APPROXIMATE
METHOD
A t3SORP T I O N - S T R I P P I N G I. A. Aleksandrov, a n d E. N. T u r e v s k i i
OF C A L C U L A T I N G TOWERS S. A . G r o i s m a n ,
UDC 541.183:66,033.23
In the separation of natural and petroleum gases and the stabilization of hydrocarbon condensates, absorptionstripping towers (AST) are used for deethanization of saturated absorbent or condensate. It is well known that the most r e l i a b l e method for calculating towers is the t r a y - b y - t r a y method, taking into account the changes in mass flux and temperature from tray to tray. Such a method of calculation is accomplished in a computer. Without resorting to a t r a y - b y - t r a y calculation, the basic parameters of the process m a y be obtained by approximate c a l c u l a t i o n methods; these are also easier to use when computerized. A certain method of calculation given in [1] is usually used for the approximate calculation of an AST. In spite of a number of assumptions in deriving the original equations and the comparative c o m p l e x i t y of realizing this method in practice, it has remained the only method suitable for rapid calculation of an AST [2, 3]. tn this article, we are proposing a comparatively simple and sufficiently precise method for the approximate calculation of an AST. It is based on the recurrent relationships of Edmister [4J, which are obtained as a result of joint solution of the m a t e r i a l balance and phase equilibrium equations. Let us e x a m i n e the derivation of the recurrent relationships and the c a l c u l a t i o n a l equations. In Fig. 1, we show a simplified diagram of an AST with the principal streams of vapor and liquid, feedstock, and lean absorbent. Numbering the trays in e a c h section of the tower from the top downward, we witl designate the upper tray j = 1 and the lower tray j = n, so that the lean absorbent will be indicated by the subscript zero (0), and the gas entering the lower tray of the absorption section of the tower will have the subscript n + 1. A similar notation is adopted for the lower part of the tower with a total number of trays N. Let us examine the balance of streams by component, which can be written around each tray or for an e n velope including the part of the column from one end to the i n t e r m e d i a t e section. Solving the stream m a t e r i a l balance equation for the i - t h component around the first tray, together with the phase equilibrium equation vi,~, :
vi,l + li,1 - - li,o.
141 . : A 4 t . v i , t ,
(1)
w e obtain
v i , ~ = v i , 1 (! -k Ai,1) - - l i , 0,
(2)
where At, 1= L1/Ki, 1" Vi is the absorption factor of the i - t h component; L and V are respectively the total flows of liquid and vapor; and K is the phase equilibrium constant. In a similar manner, for the second tray we obtain v4.~ ~ v i , 2 (1 + A42 ) --14o.
(3)
Substituting the value of vi, z from (2) into (3), we have vi,3.----vi, l (I -k Ai,~ + Ai,l.Ai,~) - - l i , o (1 + Ai,,.).
(3a)
A l l - Union Sciennific-Research and Planning-Design Institute of the Petroleum Industry (VNIIPIneft'). All-Union Scientific-Research Institute of Natural Gas (VNIIgaz). Translated from Khimiya i Tekhnologiya Topliv i Masel, No. 12, pp. 27-30, December, 1973. 9 1974 Consultants Bureau, a division of Plenum PublishingCorporotion, 227 West 17th Street, N e w York, N. Y. 10011. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
940
Continuing, we obtain for the j-th tray the following recurrent relationship between the vapor fluxes of the i-th component entering the j-th tray and leaving the first tray:
t
Zo, ~t,._.~o
06 f+ 1 = vi,l.Bi, ] - - li, o. B], ]--1
zri,z
--
(4)
~"~, 1
Bid-~-I + A i d + Ai,i_ t . A i d +
g
. . . + Ai,t.Ai,i. t
(5)
Carrying out analogous transformations of the system of equations (1) relative to the component fluxes in the liquid li, j, we can obtain the following recurrent relationship between the fluxes li, j and li, o:
if, V
S
l i,iDi,] = 11,o + vi,i+ t .Di,i_ 1
(6)
D i , i = 1 + Si, x + Si,l.Si,s + . . . + S i , t . S i d ,
(7)
where Si, j = Ki, j ' ( V j / L j ) is the stripping factor. On the basis of the recurrent relationships for the upper and lower sections of the AST and the material balance equation for the lower section, we obtain the following calculational expression which permits us to determine the composition of the bottom product from the tower: fl,V + li,o li,N
fi, L "4-
--
Di,N ~
i
Oi'n Dt, N - - l
(8) '
fDi,n
Fig. 1. Diagram of absorption-stripping tower with external and internat fluxes: F) saturated absorbent; L0) lean absorbent; V 1) dry gas; LN) deethanized absorbent; fi, Z, fi, V) quantities of i -th component in liquid and vapor phases of feed; vi, i, Zi, N) quantities o f i - t h component in dry gas and stripped absorbent; 1, 2 ... n) tray numbers in absorption section; 1, 2 ... N) tray numbers in stripping section.
