- Email: [email protected]
Modelling of a crude distillation column
009%1354/91 53.00 + 0.00 copyright Q 1991 PerganlonPress plc
Computers&em. Engng, Vol. 15, No. 2. pp. 133-139, 1991 Printed in Great Britain.All rightsreserved
SHORT MODELLING
OF A CRUDE
P. LANG', G. Department ‘
(Received
NOTE DISTILLATION
SZALP&S~, G. CHIKANY'
COLUMN
and S. KEMI%NY'
of Chemical Engineering, Technical University of Budapest, Mtiegyetem rakpart 3, H- 152 1, Budapest XI, Hungary ZHungarian Hydrocarbon Institute, Hungary
7 January
1987; Final revision received 3 August
1990; received for publication
28 August
1990)
algorithm and a FORTRAN program have been developed for modelling of crude distillation and vacuum columns on smaller computers. Wang-Henke and Sum of Rates methods are combined in a new way. The memory requirement is low even in the case of a great number of pseudocomponents. An atmospheric crude distillation column has been simulated. Crude oil is described with 50 pseudocomponents chosen on the basis of the TBP curve of the feed. Calculated and experimental results are compared.
Abstract-An
the method were demonstrated and compared. Water was already regarded as being distributed between the vapor and liquid phases on stages except the condenser. The rates of side products withdrawn from sidestrippers are not specified by Hess and Holland, which is very uncomfortable when modeliing. This method has the following disadvantages:
INTRODUCYl’ION In order to successfully simulate a complex crude distillation column (Fig. 1) the following difficulties must be overcome: -Since the crude oil is a complex mixture containing more than a hundred components and oil is separated into many products, computation must be carried out with a great number of pseudocomponents. -Sidestrippers
-Time consumption of one iteration step is very high (almost (2N + 1) times greater than that of the BP method).
and pumparounds must be modelled.
-In the upper section the temperature increases downwards to a great extent while in the lower part temperature decreases because the main column has no reboiler. The column operates in a very wide temperature range. -Watersteam account. -Simple used.
-Its memory requirement is also higher than that of the BP or SR methods. -It
used for stripping must be taken into
and fast VLE
needs good initial estimates in order to converge successfully.
Its advantages are the following: and enthalpy models must be
Amundson et al. (1959) were the first who modelled a distillation column with a sidestripper extending their algorithm of the BP type. This method involved separate convergence of the main column assuming compositions of the vaporreturn streams from the sidestrippers. After each sidestripper is converged, revised vapor-return streams are used to converge the main column. Dickey et uZ.(1962) and Cechetti el al. (1963) suggested simultaneous modelling of the main column and sidestrippers using the 8 method. In these earlier works water was treated as a single-phase light (SPL) component. These algorithms of the BP type may fail to converge when modelling a crude oil distillation tower having no reboiler. The t, L and V profiles of the lower part of the main column cannot be precisely calculated by BP methods. The “multi-8 method” was applied by Hess and Holland (1977) and Hess et al. (1977) for modelling of absorber-type pipestills since the 0 method had failed to converge for columns of this type. This method belongs to the “2NNewton-Raphson methods” originated by Tomich (1970). The plate temperatures and the L/l’s were considered as independent variables. Three different numerical versions of TStripping factors: Sj = Kb. ( VjfLr). Withdrawal factors: RLj = 1 + Ul/Lj and R,, = 1 + Wj/ V,.
-It
converges more rapidly mainly in the vicinity of the solution than BP and SR methods, therefore fewer iteration steps are needed.
-It
can be used for the whole range of tower types because of its generality.
Russel(l983) published a method belonging to the “inside class of methods originated by Boston and Sullivan (1974) which was also used for solving crude-distillationcolumn problems. In the inner loop, stripping and sidestream withdrawal factors? are converged with relative volatilities assumed (and kept constant in the inner loop) using the quasi-Newton method to achieve all enthalpy balances. After solving component-material balances, temperatures are computed with the “Kb method”. Enthalpies are calculated using a simple enthalpy model. The component flow summations give new V, (and Lj) values. In the outer loop relative volatilities are updated and enthalpies are calculated rigorously. (The removal of time-consuming Kand enthalpy calculations to an outer loop gave rise to the term “insideout”). This method allows a wide variety of performance specifications and provides good speed, but it is rather complicated. Algorithms of the global Newton-Raphson type [e.g. Naphtali and Sandholm (1971), Gallun and Holland
133
our”
Short Note
134
CONDENSER
---c
___ -5:
feed crude
NO. 3.
H I-----
steam ---w-J
water
heavy gas oil steam
oil
Fig. 1. Crude distillation column with actual plate numbers. (1976) and KubiEek et al. (1976)] are not applicable to solve crude distillation problems with a great number of pseudocomponents on small computers because of their great memory requirements. ALCOR~M
PROPOSED
In this paper only the main characteristics of the new algorithm are summarized. In the new method, BP and SR
methods were combined for rnodelling further developing the idea of Tim&r et al. (1979). (The above authors suggested modelling of the upper part of the reboiled absorbers by SR and that of the lower section by BP methods.) The Wang-Henke algorithm (Wang and Henke, 1966) is used for modelling the upper rectifying section (plates above the feed plate) of the main column. For simulating the lower stripping section of the main column and sidestrippers the Sum of Rates (SR) method of Burningham and Otto (1967)
1 _---_+
a.)
usuai
b.)
specified calculated
modif ied
Fig. 2. Usual and modified specification of feed and product rates.
