Constant molar overflow

Operating Lines The McCabe-Thiele method is based upon representation of the material-balance equations as operating lines on the y-x diagram. The lines are made straight (and the need for the energy balance obviated) by the assumption of constant molar overflow. The liqmd-phase flow rate is assumed to be constant from tray to tray in each sec tiou of the column between addition (feed) and withdrawal (produc t) points. If the liquid rate is constant, the vapor rate must also be constant. 

The constant-molar-overflow assumption represents several prior assumptions. The most important one is equal molar heats of vaporization for the two components. The other assumptions are adiabatic operation (no heat leaks) and no heat of mixing or sensible heat effects. These assumptions are most closely approximated for close-boiling isomers. The result of these assumptions on the calculation method can be illustrated with Fig. 13-28, vdiich shows two material-balance envelopes cutting through the top section (above the top feed stream or sidestream) of the column. If L + i is assumed to be identical to L 1 in rate, then 9 and the component material balance... 

However, the total number of equilibrium stages N, N/N,n, or the external-reflux ratio can be substituted for one of these three specifications. It should be noted that the feed location is automatically specified as the optimum one this is assumed in the Underwood equations. The assumption of saturated reflux is also inherent in the Fenske and Underwood equations. An important limitation on the Underwood equations is the assumption of constant molar overflow. As discussed by Henley and Seader (op. cit.), this assumption can lead to a prediction of the minimum reflux that is considerably lower than the actual value. No such assumption is inherent in the Fenske equation. An exact calculational technique for minimum reflux is given by Tavana and Hansen [Jnd. E/ig. Chem. Process Des. Dev., 18, 154 (1979)]. A computer program for the FUG method is given by Chang [Hydrocarbon Process., 60(8), 79 (1980)]. The method is best applied to mixtures that form ideal or nearly ideal solutions. 

Pressure drops in the column will he neglected, and the K values will he read at 827 kPa (120 psia) in both column sections from the DePriester nomograph in Fig. 13-14. When constant molar overflow is assumed in each section, the rates in pound-moles per hour in the upper and lower sections are as follows ... 

The system is ideal, with equilibrium described by a constant relative volatility, the liquid components have equal molar latent heats of evaporation and there are no heat losses or heat of mixing effects on the plates. Hence the concept of constant molar overflow (excluding dynamic effects) and the use of mole fraction compositions are allowable. 

CONSTANT MOLAR OVERFLOW AND CONSTANT PLATE HOLDUP CONSTANT HOLDUP IN REBOILER AND SURGE DRUM... 

A batch still corresponding to a total separation capacity equivalent to eight theoretical plates (seven plates plus the still) is used to separate a hydrocarbon charge containing four (A, B, C, D) simple-hydrocarbon components. Both the liquid and vapour dynamics of the column plates are neglected. Equilibrium data for the system is represented by constant relative volatility values. Constant molar overflow conditions again apply, as in BSTILL. The problem was originally formulated by Robinson (1975). 

To illustrate the procedure the calculation will be shown for the reboiler and bottom stage, assuming constant molar overflow. 

With the feed at its boiling point and constant molar overflow the base flows can be calculated as follows ... 

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 ... 

In some computer applications of the method, where the assumption of constant molar overflow is not made, it is convenient to start the calculations by assuming flow and temperature profiles. The stage component compositions can then be readily determined and used to revise the profiles for the next iteration. With this modification the procedure is similar to the Thiele-Geddes method discussed in the next section. 

Start by considering the material balance for the part of the column above the feed, the rectifying section. Figure 9.6 shows the rectifying section of a column and the flows and compositions of the liquid and vapor in the rectifying section. First, an overall balance is written for the rectifying section (assuming L and V are constant, i.e. constant molar overflow) ... 

However, to fully understand the design of the column, the material balance must be followed through the column. To simplify the analysis, it can be assumed that the molar vapor and liquid flowrates are constant in each column section, which is termed constant molar overflow. This is strictly only true if the component molar latent heats of vaporization are the same, there is no heat of mixing... 

Again, assuming constant molar overflow (L and V are constant), these expressions can be combined to give an... 

The McCabe-Thiele Method is restricted in its application because it only applies to binary systems and involves the simplifying assumption of constant molar overflow. However, it is an important method to understand as it gives important conceptual insights into distillation that cannot be obtained in any other way. 

The Underwood Equations tend to underestimate the true value of the minimum reflux ratio. The most important reason for this is the assumption of constant molar overflow. As mentioned previously, the Underwood Equations assumed constant molar overflow between the pinches. So far, in order to determine the reflux ratio of the column, this assumption has been extended to the whole column. However, some compensation can be made for the variation in molar overflow by carrying out an energy balance around the top pinch for the column, as shown in Figure 9.16. Thus... 

In Chapter 9, it was shown how the Underwood Equations can be used to calculate the minimum reflux ratio. A simple mass balance around the top of the column for constant molar overflow, as shown in Figure 11.3, at minimum reflux gives ... 

