripped to regenerate the solvent for recirculation back to the absorber, as depicted in Fig. 14-3. It is apparent that the conditions selected for the absorption step
FIG. 14-3 Gas absorber using a solvent regenerated by stripping. (a) Absorber. (b) Stripper.
FIG. 14-3 Gas absorber using a solvent regenerated by stripping. (a) Absorber. (b) Stripper.
(e.g., temperature, pressure, LM/GM) will affect the design of the stripping tower, and conversely, a selection of stripping conditions will affect the absorber design. The choice of optimum operating conditions for an absorber-stripper system therefore involves a combination of economic factors and practical judgments as to the operability of the system within the context of the overall process flow sheet. In Fig. 14-3, the stripping vapor is provided by a reboiler; alternately, an extraneous stripping gas may be used.
An appropriate procedure for executing the design of an absorberstripper system is to set up a carefully selected series of design cases and then evaluate the investment costs, the operating costs, and the oper-ability of each case. Some of the economic factors that need to be considered in selecting the optimum absorber-stripper design are discussed later in the subsection "Economic Design of Absorption Systems."
Importance of Design Diagrams One of the first things a designer should do is to lay out a carefully constructed equilibrium curve y0 = F(x) on an xy diagram, as shown in Fig. 14-4. A horizontal line corresponding to the inlet-gas composition yi is then the locus of feasible outlet-liquor compositions, and a vertical line corresponding to the inlet-solvent-liquor composition x2 is the locus of outlet-gas compositions. These lines are indicated as y = y1 and x = x2, respectively on Fig. 14-4.
For gas absorption, the region of feasible operating lines lies above the equilibrium curve; for stripping, the feasible region for operating lines lies below the equilibrium curve. These feasible regions are bounded by the equilibrium curve and by the lines x = x2 and y = y1. By inspection, one should be able to visualize those operating lines that are feasible and those that would lead to "pinch points" within the tower. Also, it is possible to determine if a particular proposed design for solute recovery falls within the feasible envelope.
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