W I L L I A M R. OWENS ROBERT N. M A D D O X
Short-cut Absorber Culculatr'ons is essentially a vapor pressure phenomenon. A bsorption The driving force is the difference between the partial pressure of a constituent in the gas and the vapor pressure due to the portion absorbed in the liquid ." These were the words of Alois Kremser (9) that started theoretical analysis of the absorption process in 1930. Since then, many useful and helpful additions have been made to the solution of absorption problems. Absorption is a mass transfer operation, principally occurring in one direction. I n the petroleum industry, absorption describes a multicomponent separation with countercurrent flow to increase concentration driving forces. A gas stream rich in heavy components is fed into the bottom of the absorber to rise through contacting devices. I t is the in-gas, wet gas, or rich gas. A sponge or absorbing oil is fed in the top. I t is the lean oil. The two streams pass countercurrently and the gas stream leaving the absorber is denoted the discharge gas, lean gas, or dry gas; the oil leaving, the rich oil. The design or evaluation of an absorber represents time and capital investment. Thus, speed and accuracy are plied against one another. The accuracy of solution, in turn, is a function of the accuracy of the data supplied and the method of calculation. Design calculations began with little data and easy to use methods. Time brought improved equilibrium and enthalpy data and led to more exact calculation methods. The advent of the computer made possible rigorous calculation methods; however, not everyone has access to a computer and a program for such calculations. Need still exists for a simple hand method that incorporates absorption calculations, heat balance calculations, and a minimum number of assumptions for a broad range of absorber operating conditions. Such a method would find application in preliminary designs, economic feasibility studies, initial profiles for rigorous calculation, or even final designs in the absence of exact methods. 14
INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY
Figure 7.
A simple absorber
A simple hand method that incorporates absorption calculations, heat balance calculations, and a minimum number of assumptions for a broad range of absorber operating conditions
Background
K =
Design variables.
From an analysis of design variables (15) for an n-tray, C-component absorber with only two feeds, a designer is faced with
2C
+ 2n + 5
degrees of freedom-i.e., variables. A unique absorber could then be described by specifying Pressure in each stage Heat leak in each stage Lean oil composition and pressure Lean oil rate and temperature In-gas composition and pressure In-gas rate and temperature Number of stages
n n
C 2 C
2C
+ 2n + 5
If a desired recovery of a component is specified, then that specification replaces one in the list above-for instance, the lean oil flow rate. Basic absorber design methods, rigorous and otherwise, begin with these specifications. Algebraic development. If we consider the ith stage with a vapor stream entering the bottom, a liquid stream entering the top, and a liquid and a vapor stream leaving, then material balance equation for each component is (Figure 1) uz+1
+
=
+4
(1) The equation around the ith tray and the top of the column for a given component is where:
I t 4
ut
= moles of component leaving in the dry gas lo = moles of component entering the lean oil
u1
When we define a theoretical stage to have the liquid and vapor leaving in equilibrium, the equilibrium ratio K becomes
u/V l/L
_I -_ - L
VK
u
(3)
3 -
where V and L are the total streams. the equation yields
By rearranging,
= A
(4)
for each component on each tray. The ratio A has become known as the absorption factor. When we rearrange Equation 1 for the top tray of an absorber v2 = Vl(A1 1) - lo (5) then the liquid leaving tray 2 would be
+
2
1
mole fraction vapor mole fraction liquid
12
= ~ z A z= Ul(A1A2
+ Az) - loA2
(6)
When Equations 2 and 4 are used to obtain the vapor rising to a given tray and its equilibrium liquid alternately, the equation for the liquid leaving tray n is 1, = Ui(AiAzA3. . . A n
+ AzAa. . . A n + . . . + A,) lo(A2. . .An
+ . + An) 5
-
.
(7)
The convention presented by Edmister (3) defines TA
ZA
.
= AiAzAs. . A n
and = AiAz.. .An
+ AZA3.. . A , + . . . + A ,
(8)
(9)
By use of these definitions, Equation 7 becomes In = V l Z A - lO(ZA - T A ) (10) Design information usually consists of both feed streams rather than a feed and a product stream. Applying an over-all component balance to Equation 10 yields
where V I is the moles in the dry gas; vn+l the moles in the wet gas; and lo the moles in lean oil. VOL. 6 0
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DECEMBER 1 9 6 8
15
Literature survey. Solution of the mathematical model for absorber calculations depends upon the method of evaluating the absorption factor for each individual tray and component. The simplest method is to assume the absorption factor is constant throughout the column. A refinement of that method is to use an “effective” absorption factor that will give the same value as the rigorous solution. The most difficult method is to evaluate each absorption factor on every tray for all components. Rigorous solutions for multicomponent systems are difficult and time-consuming and, without good thermodynamic data, unwarranted. Significant contributions to the average absorption factors methods were made by Kremser (Q), Brown and Souders ( I ) , and Landes and Bell ( I O ) . The case for “effective” absorption factors has been provided by Horton and Franklin (7), Edmister (2-4), and Hull and Raymond (8). Sujata (77) and Holland (6) have presented tray-by-tray methods for computer solution to supplement the Lewis-Matheson and Thiele-Geddes methods for distillation. I n 1930 Kremser ( 9 ) presented a mathematical analysis of the relations of the oil absorption process. T o simplify calculations, the assumption was made that pressure, oil rate, gas rate, and temperature were constant throughout the absorber. Kremser noted these assumptions were not fulfilled with rich gas feed or high pressure plants. Using a material balance similar to Equation 7 and a constant absorption factor, Kremser developed Equation 12 which is analogous to Equation l l :
Souders and Brown rearranged Equation 12 to the form un+l - u1 - An+l - A (13) un+l - U O An+l - 1 which made calculations more convenient when changing the composition of the lean oil. The left side of Equation 13 is the ratio of the actual change in composition of the gas to the maximum change in composition were it in equilibrium with the lean oil. The assumptions of this method were substantially valid for moderate pressures and lean gases, hence little absorption. Souders and Brown recommended that with greater absorption, the equilibrium values should be evaluated a t some intermediate temperature between the top and bottom. This value combined with the oil rate a t the top, L, and the gas flow a t the bottom, V , produced ultraconservative values for design work in this range. 16
INDUSTRIAL AND E N G I N E E R I N G CHEMISTRY
Recently a method has been presented which incorporates the heat balance into the method of Kremser, Souders, and Brown. Landes and Bell ( I O ) used the Souders and Brown method and an estimated average temperature to provide a first estimate of the average absorption factor. The top tray temperature was assumed and the dew point calculated filling the void with lean oil. A heat balance was made around the top tray using an assumed temperature for the second tray. The same procedure was then followed for the second tray. The assumed temperature for the third tray was left unchecked. An over-all heat balance yielded the temperature of the rich oil stream. After the temperature-tray profile had been plotted, the oil-vapor ratios were calculated. The L / V of the top tray had been found during the top tray analysis. The L / V ratio for the bottom tray was calculated by assuming equal shrinkage on all trays except the top. By use of plotestimated values for temperatures and L/V’s, the absorption factor for the key component was calculated for each tray and graphically averaged for the second iteration. Absorption factors for other components were found by the ratio of equilibrium values and the absorption factor of‘the key component. I n 1940 Horton and Franklin (7) presented two separate methods to calculate absorber performance. The primary method was based on evaluating the absorption factor on each tray with temperature and vapor profiles calculated by empiricisms.
