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Predictions of products and feeds from operating conditions of crude fractionator
IFAC
Copyright © IF AC Dynamics and Control of Process Systems, Jejudo Island, Korea, 2001
c:
0
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Publications www.elsevier.com!1ocate/ifac
PREDICTIONS OF PRODUCTS AND FEEDS FROM OPERATING CONDITIONS OF CRUDE FRACTIONATOR Doug Hyung Lee, Kyong Churl Bae, Euy Soo Lee, In Soo Lee*, Sang Jin Park *Kyungpook National University, Kyungpook, Korea Choong-Ku, Pil-Dong, 3-26, Dongguk University, Seoul, Korea Abstract: This paper is to provide the information of the products and feeds of crude fractionator, hard to get from hardware system, by using inferential model for real-time operating conditions. Knowing that the characteristic of each product of crude distillation tower follows the probability function, it has become possible to consider the variables of the the probability function as operating conditions. The proposed model can provide tool for doing more efficient operations to maximize profit. In this study, Partial Least Squares Projections to Latent Structures~LS) technique was also used to make inferential model. Copyright '2000IFAC Keywords: Crude product quality, Crude TBP curve, Probability density functions, Parameter estimation, PLS , Optimization, Regression, Inferential model 1.
because all properties of a pseudocomponent are predicted by TBP data and specific gravity
INTRODUCTION
It is well recognized to know the characteristics of operating feed for more efficient operations of Crude Unit (CDU). Characteristics of feed can be utilized for the production and control strategy that all products meet their quality target so as to maximize the profit.
In this research, a set of real operation data for LGCaltex located in southern part of Korea was used with PRO/ll with PROVISION together.
2. Many approaches were performed to control the crude product qualities. Friedman(1994) proposed the model-based control of crude product qualities by using simplified heat-balance equations for estimating the crude TBP curve. But the model underpredicted the slope about 5%.
PRODUCT QUALITY AND PROBABILITY FUNCTION
Generally, there are several products in CDU, LPG gas, Naphtha, Light Kerosene(LK), Heavy Kerosene{HK), Light Gas Oil(LGO), Heavy Gas Oil(HGO), Residue Crude(RC). Each product has boiling point ranges as specifications by separation of crude oil and the specifications are controlled by operating environment. True boiling point(TBP) is a major characteristic of CDU product and feed. TBP data of crude feed oil for products range are shown in Figure 1 and TBP for each product is shown in Figure 2.
Model predictive control(MPC) technology and neural network model were commonly used by numbers of researchers for the optimum product control. On-line analyzers can be strategically placed along the process vessels to supply the required product quality information to multivariable controllers. However, on-line analyzers are very costly and are limited to maintain the product specification. In this paper, an attempt to identify the feed and product is proposed, which is able to provide the information for prediction scheduling and controlling. Two key ideas were used to identify the feed characteristic. The first one is that the characteristic of each product follows a specific probability function. The other is that the variables of the function depend on operating conditions. TBP curve is a major characteristic of feed and products in CDU
Probability density to the product TBP is shown in Figure 3 and 4. It should be notice that the probability temperature density of product TBP can be utilized by general probability function.
555
1000
18 900 800
'Z
700
e.a.'"
600
I-
500
G
m
_· 1
,------------------------------=== .
, .6 1.4
. . .:.0,
RC
lPG
-, --_.-,
' 0:..,
1:-;' :g:-.
400 0.4
300
0.2
200 10
20
30
40
50
60
70
80
90
100
0.0 +-'-."""~----._----r_--_.----~--------j 750 700 450 500 550 600 650
Distillated Percent(Liquid Volume)
TBP of HGO product (Dog. K)
Figure 1 TBP data of Crude Oil and product range Figure 4 Probability temperature density of HGO product '000,--------------------------------,
Two probability functions are utilized to represent the TBP data of product. One is Hill's equation and the other is developed. These functions are expressed in the integrated form of probability density function. o 200
Hill's equation
..... LPG ··0·· NAPHTHA
v~
-r-
LK
...... . HI<
......... lGO
Distillate (%), D = a /«TH / T)B" + 1)
-{} . HGO RC
Where,
-+20
40
60
100
80
(1)
a, T H ' B H : Parameter for Hill' s equation T : True Boiling Point
Distillated liquid volume percent
New equation Distillate(%)=a/exp«TL -T) / BL)2 ,(at, TL > T)
Figure 2 TBP for CDU products
(2)
Distillate(%) = a, (at, TL < T) Where,
a. TL,B L : Parameter for the New equation T : True Boiling Point
,.8
,-----------------------------=== +-0 ..'
1.6
·0
OM&!
....