Short Note initial
Give
toted Calculate
tj
from
Q’
Lj
,
values
mater ial
from
s
135 (Vi;,5
are
balances
colcu-
)
component-material
balances
+ Normalize
xi _ i mole-fractions
4 Compute
bubble-points
tj
the
Update
I
part
Vj
(and
main
Lj -1)
molar
of the main column
Calculate
new of the
tj
in
upper
part
of
flows
in the
lower
using SR methcd (j-f....,N’
temperatures
main
the
column
column
in (SR
the
)
I
lower part
method)
I Compute (Li_: s
new Vi s and
rates
sidestrippers
1Update
(and (from
Vi;,s)
are
t’ s
for the sidestrippers L15ing 5R method of liquid
entering the
from material balances
1
la the sidestriFpers (SR method) 1
in the upper
l-eat and
sidestreams
calculated
material
port
of the main column
balances
f
using CC method)
Yes
END
Fig. 3. Simplified block diagram of the algorithm.
is suggested. The SR method is applied with a modified type of specification in order that liquid product rates leaving the bottoms of the stripping section and sidestrippers could be kept constant. When applying the SR method (e.g. for the simple absorber shown in Fig. 2a) feed rates (F, and FN) are usually specified. In this case there is no possibility of fixing a product rate because of the lack of degrees of freedom. By the modified type of specification applied in the new algorithm instead of the upper feed rate (F,) the bottom product rate (LN) is fixed (“lower end specification”). For the stripping section and sidestrippers the modified type of specification is more advantageous. (Rate of a product of the crude distillation tower is fixed instead of the rate of an inner liquid stream.) This “lower end specification” requires a slight modification in the original SR algorithm. Instead of 4s the vapor flowrates (V,s) must be updated by the summation equations (For modelling of sidestrippers the BP
method can be applied in the computer program, too, but in our experiences the SR method usually provides better convergence.) For solving the almost tridiagonal set of component material balance equations (see later in this paper) KubiEek’s algorithm (1973) is applied. Water may be regarded as being distributed between the vapor and liquid phases or as an SPL component. When solving heat balance equations by the BP method, the constant-composition method of Weisenfelder et al. (1961) is used in a modified form which is very advantageous in the case of a complex column with many feeds and sideproducts. (Enthalpy and material balances are written around the individual plates.) In order to give more accurate initial temperature and molar flow profiles the conception of “disturbed plates” [e.g. Pierucci er al. (198211 is applied. Appropriate damping technics usual at BP and SR methods based on experience are used when updating xU
Short Note COMPONENT-MATERIAL
BALANCES
For the column shown in Fig. 1. a model column with theoretical plates was created (sea Fig. 4). For this model column the coefficient matrix of the set of equations of component-material balances differs from a tridiagonal matrix by the appearance of three non-zero elements to the left and three non-zero elements to the right of the tridiagonal band of elements which result from the introduction of the sidestreams (U,, U,, and U,,) to the sidestrippers and from the return of the vapor streams (V,, , V,, and V,) from the sidestrippers, respectively. The abbreviated matrix display for the set of equations of component-material balances is shown in Fig. 5. (Component indices and off-band zeros are omitted.) Liquid pumparounds from one theoretical stage returning to the same or to an adjacent stage result in no further off-band elements. A pumparound from one theoretical stage to a non-adjacent stage somewhere above would result in a non-zero off-band element to the right of the tridiagonal band. PROPERTTRE OF PREUDOCOMPONENTS
Fig. 4. Model column with theoretical plates.
liquid mole fractions, tj temperatures and Li, Vi molar flowrates. A simplified block diagram of the new algorithm is given in Fig. 3. Instead of the Wang-Henke method it would be worth trying to apply the Jedlovsxky (1974) algorithm. (This method usually provides better convergence for the rectification of hydrocarbon mixtures.) r
In order to define psuedocomponents and calculate physicochemical properties, a TBP curve of the crude oil was determined. The crude oil was separated into 30 fractions on a ASTM D 2892-78 standard distillation column. Boiling temperatures, densities and molecular weights of the fractions were measured, and correlated with a polynomial of fifthorder as the function of the relative amount boiled off. The possibility of assigning pseudocomponents of an arbitrarily narrow boiling temperature range (e.g. 1O’C) was provided by the use of these polynomials. On the bases of the boiling points, densities and molecular weights of the pseudocomponents, their critical parameters were estimated by the method of Riaxi and Daubert (1980). The ideal gas enthalpy polynomial coefficients can be determined by the method of Daubert and Danner (1983). Enthalpies of the real fluids on the pressure and temperature of the industrial column were
_
a, a2
.
.
. .a7
.
.
-
‘b, c7 --------’ .’ . 1 :. 1. * .
--c W21 I I 7 -
-.
I I
I I
I
)
lJ,3+____---_0
I I bzz I_a22 10 I 1 I
0
/
b,
f
L --V2s-K25
j----,
0
. 4
x2
dz
X3 .
d,
X12
‘Jzs’K2.
1
-_
_
X? . . .
I
1 aI2 bq2 c,> -----.
_ Xl
I
Xl3 . .
k3 . ..
=
X20
c21
X21
da
x22
6,
X23
63
X24
d24
I I I “,a-
__-__
--____.o
Fig. 5. Set of equations of component-material
1I 1 bzs
~25
X23
d,
02s
bzs
X26
4,
balances.
_
Short Note Table Pseudocomponent No.
1. Composition
of the hydrocarbon
Pseudo-
component
Mel% I
1 2 3 4 5 6 7 8 9
8.1 2.9 2.8 3.5 4.2 4.1 4.1 3.0 5.8
10 11 12 13 14 15
3.5 3.3 3.2 1.9 2.4 3.4
No.
Mel% 2
16 17 18 19 20
2.8 2.7 2.6 2.0 1.4 2.3 1.8 1.7 2.1 1.2 1.9 1.1 1.1 1.1 1.0
;: 23 24 25 26 27 28 29 30
feed
Pseudocomponent No.
