Height of column based on conditions in liquid film
A similar analysis may be made in terms of the liquid film. Thus from equations 1
and 2
(6)
where the concentrations C are in terms of moles of solute per unit volume of liquor. If
CT = (moles of solute + solvent) (volume of liquid), then:
Where (7)
The transfer equation (6) may now be written as:
Thus (8)
and for dilute concentrations this gives
(9)
where CT and kL have been taken as constant over the column.
Height based on overall coefficients
If the driving force based on the gas concentration is written as (Y ? Ye) and the overall
gas transfer coefficient as KG, then the height of the tower for dilute concentrations becomes
(10)
or in terms of the liquor concentration as:
(11)
Equations for dilute concentrations
As the mole fraction is approximately equal to the molar ratio at dilute concentrations
then considering the gas film:
(12)
and considering the liquid film:
(13)
The operating line and graphical integration for the height of a column
Taking a material balance on the solute from the bottom of the column to any plane where
the mole ratios are Y and X gives for unit area of cross-section:
(14)
Or (15)
This is the equation of a straight line of slope Lm/Gm, which passes through the point
(X1, Y1). It may be seen by making a material balance over the whole column that the
same line passes through the point (X2, Y2). This line, known as the operating line,
represents the conditions at any point in the column. Figure 2 illustrates typical conditions for the case of moist air and sulphuric acid or caustic soda solution, where the main resistance lies in the gas phase. The equilibrium curve represented by the line FR, and the operating line is given by AB, A corresponding to the concentrations at the bottom of the column and B to those at the top of the column. D represents the condition of the bulk of the liquid and gas at any point in the column, and has coordinates X and Y . Then, if the gas film is controlling the process, Yi equals Ye, and is given by a point F on the equilibrium curve, with coordinates X and Yi . The driving force causing transfer is then given by the distance DF. It is therefore possible to evaluate the expression:
by selecting values of Y , reading off from the Figure the corresponding values of Yi, and
thus calculating 1/(Yi ? Y). It may be noted that, for gas absorption, Y > Yi and Yi ? Y
and dY in the integral are both negative. If the liquid film controls the process, Xi equals Xe and the driving force Xi ? X is given in Figure 2 by the line DR. The evaluation of the integral:
المادة المعروضة اعلاه هي مدخل الى المحاضرة المرفوعة بواسطة استاذ(ة) المادة . وقد تبدو لك غير متكاملة . حيث يضع استاذ المادة في بعض الاحيان فقط الجزء الاول من المحاضرة من اجل الاطلاع على ما ستقوم بتحميله لاحقا . في نظام التعليم الالكتروني نوفر هذه الخدمة لكي نبقيك على اطلاع حول محتوى الملف الذي ستقوم بتحميله .
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