Design for Hydrocarbon
ABSORPTION AND STRIPPING w.e. c
w
STANDARD OIL COMPANY (INDIANA), XHITINQ,
Equations are developed lor making hydroarbon absorption and stripping design calculations. W i v e absorption (or stripping) factors, o b tained by analytiul equations from the terminal (top and bottom tray) conditions, an used in this method. Absorption and stripping efficiencies an computed by equations using these effective factors and taking into account the compositions d the wet gas and the k.n oil in the use 01 absorption and rich oil, and the stripping gas in the case d stripping. The eppliition of the method is outlined. For componenb appearing in both wet and gas and Ieen oil, it is kquently necessary to apply both the absorption and stripping .quations. A cornprison of this md 0 t h methods wid phto-plate ulcuktions i n d i d that this provides an accurate and rapid short cut.
HE recovery of valuable hydrocarbons from mnlti~~ by absorption, followed component g a s e ~mixturea by Bteam stripping of the enriched solvent, is an important process in the petroleum industry. A simpMed flow diagram of thia proeeae is given in Figure 1. This system con&a of an absorber, stripper, and auxilisries. In spite of the importgnce of these operations, no rapid accurate method of design hss been proposed. Such a method is presented in this psper. If the number of theoretical plates are known or assumed, the ragired lean oil rates for absorption and the steam quantities for stripping may be found by plate-to-plate tal+ tiom involving heat and material balances and phase eqnilibria at each theoreticalcontact of vapor and liquid, a tedious and slow method. By the Kremser-Brown method, which involves the nee of absorption and stripping factors, originally pmpased by Kremser (8)and later improved by Soudera and Brown (J), d a calculations of this kind may be made more rapidly. However, the simplifying assumptions made in the development of the Kremser-Brown method often lead to serious errom, particulsrly in the design of absorbers treatingrich gssee. The h e r the gas and the greater the solvent quantity, the more reliable is the Krem9er-Brown method. A more Becurate method of making absorption and strip ping calculations is the rigorous graphical treatment of Sherwood (a. The theoretical plates are stepped off between operating. and equilibrium lines on an X-Y plot for the key component in determining the proper relation between number of plate, re cove^^, and solvent or steam rate. For this
T
I
Fr-t.ddns
INO.
plot the operating line is made straight and the equilibrium line curved to fit the equilibrium relations at both enda of the column. The Kremser-Brown absorption factor method is frquently used in making first approximations before a p plyinS this graphid method. NeVerthdW, the COlUtNCtion of an X-Y plot of d c i e n t accuracy for process design calculations is frequently too tedious and time conwming to be practical for most design problems. Recently Horton and Franklin (I) proposed two design procedures for predicting absorber performance. Their first method, which is the longer and more accurate, involves the use of separate a h r p t i o n factors for each component on each plate throughout the absorber, and the calculation of the absorption efficiency by a gehed equation. Their see ond and shorter method involves the use of an &ective absorption factor for emh component, and the calculation of absorption efficiency by the Kremser-Brown equation. In this method the effwtive absorption factor for the more volatile components is the L/KV ratio near the bottom of the a b sorber, and for the less volatile components it is the L/KV ratio near the middle of the tower. An empirical rule for locating and evaluating these &eotive absorption factors is proposed by Horton and FranLlin. Brie&. their pmoedure is ( 4 ) ta assume the total amount of gas absorbed,(b)estimate the L/V ratio and the tamperstwe at various points in the column, (c) evaluate the effective absorption factors by the propoaed method, (d) calculate the absorption e5iciency by the ILremaer-Brown equation, and (e) reviee the assumption of totsl gas absorbed and repeat the above steps. Horton and Franklin recommend this second and shorter method 88 a first trial, and their first and more rigorous method aa the final trial in the solution of absorption prohlems. A new method of making absorption and stripping design calculations by the use of effective absorption or stripping factors, which are obtained from an analytically derived equation, is presented in this paper. Plateto-plate calculations were made up to eight equilibrium stsgas, and for prsctical purposes the assumption could be made that the &e* tive absorption factor was independent of the number of plates. EWA~ONS
An algebraic solution of a platsto-plate calculation for ao absorber of n plate (Figure 1) is repwnted by the following equation, which involves only the wumption of equilibrium between vapor and liquid on each theoretical plate, where the plateg are numbered from top to bottom: A 1 A A...A.+A& ...A s + .... + A . Y.,, - Y, = ( A ,A&.. A . + A A , .A. s + ....+ A . + l ) Y.+,
LOX.
