Constant molal overflow

For preliminary studies of batch rectification of multicomponent mixtures, shortcut methods that assume constant molal overflow and negligible vapor and liquid holdup are useful. The method of Diwekar and Madhaven [Ind. Eng. Chem. Res., 30, 713 (1991)] can be used for constant reflux or constant overhead rate. The method of Sundaram and Evans [Ind. Eng. Chem. Res., 32, 511 (1993)] applies only to the case of constant remix, but is easy to apply. Both methods employ the Fenske-Uuderwood-GiUilaud (FUG) shortcut procedure at successive time steps. Thus, batch rectification is treated as a sequence of continuous, steady-state rectifications. 

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

Dechman [109] illustrates a modification to the usual McCabe-Thiele diagram that assumes constant molal overflow in a diagram that recognizes unequal molal overflow. 

Binary System Material Balance Constant Molal Overflow Tray to Ttay... 

Constant molal overflow from stage to stage (theoretical) for simple ideal systems following Raoult s Law. More complicated techniques apply for nonideal systems. 

At constant molal overflow The time required for the distillation only. 

The direct-solution method of Akers and Wade [1] is among several which attempt to reduce the amount of trial-and-error solutions. This has been accomplished and has proven quite versatile in application. The adaptation outlined modifies the symbols and rearranges some terms for convenient use by the designer [3]. Dew point and bubble point compositions and the plate temperatures can be determined directly. Constant molal overflow is assumed, and relative volatility is held constant over sections of the column. 

Heat Balance—Adjacent Key Systems with Sharp Separations, Constant Molal Overflow... 

Equilibrium Basic Consideration, 1 Ideal Systems, 2 K-Factor Hydrocarbon Equilibrium Charts, 4 Non-Ideal Systems, 5 Example 8-1 Raoult s Law, 14 Binary System Material Balance Constant Molal Overflow Tray to Tray,... 

Since vapour phase dynamics are negleeted and "Constant Molal Overflow" conditions also apply, Vn+i = Vn = V, and... 

Equations (d) and (e) contain two unknowns D and B, which can be determined once F, XF, XB, and XD are specified. In addition, if the assumption of constant molal overflow is made, then the liquid L and vapor flows V are... 

The procedure starts with the specified terminal compositions and applies the material and energy balances such as Eqs. (13.64) and (13.65) and equilibrium relations alternately stage by stage. When the compositions from the top and from the bottom agree closely, the correct numbers of stages have been found. Such procedures will be illustrated first with a graphical method based on constant molal overflow. 

Figure 13.7. Features of McCabe-Thiele diagrams for constant molal overflow, (a) Operating line equations and construction and minimum reflux construction, (b) Orientations of -lines, with slope = ql q — 1), for various thermal conditions of the feed, (c) Minimum trays, total reflux, (d) Operating trays and reflux, (e) Minimum reflux determined by point of contact nearest xD.

Molal heats of vaporization often differ substantially, as the few data of Table 13.4 suggest. When sensible heat effects are small, however, the condition of constant molal overflow still can be preserved by adjusting the molecular weight of one of the components, thus making it a pseudocomponent with the same... 

Binary systems of course can be handled by the computer programs devised for multicomponent mixtures that are mentioned later. Constant molal overflow cases are handled by binary computer programs such as the one used in Example 13.4 for the enriching section which employ repeated alternate application of material balance and equilibrium stage-by-stage. Methods also are available that employ closed form equations that can give desired results quickly for the special case of constant or suitable average relative volatility. 

The background of shortcut methods is well treated in the books of King (1980) and Henley and Seader (1981). Here attention will be directed to application of the techniques. These shortcut methods assume constant molal overflow in the rectifying and stripping zones and constant relative volatilities, which may be taken at the conditions of the feed tray or as a geometric mean of the values at the top and bottom of the column. Since the top conditions are not known completely in advance, evaluation of a mean relative volatility is an iterative process that can be started with the value at the feed tray or at the feed condition. Particular modes of variation of a sometimes are assumed. The method of Winn assumes that the vaporization equilibrium ratios vary as... 

Estimates must be made of V/L at the top and bottom and the feed zone. In distillation problems, assumption of constant molal overflow in each zone probably is within the accuracy of the method. In stripping or absorption columns, first iteration evaluations of the amounts of stripping or absorption will provide improved estimates of V/L at the key points in the columns. 

Most of the properties change somewhat from one end to the other of industrial columns for effecting separations, so that the mass transfer coefficients likewise vary. Perhaps the property that has the most effect is the mass rate of flow which appears in the Reynolds number. Certainly it changes when there is a substantial transfer of material between the two phases in absorption or stripping and even under conditions of constant molal overflow in distillation processes, the mass rate of flow changes because of differences of the molecular weights of the substances being separated. As a practical expedient, however, mass transfer coefficients are evaluated at mean conditions in a column. 

Only the important case of constant molal overflow will be considered. The material balance around the lower end of the column of Figure 13.15(b) is... 

After values of the variables 1) and Vp called tear variables, are specified, Eqs. (182)ff become a linear set in the x9 variables. Initial estimates of the vapor flows are made by assuming constant molal overflow modified by taking account of external inputs and outputs, and those of the temperatures by assuming a linear gradient between estimated top and bottom temperatures. Initially, also, the Kji are taken as ideal values, independent of composition, and for later iterations the compositions derived from the preceding one may be used to evaluate corrected values of With appropriate substitutions,... 

Box 1. Initial estimates of the temperature are made by taking linear variation between estimated overhead dewpoint and bottoms bubblepoint. The vapor rates are estimated on the basis of constant molal overflow with due regard to input or output sidestreams. 

Assuming constant molal overflow (2), the mass flow rate of component A must be related to the mass flow rate of component B... 

The initial total flow rate and temperature profiles can make the difference between success and failure of a rigorous method. Usually for distillation columns, the condenser and reboiler temperatures are estimated and a calculation that assumes constant molal overflow Sec. 2.2.2) is used to initialize tbe internal vapor and liquid flow... 

Where constant molar overflow does not work well, such as with nonideal systems or where there is a drastic difference between internal vapor and liquid rates. Section 2.2.2 discusses the applicability of constant molal overflow. 

Column operates adiabatically and constant molal overflow assumption is acceptable. 

A modified Thiele-Geddes method, programmed for an IBM 370-155, was used to perform the calculations needed to size each required column. Experimental activity coefficient data were used to allow for nonideal liquid phase behavior while energy balances, using estimated enthalpy data, were used to correct for non-constant molal overflow. The Theta Method was used for convergence, and all plate efficiencies were assumed to be 100%. (See Reference 7 for additional calculational details and a program listing.)... 

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