where = Di,./Oz,._l.
r
With the assumption of constancy for the stripping (or absorption) factor throughout the section, Eq. (7) assumes the form of a geometric series for which the sum is equal to S n+~ --
Di'n --"
1
St - - 1
(9)
From the equation that has been derived (8), it is possible to determine analytically the composition of the deethanized absorbent or condensate with known stripping factors.
In the design of an AST, the stripping factors of the key components are usually unknown, but values are assigned for the propane recovery in the bottom product and the ethane content of this product.
(IN) C3
(10)
Lc8 -- (fL + fv) c3 ' ~c2--
!IN) Ce (IN) C3 "
(10a)
The recovery coefficients of the i-th component in the absorption and stripping sections of the tower have the following form: li,n epi ~ , -; via + fi,V (11)
ViA' ~; -- li,n + [i,L
(lla)
Solving Eq. (11) together with the material balance equation for the stripping section and the conditions (10, 10a), we obtain the following expression for determining the recovery coefficients with v a p o r - l i q u i d feed of the AST:
Zc3-- [I
I - ~b~ ~ ' -
ZC3 =
-
"cO ]C3
[fL + ~'fv ]c.~ "
[fL + fV ]Cs
[( I - - ~') (fL + ?" fv)]c2( I - - ~'~0')c3 (1 - - cp-cp')c~. [(1 - - ~') (fL + tO" [v)]c~
(12) (13) 941
TABLE I. Starting Data and Results from Calculating AST for Deethanization of Saturated Absorbent (Example 1)
Component
Calculated values determined from Eqs. (5.7)
Phases of feed, kmoles/h vapor
CH4 122 C.~H~ 23,79 Calls 28,65 10,36 :gC4HIo ZCsHI~ 1,88 0,65 Absorbent Total 187,53
I~i, L
23,48 14,41 43,55 36,34 17,73 356,75 489,06
f ~om ~q. t~) 9
oN .n1 n:l n
liquid
fl, V
Bottom product, kmoles/h
11,8 9,83. I0~ 2,28 13,4 1,74 I 6,075 6,00 I ,01 2,05 l,ll 1 1,05
Itest I d~ta I a 115]
[ !
lcalc, by I method I I of [5]
3,32 3,30 71,53 71,58 46,70 46,70 16,61 16,61 489,40 520,4 627,56 658,59
Top product, kmoles/h
Ilfrom [ mate/ riq /baTance
3,30 71,585 46,70 16,61 493,09 631,285
test do,o "~" [5]
cale. by method of [5]
145,48 34,88 0,67
145,48 34,90 0,61
145,48 34,90 0,615
181,03
180,99
180,995
TABLE 2. Starting Data and Results from Calculating AST for Deethanization of Saturated Absorbent (Example 2)
Component
CH
Cs~6 CsHs C-~H,o CsHIa Absorbent Total
External fluxes, kmoles/h from Eq. (8) ..... by method [3] vl, 1
2,35 5,14 1,62
971
lt, N
,7o
15,30 7,38 6,08 77,26 106,72
vi, 1
It, N
2,35
.67 1530
5,13 1,60
9~8
7,38 6,08 77,26 106,69
Internal fluxes,9kmoles/h by method [3] from Eqs. (4) and (6) tt 9 n+~t, L [ vl,
1,80
7,84 24,62
9,05 6,53 61,43
111,27
1"
Jvi, l,+tt,
1.80 7,14 9,32 1,67 0,45
2,48 7,60 9,72 1,73 0,47
2U,38 2 oo
li, n
0,13 2,46 8,10
1,73
0.47 15,91 28,80
I~, n+fi, L
~t, 1' I"i, v+ri. v I
1,801
2,48
1,681 0,45 [
1,74 0.47
1,80 7,92 24,60 9,06 6,53
7,251 9,301
111,34
,07481'
61,43
7,61 9,70
1l, n
0,13 2,48 8,10 1,74 0,47 15,83 28,75
These equations (12, 13) permit the determination of the recovery coefficients for each section without any preliminary determination of product composition. This method is illustrated in the following paragraphs by two examples in calculating an AST for the deethanization of a saturated absorbent with the process paiameters varied over a wide range. Example 1. Calculate an AST for deethanization of a saturated absorbent under the following conditions: feedstock composition as shown in Table 1; pressure 14.5 kg/cmZ; ZCs= 0.99; ZC2= 2.9% by weight; N= 5, n= 15; top, feed, and bottom temperatures 20, 80, and 202~ respectively; molecular weight of absorbent 140. For