MC+% z
31 32 33 34
1.3 1.0 0.9 0.9 0.6 0.9 0.8
35 36 37 38 39 40 41 42 43 44
0.5 0.8 0.5 0.3 0.2 0.2 7.6
calculated by the Benedict-WebbRubin equation of state modified by Lee and Kesler (1975). The calculated enthalpies were correlated with a polynomial of third-order as a function of temperature. The vapor pressures of the pseudocomponents were also computed according to Lee and Kesler. Three data points were correlated with the Antoine equation for column calculation purposes. In the program vapor-liquid equilibria may be described with a combination of Flory-Huggins and Hildebrand models (Hildebrand and Scott, 1950) or an ideal liquid phase may be assumed. In the latter case water must be treated as a single-phase light component. EXAMPLES
The atmospheric crude distillation column shown in Fig. I is modelled. Crude oil is described as a mixture of 44 Table
2. Temperature
Temperature Plate NO. 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
(“C)
and
Liquid
molar
(km01
h-‘)
Initial
Final
Initial
Final
64.0 100.0 117.0 122.0 127.0 132.0
64.0 111.1 120.5 129.9 135.3 140.0 144.5 149.8 153.8 157.4 168.5 176.8 188.9 209.9 229.8 247.8 257.3 286.9 283.0 277.6 127.9 112.1 176.8 164.6 217.3 203.6
346.1 346.1
361.9 429.5 648.8 651.2 641.0 628.8 421.3 413.0 402.9 796.5 739.2 686.9 358.4 282.0 88.4 60.4 57.8 248.8 225.1 207.0 128.4 114.1 202.4 180.3 91.2 79.7
137.0 146.3 155.2 165.0 170.0 188.0 206.0 226.5 247.0 262.0 277.0 292.0 291.5 291 .O 137.5 138.0 198.0 190.0 238.5 230.0
534.6 534.6 534.6 534.6 398.6 398.6 398.6 775.7 775.7 775.7 575.7 575.7 485.7 485.7 485.7 694.9 694.9 207.0 125.0 114.0 190.1 180.3 84.9 79.7
Sidestream rates (kmol h-‘) Plate
NO. 7 13 15
Cm.3
15,2-E
Initial
Final
136.0 200.0 90.0
148.1 230.7 107.6
flow
profiles Vapor
(km01
hm’)
Initial
Final
-
-
903.8 903.8 903.8 903.8
731.0 798.6 1018.0 1020.3 1010.1 998.0
843.0 843.0 843.0 1220.0 1161.4 1161.4 1161.4
865.7 857.4 847.2 1240.8 1094.3 1041.9 944.1
1161.4 1112.2 1112.2 1112.2 567.3 567.3 60.8 49.9 58.6 48.8 49.2 44.0
867.7 714.9 686.9 684.3 121.2 97.5 73.0 53.2 89.3 61.1 66.7 50.4
715.3 715.3
137
pseudocompotmnts. The numbers of theoretical stages, locations of f&s. sidestreams and pumparounds can be seen in Fig. 4. The hydrocarbon f& (F,, = 754.11 km01 h-i) enters the column at 292°C. The steam enters the main column and sidestrippers as superheated vapor at 400°C with rates F,= 79.44 and Fz2= Fu= F,=38.89. The rate of top product U, = 173.05 kmol h-i. The side product-rates are specitied L, = I14.06, Lr., = 180.26 and r, = 79.7 km01 h-‘. The upper pumparound stream is to be withdrawn at the rate of F; = 63 1.92 km01 h-‘, its temperature decreases by 52°C. The rate of the lower pumparound stream F;,, = 707.27 km01 h-‘, the decrease of its temperature is 78°C. The initial value of the.reflm ratio L, /U, = 2. The pressure in the condenser is 0.953 bar, the pressures in the bottoms of the main column and the sidestrippers are 1.15 and 1.04, 1.lO and 1.I2 bar, respectively. (Linear pressure profiles are assumed in the main column and in the sidestrippers.) The temperature of the reflux is 64°C. The composition of the hydrocarbon feed is shown in Table 1. Initial temperature and molar flow profiles and results of the computation are presented in Tables 2-4. In order to show the agreement between the experimental and calculated product compositions the measured and calculated cumulative distribution curves are plotted in Fig. 6 for a similar operational state of the column. Calculated distribution curves for this latter case can be seen in Fig. 7 (dashed lines).
Table
1 2 3 4 : 7 8 9 10 11 12 13 14 15 16 17 18 19 z 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44
3. Product
comwsitions
34.49 12.14 11.36 13.35 13.83 9.22
0.96 0.61 1.04 2.40 5.84 11.64
4.55 0.77 0.28 0.02 0.00 0.00 0.00 0.00 0.00 0.00 0.00
21.32 15.39 25.78 9.89
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
3.87 1.08 0.15 0.04 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
calculated
~mol%)
0.14 0.09 0.14
0.01 0.00 0.01
0.29 0.56 0.88 1.70 1.97 7.36 8.05 10.88 11.98 7.20 8.76
0.03 0.05 0.09 0.16 0.17 0.53 0.54 0.85
11.59 8.59 7.09 5.48 3.12 1.48 1.49 0.63 0.30 0.17 0.04 0.02 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00
I.32 1.22 2.32 4.87 5.77 7.69 9.71
0.00 0.00 0.00 0.00
0.00 0.01 0.02 0.02 0.06 0.05 0.07 0.11 0.10 0.19 0.40 0.49 0.69 0.95 I .03 0.99 2.20 2.31
9.17 7.31 12.65 9.60 8.10 8.20 3.48 3.66 1.25 0.67 0.32 0.13 0.07 0.02 0.00
2.81 4.34 2.99 5.48 3.51 3.74 3.88 3.59 4.70 3.63 3.27
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
3.27 2.18 3.27 2.91 1.82 2.91 1.82 1.09 0.73 0.73 27.64
Short Note
138
Table 4. E&halpies and heat duties calculated: (a) the feed enthalpk watcrsteam = hr M hydrocarbon: hF,,s= 1.439 x loSkJkmol-‘, 4.644 x 104 kJ kmo1-‘; (b) molar entha1pika =h,,=h,,=hF.,= of liauid and vabor flows entbduics _