These equations assume constant per cent absorption on each stage and a temperature change proportional to the vapor shrinkage. The authors acknowledged that predicted material balances and stage temperatures may differ from tray-by-tray results, but their use gave results which agreed closely with over-all absorption efficiency. Horton and Franklin’s second method introduced the effective absorption factor as the value which gave the same results as the individual absorption factors. Considering the series expansion similar to Equation 10, they concluded the effective absorption factor for light components (small values of A ) corresponded to the absorption factor at a position near the bottom and for heavier components, to a position near the middle of the tower. A table was presented as a guide to the selection of effective factors.
TABLE 1.
Pressure, psia
Run
Trays
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44
8
500
8
500 500 500 500 5 00 500 500 500 500 500 500 500 500 500 5 00 5 00 200 200 1000 1000 500 500 5 00 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500
8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 2 2 12 12 8 8 8 8 8
3 3 4 4 5 5 8 8 8 8
Oil, mw 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 145 145 250 250 200 200
200 200 200 200 200 200 200 200 200 200 200 200 200 145 145 200 145
LIST OF RUNS
Oil stripped
Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No No Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes
* *
Oil )mp, F 100 50
0 100 120 0
20 100 0 100 0 100 0
100 0 100 0 100 0 100 0 100 0 100 0 100 0
100 0 75 20 10
- 10 -20 100 0 100 0 100 0 0 0 100 0
Gas temp, OF
100 50 0 120 100 20 0 100 0
100 0 100 0 100 0 100 0
100 0 100 0 100 0 100 0 100 0
100 0 75 20 10 -10 20 100 0 100
-
0 100
0 0 20 100 0
c3 Recovery
Gas composition
0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.20 0.20 0.90 0.90 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70
Average Average Average Average Average Average Average Average Average Average Average Average Average Rich Rich Lean Lean Average Average Average Average Average Average Average Average Average Average Average Average Average Average Average Average Average Average Average Average Average Average Average Rich Average Average Average
0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70
* Presaturated.
VOL. 6 0
NO. 1 2
DECEMBER 1 9 6 8
17
I n 1943, Edmister ( 2 ) presented a short-cut method based on an exact solution for a two-tray absorber. At that time Edmister presented a material balance equation
defining A , as
+
+ . . + A, + . . . + An + 1
A,"+1 - A , - A 1 A z . . . A n AO.. . A , -1 A1A2.. , A , Az.. .A,
+
,
(17) and A' as
+
+ .. + A, + .. . + A , + 1
AzA8. . . A , AS.. .A, AlAz.. .A, Az.. .A,
+
,
(18)
When the system was solved for a two-tray absorber, A , and A' could be expressed as
A,
=
VAz(A1
+ 1) + 0.25 - 0.5
Vni-1
(19 )
and
I n 1957, Edmister ( 4 ) published a new form of the material balance equation and new absorption factor functions as =
01
+
lO$A
(21)
= fraction not recovered
(22)
vn+l+A
with
'
A
1 -ZA+1 -
~
and $A
= 1
-
T A ~
ZA
+1
= lean oil fraction lost
(23)
They may be evaluated either rigorously by individual tray absorption factors or approximately by effective absorption factors based on the two-tray model as defined by Equation 19. Presenting the first short-cut method to incorporate heat balance equations, Hull and Raymond (8) pointed out that the key to over-all absorber heat balance was establishing either the discharge gas or the rich oil temperature. I n light hydrocarbon fractionators, the problem is solved by dew- and bubble-point calculations. I n absorbers this procedure is complicated by the presence of components with widely varying boiling points. 18
Hull and Raymond presented two methods for determining terminal tray temperatures. The first method, applicable to absorbers with input-oil and gas-weight ratio from 0.8 to 5.0, was based on the lean oil being the principal heat balance quantity in the top section of the column. For high-pressure absorbers where the oil-gas ratio may be very small, a correlation ~ 7 a sdeveloped between the in-gas and the rich-oil temperatures. I n each of the above cases, the remaining terminal temperature was calculated from the over-all heat balance. The column average temperature was correlated as a difference from the average of the terminal temperatures. Hull and Raymond proposed a method of evaluating A , and A', a term they denoted A,. The A , was in terms of the fractional distance between the bottom and average tower conditions while A' was in terms of the fractional distance between the bottom and top of the column. By use of their arrangement of the material balance equation, the fraction absorbed, F, of each component is
INDUSTRIAL AND ENGINEERING CHEMISTRY
un+1
-
- lo/A'
=
=
A,,+' - A , A,"+' - 1
(24)
The methods discussed above have been short-cut or approximate solutions to absorber calculations although several are capable of exact solution. With the advent of high-speed computers tray-by-tray solutions became more popular and feasible. Lewis and Matheson ( 7 7 ) developed a rigorous multicomponent distillation calculation scheme which could be modified to work on absorbers. Thiele and Geddes (78) also developed a multicomponent distillation calculation method based on the ratio of the liquid stream to the top product stream. Holland (6) adapted this method to a computer solution for absorbers using the absorption factor approach. An iterative tray-by-tray method was described by Sujata (77) and programmed for computer application by Spear (76). The Sujata method presents no new equations, but rather applies the absorption factor technique combined with a simultaneous solution for the
AUTHORS William R. Owens is a graduate assistant and Robert N . Maddox is Professor and Head of the School of Chemical Engineering, College of Engineering, Oklahoma State University, Stillwater, Okla. The authors thank the Department of Health, Education, and Weyare for the NDEA Traineeship which supported Mr. Owens during this work, and the Oklahoma State Thiversity Computing Center for computing time used.