O~
Figure 5 to 6 show characteristic feature of Hill's equation. Each function has three variables; a is a
"'V'" 0"..
"0_ -(}-O_
' .4
+ 0. .1
-<)-0_
~ 1.2 c
-0. 0 . .10 . . . . 0 . .' 1
o
-0- 0 ...12 ..... 0..')
"
· ..· 0_
1.0
~
:g 0 .8
£
weighting factor, TH,BH and TL ,E L are stand for
-o-o ..u ........ o... ' ~ '9
average and variance factor. The flow rate and characteristic of each product is expressed by these
0...,'
. . . 0 ••11
-
+0"'"
0.6
0.4
two function, i.e., a, rH' EH and
02
0.0 +-----~------._----~------._-------1 650 400 450 SOD 550 600
a, r;.,BL
.
TBP
identifications of products and feed can be expressed by these variables only. A summary for the regression result was listed on Table 1 and Table 2 This regression was performed with SigmaPlot version 5.00 software.
TBP of lGO p
Figure 3 Probability temperature density of LGO product
556
100
"
Table 2 Error for regression when New equation was used for the each product
80
E
oil
~
Deg. K
"C
.~
60
::; ~
Case
@ ~
No.
4{}
Q. "C
~
;;;
20
0
300
400
500
600
BOO
700
LPG
Naph
LK
HK
LGO
HGO
RC
2.65 30.57
1
33.08
2.08
1.72
1.59
3.51
2
10.60
3.01
1.63
2.12
2.67
2.69 17.43
3
19 .83
5.53
3.19
1.15
3.28
2.43 34.06
4
31.08
3.31
2.40
1.50
3.08
2.47 34.16
5
21.21
2.77
1 .81
2.10
2.78
2 .58 18.85
6
20.07
4.72
4.58
2.74
3.50
2.66 32.20
7
25 .20
3.06
0.97
1.74
3.16
2.69 31 .34
8
32.14
1 .38
2.29
1.40
3.40
2.66 34.02
9
19 .83
4.82
4.57
2 .73
3.37
2.76 34.29
10
16.16
3.42
1.50
1.89
2.83
2.63 20.78
900
TBP(Deg.K)
Figure 5 Hill's probability function
1.0.,.----------------------, .. _ .• - '
0.9
O.B
-
~ 0.7
... ;
'. - -
0.6
-
~ 0 .5
-
:B
e
a..
-
TBP TBP TBP TBP TBP
Y&
on 'IS
O-HiI'a(Th"SOO.BhaS) O-HiJI{Tha500,Bh"S) o 'HirI(Th:sOO,8h " 7, D-HiI'I(Ttla500,Bh"8) O-Hi4h(TtI-SOO.Bh..gj
VI .... AY9 TBP vs D-HiI'&(Th"'SOO.8h z l0) AvgTBP ... D·HiI'I(Th~. Bn= 1 1) Iwg TBP 'IS O-HiI'I(Th"SOO,Bh"'12) AvgTBPwD-HiI's(Th"500,Bh"'13) "vg TBP 'IS D·Hif't(Th -SOO, en",4) T'SP 'IS O· HiI's(Th-!'iOO ,8h=lS) Avg TBP .... D-HiI's(Thz500,8h.1 6) Avg TBP \OS D-HiI'II(Tha500,8h· 17) Avg TBP VI O·HiI'I(Th a500, 8h"'1 .!! ) Avg TBP 'IS o·HiI'9(Th_SOO.8h_1!1)
"vg
Table 3 Regression result summary for Hill's equation to the HGO product
_. "vg
o ]l
.
-
Avg Avg Avg Ayg
0.4
.
-
R = 0.99923826
Rsqr = 0.99847710
Adj Rsqr = 0.99817252
0.3
0.0 ~-""-.,.----~---.--= 400 500 600 700 300
BOO
900
P
Coefficient
Std. Error
t
TH
27.3499
1.0357
26.4081
BH
550.5835
0.765
719.7363 <0.0001
0.2
<0.0001
TBP(Deg.K)
Table 4 Regression result summary for New equation to the HGO product
Figure 6 Hill's probability density function
R
= 0.99906875
Rsqr = 0.99813837
Adj Rsqr = 0.99776604
Table 1 Error for regression when Hill's equation was used for the each product Deg . K Case No.