Molar Plate No. 1 2 3 4 : 7 f 10 11 12 13 14 15 16 17 18 19 20 21 22 :: 25 26
03 kmo1-‘)
Liquid -7.662 1.1666 1.485 1.821 2.048 2.260 2.479 2.734 2.944 3.148 3.704 4.218 5.109 4.855 8.779 1.092 1.248 1.892 1.942 1.946 1.946 1.449 4.675 4.214 8.373 7.774
x x x x x x x x x x x x x x x x x x x x x x x x x x
10’ Iti 10’ 10’ 10’ 104 lOa 10’ 10’ 10’ 104 Iti 104 Iti 104 105 10s lo5 10J 10’ 10’ 104 10’ 10’ 10’ 10’
Vapor 4.625 x 10’ 4.895 x 104 5.194 x lti 5.4cKl x lti 5.580 x lti 5.757 x Iti 5.961 x 10’ 6.118 x 104 6.258 x LO4 6.839 x 104 7.239 x lti 7.756 x IO 8.678 x 10’ 9.560 x lti 1.033 x 10s 1.058 x 10’ 1.156 x 10’ 8.642 x 104 7.285 x 10’ 5.244 x lo* 4.982 x 10’ 6.714 x 10’ 6.019 x lti 7.570 x Iti 6.440 x lo*
REMARKS
The method suggested usually provides good convergence. However, in the vicinity of the solution convergence becomes slower as is usual with methods of total decomposition. Generally 50-60 iteration steps are enough to achieve a result of sutiicient accuracy for a chemical engineer. When water is treated as being distributed between liquid and vapor phases at least one product rate must not be fixed, therefore in most of the calculations water was considered an SPL component. The program was also successfully used for modelling a complex vacuum unit without condenser. The algorithm proposed can also serve for providing appropriate initial values for other computation methods which am more sensitive to the starting estimates. A detailed algorithm including the damping techniques applied and the characteristics of the pseudocomponents will be sent upon request. Acknowiedgemenrs-The authors are indebted to Dr A. Deak, Mr Gy. Vancsura of the Technical University, Budapest and Z. Merth of the Hungarian Hydrocarbon Institute for their help in making parts of the computation work. NOMENCLATURE II, b, c = Coefficients in the set of component
the enthalpies of the pumparound streams after cooling Plate
Enthaluy (kJ LmOizl)
3 10
3.587 x 102 5.158 x 103
(c) heat duties of the condenser and pumparound heat exchangers Plate
Heat duties (LJ h-‘)
: 10
-3.325 x 10’ -9.155 x 106 - 1.862 x 10’
Figure 7 illustrates the modification of calculated distribution curves due to the change in product rates when an LGO fraction containing pseudocomponents from 8 to 15 had to be produced in a larger quantity.
material balance equations d = Right-hand side elements in the set of component material balance equations f = Number of feed plate of crude oil F = Total flowrate of a feed F’ = Molar flowrate of a liquid pumparound h = Molar liquid enthalpy U = Molar vapor enthalpy K = Vapor-liquid equilibrium constant
L N R S U U’ V x y z
= = = = = = = = = =
Liquid molar flowrate Number of trays Withdrawal factor Stripping factor Liquid sidestream Water stream Vapor molar flowrate Molar liquid fraction Molar vapor fraction Molar fraction in a feed
-
Measured 0
Pseudocomp.
No.
Fig. 6. Measured and calculated product compositions.
Calculated
Short Note
139
25
---
Bask
-
Modified
15
10
5
0
Pseudocamp.
Fig. 7. Modification Subscripts
b = F = i= j = L = V =
Base component Feed Component Tray Liquid Vapor
Superscripts I = Main column
II, III,
No.
of product distribution curves.
= Side-stripper
REFERENCES Amundson N. R., A. J. Pontinen and J. W. Tiernay, AIChE Jf 5, 295 (1959). Boston J. F. and S. L. Sullivan Jr, Can. J. Chem. Engng Feb, 52 (1974). Burningham D. W. and F. G. Otto, ffydrocarbon Process. Ott, 163 (1967). Cechetti R. C. er al., Hydrocarbon Process. 42(g), 159 (1963). Daubert T. E. and P. P. Danner, API Technical Data Book Perroieum Refining, 3rd Edn. Washington, D. C. (1983). Dickey B. R.. C. D. Holland and R. Cecchetti, Petrol. Refiner 41(2), 143 (1962).
Gallun S. E. and C. D. Holland, Hydrocarbon
Process.
55,
I37 (1976).
F. E. Hess, C. D. Holland, Hydrocarbon Process. 56(S), 241 (1977). Hess F. E. er al. Hydrocarbon Process. 56(6), 181 (1977). Hildebrand J. H. and R. L. Scott, The Solubility of NonElectrolytes. Reinhold, New York (1950). Holland C. D., G. P. Pendon and S. E. Gallun, Hydrocarbon Process. 54(l), 101 (1975). Jedlovszky P., Clrem. Engng. Sci. 29(l), 287 (1974). KubiEek M.. Commun. ACM 16(121. 760 (1973). KubiEek M., V. Hlav%ek and F.‘P&chask& Chkm. Engng. Sci. 31, 277 (1976). Lee B. I. and M. G. Kesler, AIChE JI 21, 510 (1975). Naphtali L. M. and D. P. Sandholm, AlChE JI 17(l), 148 (1971). \-~ Pieru&S. et al.. Computers &em. Engng 6, 39 (1982). Riazi M. R. and T. E. Daubert, Hydrocarbon Process. 59(3), 115 (1980). Russel R. A., Chem. Engng Ott 17, 53 (1983). Tim&r L., Z. Csermely and S. BBcskai, Hung. J. Ind. Chem. 7(4), 377 (1979). Tomich J. F., AZChE Jl 16, 229 (1970). Wang J. C. and G. E. Henke, Hydrocarbon Process. 45, 155 (1966). Weisenfelder A. J. et al., Petrol. Refiner 40(10), 175 (1961).