C o m m , Wuhinlton. D. C.
037
+
+
+
A d , ...A . AI...A. ..... + A . 1 ( A I A A . . .A. A d , . ..A. . As+ 1
+
+. .+
INDUSTRIAL AND ENGINEERING CHEMISTRY
838
The derivation of Equation 1 was presented by Horton and Franklin (1). It is an exact expression for the efficiency of an absorber of .n plates; the term to the left of the equality sign is the absorption efficiency E,, the first term to the right gives the absorption efficiency for a denuded lean oil, and the second term to the right is a correction for the presence of solute in the lean oil. An analogous equation may be written for stripping. Using average effective absorption factors instead of values for each plate makes it possible to express Equation 1 in the following simplified manner:
Val. 35, No. 8
from which A, = dA,(AI
+ 1) + 0.25 - 0.5
(11)
Equation 11 gives values of A , for use with Equation 2 . An analogous equation is written by inspection for stripping:
8,= l / s n ( S i
+ 1) + 0.25 - 0.5
(12)
Equation 12 gives values of S , for use with Equation 5. An expression for A' is derived by combining Equations 6 and 7 as follows:
from which
where A , and A' are defined by the following relations:
Equation 14 gives values of A' to use with Equation 2. An analogous equation is written for stripping:
(4)
I n a similar manner the following analogous expression is written for the stripping efficiency:
where S, and S' are defined in the same way A , and A' are defined in Equations 3 and 4. Reference to Figure 1will make the significance of the terms in Equations 2 and 5 more clearly understood. Simple and direct equations or correlations for predicting the average effective absorption and stripping factors appearing in Equations 2 and 5 are desired. These relations have been developed by analyzing plate-to-plate calculations and test data for absorbers and strippers. From this study it was found that A , and A' are essentially independent of n, and can be expressed as functions of Al and A,, the terminal values of A , for practical design calculations with very little sacrifice in accuracy. If A , and A' are independent of n; Equations 3 and 4 may be written for any number of plates and useful equations developed. Rewriting Equations 3 and 4 for a two-plate absorber gives:
Equation 6 may be written
Factoring out [A, - I],
+
A, = 1 is always a solution to this equation but is of no interest. The other positive root is the one desired; hence,
Equation 15 gives values of S' to use with Equation 5. APPLICATION
OF METHOD
Equations 2, 5, 11, 12, 14, and 15 constitute the absorption and stripping design method proposed in this paper, These equations have been derived mathematically and are based on two fundamental assumptions: (a) Equilibrium exists between vapor and liquid on each theoretical plate, and (b) effective absorption and stripping factors are functions of terminal conditions only and independent of the number of theoretical plates. The above equations are not limited to the ideal cases of perfectly denuded lean absorption oil or stripping gas but may even be used to predict the performance of absorbers and strippers where overlapping occurs-e. g., where the same components appear in both the lean oil and wet gas. Unless a perfectly denuded and nonvolatile lean oil is used in absorbers, lean oil will be lost into the off gas due t o stripping the more volatile components of the lean oil. An analogous situation exists for strippers. Unless a perfectly inert and condensable free stripping gas is used in strippers, there will be absorption of the less volatile components of the stripping gas. Thus absorption and stripping may both occur simultaneously in the same absorber or stripper. Accordingly, both the absorption Equation 2 and the stripping Equation 5 must frequently be used in designing an absorber; the former equation is applied to all the components in the wet gas, and the latter to all components in the lean oil. I n applying Equations 2 and 5, it is convenient to have the last terms plotted graphically as a function of A , or 8, and n. Such a plot is easy to construct and therefore not presented in thie paper. For components that appear in both the wet gas and lean oil to an absorber, either absorption or stripping may take place or absorption may prevail on some and stripping on the others, depending upon the concentrations and operating conditions. It is usually possible to tell a t a glance which operation prevails for the various components in this overlapping region. If such is not the case, the first term in brackets to the right of the equality sign in either Equation 2 or 5-i. e., (1 L,XO/A'V,+1Y,+Jor (1 - V,Y,/S'L,+~X,+~)-may be applied to the components in question. One of these expressions will be negative and one positive for each of the overlapping
August, 1943
INDUSTRIAL AND ENGINEERING CHEMISTRY
839
components. The positive expression indicates the proper equation for that component. I n calculating the effective absorption or stripping factors ( A , and A’, or by Equations 11,12,14, and 15, be taken to use the proper values o
the equations presented below. The vapor contraction across any plate in an absorber is approximately represented by the following relation: Figure 1.