4
8
12
16
20
24
28
32
36
40
44
Problem Number Figure 2.
Terminal tray shrinkage
variables. Temperature and flow profiles are initially assumed. Correct flow profiles are found for given temperature profiles. Individual tray heat balances validate assumed temperature profiles or adjust them as necessary. The major iteration variable is temperature based on heat balance. Spear checked results of his program against experimental data for four industrial absorbers. Temperatures, flow rates, and material and heat balances agreed within limits of data error. In 1959 Ravicz (74) presented a calculation method which eliminated the ideal tray restriction and the concept of an over-all column efficiency. This method, utilizing the power of the computer, included nonideal mass transfer calculations, enthalpy, equilibrium, and physical correlations too tedious for hand calculations. Development of N e w Calculation Procedure
Consideration of the variables involved in the calculation of multicomponent absorbers shows that the man initiating a “grass roots” calculation faces two major problems: (1) estimating a reasonable L / V profile for the absorber and (2) estimating and checking a column temperature profile. Previous authors have considered the first of these problems in some detail in developing short-cut calculation procedures. Few have undertaken the second which is at least of equal importance. Analysis of a large number of tray-by-tray computer solutions for multicomponent absorbers showed an amazing consistency in the fraction absorbed on the two terminal trays in the column. For numbers of trays varying from three to twelve, approximately 80yo of the total material absorbed is absorbed on the top tray and the bottom tray of the column. This is illustrated in Figure 2 for the 44 problems solved. There may be considerable shift in the percentage absorption in either the top tray or the bottom tray depending on operating conditions, but the terminal fractional absorption, w , var-
Tray
Figure 3.
Typical temperatureprojle
VOL. 6 0
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DECEMBER 1 9 6 8
19
ied from only 62 to 89% with the average for all runs being very close to the 80% level. This fact can be incorporated into absorption calculations to provide a useful and valuable extension and to give considerable improvement in accuracy and reliability in comparison with tray-by-tray results. With 80% of the absorption occurring on the terminal trays, the absorption factors through the tower should be easily represented in terms of three factors: (1) the absorption factor for the top tray, (2) the absorption factor for the bottom tray, and (3) the absorption factor which represents the remaining n - 2 trays in the column. I n terms of these three absorption factors, Equations 8 and 9 become
TABLE Ill. SUMMARY OF RESULTS
Kremser-Brown Calculation Method Predicted Variable
Remarks
Methane recovery Ethane recovery Lean oil rate Temperatures: Rich oil
Average 1070 low Average 10% low Average %yohigh Specified from Sujata results Specified from Sujata results Does not apply
Lean gas Column average
Edmister Calculation Method
Methane recovery Ethane recovery Lean oil rate Temperatures: Rich oil Lean gas
Average 1 . 4 % low Average 3 . 0 % low Average 2 . 0 % high Average 1.72'F high Specified from Sujata results Does not apply
Column average
Proposed Calculation Method
T o properly evaluate the three absorption factors, temperatures of the top and bottom trays and an average temperature for the tower must be known. The temperature of the top tray of the column can be estimated by the following equation which is based on a heat balance around the top tray.
LPLO
When we use Equation 27, a value for T,, is assumed and a dewrpoint calculation is run on V D G ,adding sufficient lean oil to the calculated composition to make the sum of the mole fractions equal to unity. This provides the composition of the liquid leaving the top theoretical plate, and a material balance then provides the composition of vapor leaving plate two: For the first trial, the temperature of tray two is assumed equal to TDQ;for subsequent trials, Tz is calculated from
TABLE I I.
Camflonent
Standard
Gas Rich
Methane Ethane Propane &Butane n-Butane i-Pentane n-Pentane Lean oil Nitrogen
89.01 6.29 2.36 0.49 0.68 0.13 0.29 0.00 0.75
86.01 6.79 3.36 1.49 1.18 1.13 0.29 0.00 0.75
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
Average Average Average Average Average Average
O.6yO low 1.0Yo low 0.4YG high 1.8'F high 0.2'F high 1.4'F high
Equation 29. A heat balance around the top tray then checks the assumed value for T D O . Evaluation of the average absorption factor requires the average L / V value for the column together with the average temperature of the column. Tav,is calculated from Equation 28 T.4VE
=
TDG
+
[cPDG(T?20
-
+ (l -
TDQ)
CPD,
f
W)AHABSI
(28)
CPOIL
Equation 28 represents a heat balance around the middle n - 2 trays of the absorber. After TAvEhas been esti-
COLUMN PARAMETERS
Column conditions
20
Methane recovery Ethane recovery Lean oil rate Temperatures: Rich oil Lean gas Column average
500 psia 8 trays 9 components Oil Nanstriflped
Lean
Stripped
92.75 5 .OO 1.75 0.25 0.25 0.00 0.00 0.00 0.00
0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.005 0,005
1.000
0.970 0.000
0.000
0.010
0,010
Presaturated
0,150 0.000 0.000 0.000 0.000 0.000 0.000 0.850 0.000
mated for the tower, Equation 29
(TBTM
-
TBTM
TTOP
TTOP)
2
n
)
(29)
analysis of the temperature profile from approximately 50 tray-by-tray solutions of multicomponent absorption problems. The average L/V ratio is determined from Equation 30
is used to calculate Tz. The graphical justification for Equation 29 is shown in Figure 3. Figure 3 is based on
TABLE IV.
Run
a
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 D i d not converge.