Computers&em. Engng, Vol. 15, No. 2. pp. 133-139, 1991 Printed in Great Britain.All rightsreserved
SHORT MODELLING
OF A CRUDE
P. LANG', G. Department ‘
(Received
NOTE DISTILLATION
SZALP&S~, G. CHIKANY'
COLUMN
and S. KEMI%NY'
of Chemical Engineering, Technical University of Budapest, Mtiegyetem rakpart 3, H- 152 1, Budapest XI, Hungary ZHungarian Hydrocarbon Institute, Hungary
7 January
1987; Final revision received 3 August
1990; received for publication
28 August
1990)
algorithm and a FORTRAN program have been developed for modelling of crude distillation and vacuum columns on smaller computers. Wang-Henke and Sum of Rates methods are combined in a new way. The memory requirement is low even in the case of a great number of pseudocomponents. An atmospheric crude distillation column has been simulated. Crude oil is described with 50 pseudocomponents chosen on the basis of the TBP curve of the feed. Calculated and experimental results are compared.
Abstract-An
the method were demonstrated and compared. Water was already regarded as being distributed between the vapor and liquid phases on stages except the condenser. The rates of side products withdrawn from sidestrippers are not specified by Hess and Holland, which is very uncomfortable when modeliing. This method has the following disadvantages:
INTRODUCYl’ION In order to successfully simulate a complex crude distillation column (Fig. 1) the following difficulties must be overcome: -Since the crude oil is a complex mixture containing more than a hundred components and oil is separated into many products, computation must be carried out with a great number of pseudocomponents. -Sidestrippers
-Time consumption of one iteration step is very high (almost (2N + 1) times greater than that of the BP method).
and pumparounds must be modelled.
-In the upper section the temperature increases downwards to a great extent while in the lower part temperature decreases because the main column has no reboiler. The column operates in a very wide temperature range. -Watersteam account. -Simple used.
-Its memory requirement is also higher than that of the BP or SR methods. -It
used for stripping must be taken into
and fast VLE
needs good initial estimates in order to converge successfully.
Its advantages are the following: and enthalpy models must be
Amundson et al. (1959) were the first who modelled a distillation column with a sidestripper extending their algorithm of the BP type. This method involved separate convergence of the main column assuming compositions of the vaporreturn streams from the sidestrippers. After each sidestripper is converged, revised vapor-return streams are used to converge the main column. Dickey et uZ.(1962) and Cechetti el al. (1963) suggested simultaneous modelling of the main column and sidestrippers using the 8 method. In these earlier works water was treated as a single-phase light (SPL) component. These algorithms of the BP type may fail to converge when modelling a crude oil distillation tower having no reboiler. The t, L and V profiles of the lower part of the main column cannot be precisely calculated by BP methods. The “multi-8 method” was applied by Hess and Holland (1977) and Hess et al. (1977) for modelling of absorber-type pipestills since the 0 method had failed to converge for columns of this type. This method belongs to the “2NNewton-Raphson methods” originated by Tomich (1970). The plate temperatures and the L/l’s were considered as independent variables. Three different numerical versions of TStripping factors: Sj = Kb. ( VjfLr). Withdrawal factors: RLj = 1 + Ul/Lj and R,, = 1 + Wj/ V,.
-It
converges more rapidly mainly in the vicinity of the solution than BP and SR methods, therefore fewer iteration steps are needed.
-It
can be used for the whole range of tower types because of its generality.
Russel(l983) published a method belonging to the “inside class of methods originated by Boston and Sullivan (1974) which was also used for solving crude-distillationcolumn problems. In the inner loop, stripping and sidestream withdrawal factors? are converged with relative volatilities assumed (and kept constant in the inner loop) using the quasi-Newton method to achieve all enthalpy balances. After solving component-material balances, temperatures are computed with the “Kb method”. Enthalpies are calculated using a simple enthalpy model. The component flow summations give new V, (and Lj) values. In the outer loop relative volatilities are updated and enthalpies are calculated rigorously. (The removal of time-consuming Kand enthalpy calculations to an outer loop gave rise to the term “insideout”). This method allows a wide variety of performance specifications and provides good speed, but it is rather complicated. Algorithms of the global Newton-Raphson type [e.g. Naphtali and Sandholm (1971), Gallun and Holland
133
our”
Short Note
134
CONDENSER
---c
___ -5:
feed crude
NO. 3.
H I-----
steam ---w-J
water
heavy gas oil steam
oil
Fig. 1. Crude distillation column with actual plate numbers. (1976) and KubiEek et al. (1976)] are not applicable to solve crude distillation problems with a great number of pseudocomponents on small computers because of their great memory requirements. ALCOR~M
PROPOSED
In this paper only the main characteristics of the new algorithm are summarized. In the new method, BP and SR
methods were combined for rnodelling further developing the idea of Tim&r et al. (1979). (The above authors suggested modelling of the upper part of the reboiled absorbers by SR and that of the lower section by BP methods.) The Wang-Henke algorithm (Wang and Henke, 1966) is used for modelling the upper rectifying section (plates above the feed plate) of the main column. For simulating the lower stripping section of the main column and sidestrippers the Sum of Rates (SR) method of Burningham and Otto (1967)
1 _---_+
a.)
usuai
b.)
specified calculated
modif ied
Fig. 2. Usual and modified specification of feed and product rates.