1
Naph
LK
HK
LGO
HGO
RC
14.70 5.28
4.91
5.30
3.66
7.60
8.95 5.55
LPG
2
11 .82 10.62 4.69
5.92
3.77
6.77
3
12.12 11 .85 6.19
4.76
2 .96
7.30 11.65
4
17.99 10.33 4.97
5.76
3.22
7.44 11 .86
5
7.83
5.73
4.78
7.01
6 .93 10.54
9.95
4 .57
7 .38
5.63
3.44
6.45
2.41
7
8.16
9 .48
4 .18
5.94
3.14
7.35
9.27
4.06
7.55
9.13
8
12.74 7.81
5.09
5.26
9
7.11
3.42
6.51
2 .57
6 .83 10.55
6 .05
3.64
6.93
10
5.44
7.33 10.64 4.53
Std. Error
t
TL
705.9085
2.8991
243.4936 <0.0001
BL
100.9859
3.5443
28.4923
P
<0.0001
The mUltiple correlation coefficient(R), and Rsqr, the coefficient of determination, are both measures of how well the regression model describes the data. The t statistic tests the null hypothesis that the coefficient of the independent variable is zero, that is, the independent variable does not contribute to predicting the dependent variable. t is the ratio of the regression coefficient to its standard error. P is the P value calculated for t. The P value is the probability of being wrong in concluding that the coefficient is not zero (i.e., the probability of falsely rejecting the null hypothesis, or committing a Type I error, based on t). The smaller the P value, the
4 .88
6
Coefficient
4.20
557
1) 2) 3) 4) 5)
greater the probability that the coefficient is not zero. Figures 7 and 8 show the fitness of probability function to the product TBP. Hill's equation generally fits the product TBP and New equation fits more precisely the TBP of Naphtha, LK, HK, LGO, HGO products.
20
40
80
80
Number of trays between each product Supplied steam quantity Product draw rate Heat duty of condenser, Pump-around duties
Parameters of probability can be determined by above variables and by also dependent variables. i.e, tray temperatures, over flash ratio, outlet temperature of furnace, reflux ratio, etc for controlling the product quality. In this paper, Partial Least Squares Projections to Latent Structures(PLS) technique was used in order to predict the variables of probability function from the variables of operating system. Instead of using the ordinary least square method, PLS technique is commonly used in multivariate calibration i.e., the predictor block consists of variables that are less expensive, less time consuming, or more easily measured or calculated than the responses. The X block is often illconditioned, i.e., the separate variables are strongly correlated and there are more variables than objects.
100
Percent Distillated(Uquid Volume)
Figure 7 Provided vs calculated TBP 's by using Hill's equation
The parameters of New equation of probability can be correlated by operating variables as written in Equation 3 by PLS. TL
= f,,,, 1 C L,"
f T,., (X) .
BL =
f. C B,, ' fB ,,(X)
(3)
, ~]
Optimized parameters of the new probability equation with operating variables for LGO product was shown in Table 5. ~
~o
~
w
Table 5 Optimized parameters of the New probability equation with operating variables for LGO product
100
Percent Distillated(Liquid Volume)
Figure 8 Provided vs calculated TBP's by using New equation
fT, (x) , 'j
f •., (x) I
3.
RELATIONS BETWEEN THE PARAMETERS OF PROBABILITY FUNCTION AND OPERATING CONDITIONS BY PLS METHOD
Characteristics and quantities of products for CDU can be changed by operation and operating system, The variables are as follows
5489.8
5924 ,8
Constant
-
Calculated LK product
0.10585
Temp,
-
Calculated HK product
-0.02487
X
0.12229
X
Log(x/(I00-x))
558
C L,i
X
X
Description
CB ,i
7,0784
0.18639 8.3702
-14.279 -15.158 28.211
Temp. Calculated LGO product
21.812
Temp. Calculated HGO product Temp, LK flow ratelFeed flow
rate·IOO Log(x/(IOO-x))
21.776
30.258
HK flow rateIFeed flow rate·lOO
Log(X/(IOO-x))
Log(x/(lOO-x))
186.76
161.9
-47.734 -44.636
.6 .9
25
LOO flow rateIFeed flow rate· 100
.14
Hoo flow ratelFeed flow
.15
24
rate·IOO
.16 ."
Log(x/( lOO-x))
-26.644 -14.599
• 7 '~17 .l8 .3 .12
"~ 1l
Overflash flow ratelFeed flow rate· I 00
0
23
X
3.6998
X
-169.06 -34.318
X
-1197.4
-1270.8
.tl°
LK specific gravity
83 .896
.2 .5
HK specific gravity LGO specific gravity
22
These models are depend on the operating system of CDU: number of trays, supplied steam quantity, heat duty of condenser, pump around duties, etc. so the model should be modified to use in other systems. The models made by PLS technique predict each parameters of probability function and the TBP of each product can be calculated with these parameters. Figure 9 and 10 show comparisons between predicted and observed values of Hill's equation parameter
_13
22
24
23
$in;a-P7 .01 by Urrelri AB 2000-08-25 08:36
Figure 9 Predicted vs observed value of Hill's equation parameter: BH
-13 81 80
'12
_1~~F
79
Finally, the TBP of feed can be obtained by summing all predicted products as written III Equation 4.