comparison, results were taken from a tray-by-tray calculation on a Minsk 22 computer, and also data from a plant operating test on an AST in the Korobki gas processing plant [5]. The calculation was performed in the following sequence: first, a value was assigned for ~0C3, and, from Eq. (12), ~OC~was determined. With a known number of trays in the sections, the absorption factors for propane were found from a Kremser diagram. The conversion to ethane absorption factors was accomplished by means of the equilibrium constants, which were assumed for the average temperatures of the sections. Having obtained values for the coefficients of ethylene recovery from the Kremser diagram, the value of ZC z was calculated from Eq. (13). If the assigned and obtained values of ZC 2 were not equal, the calculation was repeated, assigning a new value of ~0Ca. After two approximations, the actual value of ~0Ca was determined by linear interpolation. From known values of ~oi, and using the Kremser diagram, absorption and stripping factors were found for the key components. Conversion to absorption factors of the remaining components was performed through the equilibrium constants. Using the values of Di, N and wi, n from Eq. (9), the composition of the deethanized absorbent was calculated from Eq. (8). The dry gas composition was determined from the material balance equation for the tower, and the compositions of the internal streams from equations given in [4, 6]. The flow rate of lean absorbent was determined in accordance with the recommendations of [6]. The results of these calculations are listed in Table 1. Satisfactory agreement was established between the results of the calculation by the proposed method (with actual compositions of products) and the results of the tray-by-tray calculation. Example 2. Determine the compositions of the external and internal streams of an AST designed for deethanization of a saturated absorbent. The starting data, equilibrium constants, and absorption and stripping factors are 942
taken from the data of [3] and are listed in Table 2. After determining the values of Bi, n. t3i, n-l, Di, N, Di, N-*, and aJi, n, the composition of the deethanized absorbent was calculated. The dry gas composition was found from the material balance, and the compositions of the internal streams from Eqs. (4) and (6). From the values of the gas and tiquid fluxes in the absorption section, the flow rate of lean absorbent was calculated [3]. The agreement of the results from the calculation is satisfactory (see Table 2). Thus, the calculation procedure presented here provides a rather simple route to the calculation of the external and internal fluxes in the apparatus, and hence can be used for engineering design of AST's and for analysis of their operation. LITERATURE 1. 2. 3. 4. 5. 6.
CITED
A . S . G1endening and C. F. Sonderson, Petrol. Processing, 4, No. 1 (1949). A . A . Kuznetsov, S. M. Kagermanov, and E. N. Sudakov, Process and Equipment Design Calculations in the Petroleum Refining Industry [in Russian], Khimiya, Moscow (1966), p. 64. I . A . Aleksandrov, Distillation and Absorption Equipment [in Russian], Khimiya, Moscow (1971), pp. 80, 247. W . C . Edmister, Ind. Eng. Chem., 35, No. 8, 837 (1957). S.P. Gnusnova, B. G. Bergo, and A. G. Boyarinov, in: Processing Gas and Gas Condensate [in Russian], No. 6 (1970), p. !4. E.N. Turevskii, I. A. Aleksandrov, and A. L. Khalif, Gaz. Delo, No. 11, 27 (1969).
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