The Silver-Bell-Ghaly Method

This method takes advantage of the rough proportionality between heat and mass transfer coefficients according to the Chilton-Colburn analogy, and employs only heat transfer coefficients for the process of condensation from a mixture. The sensible heat of the vapor is transferred through the gas film 

In terms of an overall heat transfer coefficient U that does not include the gas film, the total heat transfer Qr that is made up of the latent heat and the sensible heats of both vapor and liquid is represented by 

When the unknown intcrfacial temperature 2J is eliminated and the ratio Z of sensible and total heat transfers 

A procedure will be described for taking the vapor from its initial dewpoint Tga to its final dewpoint corresponding to the required amount of condensation. Gas temperatures are specified at intermediate points and the heat balance is applied over one interval at a time. 

Prepare the condensing curve, a plot of the vapor temperature Tg against the amount of heat removed Q, by a series of isothermal flashes and enthalpy balances. 

Since the heat ratio Z, the temperatures and the heat transfer coefficients vary with the amount of heat transfer Qj. up to a position in the condenser, integration must be done numerically. The coolant temperature is evaluated from Eq. (8.38). Bell and Ghaly (1973) examine cases with multiple tube passes. 

The basis of the method was stated by Silver (1947). A numerical solution of a condenser for mixed hydrocarbons was carried out by Webb and McNaught (in Chisholm, 1980, p. 98) comparison of the Silver-Bell-Ghaly result with a Colbum-Hougen calculation showed close agreement in this case. Bell and Ghaly (1973) claim only that their method predicts values from 0 to 100% over the couect values, always conservative. A solution with constant heat transfer coefficients is made in Example 8.11 A recent review of the subject has been presented by McNaught (in Taborek et al., 1983, p. 35). 

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Additional corrections to hw can be made because of condensation conditions, but will not be included in this solution. With the establishment of the four temperature sections in the heat exchanger, the Silver-Bell-Ghaly method can now be used to approximate the required areas in... 

Condensers 200 Condenser Configurations 204 Design Calculation Method 205 The Silver-Bell-Ghaly Method 206... 

Empirical methods approximate methods, in which the resistance to heat transfer is considered to control the rate of condensation, and the mass transfer resistance is neglected. Design methods have been published by Silver (1947), Bell and Ghaly... 

The basic fluid dynamics and heat- and mass-transfer processes for multicomponent condensation are poorly understood, and the computation is difficult available design methods are both heuristic and feasible only for computer solution. The basic model was developed by Silver [42] and put in more general form by Bell and Ghaly [43]. Computer-based design methods that have been validated against experimental data are commercially available. 

Equilibrium methods, as proposed originally by Silver [200] and extended by Bell and Ghaly [201] and others, all assume that there is local equilibrium between the vapor and the condensate throughout the condenser. Even though condensation is a nonequilibrium process, the gas temperature Tg is assumed to follow a vapor-liquid equilibrium curve at T, as the vapor mixture is cooled from the mixture dew point 7"dew to the mixture bubble temperature Tbub. These methods therefore require the generation of a cooling or condensation curve (not to be confused with the condensation curve described in Fig. 14.1), as shown in Fig. 14.25,... 

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