Lewis Matheson method

The method proposed by Lewis and Matheson (1932) is essentially the application of the Lewis-Sorel method (Section 11.5.1) to the solution of multicomponent problems. Constant molar overflow is assumed and the material balance and equilibrium relationship equations are solved stage by stage starting at the top or bottom of the column, in the manner illustrated in Example 11.9. To define a problem for the Lewis-Matheson method the following variables must be specified, or determined from other specified variables  

The usual procedure is to start the calculation at the top and bottom of the column and proceed toward the feed point. The initial estimates of the component distributions in the products are then revised and the calculations repeated until the compositions calculated from the top and bottom starts mesh, and match the feed at the feed point. 

Efficient procedures for adjusting the compositions to achieve a satisfactory mesh at the feed point are given by Hengstebeck (1976). 

Efficient procedures for adjusting the compositions to achieve a satisfactory mesh at the feed point are given by Hengstebeck (1961). Good descriptions of the Lewis-Matheson method, with examples of manual calculations, are also given in the books by Oliver (1966) and Smith (1963) a simple example is given in Volume 2, Chapter 11. 

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Hengstebeck shows how the method can be extended to deal with situations where the relative volatility cannot be taken as constant, and how to allow for variations in the liquid and vapour molar flow rates. He also gives a more rigorous graphical procedure based on the Lewis-Matheson method (see Section 11.8). 

In general, the Lewis-Matheson method has not been found to be an efficient procedure for computer solutions, other than for relatively straightforward problems. It is not suitable for problems involving multiple feeds, and side-streams, or where more than one column is needed. 

Like the Lewis-Matheson method, the original method of Thiele and Geddes (1933) was developed for manual calculation. It has subsequently been adapted by many workers for computer applications. The variables specified in the basic method, or that must be derived from other specified variables, are ... 

The Lewis-Matheson method does not work well for wide-boiling mixtures because of the required component distribution. There is also the difficulty of deciding what is a good match at the feed stage. 

The Lewis-Matheson method can be modified so that the number of stages is fixed and instead the product compositions or the reflux ratio is adjusted. The criterion of a match at the feed stage is preserved. 

The theta method. This method has been primarily applied to the Thiele-Geddes equations but a form of the theta method equation has also been applied to the equations of the Lewis-Matheson method. The main independent variable of the method is a convergence promoter, theta (or 6). The convergence promoter 0 is used to force an overall component and total material balance and to adjust the compositions on each stage. These new compositions are then used to calculate new stage temperatures by an approximation of the dew- or bubble-point equation called the Kb method. The power of the Kb method is that it directly calculates a new temperature without the sort of failures that occur when iteratively solving the bubble- or dew-point equations. 

Levapak , 427, 500, 616, 645. 665 Lewis tray efficiency cases. 371. 373 Lewis-Matheson method. 145. 146, 153 UNPACK, 159... 

Multicomponent distillation, 393 absorption factor method, 398 azeotropic, 420-426 bubblepoint (BP) method, 406-409 computer program references. 404 concentration profiles, 394 distribution of non-kevs. 395 Edmister method, 398,399 extractive, 412, 417-422 feed tray location, 397 free variables, number of 395 Lewis-Matheson method 404 MESH eauations. 405-407 molecular, 425-427 nomenclature, 405 number of theoretical trays, 397 packed towers, 433-439 petroleum, 411-415 reflux, minimum, 397 reflux, operating, 397 SC (simultaneous correction) method, 408-411... 

CALCULATION OF REQUIRED REFLUX RATIO AND CONCENTRATION PROFILES. The number of plates needed for a specified separation at a selected reflux ratio can be determined by a plate-by-plate calculation called the Lewis-Matheson method. The amount of all components in the products must be specified to start the calculation. From the composition of the distillate (which is the same as the vapor from the top if a total condenser is used), the temperature and liquid... 

The Lewis-Matheson method is also an equation-tearing procedure. It was formulated according to the Case I variable specification in. Table 6.2 to determine stage requirements for specifications of the separation of two key components, a reflux ratio and a feed-stage location criterion. Both outer and inner iterations are required. The outer loop tear variables are the mole fractions or flow rates of nonkey components in the products. The inner loop tear variables are the interstage vapor (or liquid) flow rates. The Lewis-Matheson method was widely used for hand calculations, but it also proved often to be numerically unstable when implemented on a digital computer. 

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