Short Note initial
Give
toted Calculate
tj
from
Q’
Lj
,
values
mater ial
from
s
135 (Vi;,5
are
balances
colcu-
)
component-material
balances
+ Normalize
xi _ i mole-fractions
4 Compute
bubble-points
tj
the
Update
I
part
Vj
(and
main
Lj -1)
molar
of the main column
Calculate
new of the
tj
in
upper
part
of
flows
in the
lower
using SR methcd (j-f....,N’
temperatures
main
the
column
column
in (SR
the
)
I
lower part
method)
I Compute (Li_: s
new Vi s and
rates
sidestrippers
1Update
(and (from
Vi;,s)
are
t’ s
for the sidestrippers L15ing 5R method of liquid
entering the
from material balances
1
la the sidestriFpers (SR method) 1
in the upper
l-eat and
sidestreams
calculated
material
port
of the main column
balances
f
using CC method)
Yes
END
Fig. 3. Simplified block diagram of the algorithm.
is suggested. The SR method is applied with a modified type of specification in order that liquid product rates leaving the bottoms of the stripping section and sidestrippers could be kept constant. When applying the SR method (e.g. for the simple absorber shown in Fig. 2a) feed rates (F, and FN) are usually specified. In this case there is no possibility of fixing a product rate because of the lack of degrees of freedom. By the modified type of specification applied in the new algorithm instead of the upper feed rate (F,) the bottom product rate (LN) is fixed (“lower end specification”). For the stripping section and sidestrippers the modified type of specification is more advantageous. (Rate of a product of the crude distillation tower is fixed instead of the rate of an inner liquid stream.) This “lower end specification” requires a slight modification in the original SR algorithm. Instead of 4s the vapor flowrates (V,s) must be updated by the summation equations (For modelling of sidestrippers the BP
method can be applied in the computer program, too, but in our experiences the SR method usually provides better convergence.) For solving the almost tridiagonal set of component material balance equations (see later in this paper) KubiEek’s algorithm (1973) is applied. Water may be regarded as being distributed between the vapor and liquid phases or as an SPL component. When solving heat balance equations by the BP method, the constant-composition method of Weisenfelder et al. (1961) is used in a modified form which is very advantageous in the case of a complex column with many feeds and sideproducts. (Enthalpy and material balances are written around the individual plates.) In order to give more accurate initial temperature and molar flow profiles the conception of “disturbed plates” [e.g. Pierucci er al. (198211 is applied. Appropriate damping technics usual at BP and SR methods based on experience are used when updating xU
Short Note COMPONENT-MATERIAL
BALANCES
For the column shown in Fig. 1. a model column with theoretical plates was created (sea Fig. 4). For this model column the coefficient matrix of the set of equations of component-material balances differs from a tridiagonal matrix by the appearance of three non-zero elements to the left and three non-zero elements to the right of the tridiagonal band of elements which result from the introduction of the sidestreams (U,, U,, and U,,) to the sidestrippers and from the return of the vapor streams (V,, , V,, and V,) from the sidestrippers, respectively. The abbreviated matrix display for the set of equations of component-material balances is shown in Fig. 5. (Component indices and off-band zeros are omitted.) Liquid pumparounds from one theoretical stage returning to the same or to an adjacent stage result in no further off-band elements. A pumparound from one theoretical stage to a non-adjacent stage somewhere above would result in a non-zero off-band element to the right of the tridiagonal band. PROPERTTRE OF PREUDOCOMPONENTS
Fig. 4. Model column with theoretical plates.
liquid mole fractions, tj temperatures and Li, Vi molar flowrates. A simplified block diagram of the new algorithm is given in Fig. 3. Instead of the Wang-Henke method it would be worth trying to apply the Jedlovsxky (1974) algorithm. (This method usually provides better convergence for the rectification of hydrocarbon mixtures.) r
In order to define psuedocomponents and calculate physicochemical properties, a TBP curve of the crude oil was determined. The crude oil was separated into 30 fractions on a ASTM D 2892-78 standard distillation column. Boiling temperatures, densities and molecular weights of the fractions were measured, and correlated with a polynomial of fifthorder as the function of the relative amount boiled off. The possibility of assigning pseudocomponents of an arbitrarily narrow boiling temperature range (e.g. 1O’C) was provided by the use of these polynomials. On the bases of the boiling points, densities and molecular weights of the pseudocomponents, their critical parameters were estimated by the method of Riaxi and Daubert (1980). The ideal gas enthalpy polynomial coefficients can be determined by the method of Daubert and Danner (1983). Enthalpies of the real fluids on the pressure and temperature of the industrial column were
_
a, a2
.
.
. .a7
.
.
-
‘b, c7 --------’ .’ . 1 :. 1. * .
--c W21 I I 7 -
-.
I I
I I
I
)
lJ,3+____---_0
I I bzz I_a22 10 I 1 I
0
/
b,
f
L --V2s-K25
j----,
0
. 4
x2
dz
X3 .
d,
X12
‘Jzs’K2.
1
-_
_
X? . . .
I
1 aI2 bq2 c,> -----.
_ Xl
I
Xl3 . .
k3 . ..
=
X20
c21
X21
da
x22
6,
X23
63
X24
d24
I I I “,a-
__-__
--____.o
Fig. 5. Set of equations of component-material
1I 1 bzs
~25
X23
d,
02s
bzs
X26
4,
balances.
_
Short Note Table Pseudocomponent No.
1. Composition
of the hydrocarbon
Pseudo-
component
Mel% I
1 2 3 4 5 6 7 8 9
8.1 2.9 2.8 3.5 4.2 4.1 4.1 3.0 5.8
10 11 12 13 14 15
3.5 3.3 3.2 1.9 2.4 3.4
No.
Mel% 2
16 17 18 19 20
2.8 2.7 2.6 2.0 1.4 2.3 1.8 1.7 2.1 1.2 1.9 1.1 1.1 1.1 1.0
;: 23 24 25 26 27 28 29 30
feed
Pseudocomponent No.