Predicted dry gas temperature Sujata Proposed 103.73 58.14 18.18 103.87 122.84 18.97 32.60 107.48 15.44 103.11 13.58 103.87 18.41 104.84 23,24 103.22 14.10 101.93 8.37 106.21 27.35 105.48 23.39 103.82 17.83 104.84 16.99 103.82 17.62 80.54 33.12 25.48 11.21 4.42 104.33 17.85 104.03 18.31 103.99 18.47 30.50 25.39 102.14 20.00
104.27 59.12 18.64 103.96 123.40 18.76 32.74 108.31 13.38 103.30 15.21 104.87 18.80 105.04 22.74 103.64 13.83 101.97 9.03 106.98 26.33 106.12 23.05 104.26 18.13 104.42 17.17 104.20 18.55 81.22 34.59 25.92 11.36 4.13 104.39 17.60 104.46 18.53 104.39 18.58 30.44 25.65 102.48 20.02
(L/v)AVB
=
Ln
- (vn+,- Vn) Vn - 0.05s
(30)
PREDICTED TEMPERATURES
Predicted column average temperature Sujata Proposed 106.31 61.61 18.07 113.01 120.35 32.23 21.76 103.43 9.64 105.94 19.85 105.81 17.73 112.15 34.44 103.34 8.08 103.50 14.95 107.84 20.10 107.84 18.09 105.57 16.03 106.19 17.75 105.79 17.40 83.66 35.65 26.90 9.16 0.20 106.34 18.44 106.54 18.53 106.55 18.45 35.44 34.11 105.21 17.38
Predicted rich oil temperature Sujata Proposed Edmister
108.13 63.78 20.13 114.22 121.17 36.03
105.26 61.04 21.86 106.80 123.33 28.28
21.92 104.79 9.39 107.40 21.59 107.66 19.72 114.44 38.19 104.84 9.54 104.73 17.01 110.08 21.25 109.87 19.85 107.29 17.83 106.32 17.96 108.26 20.24 85.74 37.44 29.26 10.86 1.53 107.13 19.34 107.52 19.41 107.78 19.74 38.57 37.39 107.09 19.88
31.45 106.09 12.06 104.46 19.42 105.19 21.74 108.26 34.41 103.84 13.95 102.68 12.79 107.76 28.03 107.41 24.73 105.16 20.45 105.51 17.37 105.02 21.14 82.60 37,09 29.47 14.19 6.27 105.48 19.03 105.49 20.20 105.51 21 .oo 39.93 33.88 103.92 22.62
VOL. 6 0
106.70 63.41 23.61 107.77 124.21 31.31 30.86 107.63 12.21 105.41 22.14 106.57 23.43 109.95 38.06 104.85 13.85 103.19 14.83 109.94 28.24 109.08 25.66 106.36 21.78 104.73 17.53 106.70 23.65 84.54 39.39 31.43 15.58 7.35 105.69 20.67 106.56 23.05 106.63 23.31 43.14 36.56 104.66 24.19
NO. 1 2
108.05 63.82 20.07 133.70 121.24 34.96 21.37 105.56
. . .a 107.27 22.11 108.14 20.09 114.03 38.28 104.83 9.02 104.69 17.14 109.91 18.60 110.13 19.04 108.02 20.37 106.28 18.04 108.06 20.52 85.65 37.98 29.15 10.59 0.66 107.15 19.04 107.57 19.36 107.78 19.54 39.07 37.15 107.29 20.40
DECEMBER 1 9 6 8
21
Equation 30 is a modified material balance accounting for gas shrinkage in the midsection of the column. 'The empirical 0.05 factor is based on comparison of tray-by-tray results. The bottom tray L / V ratio is determined from shrinkage across the bottom tray of the tower. The temperature of the bottom tray is determined by heat balance around the column. After the absorption factors have
TABLE V.
been determined as outlined above, they are used to evaluate Equations 25 and 26 and these factors are used in Equation 11 to calculate absorption in the column.
Testing the Proposed Procedure
The short-cut calculations proposed here, together with the Kremser-Brown analysis and Equations 8, 9, and 11
PREDICTED RECOVERIES
Predicted methane recovery Sujata
Proposed
Edmister
5.055 1 2 3.800 2,998 3 5,092 4 5.669 5 3.078 6 3.187 7 1.376 8 0.725 9 7.188 10 4.210 11 5.032 12 2.987 13 5.161 14 3.549 15 5.044 16 2,579 17 4.207 18 1.936 19 7.581 20 5.845 21 5.128 22 3.049 23 5.038 24 2.950 25 7.403 26 3.933 27 4.972 28 2.949 29 4.371 30 3.272 31 3,129 32 2.879 33 2,770 34 6.063 35 3.356 36 5.556 37 3.165 38 5.316 39 3.082 40 3.661 41 3.216 42 5.013 43 3.008 44 Did not converge.
5,058 3.801 2.943 5.089 5.641 3.005 3.136 1.389 0,717 7,166 4.138 5.030 2.935 5.208 3,424 5.036 2.570 4.214 1.938 7.530 5,671 5,128 3.004 5.036 2.901 7,396 3.939 4.990 2.923 4.379 3.246 3.080 2.818 2.707 6.076 3.359 5.541 3.124 5.304 3,030 3.553 3.142 5.091 2.996
5.108 3.789 2.812 5.221 5.625 2.988 2.948 1.422
Run
Q
22
... 7.213 3.951 5.111 2.814 5.131 3.126 5,191 2.622 4.210 1.901 7.724 5.343 5,171 2.844 5.108 2.812 7.608 3.978 5.040 2.790 4.404 3.166 2.983 2.650 2.497 6.171 3.297 5.627 3.044 5.371 2.926 3.198 3.079 5.487 2.903
I N D U S T R I A L A N D ENGINEERING C H E M I S T R Y
Predicted ethane recovery KremserBrown
Sujata
Proposed
Edmister
4.760 3.325 2.226 4.987 5.215 2.414 2,432 1.334 0.607 6.825 3.176 4.757 2,225 4.656 2.261 4.930 2,243 4.095 1.632 7.004 4.142 4.788 2,253 4.755 2.213 7.345 3.433 4.681 2.184 4,000 2.627 2.420 2.043 1.871 5.863 2.739 5.305 2.482 5.040 2.358 2.305 2.460 9.954 3,899
1.690 1.513 1.402 1,673 1.783 1.378 1.459 0,467 0,358 2.405 1.947 1.687 1.400 1.871 1.685 1.313 0,992 1.514 1.109 2.009 1.825 1.702 1,422 1.689 1.392 2.277 1.771 1.666 1.385 1.597 1.436 1.418 1,389 1.376 1.991 1.559 1.849 1.475 1.774 1.438 1.723 1,422 1.684 1.409
1.684 1.504 1.371 1.670 1.772 1.341 1.434 0.469 0.355 2.393 1.915 1.680 1.370 1.872 1.624 1.307 0.980 1.511 1.102 1.994 1.776 1.695 1.394 1,682 1.364 2.276 1.772 1.660 1.361 1.591 1.419 1.390 1.355 1.342 1.991 1.556 1.844 1.460 1.768 1.415 1.668 1.382 1.693 1.390
1.686 1.485 1.300 1.696 1.757 1.322 1.342 0.475
... 2.398 1.823 1.686 1.300 1.846 1.492 1.327 0,978 1.510 1.078 2.005 1.665 1.694 1.313 1.686 1.299 2.300 1.780 1.661 1.284 1.585 1.370 1.334 1.266 1.234 2.008 1.534 1.857 1.419 1.776 1.361 1.515 1.345 1.665 1.290
KremserBrown
1.635 1.394 1.140 1.667 1.698 1.190 1.195 0.458 0.315 2.346 1.632 1.634 1.140 1.774 1.264 1.296 0.890 1.495 1.004 1.918 1.436 1.639 1.148 1.634 1.137 2.273 1.662 1.608 1.120 1.517 1.243 1.197 1.088 1.036 1.968 1.391 1.812 1.269 1.728 1.207 1.276 1.202 1.632 1.142
TABLE V I .