If the feed is partially vaporized, the vapor flow below the feed will be lower than the top of the column. For above ambient temperature separations, the cost of operating the distillation will be dominated by the heat load in the reboiler and the vapor flow in the bottom of the column. For below ambient temperature separations, the cost of operating the column will be dominated by the cost of operating the refrigerated condenser and hence the vapor flow in the top of the column. If constant molar overflow is assumed, the vapor flow in the bottom of the column V is related to the vapor flow in the top of the column by... 

The number of molecules passing in each direction from vapour to liquid and in reverse is approximately the same since the heat given out by one mole of the vapour on condensing is approximately equal to the heat required to vaporise one mole of the liquid. The problem is thus one of equimolecular counterdiffusion, described in Volume 1, Chapter 10. If the molar heats of vaporisation are approximately constant, the flows of liquid and vapour in each part of the column will not vary from tray to tray. This is the concept of constant molar overflow which is discussed under the heat balance heading in Section 11.4.2. Conditions of varying molar overflow, arising from unequal molar latent heats of the components, are discussed in Section 11.5. 

This method is one of the most important concepts in chemical engineering and is an invaluable tool for the solution of distillation problems. The assumption of constant molar overflow is not limiting since in very few systems do the molar heats of vaporisation differ by more than 10 per cent. The method does have limitations, however, and should not be employed when the relative volatility is less than 1.3 or greater than 5, when the reflux ratio is less than 1.1 times the minimum, or when more than twenty-five theoretical trays are required(13). In these circumstances, the Ponchon-Savarit method described in Section 11.5 should be used. 

Assuming constant molar overflow, then for the part of the column above the sidestream the operating line is given by ... 

The enthalpy-composition approach may also be used for multiple feeds and sidestreams for binary systems. For the condition of constant molar overflow, each additional sidestream or feed adds a further operating line and pole point to the system. 

The HETP of a column, valid for either distillation or dilute-gas absorption and stripping systems in which constant molar overflow can be assumed, and in which no chemical reactions occur, is related to the height of one overall gas-phase mass-transfer unit, HQG, by the equation ... 

Equation (14-135) is based on the assumption of constant molar overflow and a constant value of Emv from tray to tray. It needs to be applied separately to each section of the column (rectifying and stripping) because GM/LM, and therefore X, varies from section to section. Where molar overflow or Murphree efficiencies vary throughout a section of column, the section needs to be divided into subsections small enough to render the variations negligible. 

For single separation duty, Farhat et al. (1990) considered the operation of an existing column for a fixed batch time and aimed at maximising (or minimising) the amount of main-cuts (or off-cuts) while using predefined reflux policies such as constant, linear (with positive slope) and exponential reflux ratio profile. They also considered a simple model with negligible liquid holdup, constant molar overflow and simple thermodynamics, but included detailed plate to plate calculations (similar to Type III model). 

Constant molar overflow. This assumption is a substitute for the energy balances, It states that the mixture has a constant heat of vaporization and that sensible heat and heat of mixing effects are negligible. Equations (2.7) and (2.8) give a mathematical expression of this assumption, Detailed thermodynamic implications of this assumption are described elsewhere (e.g, Hefs. 6-8),... 

Generally, constant molar overflow holds well for systems where tbe components are similar in nature and molecular weights, and... 

When latent heat varies from stage to stage, so do the LfV and L FV ratios. For this reason, when the constant molar overflow assumption (Sec. 2.2.2) does not apply, the component balance relationship becomes a curve instead of a straight line. 

Minimum reflux can be determined by graphical (Secs. 2.3.5, 2.4.1), shortcut (Secs. 3.2.2 to 3.2.4), or rigorous techniques. Most graphical and shortcut methods give good results either when constant molar overflow (Sec. 2.2.2) applies, or when the method is corrected for energy balance. Unfortunately, shortcut methods in most commercial simulations apply no energy balance correction, and wBd minimum reflux predictions are not uncommon. 

Underwood s method (36). This method solves an equation which relates feed composition, thermal condition of the feed, and relative volatility at the average temperature of the column for a factor 6 which lies numerically between the relative volatilities of the keys. This factor is substituted in a second equation which relates minimum reflux to relative volatility and distillate composition. The method assumes constant relative volatility at the mean column temperature and constant molar overflow (Sec. 2.2.2). This method gives reasonable engineering accuracy for systems approaching ideality (28). The Underwood method has traditionally been the most popular for minimum reflux determination, When no distributed key components are present, the method is... 

The Colburn method (39) This method calculates the minimum reflux ratio of the key components as if they formed a binary system, then corrects this value for light and heavy nonkeys. The Colburn method assumes constant molar overflow and constant relative volatility in each zone of constant composition in the column. This method is more elaborate, but has been recommended (28) as probably the most accurate shortcut method for minimum reflux. 

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