MC+% z
31 32 33 34
1.3 1.0 0.9 0.9 0.6 0.9 0.8
35 36 37 38 39 40 41 42 43 44
0.5 0.8 0.5 0.3 0.2 0.2 7.6
calculated by the Benedict-WebbRubin equation of state modified by Lee and Kesler (1975). The calculated enthalpies were correlated with a polynomial of third-order as a function of temperature. The vapor pressures of the pseudocomponents were also computed according to Lee and Kesler. Three data points were correlated with the Antoine equation for column calculation purposes. In the program vapor-liquid equilibria may be described with a combination of Flory-Huggins and Hildebrand models (Hildebrand and Scott, 1950) or an ideal liquid phase may be assumed. In the latter case water must be treated as a single-phase light component. EXAMPLES
The atmospheric crude distillation column shown in Fig. I is modelled. Crude oil is described as a mixture of 44 Table
2. Temperature
Temperature Plate NO. 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
(“C)
and
Liquid
molar
(km01
h-‘)
Initial
Final
Initial
Final
64.0 100.0 117.0 122.0 127.0 132.0
64.0 111.1 120.5 129.9 135.3 140.0 144.5 149.8 153.8 157.4 168.5 176.8 188.9 209.9 229.8 247.8 257.3 286.9 283.0 277.6 127.9 112.1 176.8 164.6 217.3 203.6
346.1 346.1
361.9 429.5 648.8 651.2 641.0 628.8 421.3 413.0 402.9 796.5 739.2 686.9 358.4 282.0 88.4 60.4 57.8 248.8 225.1 207.0 128.4 114.1 202.4 180.3 91.2 79.7
137.0 146.3 155.2 165.0 170.0 188.0 206.0 226.5 247.0 262.0 277.0 292.0 291.5 291 .O 137.5 138.0 198.0 190.0 238.5 230.0
534.6 534.6 534.6 534.6 398.6 398.6 398.6 775.7 775.7 775.7 575.7 575.7 485.7 485.7 485.7 694.9 694.9 207.0 125.0 114.0 190.1 180.3 84.9 79.7
Sidestream rates (kmol h-‘) Plate
NO. 7 13 15
Cm.3
15,2-E
Initial
Final
136.0 200.0 90.0
148.1 230.7 107.6
flow
profiles Vapor
(km01
hm’)
Initial
Final
-
-
903.8 903.8 903.8 903.8
731.0 798.6 1018.0 1020.3 1010.1 998.0
843.0 843.0 843.0 1220.0 1161.4 1161.4 1161.4
865.7 857.4 847.2 1240.8 1094.3 1041.9 944.1
1161.4 1112.2 1112.2 1112.2 567.3 567.3 60.8 49.9 58.6 48.8 49.2 44.0
867.7 714.9 686.9 684.3 121.2 97.5 73.0 53.2 89.3 61.1 66.7 50.4
715.3 715.3
137
pseudocompotmnts. The numbers of theoretical stages, locations of f&s. sidestreams and pumparounds can be seen in Fig. 4. The hydrocarbon f& (F,, = 754.11 km01 h-i) enters the column at 292°C. The steam enters the main column and sidestrippers as superheated vapor at 400°C with rates F,= 79.44 and Fz2= Fu= F,=38.89. The rate of top product U, = 173.05 kmol h-i. The side product-rates are specitied L, = I14.06, Lr., = 180.26 and r, = 79.7 km01 h-‘. The upper pumparound stream is to be withdrawn at the rate of F; = 63 1.92 km01 h-‘, its temperature decreases by 52°C. The rate of the lower pumparound stream F;,, = 707.27 km01 h-‘, the decrease of its temperature is 78°C. The initial value of the.reflm ratio L, /U, = 2. The pressure in the condenser is 0.953 bar, the pressures in the bottoms of the main column and the sidestrippers are 1.15 and 1.04, 1.lO and 1.I2 bar, respectively. (Linear pressure profiles are assumed in the main column and in the sidestrippers.) The temperature of the reflux is 64°C. The composition of the hydrocarbon feed is shown in Table 1. Initial temperature and molar flow profiles and results of the computation are presented in Tables 2-4. In order to show the agreement between the experimental and calculated product compositions the measured and calculated cumulative distribution curves are plotted in Fig. 6 for a similar operational state of the column. Calculated distribution curves for this latter case can be seen in Fig. 7 (dashed lines).
Table
1 2 3 4 : 7 8 9 10 11 12 13 14 15 16 17 18 19 z 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44
3. Product
comwsitions
34.49 12.14 11.36 13.35 13.83 9.22
0.96 0.61 1.04 2.40 5.84 11.64
4.55 0.77 0.28 0.02 0.00 0.00 0.00 0.00 0.00 0.00 0.00
21.32 15.39 25.78 9.89
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
3.87 1.08 0.15 0.04 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
calculated
~mol%)
0.14 0.09 0.14
0.01 0.00 0.01
0.29 0.56 0.88 1.70 1.97 7.36 8.05 10.88 11.98 7.20 8.76
0.03 0.05 0.09 0.16 0.17 0.53 0.54 0.85
11.59 8.59 7.09 5.48 3.12 1.48 1.49 0.63 0.30 0.17 0.04 0.02 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00
I.32 1.22 2.32 4.87 5.77 7.69 9.71
0.00 0.00 0.00 0.00
0.00 0.01 0.02 0.02 0.06 0.05 0.07 0.11 0.10 0.19 0.40 0.49 0.69 0.95 I .03 0.99 2.20 2.31
9.17 7.31 12.65 9.60 8.10 8.20 3.48 3.66 1.25 0.67 0.32 0.13 0.07 0.02 0.00
2.81 4.34 2.99 5.48 3.51 3.74 3.88 3.59 4.70 3.63 3.27
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
3.27 2.18 3.27 2.91 1.82 2.91 1.82 1.09 0.73 0.73 27.64
Short Note
138
Table 4. E&halpies and heat duties calculated: (a) the feed enthalpk watcrsteam = hr M hydrocarbon: hF,,s= 1.439 x loSkJkmol-‘, 4.644 x 104 kJ kmo1-‘; (b) molar entha1pika =h,,=h,,=hF.,= of liauid and vabor flows entbduics _
