OPTIMIZATION PETROLEUM P.M.
OF T H E P R O C E S S
OF R E F I N I N G
FEED F O R L U B R I C A T I N G - O I L
RESIDUAL
PRODUCTION UDC 65.018.2:665.543:547.53
Nesterov
In the refining of residual phenol-deasphalted feedstock in an extraction column (usually packed) the influence of the inlet conditions on the quality and quantity of the raffinate varies and has as yet been little studied. Extraction column operating conditions are selected intuitively by the plant technologist and operator. Therefore, selection of the best conditions depends on the training and experience of the plant technologist and operator. This resuits in loss of lubricating-oii components. The object of this article is to determine optimal regions of the process, by obtaining a quantitative assessment of inlet and outlet conditions in the form of a mathematical model which adequately describes the optimal process conditions of lubricant refining under plant conditions. For this purpose, the operating condition of a solvent-extraction column 2.6 mm diameter and 22 m high at the Fergana oil refinery (FNPZ) in which residual, deasphalted Fergana crudes were refined were studied in four stages. First
Stage.
Study of the operating conditions of the extraction column lead to the construction of a mathematical model in the form of linear regression equations (1)-(3). These equations approximately describe the extraction process in an industrial column under 'normal' operating conditions. They can also be used for approximate assessment of the physicochemical relationships of the process and to select a strategy of experimentation under full-scale conditions within the optimal region. The regression coefficients were significant for a 5% significance level. Correction of these coefficients for the number of parameters gave a result in the form of ~1 == 0,375;
~e = 0,376;
~s ---- 0,418
R1 = 0,365Xx -}- 0,313X4 - - 0,36X~
(1)
Re =: 0,306X1 -~ 0,215X. -- 0,331X4 - - 0,446X5 @ 0,33X e - - 0,434Xs -t- 0,345X9 -}- 0,423X14- 0,112Xl~ Ra == 0,281X1 -~- 0,238X 2 - - 0,21X3 - - 0,493X5
(.2)
@ 0 , 2 2 6 X 6 - 0,287X8-47 0 , 2 4 8 X 9 - 0,248Xio -I- 0,348Xle - - 0,2Xla -}- 0,21X15,
(3)
where XI is the feedstock flow rate, mS]h; X 2 is the phenol flow rate, mS/h; Xs is the temperature in the upper part of the column, ~ X4 is the flow rate of antisolvent delivered to the bottom of the column, mS/h; X s is the phenol tefnperature, *C; X6 the temperature in the middle part of the column *C; X 7 the temperature in the lower part of the column, *C; Xs the feedstock viscosity, cS; X9 the feedstock flashpoint, *C; X10 the feedstock color, mm (on the KN-51 instrument scale); Xil the feedstock density, g/cmS; Xlz the melting point of phenol, *C; Xm the quantity of oil in the phenol, %; X14 the quantity of water in the phenol, %; RI the yield of end product, % on feedstock; Rs the quantity of coke in the raffinate, %; R2 the flashpoint of the product, ~ Xls the quantity of coke in the feedstock, %. The magnitude of corrected multiple correlation coefficients indicates the presence of undefined factors in the regression equations.
Translated from Khimiya i Tekhnologiya Topliv i Masel, No. I0, pp 38-44, October, 1969.