-14 ·2 "'5
78 77
(4) D(T,L"L"L) , L .. L"L. ,L7 ,
25
Predicted
'1
76
-7
)
75 74
: Liquid volume distillate percent at temperaure T D /T) : Liquid volume distillate percent at temperature T
_t9
where, D
74
: Std. Liquid volume of each product
77
~
~
W
M
Si'n::a--P7 .01 by UTetri AB 2000-08-25 08:47
It should be noticed that for desired product spec., the two points of TBP can be utilized to get full curve ofTBP by applying the probability function. Equation 5 shows how to calculate the parameters for Hill's equation when we know TBP 50% and TBP 90%. For the case of New equation is shown equation 6.
Figure 10 predicted vs observed value of New equation parameter: BL
T -
Jln(2)· TB?,o -Jln(IO / 9) ·TBPso
-'--...:.....:..----r~'---'>==~~--=
M
L -
-Jln(lO / 9)
B _ TL -TBPso L-
TH = TBPso
~
Predicted
of each product
L,
~
~
(6)
where, TL ,B L are parameter for the New equation
(5)
TBPso is temperature at 50% Distillate
1"(1/9) B" : In(111Pso / TBp." )
TBP"" is temperature at 90% Distillate
where, TBPso is temperature at 50% Distillate TBp." is temperature at 90% Distillate
Finally, the TBP of feed can be calculated with all
Tu ,B" are parameterfor Hill 's equation
559
predicted product TBP by using equation 4. Anders Berglund, "Some Extensions of PCA and PLS", Solfjadern Offset AB, Umea, (1998) ,00r-------------------~;;;:~
Bo-Nan Jiang, "On the Least-squares Method", Comput. Methods Appl. Mech. Engrg. 152, p239257, (1998)
80
Bjorn K. Alsberg, Douglas B. Kell, and Royston Goodacre, "Variable selection in Discriminant Partial Least-Squares Analysis", Anal. Chem. 70, p4126-4133 ,( 1992)
20
-
Predicted TBP from HII's Eq.
-
Predicted TBP from New Eq.
_ _ Provided Feed TBP
200
300
400
500
600
700
800
900
1000
1100
TBP(Deg. K)
Chorng H. TWU, "An internally consistent correlation for predicting the critical properties and molecular weights of petroleum and coal-tar liquids", Fluid phase equilibria, 16, p137-150, (1984)
Figure 11 Comparison of predicted TBP's of feed for using different probability equations
4.
Jefferson W. Tester, Michael Modell, "Thermodynamics and its applications", Prentice Hall PTR, 3rd edition
CONCLUSION
Knowing that the characteristic of each product of crude distillation tower follows the probability function, it has become possible to consider the variables of the probability function as operating conditions.
John B. Cooper, Kent L. Wise, James Groves, and William T. Welch, "Determination Octane numbers and Reid Vapor pressure of Commercial Petroleum Fuels Using FT-Raman Spectroscopy and Partial Least-Squares Regression Analysis", Analytical Chemistry, Vol. 67, No . 22. November 15, p40964100, (1995)
Utilizations of the proposed probability equation and PLS technique has enabled to correlate the operating conditions with TBP 's of each product and resulting feed. The choice of probability function is rather arbitrary and other equally versatile distribution functions or combined functions can be used.
Nickey J. Messick. John H. Kalvas and Patrick M. Lang, "Selecting Factors for Partial Least Squares", Microchemical, Journal, 55, 200-209,article No. MJ961413, (1997)
It should be also noted that for desired product specification, the two points of TBP can be utilized to get feed and product TBP's by applying the probability function.
Srikanth Voorakaranam and Joseph, "Model Predictive Inferential Control with Application to a Composites Manufacturing Process", Ind. Eng. Chem. Res. 38, p433-450,(1999)
Overall, the proposed method can be effectively used for controlling optimization of process, the downstream operation for better profit.