This equation says that the vapor contraction per plate is the same percentage of the vapor to the plate in question for all plates in an absorber. Applying Equation 16 to the top plate gives the following expression for the vapor leaving the second plate:
vz = V I (V*+l T).
I
Applying Equation 16 to the bottom plate gives the following expression for the vapor leaving the bottom plate:
ows that the proposed method is almost e calculations for a four-plate absorber. is shorter than Horton and Franklin’s rable accuracy ( I ) , although not more accurate. The method is more rapid and more accurate than Horton and Franklin’s Method 2. A comparison for absorbers containing more plates would be desirable. A A, A’
Equations 17 and 18 plus material balances around each plate will give the approximate L and V quantities for each plate. Temperatures on the top and bottom plates may be estimated by heat balances and the assumption that the temperature change per plate is proportional to the gas contraction. The accuracy of any method of making absorption and stripping design calculations is dependent upon the estimation of temperatures and liquid and vapor quantities. The initial assumption of total absorption for the liquid and vapor quantities and the heat balances for temperatures can be checked after the calculations of the absorption of each component are complete. It is frequently necessary to make a second set of calculations in order to bring the initial estimates and the final results into closer agreement. With experience these items may be estimated closely enough so that a second trial is unnecessary. C O M P A R I S O N OF M E T H O D S
Absorption efficiencies computed by this method are compared with those obtained by other methods in the following tabulation of “fraction absorbed” which means the amount of the component in the wet gas:
Methane Ethane Propsne n-Butane n-Pentane
Plate-to-Plate 0.0336 0.125 0.506 0.9185 0.9568
Hortm and Franklin Method 1 Method 2 0.0328 0.0327 0.122 0.127 0.501 0.509 0.916 0.921 0.956 0.9588
This Method 0.033 0.125 0.506 0.918 0 956 I
Flow Diagram for Absorbing-Stripping System
-
NOMENCLATURE
absorption factor = L / V K effective absorption factor effective absorption factor S = stripping factor = V K / L 8, = effective stripping factor S’ = effective stripping factor L = moles of liquid V = moles of vapor X = moles of any com onent in the liquid phase per mole of liquid entering atsorber or stripper x = mole fraction of any component in liquid Y = moles of any component in liquid phase per mole of vapor entering absorber or stripper mole fraction of any component in vapor phase equilibria constant = y/x E. = absorption efficiency = (Yn+l - YI)/Y,+1 E, = stripping efficiency = (Yn+l - Xt)/Xn+l Subscripts = conditions at top of absorber or bottom of stripper0 I. e., reference to lean oil for absorbers and to stripping medium for stripping 1,2,3.. . .n = plate numbers, top to bottom for absorbers, bottom to tou for striuuers -_ m = any late n 1 = cond?tions at bottom of absorber or at tor, of s t r i p per-i. e., reference to entering wet gits for absorbers and to entering rich oil for strippers = =
%’
+
LITERATURE CITED
(1) Horton, George, and Franklin, W. B., IND.ENC. CHEM.,32,
1384 (1940). (2) Kremser, A., Nail. Petroleum News, 22, No. 21 (May 21, 1930). (3) Sherwood, T. K., “Absorption and Extraction”. New York, McGraw-Hill Book Go., 1937. (4) Souders, Mott, Jr., and Brown. G . G., IND. ENQ.CHHIM., 24, 519
(1932).
PRI~SEINT~DD before the Division of Petroleum Chemistry at the 105th Meeting of the A M ~ R I C ACHI~MICAL N S O C I ~ T Detroit, Y, Mich.