EQUILIBRIUM CONSTANT VALUES FOR T H E EQUATION
In K = A
+ BIT + C / T a+ D/Ta
D
Component
A
B 200 psia
C
Methane Ethane Propane i-Butane n-Butane i-Pentane n-Pentane 200 mw oil Nitrogen
0.62936 1 ,89355 1.41560 1.06618 1.70875 1.55110 1.45431 6.27465 - 4,32824
41.67177 27.73705 31 ,66986 37.21840 28.09457 26.85196 28.93027 - 65.07498 -15.77304
-222.35380 -254.60420 -302.31800 -363.29280 -337.54400 -345.38220 -365.60330 -174.09260 84.92576
302.69330 408.75500 442,47130 531 .47560 504.89700 474.47930 500.95320 245 ,73240 -151.42850
Methane Ethane Propane &Butane nButane i-Pentane n-Pentane 200 mw oil Nitrogen Decane 250 mw oil
0.86989 2.78127 2.67452 2.10888 2.84696 2.28437 2.78643 6.81646 -5.18179 12.66661 -5.45264
500 psia 26,59536 1.13197 0.07913 6.29061 - 3.14933 3.43893 - 3.21470 -34.68934 - 15.63904 -164.81940 - 12.38642
-149.53520 -122.21500 -143.93070 -189.73140 -166.11700 -217.79740 - 199.56500 -508.67470 78.55727 368.43090 66.67615
180.98960 211.40340 205.87790 241.37350 225.79970 278.51110 257.36800 701.43180 -130.90850 -402.67520 -118.86150
Methane Ethane Propane &Butane n-Butane i-Pentane n-Pentane 200 mw oil Nitrogen
-0.60247 1.98596 1.74780 1.21320 1.71057 1.11933 1.78504 19.15638 6.65472
1000 psia 42.93807 2.60610 1.27734 7.51930 1.19572 9.60301 - 0.54964 -276.73060 - 4.10338
-248.92420 -122.12060 -124.64890 -169.46260 -155.51380 -219.32000 -177.99260 829.38210 22.03521
375.15760 235.75920 182.44810 222.95100 212.94260 296.40310 227.70500 -798.32900 -39.18790
-
evaluated using the effective absorption factor proposed by Edmister, was compared with the results of tray-bytray calculations for 44 sample problems. T h e trayby-tray calculation procedure was that of Sujata (77) as programmed and tested by Spear (76). Table I shows the complete list of problems run to evaluate the proposed procedure. T h e number of theoretical plates varied from two to 12, with eight being used most frequently because most industrial absorbers are designed with six to 10 theoretical trays. Tower pressures ranged from 200 to 1000 psia, with 500 psia being used most often. Temperatures ranged from -20” to 120°F. Key component recovery ranged from 20 to 90%. I n most cases, absorption oil was stripped, but both nonstripped and presaturated oils were tested. Gas compositions were varied, with arbitrarily assigned designators of lean, average, and rich. The range of lean oil and rich gas compositions used is shown in Table 11. Results of these calculations are summarized in Table 111. Comparative results for key variables are shown
-
in Tables IV, V, a n d VIII. I n all calculations, the same equilibrium and enthalpy data were used for all methods. Equation coefficients for these properties are shown in Tables V I and VII. Data for the curve fits were taken from the 1957 edition of the NGSMA Engineering Data Book (72). Results from the Kremser-Brown calculation procedures are the poorest of the short-cut procedures investigated. This is to be expected because of the assumptions necessary in making the calculations. Dry-gas and rich-oil temperatures were provided from tray-by-tray results on that problem. T h e average absorption temperature was assumed to be the average of the four terminal stream temperatures. The L / V ratio was assumed to be the ratio of the lean oil to the rich gas. The relatively large errors in component recovery and lean oil rate indicate that the Kremser-Brown technique should find major application in providing “first-guess” information for one of the other calculating techniques. Equations 8, 9, and 11 evaluated using the two-tray effective factors presented by Edmister give, over-all, VOL. 6 0
NO. 1 2
DECEMBER 1 9 6 8
23
good results. When this procedure was used, a linear absorption profile was assumed in the column. Lean-oil and rich-gas temperatures were specified. Since this procedure does not include independent calculation of terminal stream temperatures, one other stream temperature had to be fixed. For the cases considered, the dry-gas temperature was fixed from tray-by-tray results. T h e rich-oil temperature could then be calculated from a column heat balance.
TABLE V I I .
The proposed method of calculation gave the closest agreement with tray-by-tray results for component recoveries, lean-oil rates, and temperatures of any of the short-cut procedures investigated. Maximum deviations from tray-by-tray results are small. Top and bottom tray temperatures predicted by the short-cut procedure are in excellent agreement with those from tray-by-tray calculations over the full range of problems studied.