Yucai Zhu, Michiel van Wijck, Eric Janssen, Ton Graaf, Kees van Aalst and Leo Kieviet, "Crude Unit Identification for MPC using ASYM Method", Proceedings of the American Control Conference, Albuquerque, New Mexico, June,(1997)
REFERENCES Y.Z. Friedman, "Model-based control of Crude Product Qualities", Hydrocarbon Processing, Feb. 1994, p97-105
A.S .Pandya and R.R.Szabo, "Prediction of Petrochemical Product Property", SPIE Vo1.3390, pI97-207,(1998)
560
Copyright © IF AC Dynamics and Control of Process Systems, Jejudo Island, Korea, 2001
c:
0
C>
Publications www.elsevier.com!1ocate/ifac
PREDICTIONS OF PRODUCTS AND FEEDS FROM OPERATING CONDITIONS OF CRUDE FRACTIONATOR Doug Hyung Lee, Kyong Churl Bae, Euy Soo Lee, In Soo Lee*, Sang Jin Park *Kyungpook National University, Kyungpook, Korea Choong-Ku, Pil-Dong, 3-26, Dongguk University, Seoul, Korea Abstract: This paper is to provide the information of the products and feeds of crude fractionator, hard to get from hardware system, by using inferential model for real-time operating conditions. Knowing that the characteristic of each product of crude distillation tower follows the probability function, it has become possible to consider the variables of the the probability function as operating conditions. The proposed model can provide tool for doing more efficient operations to maximize profit. In this study, Partial Least Squares Projections to Latent Structures~LS) technique was also used to make inferential model. Copyright '2000IFAC Keywords: Crude product quality, Crude TBP curve, Probability density functions, Parameter estimation, PLS , Optimization, Regression, Inferential model 1.
because all properties of a pseudocomponent are predicted by TBP data and specific gravity
INTRODUCTION
It is well recognized to know the characteristics of operating feed for more efficient operations of Crude Unit (CDU). Characteristics of feed can be utilized for the production and control strategy that all products meet their quality target so as to maximize the profit.
In this research, a set of real operation data for LGCaltex located in southern part of Korea was used with PRO/ll with PROVISION together.
2. Many approaches were performed to control the crude product qualities. Friedman(1994) proposed the model-based control of crude product qualities by using simplified heat-balance equations for estimating the crude TBP curve. But the model underpredicted the slope about 5%.
PRODUCT QUALITY AND PROBABILITY FUNCTION
Generally, there are several products in CDU, LPG gas, Naphtha, Light Kerosene(LK), Heavy Kerosene{HK), Light Gas Oil(LGO), Heavy Gas Oil(HGO), Residue Crude(RC). Each product has boiling point ranges as specifications by separation of crude oil and the specifications are controlled by operating environment. True boiling point(TBP) is a major characteristic of CDU product and feed. TBP data of crude feed oil for products range are shown in Figure 1 and TBP for each product is shown in Figure 2.
Model predictive control(MPC) technology and neural network model were commonly used by numbers of researchers for the optimum product control. On-line analyzers can be strategically placed along the process vessels to supply the required product quality information to multivariable controllers. However, on-line analyzers are very costly and are limited to maintain the product specification. In this paper, an attempt to identify the feed and product is proposed, which is able to provide the information for prediction scheduling and controlling. Two key ideas were used to identify the feed characteristic. The first one is that the characteristic of each product follows a specific probability function. The other is that the variables of the function depend on operating conditions. TBP curve is a major characteristic of feed and products in CDU
Probability density to the product TBP is shown in Figure 3 and 4. It should be notice that the probability temperature density of product TBP can be utilized by general probability function.
555
1000
18 900 800
'Z
700
e.a.'"
600
I-
500
G
m
_· 1
,------------------------------=== .
, .6 1.4
. . .:.0,
RC
lPG
-, --_.-,
' 0:..,
1:-;' :g:-.
400 0.4
300
0.2
200 10
20
30
40
50
60
70
80
90
100
0.0 +-'-."""~----._----r_--_.----~--------j 750 700 450 500 550 600 650
Distillated Percent(Liquid Volume)
TBP of HGO product (Dog. K)
Figure 1 TBP data of Crude Oil and product range Figure 4 Probability temperature density of HGO product '000,--------------------------------,
Two probability functions are utilized to represent the TBP data of product. One is Hill's equation and the other is developed. These functions are expressed in the integrated form of probability density function. o 200
Hill's equation
..... LPG ··0·· NAPHTHA
v~
-r-
LK
...... . HI<
......... lGO
Distillate (%), D = a /«TH / T)B" + 1)
-{} . HGO RC
Where,
-+20
40
60
100
80
(1)
a, T H ' B H : Parameter for Hill' s equation T : True Boiling Point
Distillated liquid volume percent
New equation Distillate(%)=a/exp«TL -T) / BL)2 ,(at, TL > T)
Figure 2 TBP for CDU products
(2)
Distillate(%) = a, (at, TL < T) Where,
a. TL,B L : Parameter for the New equation T : True Boiling Point
,.8
,-----------------------------=== +-0 ..'
1.6
·0
OM&!
....
