Symposium on Distillation Held under t h e auspices of the Division of Industrial and Engineering Chemistry of the American Chemical Society a t the Massachusetts Institute of Technology, Cambridge, Mass., December 28 and 29, 1934.
#+*-
Design of Fractionating Columns
A simplified method of computing the number of equilibrium plates required for the separation of complex mixtures was developed and found reliable as compared with theoretically rigorous calculations and with test data on commercial equipment. The over-all plate efficiency of a natural gasoline fractionator was found to be close to 100 per cent.
Number of Plates for Gas and Gasoline Fractionators'
11,
HE absorption factor concept proposed by Kremser (3) and applied by Souders and Brown (6) to gas absorbers and oil strippers has been previously suggested (1) as an apparent satisfactory basis for calculating the number of equilibrium plates required in fractionating columns. The original procedure included some unsatisfactory assumptions which have been eliminated in the improved and simplified method herein described.
GEORGE GRAYGER BROWN, MOTT SOUDERS, JR., H. V. NYLAND,* AND WILLIAM W. HESLER3 University of Michigan, Ann Arbor, Mich.
Improved Absorption Factor Method The absorption factor method uses an absorption or stripping factor in an equation which involves the number of equilibrium plates required over a section of a column to effect the change in terminal concentrations of an individual component. The method may be applied to one component at a time and is not limited to relatively complete separations between adjacent components. If the quantities of ascending vapor and descending liquid are assumed to be constant, a material balance for any one component and around any plate above the feed gives the equation : I/n+1
=
Yn
+ L - 7L 72"
Where yn + y,
zo
Ki
n ,4
(1)
xn-1
Under equilibrium conditions y
If the absorption factor, A , is a constant, the equation may be written as shown in Equation 5 .
=
Kz
(2)
A similar derivation for a section of the stripping column leads to the equation:
Substituting Equilibrium Equation 2 and the absorption factor, A , = L/K,V, the equation becomes: Ynt 1
= (1
+ An)
~n
- A n - I yn-1
(3)
Application of this equation to a number of successive plates leads to the general equation: Y ~ + I=
+ + + ++ . . ++An 1) yi - Ai + 1) Ktra
(Ai. .An Az. . A n .. (-42. .An Aa. . A n
R
An
(4)
here
zL = concn. of any component in the liquid entering LL
section of the stripping column xm = concn. of same component in liquid overflowing from bottom plate of the section ym+ 1 = concn. of same component in vapor entering bottom plate of the section K , = equilibrium constant for same component at temp. of bottom plate of the section m
1 2
a
concn. of any component in vapor entering a section of the rectifying column = concn. of same component in vapor rising from top plate of the section = concn. of same component in liquid entering top plate of the section = equilibrium constant for same component a t temp. of top plate of the section = number of theoretical plates in the section = L / K A V ,in which K A is the equivalent constant value of the equilibrium constant for the same component =
=
number of theoretical plates in the section
S = K S ~ &in which K s is the equivalent constant value of the equilibrium constant for the same
Part I appeared in January, 1934, pages 98 t o 103. Present address, Sinclair Oil Refining Company, East Chicago, Ind. Present address, Parsons Engineering Company, Mount Vernon, Ohio
component
383
INDUSI'I\IAI, 4 N D ENGINEERING CIiE~MlSTHY
,384
In setting up the conditions for a design problem for a given complex feed, only total pressure, reflux ratio, quantity of distillate, mole fraction of one component in tlie distillate, and mole fraction of another component in the bottoms may be fixed. All other compositions and quantities are dependent. Usually the more volatile components may be assumed to be ahsent from the bottorns and the less volatile components absent from tlie distillate, leaving only two or t h e e components to be distributed between distillate and bottoms. TIE composition of tlie distillate and biittoms computed on this assumption are adea ances. quate for making material 13.1