734
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Fig. 1, Motion in the optimum regmn of outlet* quantities Ri. From Eq. (1) it is seen that the end-product yield is reduced by reducing the flow rate of antisolvent delivered to the bottom of the extraction column and by reducing the feedstock flow rate but it is increased by reducing the feedstock viscosity. Analysis of gq. (2) indicates that the product (raffinate) flashpoint rises as the feedstock visocity and quantity of antisolven~ delivered to the column are reduced. It follows from Eq. (3) that raffinate coke content is mainly increased by reducing the solvent ratio of phenol to feedstock, the feedstock viscosity and the temperature gradient. On increasing the flow rate of antisolvent delivered to the bottom and top of the extraction column by 8.g% there is a 0.001% increase in the phenol content of the raffinate, an increase of 0.025% in coke content and a reduction of 8~ in flashpoint. According to the manufacturing specification the flash point of the residual feedstock should not be below 220~ For most of the time the extraction column operates with deasphalted residual feedstock having a flashpoint of 220 to 221~ These values correspond to 2% higher raffinate yield and satisfactory quality. By analyzing the mathematical model (1)-(3) and comparing it with the manufacturing specification it was found that the inlet parameters: x t = l T - l q . 8 m S / h ; Xz=82-3S.gmS/h; xs=89oc; X6=79oC; X7=76oc; Xs = 19-20 cS; x~= 0.8%; Xl4 = 0.8% correspond (approximately) to maximum and product yield. From the results of the investigation it appears that the 1.0-2.5% reduction of end product yield and the quality impairment with increase in the oil and water contents of phenol above 0.8~ calculated on phenol, are consequences of reduction in the activity of the solvent and reduction in the solvent-to-feedstock ratio. When the oil content of the phenol is high, removal of asphaltic-resinous substances from the feedstock in the upper part of the column is retarded. This increase in the content of asphaltic-resinous substances in the raffinate can be somewhat reduced by raising the temperature at the top of the column. This effect is compensated by increased loss of end-product lubricating oil components which are dissolved in the phenol and carried away in the extract. *As in Russian o r i g i n a l - Publisher.
786
Second
Stage
It is e x t r e m e l y important to determine the best size of steps of change because during changes within the o p t i m a l region, a s m a l l rise in even one of the parameters can increase end-product loss or cause unacceptable i m p a i r m e n t of quality. In the present work the m u l t i p l e x method (2) was used to determine optimum increments AX i. The m a x i m u m i n c r e m e n t a l steps in the function R, with allowance for limitations is --
Xi-
n
Xi
x j%
when
X in > 0
-x?
when
X~ < 0
xx'] =
(4)
The m i n i m u m value of these parameters AX~min restricts the m a x i m u m increment of the function tL The quantity AXP min was used to c a l c u l a t e the variables Xj and the m a x i m i z e d function R with the approximation adopted
x,."+' =
x, + Axj%x7 /
R n+~ -~ R n @ X i 6 A X i min
J
(a) n
The foliowing conditions apply to recursion coefficients: the recursion coefficient Bi should not be negative if the function R has reached its limiting value. In this case when Bn is negative and the variables X i have reached their permissible m a x i m u m / X i m a x / the variable Xi that corresponds to the greatest absolute value of Bi is excluded from the recursion analysis. This continues until all the reeursion coefficients satisfy the corresponding requirements. The value of AX c for quadratic optimization is given by the formula* Xt.6
aXZ0= CO-1,~ E BkmXkXm k
Further,
we
(6)
m
d e t e r m i n e the optimizing p a r a m e t e r R c+l = R e -1- A X i max XiC8
(7)
-~- ~ (AXi max)~ ~" 2 B kmXkXm k rn
The p a r a m e t e r AxC0 is used to exclude the possibility of reaching the m a x i m u m value at any point before crossing the boundary of m a x i m u m of the function R. The m i n i m u m value of the quantities (including AxC0) is used to c a l culate a new point. The size of the step of change, equation 6, c o m m e n c i n g with the second was diminished by an amount C c - i This approach to solutionJ0f the coupling equations between inlet and outlet parameters of the obj e c t investigated provided the required information about the surface of response at each new point on the path to the optimum and enabled optimum values of the inlet parameters to be determined. The calculations were made on a 'Promin' computer and are given in Fig. 1. Third
Stage
The response surfaces were described on the basis of results of an active experiment using the rotatable plans scheme [3] for the parameters X~, X 2, Xs, X s. The results of this experiment on a f u l l - s c a l e extraction column were processed on a Minsk-22 computer and a m a t h e m a t i c a l m o d e l was obtained, in the form of second-order regression equations, which adequately describes the optimal conditions of the extraction process: * C is the number of steps of change of inlet parameters; Bkm is the mutual correlation coefficient between inlet parameters X k, Xm; k, m are order numbers of mutually correlated inlet parameters.
736
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75
70 6'5
o
10
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17
t8
20
I
I
I
l
~s
~o
~s
~op
Fig. 3. Graph of conditional extremums of response function RI= fix): p) Eigenvalue of canonical equations, X) Lagrange multiplier, p) sphere radius.
X;
Fig. 2. Canonical sections of response surface: section XsX3 is a hyperbola, section XsX i is an ellipse.