O~
Figure 5 to 6 show characteristic feature of Hill's equation. Each function has three variables; a is a
"'V'" 0"..
"0_ -(}-O_
' .4
+ 0. .1
-<)-0_
~ 1.2 c
-0. 0 . .10 . . . . 0 . .' 1
o
-0- 0 ...12 ..... 0..')
"
· ..· 0_
1.0
~
:g 0 .8
£
weighting factor, TH,BH and TL ,E L are stand for
-o-o ..u ........ o... ' ~ '9
average and variance factor. The flow rate and characteristic of each product is expressed by these
0...,'
. . . 0 ••11
-
+0"'"
0.6
0.4
two function, i.e., a, rH' EH and
02
0.0 +-----~------._----~------._-------1 650 400 450 SOD 550 600
a, r;.,BL
.
TBP
identifications of products and feed can be expressed by these variables only. A summary for the regression result was listed on Table 1 and Table 2 This regression was performed with SigmaPlot version 5.00 software.
TBP of lGO p
Figure 3 Probability temperature density of LGO product
556
100
"
Table 2 Error for regression when New equation was used for the each product
80
E
oil
~
Deg. K
"C
.~
60
::; ~
Case
@ ~
No.
4{}
Q. "C
~
;;;
20
0
300
400
500
600
BOO
700
LPG
Naph
LK
HK
LGO
HGO
RC
2.65 30.57
1
33.08
2.08
1.72
1.59
3.51
2
10.60
3.01
1.63
2.12
2.67
2.69 17.43
3
19 .83
5.53
3.19
1.15
3.28
2.43 34.06
4
31.08
3.31
2.40
1.50
3.08
2.47 34.16
5
21.21
2.77
1 .81
2.10
2.78
2 .58 18.85
6
20.07
4.72
4.58
2.74
3.50
2.66 32.20
7
25 .20
3.06
0.97
1.74
3.16
2.69 31 .34
8
32.14
1 .38
2.29
1.40
3.40
2.66 34.02
9
19 .83
4.82
4.57
2 .73
3.37
2.76 34.29
10
16.16
3.42
1.50
1.89
2.83
2.63 20.78
900
TBP(Deg.K)
Figure 5 Hill's probability function
1.0.,.----------------------, .. _ .• - '
0.9
O.B
-
~ 0.7
... ;
'. - -
0.6
-
~ 0 .5
-
:B
e
a..
-
TBP TBP TBP TBP TBP
Y&
on 'IS
O-HiI'a(Th"SOO.BhaS) O-HiJI{Tha500,Bh"S) o 'HirI(Th:sOO,8h " 7, D-HiI'I(Ttla500,Bh"8) O-Hi4h(TtI-SOO.Bh..gj
VI .... AY9 TBP vs D-HiI'&(Th"'SOO.8h z l0) AvgTBP ... D·HiI'I(Th~. Bn= 1 1) Iwg TBP 'IS O-HiI'I(Th"SOO,Bh"'12) AvgTBPwD-HiI's(Th"500,Bh"'13) "vg TBP 'IS D·Hif't(Th -SOO, en",4) T'SP 'IS O· HiI's(Th-!'iOO ,8h=lS) Avg TBP .... D-HiI's(Thz500,8h.1 6) Avg TBP \OS D-HiI'II(Tha500,8h· 17) Avg TBP VI O·HiI'I(Th a500, 8h"'1 .!! ) Avg TBP 'IS o·HiI'9(Th_SOO.8h_1!1)
"vg
Table 3 Regression result summary for Hill's equation to the HGO product
_. "vg
o ]l
.
-
Avg Avg Avg Ayg
0.4
.
-
R = 0.99923826
Rsqr = 0.99847710
Adj Rsqr = 0.99817252
0.3
0.0 ~-""-.,.----~---.--= 400 500 600 700 300
BOO
900
P
Coefficient
Std. Error
t
TH
27.3499
1.0357
26.4081
BH
550.5835
0.765
719.7363 <0.0001
0.2
<0.0001
TBP(Deg.K)
Table 4 Regression result summary for New equation to the HGO product
Figure 6 Hill's probability density function
R
= 0.99906875
Rsqr = 0.99813837
Adj Rsqr = 0.99776604
Table 1 Error for regression when Hill's equation was used for the each product Deg . K Case No.