TEKPEKATUI~E OF F E E DP L A T E . Since tire vapor rising from the feed plate is the feed to the rectifying section, and the liquid overflow from the feed plate is the feed to t.he stripping section, it is necessary to calculate the conipositions a t tlie feed plate ilepending upon tlie temperature of the feed plate. T i it is assnmed tiiat tlie tenrperatnre gradient between top and bottom terminal plates is linear, tlre tempcra.ture of tlie feed plate niay be calcrilated frnm the equation: :I =
where h
2'
n
t n--t m
(21
- 1')
(7)
VOL. 27, NO. 4
lationship, to determine the bottom terminal p l a t e f o r t h e s t r i p p i n g factor. COMPOSITION AT FEED PLATE. The computed composition of tlie liquid leaving the feed plate must have as its bubble point the temperature of tlie f e e d p l a t e e s t i m a t e d i n t h e mariner described. In order to fix this cornposition at the feed plate, it is necessary to know tlie temperature and pressure and t.he concentrations of all but two of the components. For components which do not a p pear iir the bottoms it may be assuined t,liat the mole fraction in the liquid leaving the feed plate is the so same as that of tlie plate above (4) t h a t , E q u a t , i o n 8 may be applied. Similarly, for coniimnentt. which do not appear in the distillate, Equation 9 may be used. Under these conditions a material balance for the more volatile components becomes Ka,
L
zq = V zo(
+ -nV ZOD
aiid.for lesb volatile components,
= temp of tup termirral plate,
Sini:e the uuinber of plat,ea above arid below tlie feed is not yet known, this equation involves a trinl a i d error procedure, wliich rapidly yields a satisfactory solution.
TEMPERATURE AND COMPOSITION AT TOP PLATE. By n e f f l e c t i n g ..,
as conservative practice, airy fractionation in the ovcriiead condenser, tlie vapor rising from the top plate niay be assumed to have the same composition as tlie top overhead distillate or product. The equilibrium tenipcrature a t the tap plate may then be calculated from the corup~mili~~n of this vapor (3). In many cases the temperature gradient betweeti thc plates a t tlie top of the coliimii is not linear. Til such cases Equations 1and 2 sliould he used t o compute tlle compositions and equilibriuni temperatures for a few plates belorn the top or, until the temperatnre gradient between successive plates is substantirdly uniform, to determine a plate that may Ilc used as tlie top terminal plate for applicatinii of the absorption factor. TELIPER~TURE AND COMPOSITION AT Borrow I'LATE. The composition of the liquid leaving the bottom plate niiiy lie calculated by assuming that the bottoms product is in eqnilibrium with the vapor entering the bottom plate and by making a material halance around tlie reboiler or kettle. The temperature difference between successive plates near the bottom is usually far from uniform, and it is advisable to use Equations 1 and 2 to compute the temperatures for a few plates until the temperature gradient approaches it liricar re-
Wlion there are thrce cotnponents wliich appear in significant quantities in both overliead and bottoms. Euuatiorr 8 may be applied to the most volatile of these three ;omponents if the mole fraction of this component in the bottoms is sinall and the ratio of the number of plates above the feed to the number below tlie feed (n/m) is greater tlran two. The nrualler tlie mole fraction in tlie bottoms arid tlie larger the ratio of plates, the more applicable is Equation 8. Equation 0 may be applied to t.he least volatile component appearing in Imt,ii overhead and bott.oms if the inole fraction of this conipouent, in the distillate is sinal1 and the ratio n/m is less tliarr one-third. The smaller the mole fract,ion in the distillate and tlie strraller the ratio of dates. the more aunlicable .. is Eqiiatiou 9. The mole ir:rctions of all bilt two cornironeirts in the liouid leaving the iecd plate may usnally be determined as descriied. Tlic mole fractions of these two intermediate components may be determined from the entimated tenrperature of the feed plate and the two relationships: (1) Sum oi isrole fractions of all components in the liquid leaving the feed plate is iinit.y; and (2) sum of products of I