R1 =: 80,24 + 0,17Xt @ 0,09X2 -F 0,03Xs ~- 0,04X8 - - 0,16X1Xe Jr- 0,09XtXa - - 0,001X1Xs - - 0,15X2X a
+ O,04X~X8 + O,06X3Xs + 0,02X~ - - 0,001Xl - - 0,01X~ + 0,02X~
(8)
R~ = 0,4 @ 0,01X1 - - 0,04X 2 + 0,0IX3 -[- 0,001Xs + 0,05X:tX z + 0,022XtX3 ~ 0,113X1Xs H- 0,1X2)f'a - - 0,26X2Xs - - 0,027X3Xs - - 0,04X~4-, 0, iX~ - - 0,2X~ - - 0,01X~
(9)
R5 = 12,144 + 0,08X1 - - 0,003X2 - - 0,883X3 -F 0, lXs - - 0,125X1X2 - - 0,25X~ - - 0,375X~ - - 0,2X1Xn - - 0,125X1X s - - 0,75X2Xs -F 0,245X~ -F 0,06X~ @ 0,5XzXs - - 0,4X3X a
(10)
After converting Eqs. (8)-(10) to canonical form we obtain a two-dimensional section of the response surface. An e x a m p l e of such a section is given in Fig. 2. Two dimensional sections c a n b e used to follow how equal yield curves are distributed on altering two of the factors and stabilizing the third and fourth. By using two-dimensional sections the process can be controlled to m e e t the requirements that are applied to the end product and to the resulting real conditions. In order to d e t e r m i n e certain e x t r e m a l points a system of equations was formulated by the Lagrange m u l t i p l i e r method in the form
art ~ OR~ OX~ T X - E 2 ~ = 0
I
(11) OR1 ax~ §
OR2
--~
I
,
where X is a Lagrange multiplier. A conditional e x t r e m u m of the response function is shown in Fig. 3. It foUows from Fig. 3 that it is impossible to obtain more end product than we obtained under f u l l - s c a l e c o n ditions. Fourth
Stage
The m a t h e m a t i c a l model of the process, Eqs. (8)-(10), includes a total of four inlet parameters. Therefore, this model is suitable for determining the o p t i m a l region but it is not suitable for o p t i m a l control because a large number of inlet parameters influence the performance of the extraction process.
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'738
TABLE 1. Technological Chart of Optimum Control of Process of Refining Short Residue Deasphalted with Phenol Condi2 Values of unValues of contions controlled para, trolled para.
Prediction of outlet para.
X8 X9 X~. X1, I X 1 X 2 X3 X4 18 220 0,5 0,6 18,2 33 85 2,0 22 221 0,9 0,7 17,1 34 85 2,2
R1
R~ Ra
80,3 220 0,35 78,6 222 0,320
A m a t h e m a t i c a l model with a large number of inlet parameters cannot be derived by traditional methods (experiment planning methods, m u l t i p l e correlation method, etc) because of the need to obtain a great d e a l of e x p e r i m e n t a l data under f u l l scale conditions. Therefore, in the present work we attempted to derive a m a t h e m a t i c a l m o d e l by a g r a p h i c a l - a n a l y t i c a l method. The m o d e l of the process for eight inlet p a r a meters is as follows:
R1 = 80,1 - - 6,002X1 @ O,O01X 2 - - O,O0001Xa'-- O, 1X 4 -t- O,O001Xs @ 0,000021X9 q- O,O01Xla -{- 0,015X14 - - O,O0031X1X 2 - - O,O01X1Xa @ O,O01X1X4-- O,O0012X1Xs - - O,O001XIX9 - - O,O0035X1Xla -~- O,O00033X1X14 q- O,O035X2Xa - - O,O002X2Xa ~i--O,O0005X2Xs 'I- O,O003X2X9 q- O,O01X2Xaa - - O,O015X2X14 -t- O,O023XaX4 -~- O,O002XaXs!-- O,O00051X3X9 - - 0,000001XaXla - - O,O0027X3Xl~ - - O, 1X4X 8 -J- O,O07X4X~ - - O,O02X4X:m @ O,O1X4X14: - O,O00012XsX9 + O,OO631XsX13 q- O,O0022XsX14 O, 01XgXx3 - - O, O083XgXa4 - - O, O0336XlaXa4~-- O, 0001X~ - - O, O000015X~ - - O, O000006X~
- - 0,023X~ q- O,O0003X~ - - O,O005X~ 7- 0,024X~a @ 0,023X~a
(12)