1
Naph
LK
HK
LGO
HGO
RC
14.70 5.28
4.91
5.30
3.66
7.60
8.95 5.55
LPG
2
11 .82 10.62 4.69
5.92
3.77
6.77
3
12.12 11 .85 6.19
4.76
2 .96
7.30 11.65
4
17.99 10.33 4.97
5.76
3.22
7.44 11 .86
5
7.83
5.73
4.78
7.01
6 .93 10.54
9.95
4 .57
7 .38
5.63
3.44
6.45
2.41
7
8.16
9 .48
4 .18
5.94
3.14
7.35
9.27
4.06
7.55
9.13
8
12.74 7.81
5.09
5.26
9
7.11
3.42
6.51
2 .57
6 .83 10.55
6 .05
3.64
6.93
10
5.44
7.33 10.64 4.53
Std. Error
t
TL
705.9085
2.8991
243.4936 <0.0001
BL
100.9859
3.5443
28.4923
P
<0.0001
The mUltiple correlation coefficient(R), and Rsqr, the coefficient of determination, are both measures of how well the regression model describes the data. The t statistic tests the null hypothesis that the coefficient of the independent variable is zero, that is, the independent variable does not contribute to predicting the dependent variable. t is the ratio of the regression coefficient to its standard error. P is the P value calculated for t. The P value is the probability of being wrong in concluding that the coefficient is not zero (i.e., the probability of falsely rejecting the null hypothesis, or committing a Type I error, based on t). The smaller the P value, the
4 .88
6
Coefficient
4.20
557
1) 2) 3) 4) 5)
greater the probability that the coefficient is not zero. Figures 7 and 8 show the fitness of probability function to the product TBP. Hill's equation generally fits the product TBP and New equation fits more precisely the TBP of Naphtha, LK, HK, LGO, HGO products.
20
40
80
80
Number of trays between each product Supplied steam quantity Product draw rate Heat duty of condenser, Pump-around duties
Parameters of probability can be determined by above variables and by also dependent variables. i.e, tray temperatures, over flash ratio, outlet temperature of furnace, reflux ratio, etc for controlling the product quality. In this paper, Partial Least Squares Projections to Latent Structures(PLS) technique was used in order to predict the variables of probability function from the variables of operating system. Instead of using the ordinary least square method, PLS technique is commonly used in multivariate calibration i.e., the predictor block consists of variables that are less expensive, less time consuming, or more easily measured or calculated than the responses. The X block is often illconditioned, i.e., the separate variables are strongly correlated and there are more variables than objects.
100
Percent Distillated(Uquid Volume)
Figure 7 Provided vs calculated TBP 's by using Hill's equation
The parameters of New equation of probability can be correlated by operating variables as written in Equation 3 by PLS. TL
= f,,,, 1 C L,"
f T,., (X) .
BL =
f. C B,, ' fB ,,(X)
(3)
, ~]
Optimized parameters of the new probability equation with operating variables for LGO product was shown in Table 5. ~
~o
~
w
Table 5 Optimized parameters of the New probability equation with operating variables for LGO product
100
Percent Distillated(Liquid Volume)
Figure 8 Provided vs calculated TBP's by using New equation
fT, (x) , 'j
f •., (x) I
3.
RELATIONS BETWEEN THE PARAMETERS OF PROBABILITY FUNCTION AND OPERATING CONDITIONS BY PLS METHOD
Characteristics and quantities of products for CDU can be changed by operation and operating system, The variables are as follows
5489.8
5924 ,8
Constant
-
Calculated LK product
0.10585
Temp,
-
Calculated HK product
-0.02487
X
0.12229
X
Log(x/(I00-x))
558
C L,i
X
X
Description
CB ,i
7,0784
0.18639 8.3702
-14.279 -15.158 28.211
Temp. Calculated LGO product
21.812
Temp. Calculated HGO product Temp, LK flow ratelFeed flow
rate·IOO Log(x/(IOO-x))
21.776
30.258
HK flow rateIFeed flow rate·lOO
Log(X/(IOO-x))
Log(x/(lOO-x))
186.76
161.9
-47.734 -44.636
.6 .9
25
LOO flow rateIFeed flow rate· 100
.14
Hoo flow ratelFeed flow
.15
24
rate·IOO
.16 ."
Log(x/( lOO-x))
-26.644 -14.599
• 7 '~17 .l8 .3 .12
"~ 1l
Overflash flow ratelFeed flow rate· I 00
0
23
X
3.6998
X
-169.06 -34.318
X
-1197.4
-1270.8
.tl°
LK specific gravity
83 .896
.2 .5
HK specific gravity LGO specific gravity
22
These models are depend on the operating system of CDU: number of trays, supplied steam quantity, heat duty of condenser, pump around duties, etc. so the model should be modified to use in other systems. The models made by PLS technique predict each parameters of probability function and the TBP of each product can be calculated with these parameters. Figure 9 and 10 show comparisons between predicted and observed values of Hill's equation parameter
_13
22
24
23
$in;a-P7 .01 by Urrelri AB 2000-08-25 08:36
Figure 9 Predicted vs observed value of Hill's equation parameter: BH
-13 81 80
'12
_1~~F
79
Finally, the TBP of feed can be obtained by summing all predicted products as written III Equation 4.