ENTHALPY COEFFlCl ENTS
For the Equation HV = A Component
B
C
Methane Ethane Propane i-Butane n-Butane i-Pentane n-Pentane 200 m w oil
200 psia 1293.00 2808.80 4344.10 6590.80 6590.80 8353.80 8353.80 28028.00
636.43 1008.30 1277.50 1346.40 1346.40 1541.10 1541.10 1311.70
24,000 39.328 60.454 92.632 92.632 116.350 116.350 561 ,760
Methane Ethane Propane i-Butane +Butane i-Pentane n-Pentane Decane 200 mw oil 250 mw oil
500 psia 612.61 594,36 4928.90 7759.90 7759.90 9254.40 9254,40 12873.00 16600.00 16600.00
777.21 1450.00 573.48 132.25 132.25 212.11 212.11 1413.60 1985.20 1985.20
15.010 15.633 136.510 218.040 218.040 251.650 251.650 390.560 549.190 549.190
Methane Ethane Propane i-Propane +Butane i-Pentane n-Pentane 200 mw oil
1000 psia 518.18 528.86 5615.70 8108.50 8108.50 10630.00 10630.00 37289.00
716.74 1317.40 170.98 -190.91 -190.91 -525.51 -525.51 - 5889.70
21.001 28.629 166.830 234.360 234.360 297.240 297.240 11160.600
Component
Methane Ethane Propane i-Butane n-Butane i-Pentane n-Pentane Decane 200 mw oil 250 mw oil
24
A
+ BT + CT2
For the equation H L = A A 828.12
- 1759.90 -807.45
-3040.00 -3040.00 - 51 1 4 . 8 0 - 5114.80 - 10001.00 - 14782.00 - 14782.00
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
+ BT + CT2 B -812.57 97.65 - 263.30 587.75 587.75 1327.20 1327.20 2420.70 3403.50 3403.50
C
257.710 235,070 305,330 279.520 279.520 261.530 261.530 479.370 673.800 673.800
TABLE V I I I . Run
Suiata
Probosed
Edmister
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44
26.568 14.705 7.006 27.614 32.018 8.606 8.036 6.146 0.317 38.679 11.137 26.710 6.996 25.673 7.797 27.875 6.982 60.370 15.765 16.783 4.533 27.259 7.195 26.573 6.785 40.222 IO. 374 26.021 6.766 20.042 9.710 8.311 5.796 4.670 32.474 8.352 29.543 7.660 28.138 7.350 8.374 9.345 30.815 8.218
26.771 14.907 6.988 27.674 31 ,972 8.643 7.860 6.274 0.265 38.737 11.056 26.914 6.985 25.886 7.666 28.046 7.042 60.690 16.010 16.873 4.389 27,487 7,192 26.728 6.768 40,204 10.417 26.353 6.916 20.280 9.759 8.330 5.740 4.597 32.714 8.453 29.781 7.640 28.304 7.302 8.269 9.350 31.200 8.398
27.574 15.361 6.934 28.880 32.392 8,868 7.607 6.605
a
duction of the terminal fractional absorption constant Average results of the proposed method predicted all temperatures within 1.8”F. of Sujata calculation results and all component and oil rates within 1.0%. The method is recommended for use in the space between rough guesses and rigorous calculation for any simple absorber. The time requirement, either by hand or computer, will be only slightly greater than for other methods with heat balance included.
PREDICTED LEAN O I L RATE
. . .a 39.707 11.075 27.610 6.944 26.716 7.283 28.877 7.341 61.094 16.050 18.101 4.436 28.200 6.987 27,578 6.958 40.008 10,498 27.343 6.942 20.938 9.938 8.384 5.566 4.274 32.777 8.368 30,070 7.580 28.806 7.223 7.712 9.462 30.863 7,848
w.
KrernserBrown 35,360 20.878 11.174 37.773 40,227 12.717 12.863 9.918 2.997 50.661 15,879 35.328 11.170 36.336 12.225 25.054 10.592 68.990 18,030 28.156 11.312 35.650 11.396 35.303 11.074 54.947. 17.223 34.756 10.944 27,490 14.531 12.771 9.731 8.430 43.581 13.753 39.521 12.469 37.454 11.601 12.601 13.104 35.123 11.222
Did not converge.
Conclusions
The proposed method for making short-cut absorption calculations provides design information closer to rigorous calculation results than any other short-cut method tested. This method incorporates heat balances and absorption factors with no empirical graphs or charts. The only nonexplicit assumption is the intro-
Nom en clat ure A A, A’ c
absorption factor defined as A = L / K V = effective absorption factor defined by Equation 17 = absorption factor defined by Equation 18 = number of components =
= heat capacity of specified stream C, F = component fraction absorbed A H A= ~ heat ~ of absorption K = component equilibrium constant defined by K = y / x L = total liquid rate leaving a tray, moles = component liquid rate leaving a tray, moles I = number of trays in the column n S = total wet gas shrinkage, moles T = temperature = total vapor rate leaving a tray, moles V V = component vapor rate leaving a tray, moles X = liquid mole fraction Y = vapor mole fraction
Greek Symbols
.
LIA
= AiAzAs. .A, = AiAzAa.. . A ,
+A
=
KA
$4
w
+ AzA3.. .A,
f ...
+ A,
fraction of any wet-gas component not recovered = fraction of any lean-oil component leaving in the dry gas = fraction of total gas absorption that occurs on the terminal trays
Subscripts AVE
!
BTM DG i IG LO n 0 OIL RO TOP 1 2
= =
= =
= = = = =
= = =
=
column average bottom tray discharge gas stream tray reference in-gas stream lean-oil stream total number of trays (last tray) reference for stream entering tray I average of lean-oil and rich-oil streams rich oil stream top tray first tray second tray
BI BL IOG RAPHY (1) Brown, G. G., and Souders, M., Jr., IND.ENC.CHEM.,24,519 (1932). (2) Edmister, W. C., i b d , 35, 837 (1943). (3) Edmister, W. C., ThePetroleum Engineer, 18, No. 13 (September 1947). (4) Edmister, W. C., A.I.Ch.E. J., 3, No. 2, 165 (June 1957). ( 5 ) Erbar, J. H., Oklahoma State University, Stillwater, Okla., private communication. (6) Holland, C. D., “Multicomponent Distillation,” Prentice-Hall, Inc., 1963. (7) Horton, G., and Franklin, W. B., IND.ENO.CHEM.,92,1384 (1940). (8) Hull, R. J., and Raymond, K., Oil B Gus J. (Nov. 9, 16,.23, and 30, Dec. 7, 14, and 28, 1953). (9) Kremser, Alois, Not. Petrol. News, 22, 48, (May 21, 1930). (10) Landes, S. H., and Bell, F. W., Petrol. Refiner, 39, No. 6 , 201 (1960). (11) Lewis, W. K., and Matheson, G. L., IND. ENC.CHEM.,24,494 (May 1932). (12) Natural Gasoline Supply Men’s Association, “Engineering Data Book,” 7th ed., Tulsa, Okla., 1957. (13) Nielsen, K.L., “Methods in Numerical Analysis,” Macmillan Co., 1964. (14) Ravicz, A. E., “Non-Ideal Stage Multicomponent Absorber Calculations by Automatic Digital Computer,” Ph.D. Thesis, University of Michigan, Ann Arbor, Mich. (1959). (15) Smith, B. D., “Design of Equilibrium Stage Process,” McGraw-Hill, 79 pp, 1963. (16) Spear, R. R., “An Evaluation of the Sujata Absorption Calculation Method,” Master’s Thesis, Oklahoma State University, Stillwater, Okla., 1966. (17) Sujata, A. D., Petrol. Refiner, 40 (12), 137 (December 1962). (18) Thiele, E. W., and Geddes, R. L., IND. ENO.CHEM.,25,289 (March 1933).