Equation (12) was statistically analyzed by variance analysis [5]. It was found that Eq. (12) adequately describes the process in the o p t i m a l region with a 5% significance level. The m a t h e m a t i c a l model (12) was based on operating results on a f u l l - s c a l e extraction column under normal operating conditions and on the results of active experiments conducted on the same column. The m a t h e m a t i c a l model was obtained in the following way: the boundaries of i n l e t and outlet parameters were first determined for 290 observation results of the passive experiment and 32 results of the active e x p e r i m e n t in the form X i rain -< Xi<_ Xi m a x are the physical limitations applied to the parameters. Xg min <- X - X g max > < ' g is the range of actual change of the parameters considered; < Xg rain' X . max ~ Xi m a x ' Xi min is the r e quired range of change of these parameters; a-< X <-b is the m i n i m u m difference between two states of the sets. After the boundaries of permissible values of e a c h input and output p a r a m e t e r had been determined, p a r t i c u larly outstanding points were assessed. Values that were outside the permitted limits of the Manufacturing S p e c i f i c a tion of the Fergana refinery (FNPZ) were not taken into account. The graphical part of the work consisted in constructing scatter diagrams of effects for all stages of extraction column operation in uniform scale (fig. 4). The effect scatter diagrams were compared with respect to closeness of inlet and outlet parameters and then a n a l y t i c a l l y from the r-distribution they were assessed by statistical methods
[51. Sharply outstanding parameters R1, R2..... Rn, X 1, X 2.... X n having m a x i m u m or m i n i m u m distribution were assessed by the formulas ri max - -
Xmax - - X
S.
rimax--
~
Rmax-- g
n--I
SR
ri rain --
V
n
X - - Xmax
S.
'
rimin - -
-
~ - - *?ma~ ~ - - , n--1
SR ~
(14)
/ n
where Ri, Xi, -R,X are instantaneous and m e a n values of the parameters; 8 z is the scatter. Values of each inlet p a r a m e t e r c a l c u l a t e d from the r-distribution and of e a c h outlet p a r a m e t e r were compared with tabulated values for the 5% significance level. If the c a l c u l a t e d values (rcalc) were less than the tabulated values (rtab) the results were accepted, but if they were greater than rta b they were discarded. For instance this selection resulted in rejection of 49% of the quality indices of the end product (color, flashpoint, coke content of raffinate) and 25% of the yield values.
739
From the mathematical model (12) a series of optimal values of inlet and outlet parameters of the object was obtained. For example, for the case of refining deasphalted residue of Fergana crude optimum conditions were obtained with controlled parameter values given in Table 1. Any number of similar technological conditions can be derived. The calculated values of inlet and outlet parameters should then be compared with effect scatter diagrams. CONCLUSIONS 1. A mathematical model was derived for the process of extractions which describes the optimal process conditions. The mathematical model adequately described the real process for a 5% significance level. If the mathematical model is used in process control the extraction process can be controlled unde r optimum conditions, which increases the end product yeild by 2.5% and results in economy of over 300,000 rubles per year at the FNPZ (Fergana) refinery. 2. A formula was derived for the size of step of change of inlet parameters during changes within the optimal region of the extraction process. 3. A method is given for obtaining a non-linear model which adequately describes the optimal region for eight inlet parameters with minimum expenditure of time on experimentation under full-scale conditions. LITERATURE 1.
2. 3. 4. 5. 6. 7.
740
CITES
P. M. Nesterov, V. V. Kafarov, and V. V. Shestopalov, Zavod. Lab. No. 1 (1967). B. Bode, Messen, Stenem Regeln, 6, No. 12 (1963). N. R, Draper, Annals Mathematical Statistics, 34 No. 4 (1960). P. M. Nesterov, L. P. Chemyshova, and V. V. Kafamv. Optimization of the Extraction Process. Summary of Reports of the D. I. Mendeleev MKhTi, 1967. V. V. Nalimov, The Use of Mathematical Statistics for the Analysis of Matter [in Russian], Fizmatgiz (1960). G. E. Box, Applied Statistics, 6, No. 2 (1957). G. E. P. Box, and D. R. Genks, J. of Rayal, 24, No. 2,297 (1962).