Molar Plate No. 1 2 3 4 : 7 f 10 11 12 13 14 15 16 17 18 19 20 21 22 :: 25 26
03 kmo1-‘)
Liquid -7.662 1.1666 1.485 1.821 2.048 2.260 2.479 2.734 2.944 3.148 3.704 4.218 5.109 4.855 8.779 1.092 1.248 1.892 1.942 1.946 1.946 1.449 4.675 4.214 8.373 7.774
x x x x x x x x x x x x x x x x x x x x x x x x x x
10’ Iti 10’ 10’ 10’ 104 lOa 10’ 10’ 10’ 104 Iti 104 Iti 104 105 10s lo5 10J 10’ 10’ 104 10’ 10’ 10’ 10’
Vapor 4.625 x 10’ 4.895 x 104 5.194 x lti 5.4cKl x lti 5.580 x lti 5.757 x Iti 5.961 x 10’ 6.118 x 104 6.258 x LO4 6.839 x 104 7.239 x lti 7.756 x IO 8.678 x 10’ 9.560 x lti 1.033 x 10s 1.058 x 10’ 1.156 x 10’ 8.642 x 104 7.285 x 10’ 5.244 x lo* 4.982 x 10’ 6.714 x 10’ 6.019 x lti 7.570 x Iti 6.440 x lo*
REMARKS
The method suggested usually provides good convergence. However, in the vicinity of the solution convergence becomes slower as is usual with methods of total decomposition. Generally 50-60 iteration steps are enough to achieve a result of sutiicient accuracy for a chemical engineer. When water is treated as being distributed between liquid and vapor phases at least one product rate must not be fixed, therefore in most of the calculations water was considered an SPL component. The program was also successfully used for modelling a complex vacuum unit without condenser. The algorithm proposed can also serve for providing appropriate initial values for other computation methods which am more sensitive to the starting estimates. A detailed algorithm including the damping techniques applied and the characteristics of the pseudocomponents will be sent upon request. Acknowiedgemenrs-The authors are indebted to Dr A. Deak, Mr Gy. Vancsura of the Technical University, Budapest and Z. Merth of the Hungarian Hydrocarbon Institute for their help in making parts of the computation work. NOMENCLATURE II, b, c = Coefficients in the set of component
the enthalpies of the pumparound streams after cooling Plate
Enthaluy (kJ LmOizl)
3 10
3.587 x 102 5.158 x 103
(c) heat duties of the condenser and pumparound heat exchangers Plate
Heat duties (LJ h-‘)
: 10
-3.325 x 10’ -9.155 x 106 - 1.862 x 10’
Figure 7 illustrates the modification of calculated distribution curves due to the change in product rates when an LGO fraction containing pseudocomponents from 8 to 15 had to be produced in a larger quantity.
material balance equations d = Right-hand side elements in the set of component material balance equations f = Number of feed plate of crude oil F = Total flowrate of a feed F’ = Molar flowrate of a liquid pumparound h = Molar liquid enthalpy U = Molar vapor enthalpy K = Vapor-liquid equilibrium constant
L N R S U U’ V x y z
= = = = = = = = = =
Liquid molar flowrate Number of trays Withdrawal factor Stripping factor Liquid sidestream Water stream Vapor molar flowrate Molar liquid fraction Molar vapor fraction Molar fraction in a feed
-
Measured 0
Pseudocomp.
No.
Fig. 6. Measured and calculated product compositions.
Calculated
Short Note
139
25
---
Bask
-
Modified
15
10
5
0
Pseudocamp.
Fig. 7. Modification Subscripts
b = F = i= j = L = V =
Base component Feed Component Tray Liquid Vapor
Superscripts I = Main column
II, III,
No.
of product distribution curves.
= Side-stripper
REFERENCES Amundson N. R., A. J. Pontinen and J. W. Tiernay, AIChE Jf 5, 295 (1959). Boston J. F. and S. L. Sullivan Jr, Can. J. Chem. Engng Feb, 52 (1974). Burningham D. W. and F. G. Otto, ffydrocarbon Process. Ott, 163 (1967). Cechetti R. C. er al., Hydrocarbon Process. 42(g), 159 (1963). Daubert T. E. and P. P. Danner, API Technical Data Book Perroieum Refining, 3rd Edn. Washington, D. C. (1983). Dickey B. R.. C. D. Holland and R. Cecchetti, Petrol. Refiner 41(2), 143 (1962).
Gallun S. E. and C. D. Holland, Hydrocarbon
Process.
55,
I37 (1976).
F. E. Hess, C. D. Holland, Hydrocarbon Process. 56(S), 241 (1977). Hess F. E. er al. Hydrocarbon Process. 56(6), 181 (1977). Hildebrand J. H. and R. L. Scott, The Solubility of NonElectrolytes. Reinhold, New York (1950). Holland C. D., G. P. Pendon and S. E. Gallun, Hydrocarbon Process. 54(l), 101 (1975). Jedlovszky P., Clrem. Engng. Sci. 29(l), 287 (1974). KubiEek M.. Commun. ACM 16(121. 760 (1973). KubiEek M., V. Hlav%ek and F.‘P&chask& Chkm. Engng. Sci. 31, 277 (1976). Lee B. I. and M. G. Kesler, AIChE JI 21, 510 (1975). Naphtali L. M. and D. P. Sandholm, AlChE JI 17(l), 148 (1971). \-~ Pieru&S. et al.. Computers &em. Engng 6, 39 (1982). Riazi M. R. and T. E. Daubert, Hydrocarbon Process. 59(3), 115 (1980). Russel R. A., Chem. Engng Ott 17, 53 (1983). Tim&r L., Z. Csermely and S. BBcskai, Hung. J. Ind. Chem. 7(4), 377 (1979). Tomich J. F., AZChE Jl 16, 229 (1970). Wang J. C. and G. E. Henke, Hydrocarbon Process. 45, 155 (1966). Weisenfelder A. J. et al., Petrol. Refiner 40(10), 175 (1961).