VOL. 6 0
NO. 1 2
D E C E M B E R 1968
25
APPEND1 X ABSORBER CALCU LATl ONS Solutions can be reached without estimates but will require more iterations. Perhaps the best way is to perform a simple Kremser-Brown type absorption calculation assuming an average tower temperature of 90°F. For purposes of this solution assume a total absorption of 9.6 moles/100 moles rich gas. The second step is to assume a value for the percentage of the total absorption that takes place on the two terminal trays. This value can range from about 75y0to 90% with 80% being a good over-all average value. Now we must estimate the ( L / V ) ratio for the tower.
To simplify understanding, an illustrative example will be presented. Explanatory notes and comments will be interspersed with the calculations. The calculation procedure can be divided into five distinct areas: Preliminary calculations Absorption calculations Terminal tray calculations Heat balance calculations Adjusting section In order to carry out these short-cut calculations, the same information must be known as is generally required for other short-cut methods of calculation. The single exception to this is terminal-stream temperatures. Neither the dry-gas nor the rich-oil temperature is required. Both are independently calculated during the course of the calculation.
( L / V ) = (lean oil
I n the preliminary calculations, this will be assumed constant across the tower. B. We now must calculate the enthalpy and heat capacity of the feed streams to the tower. These are calculated as the mole fraction average of the individual component values.
Problem Statement
An absorber operates at 300 psia and contains the equivalent of eight theoretical trays. Lean oil (assumed to have characteristics of octane) enters at G O O F and a fixed rate of 20 moles per 100 moles of rich gas. The rich gas enters at 70°F. The composition of the rich gas is shown in column 1 of the tabular calculations attached (Table IX). Calculate the product stream compositions and temperatures.
Rich gas enthalpy = Z(mo1es of component X component enthalpy) = Z: [(I) x ( 3 ) ] (referring to columns in table of calculations) = 637,200 Btu
Solution
I n like manner:
Preliminary calculations. A. The first step in the solution is the assumption of the total moles of material absorbed in the tower. A good initial estimate is important since the total shrinkage is the major iteration variable.
Combonent
( 7) Wet gas, moles
C1 CZ c 3
CS
0.0308 0.1831 0.5880 133.6
26
ABSORBER CALCULATIONS
(3)
(4)
Gas at 70'F
~
Lean oil, moles
80 10 10 0
0
0 0
20
~
HV
Btu/mole
5257 9122 12537 47838
0.0304 0.1771 0.5606 121 .I
( 78)
CP
Btu/mole,
OF
8.80 14.63 19.06 70.77
(5) (6) Liquid at 60°F HL CP Btu/mole Btu/mole, 3524 5104 6080 21136
(7) O F
18.69 25.42 29.12 104.11
77.568 8.229 4.417 0.149
2,432 1.771 5.583 19.851
0,0894 0.0563 0,0970 ...
2,361 1.487 2.562 20.000
90.363
29,637
0.2427
26.410
K Values
Hv 73.04"F Btu/mole
77.0 F Btulmole
8.82 14,67 19.11 71.16
5284 9167 2595 8053
3849 5543 6583 22925
HL @ ,
77'F
9.5968 1.6165 0.5034 0.002215
9.7309 1.6713 0.5281 0,002444
1513 3727 6131 25550
(23)
A TOP
(21) ABTM
0.0305 0,1808 0.5687 131.8
0.0308 0,1797 0.5464 122.9
(20)
INDUSTRIAL A N D ENGINEERING CHEMISTRY
(8)
73'F
( 79)
(77) CP,VEXT Btubmole, F
@
Rich-gas heat capacity = Z[(1) x (4)] = 1041 Btu/OF Lean-oil enthalpy = 2 [ ( 2 ) X (5)] = 422,700 Btu Lean-oil heat capacity = Z[(2) x (6)] = 2082 Btu/OF
TABLE IX.
(2)
+
shrinkage)/rich gas 20f96 ( L / V ) = A = 0.296 100
73.929 9.716 6.979 0.149
(24)
Rich oil,
AAVE
Dry gas, moles
0.0296 0.1726 0,5464 118.1
77.538 8.216 4.457 0,153
2.462 1.784 5,543 19.847
90.364
29,636
(22)
moles
C. Estimate the column temperatures, top, bottom, and average. With the lean oil entering at GOOF and the rich gas a t 70°F, good estimates are:
TDG = 73'F T R O = 77'F TAVE= 77'F Again final results are not dependent upon the initial estimates, but covergence is hastened by good values. Absorption Section
A. Equilibrium constant values must be determined for each component a t various column temperatures. The values shown in columns 7 and 8 were calculated from curve-fitted data from the NGPSA Engineering Data Book (12). B. Absorption factors are calculated for each component. For the first iteration the L/V ratio is constant and AAVE= ABTM because the rich-oil and column-average temperatures were also assumed equal. The calculated values are shown in columns 9 and 10. C. Calculate the dry gas composition using Equations 21-23 and 26 as shown below Equation 21 u1
=
+ + l o ( l - *)
The resulting composition is tabulated in column 13. B. The mole fraction of lean oil in equilibrium with the dry gas is set a t the value required to make the sum of the mole fractions in the liquid equal to unity. x i e s n oil
xieana i l
ZA ___ 1
+1AAVE- 1.0
+ AAVE- ABTM- 1.0
D. The component flow rates in the top tray liquid may be calculated by: li =
LiX,
(13)
= 2[(14)
-
(2)] X (15)
F. The first step is to calculate the amount and composition of the vapor entering tray from tray two. =
u2
u1
+ 11 - lo
(16) = (11)
+ (14) - (2)
G. Next, we calculate the heat capacity of (CPNEXT).
+ 1 - 1.0 -
TA
A A V-~ 1.0 AAVE- ABTM - 1.0 Equation 26 modified to fit the three-tray model TA
x
(14) = 26.410
E. The heat of absorption released on the top tray can be calculated because an estimate of the material absorbed on the top tray is known.
