Rigorous Distillation Calculations

FIG. 13-32 Comparison of rigorous calculations with Gilliland correlation. [Henley and Seader, Equilibrium-Stage Separation Operations in Chemical Engineering, Wiley, New York, 1981 data of Van Winkle and Todd, Chem. Eng., 78(21), 136 (Sept. 20, 1971) data of Gilliland, Elements of Fractional Distillation, 4th ed., McGraw-Hill, New York, 1950 data of Brown and Martin, Trans. Am. Inst. Chem. Eng., 35, 679 (1939).]... 

Fletcher, J. P., A Method for the Rigorous Calculation of Distillation Columns Using a Generalized Efficiency Model, The Institution of Chemical Engineers Symposium Series No. 104, Distillation and Absorption 1987, A437-A447 (1987). 

Design versus Rating Models for Rigorous Distillation Stage Calculations... 

Before the 1950s, distillation column calculations were performed by hand. Although rigorous calculation procedures were available, they were difficult to apply for all but very small columns. Shortcut methods were therefore the primary design tool. Rigorous procedures were seldom used. Inaccuracies and uncertainties in the shortcut procedures were usually accommodated by overdesign. 

By default, a distillation column includes a condenser and rcboiler Heats or cools a single process stream, exchanges heat between two process streams or between a process and utility stream Rates a TEMA shell-and-tube heat exchanger, rigorously calculating heat transfer and pressure drop... 

Shortcut calculations provided by the Fenske-Underwood-Gilliland are most effective for a preliminary design before the use of distillation simulation software that utilizes much more rigorous calculation methods. 

Commercial computer services are available to do rigorous distillation calculations. Perhaps the licensor will provide copies of rigorous computer runs to validate his balances. Alternately, the operating company can make such runs. For highly non-ideal systems, literature data for binary pairs may have to be sought. In some cases, laboratory equilibrium data may have to be obtained in-house or contracted out to one of several organizations or universities that are in this business. 

Haas, J. R. (1992) Rigorous Distillation Calculations, in Distillation Design, Kister, H. Z. (McGraw-Hill). 

To solve Equation 9.51, it is necessary to know the values of not only a ,-j and 9 but also x, d. The values of xitD for each component in the distillate in Equation 9.51 are the values at the minimum reflux and are unknown. Rigorous solution of the Underwood Equations, without assumptions of component distribution, thus requires Equation 9.50 to be solved for (NC — 1) values of 9 lying between the values of atj of the different components. Equation 9.51 is then written (NC -1) times to give a set of equations in which the unknowns are Rmin and (NC -2) values of xi D for the nonkey components. These equations can then be solved simultaneously. In this way, in addition to the calculation of Rmi , the Underwood Equations can also be used to estimate the distribution of nonkey components at minimum reflux conditions from a specification of the key component separation. This is analogous to the use of the Fenske Equation to determine the distribution at total reflux. Although there is often not too much difference between the estimates at total and minimum reflux, the true distribution is more likely to be between the two estimates. 

Thirty years ago these computed variables were calculated using pneumatic devices. Today they are much more easily done in the digital control computer. Much more complex types of computed variables can now be calculated. Several variables of a process can be measured and all the other variables can be calculated from a rigorous model of the process. For example, the nearness to flooding in distillation columns can be calculated from heat input, feed flow rate, and... 

Another evident trend is the application of mechanical computers for the rapid calculation of distillation problems. At least two papers have already appeared, one by Weil (57) on the use of an electronic computer, and the other by Rose and Williams (47) on the application of the IBM card punch technique. If a short rigorous method is not forthcoming, machine calculations may be the answer to accurate design of fractionating equipment. 

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