Tower Theory

The cooling tower cools hot water tvith cool air by countercurrent (or cross-current) fiow of the tw o fluids past each other in a tower filled with packing. This involves both mass and heat transfer. The water surface that exists on the tower packing is covered with an air film assumed to be saturated at the water temperature. The heat is transferred between this film and the main body of air by diffusion and convection. Detailed presentations of the development of cooling tower theory are given in References 39 and 46. 

In packed towers, the variation of conditions from top to bottom is continuous and not interrupted as at trays. Nevertheless, it is convenient to speak of packing heights equivalent to a theoretical tray (HETU), so that tray tower theory can be applied to the design of packed towers. 

Cooling Tower Theory The most generally accepted theory of the coohng tower heat-transfer process is that developed by Merkel (op. cit.). This analysis is based upon enthalpy potential difference as the driving force. 

Equation 39 can often be simplified by adopting the concept of a mass transfer unit. As explained in the film theory discussion eadier, the purpose of selecting equation 27 as a rate equation is that is independent of concentration. This is also tme for the Gj /k aP term in equation 39. In many practical instances, this expression is fairly independent of both pressure and Gj as increases through the tower, increases also, nearly compensating for the variations in Gj. Thus this term is often effectively constant and can be removed from the integral ... 

The stagnant-film model discussed previously assumes a steady state in which the local flux across each element of area is constant i.e., there is no accumulation of the diffusing species within the film. Higbie [Trans. Am. Jn.st. Chem. Eng., 31,365 (1935)] pointed out that industrial contactors often operate with repeated brief contacts between phases in which the contact times are too short for the steady state to be achieved. For example, Higbie advanced the theory that in a packed tower the liquid flows across each packing piece in laminar flow and is remixed at the points of discontinuity between the packing elements. Thus, a fresh liquid surface is formed at the top of each piece, and as it moves downward, it absorbs gas at a decreasing rate until it is mixed at the next discontinuity. This is the basis of penetration theoiy. 

Mass-transfer theory indicates that for trays of a given design the factors most hkely to inflnence E in absorption and stripping towers are the physical properties of the flnids and the dimensionless ratio Systems in which the mass transfer is gas-film-controlled may be expected to have plate efficiencies as high as 50 to 100 percent, whereas plate efficiencies as low as 1 percent have been reported for the absorption of gases of low sohibility (large m) into solvents of relatively high viscosity. 

Much of the basic theory of reaction kinetics presented in Sec. 7 of this Handbook deals with homogeneous reaclions in batch and continuous equipment, and that material will not be repeated here. Material and energy balances and sizing procedures are developed for batch operations in ideal stirred tanks—during startup, continuation, and shutdown—and for continuous operation in ideal stirred tank batteries and plug flow tubulars and towers. 

Parameter Estimation Relational and physical models require adjustable parameters to match the predicted output (e.g., distillate composition, tower profiles, and reactor conversions) to the operating specifications (e.g., distillation material and energy balance) and the unit input, feed compositions, conditions, and flows. The physical-model adjustable parameters bear a loose tie to theory with the limitations discussed in previous sections. The relational models have no tie to theory or the internal equipment processes. The purpose of this interpretation procedure is to develop estimates for these parameters. It is these parameters hnked with the model that provide a mathematical representation of the unit that can be used in fault detection, control, and design. 

Thus either the penetration theory or the film theory (equation 10.144 or 10.145) respectively can be used to describe the mass transfer process. The error will not exceed some 9 per cent provided that the appropriate equation is used, equation 10.144 for L2 jDt > n and equation 10.145 for L2/Dt < n. Equation 10.145 will frequently apply quite closely in a wetted-wall column or in a packed tower with large packings. Equation 10.144 will apply when one of the phases is dispersed in the form of droplets, as in a spray tower, or in a packed tower with small packing elements. 

Wood, B. and Betts, P. Proc. Inst. Mech. Eng. (Steam Group) 163 (1950) 54. A contribution to the theory of natural draught cooling towers. 

The Tower of Alchemy is filled with intensely valuable occult principles, which are so often omitted, distorted, or unknown by other authors. The author also provides the reader with a series of exercises, which take the aspirant well beyond the scope of intellectual theory by actively involving the various levels of the personality in the practical application of the alchemical wisdom. It reveals a living tradition, whose aim is real transformation, not the mere accumulation of facts... 

As Sherwood and Pigford(3) point out, the use of spray towers, packed towers or mechanical columns enables continuous countercurrent extraction to be obtained in a similar manner to that in gas absorption or distillation. Applying the two-film theory of mass transfer, explained in detail in Volume 1, Chapter 10, the concentration gradients for transfer to a desired solute from a raffinate to an extract phase are as shown in Figure 13.19, which is similar to Figure 12.1 for gas absorption. 

Theory of the Action in the Gay-Lussac and Glover Towers.— The gases issuing from the chambers consist mainly of nitrogen dioxide, nitric oxide and atmospheric nitrogen. The two former are dissolved by the sulphuric acid in the Gay-Lussac tower with formation of a solution of nitrosylsulphuric acid in excess of sulphuric acid (see also below) ... 

An advantage possessed by this series of changes is that it explains more satisfactorily than the preceding theory why much sulphuric acid can be formed in the Glover tower. In the lead chambers the acid formed is so weak that the nitrososulphonic acid stage is possibly absent from the series. 

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