Equation 23 modified to fit the three-tray model
ZA
- 0.2427
L1 = moles lean oil/mole fraction lean oil L1 = 20/0.7573 = 26.410 moles
AHTOP= 2[(11- lo) (AHi)] AHTop = 24,800 Btu
- -1
I---
-
= 1.0 Z(13) = 1.0 = 0.7573
C. Determine the flow rate of liquid leaving the top tray. The assumption is made that a negligible amount of lean oil is vaporized into the dry gas stream.
1
Un+l
Equation 22 modified to fit the three tray model
ZA
A. Using the equilibrium constant values a t 73'F, calculate the liquid mole fraction for all components appearing in the dry gas, except for the lean oil. Numbers in parentheses refer to column numbers in Table IX.
CPNEXT CPNEXT
Terminal (Top) Tray Evaluation
The initial temperatures should be improved for the next iteration. The top tray temperature is refined by combining pseudo-dew-point and heat-balance calculations. This procedure is iterative, but experience and insight should override where applicable. The procedure consists of comparing an initial temperature with the value calculated using the initial value. When the two values are the same, the top tray temperature has been found.
x
(16)]
H. Estimate the temperature on tray 2. The estimate is based on a linear interpolation between terminal temperatures plus a correction factor as in Equation 29.
=A T O ~ A ~ & ~ ~ ~ ~
The composition of the dry gas which results from these calculations is shown in column 11 of the calculations table. D. The rich-oil rate and composition are obtained from component and over-all material balances around the absorber. The rich oil is shown in column 12. The shrinkage is calculated to be 9.637 moles.
= C,V, = 2[(17) = 974 Btu/"F
Vz
Tz
=
+ T B T M -TTOP
TTOP
- 73.0
+ 8 Tz = 73.0 + 0.5 + 2.0 Tz
= 73.0
Tz
= 75.5'F
77.0
+
TTOP TBTM
+ [77.0 - (77.0
2 73.0)j
I. Calculate a new estimate of the top tray temperature, TDG from Equation 27 : (TDG - Tz) + AHTop - (CPNEXT) CPLO
TDG= TLO
(73.0 - 75.5) + 24,800 - (974) 2082 = 60 + 13.08
= 60
= 73.08'F
VOL. 6 0
NO. 1 2
DECEMBER 1968
27
APPEND I X (Continued) Ordinarily, the calculation of TDG will have to be repeated until the assumed and calculated values are in good agreement. In this case, the two values are close enough together for an example, and we will proceed with further calculations using the average.
TDG= (73.0
+ 73.08)/2
= 73.04'F
Implicit here is the assumption that the small change made in total absorption will cause negligible change in the operation of the top tray. If a major change were being made in the total absorption, the top tray calculation outline earlier would have to be repeated to have an accurate value for the top tray, L / V . Bottom tray
Heat Balance Section
A.
Calculate the enthalpy of the dry gas stream at TDQ.
= rich gas
(L/v)ET'w
HVDG= 2[(11) X (18)] = 548,100 Btu B.
Calculate the enthalpy of the rich oil a t the assumed temperature of 77.0'F.
HLRO = Z[(12) X (19)]
= 511,000 Btu
C. Check the assumed rich oil temperature by an over-all heat balance. Entering Lean oil Rich gas
Leaving
422,700 637,200 1,059,900'
Rich oil Dry gas
E. Revise the total heat of absorption based upon calculated amounts of absorption and heat of absorption a t the top tray temperature.
-
(ll)]
x
+
+
CPD,
+ CPLO
The only new term in this equation is w . From examination of tray-to-tray results, approximately 80% of the total absorption in the column occurs on the terminal trays of the column, and only about 20y0 on internal trays. For this reason, in the absence of specific information on the column under consideration, w will have a value of 0.8.
TAVE = 73.04
+
900 (77.0 - 73.04) 900
+ (1.0 - 0.8) 40,700 + 2082
1
= 76.99'F
For the foregoing calculation, the assumed value of shrinkage was 9.6 moles. The value calculated was 9.637 moles. A new value should be assumed and the calculations repeated to bring the assumption and final result into better agreement. Direct iteration will suffice. A. Determine the L / V values a t the top tray, bottom tray, and the average L / V for the column. Top tray liquid leaving tray 1 (L/V)TOP = dry gas
28
~
-
29.637 = -29'637 100.0 - 1.3 98.7 Average value
-
a
- 20.0)]
0.3003
rich oil - bottom tray shrinkage (L/v)AvE = bottom tray vapor - shrinkage x 0.03 29.637 - 1.300 = 0.2885 98.7 - (9.637 X 0.05)
With all three ( L / V ) values determined, calculations now revert to the absorption section. The individual absorption factors are determined and the recovery calculations made as before. A. Calculate individual component absorption factors for the top tray.
B. Calculate individual component absorption factors for the bottom tray. C. Calculate individual component absorption factors using the average value of L / V .
D. Calculate the dry-gas composition using the absorption factors determined above and Equation 21. 01
=
U,+l(&
26.410 = 0.2923 90.363
INDUSTRIAL A N D ENGINEERING CHEMISTRY
+ l o (1
1
-
)
= (23)
E. Determine the rich oil composition from component material balances around the tower. Total dry gas = Z(23) = 90.364 moles Total rich oil
Adjusting Section
=
29.637 [0.8(9.637) (26.410
(15) = 40,700 Btu
F. Calculate the average column temperature from Equation 28. CPDG(TRO- T D G ) (1 -
T A V E= TDG
-
rich oil gas shrinkage across bottom tray
Absorption Section
= 2[(11) X (17)] = 900Btu/'F
AHTOT= Z[(1)
= 100.0
-
51 1,000 548,100 1,059,100
The assumed rich oil temperature is correct. If the heat balance had been appreciably in error, a new value for TRo would have to be assumed, and calculations would revert to part B of this heat balance section. D. Compute the dry-gas heat capacity a t 73.04'F.
Cp,,
(L'Y)ETM
-
=
Z(24)
=
29.636 moles
Shrinkage = 100.0 - 90.364
=
9.636 moles
The estimated shrinkage (9.637 moles) and the calculated value (9.636 moles) are almost equal, indicating a solution to the problem. The solution to this problem was aided by fortuitous initial shrinkages and temperature assumptions. This sample problem presents only the calculational format of the proposed short-cut absorber calculation method. Tray-by-tray results of the Sujata procedure programmed by Spear (76) predict the rich-oil temperature to be 76.3'F and the dry-gas temperature to be 74.2'F. The dry-gas composition was 77.562 moles methane, 8.231 ethane, 4.545 propane, and 0.156 octane.