-14 ·2 "'5
78 77
(4) D(T,L"L"L) , L .. L"L. ,L7 ,
25
Predicted
'1
76
-7
)
75 74
: Liquid volume distillate percent at temperaure T D /T) : Liquid volume distillate percent at temperature T
_t9
where, D
74
: Std. Liquid volume of each product
77
~
~
W
M
Si'n::a--P7 .01 by UTetri AB 2000-08-25 08:47
It should be noticed that for desired product spec., the two points of TBP can be utilized to get full curve ofTBP by applying the probability function. Equation 5 shows how to calculate the parameters for Hill's equation when we know TBP 50% and TBP 90%. For the case of New equation is shown equation 6.
Figure 10 predicted vs observed value of New equation parameter: BL
T -
Jln(2)· TB?,o -Jln(IO / 9) ·TBPso
-'--...:.....:..----r~'---'>==~~--=
M
L -
-Jln(lO / 9)
B _ TL -TBPso L-
TH = TBPso
~
Predicted
of each product
L,
~
~
(6)
where, TL ,B L are parameter for the New equation
(5)
TBPso is temperature at 50% Distillate
1"(1/9) B" : In(111Pso / TBp." )
TBP"" is temperature at 90% Distillate
where, TBPso is temperature at 50% Distillate TBp." is temperature at 90% Distillate
Finally, the TBP of feed can be calculated with all
Tu ,B" are parameterfor Hill 's equation
559
predicted product TBP by using equation 4. Anders Berglund, "Some Extensions of PCA and PLS", Solfjadern Offset AB, Umea, (1998) ,00r-------------------~;;;:~
Bo-Nan Jiang, "On the Least-squares Method", Comput. Methods Appl. Mech. Engrg. 152, p239257, (1998)
80
Bjorn K. Alsberg, Douglas B. Kell, and Royston Goodacre, "Variable selection in Discriminant Partial Least-Squares Analysis", Anal. Chem. 70, p4126-4133 ,( 1992)
20
-
Predicted TBP from HII's Eq.
-
Predicted TBP from New Eq.
_ _ Provided Feed TBP
200
300
400
500
600
700
800
900
1000
1100
TBP(Deg. K)
Chorng H. TWU, "An internally consistent correlation for predicting the critical properties and molecular weights of petroleum and coal-tar liquids", Fluid phase equilibria, 16, p137-150, (1984)
Figure 11 Comparison of predicted TBP's of feed for using different probability equations
4.
Jefferson W. Tester, Michael Modell, "Thermodynamics and its applications", Prentice Hall PTR, 3rd edition
CONCLUSION
Knowing that the characteristic of each product of crude distillation tower follows the probability function, it has become possible to consider the variables of the probability function as operating conditions.
John B. Cooper, Kent L. Wise, James Groves, and William T. Welch, "Determination Octane numbers and Reid Vapor pressure of Commercial Petroleum Fuels Using FT-Raman Spectroscopy and Partial Least-Squares Regression Analysis", Analytical Chemistry, Vol. 67, No . 22. November 15, p40964100, (1995)
Utilizations of the proposed probability equation and PLS technique has enabled to correlate the operating conditions with TBP 's of each product and resulting feed. The choice of probability function is rather arbitrary and other equally versatile distribution functions or combined functions can be used.
Nickey J. Messick. John H. Kalvas and Patrick M. Lang, "Selecting Factors for Partial Least Squares", Microchemical, Journal, 55, 200-209,article No. MJ961413, (1997)
It should be also noted that for desired product specification, the two points of TBP can be utilized to get feed and product TBP's by applying the probability function.
Srikanth Voorakaranam and Joseph, "Model Predictive Inferential Control with Application to a Composites Manufacturing Process", Ind. Eng. Chem. Res. 38, p433-450,(1999)
Overall, the proposed method can be effectively used for controlling optimization of process, the downstream operation for better profit.
Yucai Zhu, Michiel van Wijck, Eric Janssen, Ton Graaf, Kees van Aalst and Leo Kieviet, "Crude Unit Identification for MPC using ASYM Method", Proceedings of the American Control Conference, Albuquerque, New Mexico, June,(1997)
REFERENCES Y.Z. Friedman, "Model-based control of Crude Product Qualities", Hydrocarbon Processing, Feb. 1994, p97-105
A.S .Pandya and R.R.Szabo, "Prediction of Petrochemical Product Property", SPIE Vo1.3390, pI97-207,(1998)
560