The Smoker equations

The equations can be easily programmed for solution on Personal Computers. A program written in GWBASIC is given in Table 11.1. 

Eliminating y from these equations gives a quadratic in x  

For any particular distillation problem equation 11.28 will have only one real root A between 0 and 1 

N = number of stages required to effect the separation represented by the concentration change from 

30 PRINT ALLOWS DIFFERENT REL. VOLS. IN STRIPPING AND RECTIFYING SECTIONS 40 PRINT 

For a column with a single feed and no side streams  

If the feed stream is not at its bubble point, z/ is replaced by the value of x at the 

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The Smoker equation (59) is convenient to use in binary separations with a large number of stages. The equation assumes constant relative volatility and constant molar overflow. The main application is in superfractionators such as ethylene-ethane and isobutane-n-butane separations. The Smoker equation is essentially an analytical solution... 

The Smoker equation must be applied individually for the rectifying and stripping sections. The values used for the rectifying section are... 

Hohmann (60) presents an extension of the Smoker equation to complex columns. ... 

Equation-Based Design Methods Exact design equations have been developed for mixtures with constant relative volatility. Minimum stages can be computed with the Fenske equation, minimum reflux from the Underwood equation, and the total number of stages in each section of the column from either the Smoker equation (Trans. Am. Inst. Chem. Eng., 34, 165 (1938) the derivation of the equation is shown, and its use is illustrated by Smith, op. cit.), or Underwoods method. A detailed treatment of these approaches is given in Doherty and Malone (op. cit., chap. 3). Equation-based methods have also been developed for nonconstant relative volatility mixtures (including nonideal and azeotropic mixtures) by Julka and Doherty [Chem. Eng. Set., 45,1801 (1990) Chem. Eng. Sci., 48,1367 (1993)], and Fidkowski et al. [AIChE /., 37, 1761 (1991)]. Also see Doherty and Malone (op. cit., chap. 4). 

DETERMINATION OF PLATES IN FRACTIONATING COLUMNS BY THE SMOKER EQUATIONS ... 

THIS PROGRAM CALCULATES THE NUMBER OF EQUILIBRIUM STAGES USING THE SMOKER EQUATIONS. 

Batch Rectification at Constant Reflux Using an analysis similar to the simple batch still, Smoker and Rose [Trans. Am. Inst. Chem. Eng., 36, 285 (1940)] developed the following equation ... 

Although Smoker and Rose presented the calculation method independent of time, the time can be introduced through the vapor boilup rate V of the reboiler. The resulting equation for determining total batch time is given by ... 

Model equations can be augmented with expressions accounting for covariates such as subject age, sex, weight, disease state, therapy history, and lifestyle (smoker or nonsmoker, IV drug user or not, therapy compliance, and others). If sufficient data exist, the parameters of these augmented models (or a distribution of the parameters consistent with the data) may be determined. Multiple simulations for prospective experiments or trials, with different parameter values generated from the distributions, can then be used to predict a range of outcomes and the related likelihood of each outcome. Such dose-exposure, exposure-response, or dose-response models can be classified as steady state, stochastic, of low to moderate complexity, predictive, and quantitative. A case study is described in Section 22.6. 

Jafarey et al. (61) derived a simple, approximate equation for binary distillation by simplifying the solution to Smoker s equation. Their equation is powerful for predicting the effect of disturbances on column performance. This makes their equation particularly useful in computer and microprocessor control, where it can be applied to estimate the effect of disturbances and the control action needed to compensate for them. This application is highlighted in Examples 3.8 and 3.9. The Jafarey et al, equation is... 

This chapter considers the vapor-liquid equilibrium of mixtures, conditions for bubble and dew points of gaseous mixtures, isothermal equilibrium flash calculations, the design of distillation towers with valve trays, packed tower design. Smoker s equation for estimating the number of plates in a binary mixture, and finally, the computation of multi-component recovery and minimum trays in distillation columns. 

Smoker s equations start by considering Raoult s law for a binary mixture, where a is a constant and represents the vapor-liquid equilibrium relationship. From Equation 7-25... 

Smoker s equation is not limited to the range of small concentrations, but can be used for stage calculation over the entire range. In such instances, the equation is written twice, one for each section of the tower. The average relative volatilities for the rectifying section and for the stripping section are determined. 

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