8594
Ind. Eng. Chem. Res. 2008, 47, 8594–8601
Simple Procedure for Interpreting Hydrotreating Kinetic Data Ezra K. T. Kam,* Hamza Al-Bazzaz, and Jamal Al-Fadhli Petroleum Research Center, Kuwait Institute for Scientific Research, P.O. Box 24885, Safat 13109, Kuwait
A simple procedure is developed to determine the apparent rate constants, reaction orders, and activation energies of various hydrotreating reactions, such as the hydrodesulfurization (HDS), hydrodemetalation (HDM), hydrodenitrogenation (HDN), and asphaltene cracking (HDAsph) of hydrotreating catalysts loaded in multiplereactor fixed bed units. The procedure is derived from the basic kinetic and engineering principles. The only required input parameters are the sulfur, vanadium, nickel, nitrogen, and asphaltenes contents in the feedstock and products, reaction temperatures, and liquid hourly space velocity (LHSV). These parameters are normally available from laboratories performing the kinetic studies. Since there is no correlation coefficient in the developed kinetic expression, the apparent reaction rate constant and activation energy for various hydrotreating reactions can be determined directly once the optimum value of the reaction order has been identified. To demonstrate how the procedure works, it has been applied to calculate the kinetic values published in the open literature. Excellent agreements are obtained. The procedure is further verified with kinetic parameters from experiments undertaken in our pilot plants. In some cases, kinetic values which were unable to be determined in our pervious studies can now be obtained. The overall absolute average deviation (AAD) is less than 10%. 1. Introduction The desire to enhance and optimize the performance of residue hydrotreating units is increasingly important to refinery operations worldwide. This trend is mainly due to the rocketing price in crude oils,1 the continuous depletion of crude oil quality,2 world increasing demand for middle distillates,3 ever more stringent environmental regulations,4–6 and improvement of profit margins.7,8 One of the most popular hydroprocessing units based on the hydrogen addition technology is the atmospheric hydrodesulfurization (ARDS) process.9 The ARDS process utilizes a system of graded catalysts consisting of several types of hydrotreating catalysts. The front-end catalyst normally has wider pores and is normally referred to as hydrodemetalation (HDM) catalyst. The mid-catalyst bed is normally loaded with highly active hydrodesulfurization (HDS) catalyst mainly for desulfurization. The back-end is normally known as the “finishing” catalyst, which typically has high denitrogenation (HDN) activity and sometimes-high hydrocracking (HC) activity.10 The performance of the process is strongly affected by the catalyst.11–14 Moreover, catalyst selection is very critical and it is normally assessed from pilot-plant study where the catalysts are tested under conditions similar to those employed at the refinery. However, whenever a new catalyst is developed, kinetic study has to be conducted to ensure its performance before a warranty can be issued. In this respect, a series of kinetic experiments are undertaken using different space velocities and temperature conditions. The effect of above process parameters on the extent of different hydrotreating reactions for sulfur, vanadium, nickel, asphaltenes, and conradson carbon removals (HDS, HDV, HDNi, HDAsph, and HDCCR) must be examined. The importance of the kinetic information on hydrodesulfurization (HDS) of petroleum residue oils has been highlighted by Ozaki et al.15 in terms of reactor design, catalyst activation and deactivation, and process optimization. In their study, the apparent HDS reaction order and activation energy were found * To whom correspondence should be addressed. E-mail: ekam@ prsc.kisr.edu.kw.
to decrease with a rise in reaction temperature. The change in HDS reaction order was due to the wide variety of sulfur compounds in the residual oils. The proposed reaction rate expressions for the nth order kinetics was
(
kT ) (LHSV)
)(
)
1 1 -1 n-1 (n - 1)cf (1 - c)n-1
(1)
where kT is the rate constant, LHSV is the liquid hourly space velocity, cf is the sulfur content in the feed oil, c is the fractional conversion of sulfur, and n is the reaction order. For the first order kinetics the expression became
(
( ))
C
kT ) MT 1 -
exp
D t
(2)
where C, D, and MT are correlation coefficients, which are functions of temperature, and t is the reciprocal of LHSV. Based on the Arrhenius rule, the rate equation was expressed as
( )
kT ) AO exp
-∆E RgT
(3)
The pre-exponential frequency factor, AO, was reported to be 3.35 × 107, and the activation energy, -∆E, was 22.1 kcal/ mol. The temperature range for the kinetic study was between 593 and 713 K while the reaction order, n, was varying from 4.25 to 1.42, respectively. The same set of kinetic data was later analyzed by Oyekunle and Kalajaiye16 using a power law model and involving a lengthy procedure for the determination of reaction order and transformation of error distribution. The procedure involved several steps covering both numerical crunching and graphical visualization methodologies. An array of reaction orders and a rate constant were obtained indirectly while values of the AO at 3.42 × 108 and -∆E at 29.7 kcal/mol were subsequently determined at the same temperature range. In a review of catalyst hydrometalation (HDM) of petroleum by Quann et al.,17 a summary of HDM kinetic studies was presented, covering a variety of feed stocks and catalysts. The apparent HDM reaction order over a CoMo/Al2O3 catalyst was
10.1021/ie8002705 CCC: $40.75 2008 American Chemical Society Published on Web 10/30/2008
Ind. Eng. Chem. Res., Vol. 47, No. 22, 2008 8595
found to be varying between 1 and 2, which was attributed to the different classes of metal compounds reacting at different rates.18–20 However, a reaction order of less than unity for HDM reactions was presented when using a manganese nodule catalyst.19,21 The diversity in HDM reaction order found in the open literature was mainly due to the variety in feedstock characteristics, catalyst type, reactor configuration, and process conditions employed by different research groups. Recently, two comprehensive studies on the hydrotreating kinetics of Kuwait atmospheric residual oil over a graded catalyst system were conducted by Marafi et al.3,22 One study was focused on the effect of catalyst type, while the other was concentrated on the effect of the original and treated feed stocks. In both studies, the kinetics data was obtained from an integral flow reactor, in which the kinetic experiments were conducted in a range of temperatures and LHSV’s. The influence of LHSV and temperature on the reaction kinetic parameters, such as the rate constant, activation energy and order of reaction can be established. However, the only measurable parameter from the kinetic experiments due to changes in LHSV and temperature is the concentration of the concerned products. Since the reactions are assumed following a simple integral reaction order with respect to the reactant concentration in the feed oils, the mass conservation can be described by 1 ) LHSV
∫
cp d(c) cf
(4)
-(r)
where -(r) is the reaction rate and can be expressed as a function of temperature, T, as
[ (
-(r) ) (kTo) exp
)]
To -∆E 1 (c)n RgTo T
by eq 9 to achieve the minimum error. However, there are four coefficients to be determined, and the solution depends mainly on the resultant values of these coefficients and hence becomes more complicated. In essence, it is very expensive, time-consuming, and labor intensive to conduct pilot-plant test on hydrotreating atmospheric residual oil; hence, it will be advantage to have a simple procedure to determine the hydrotreating kinetics from experimental data obtained either from life tests or dedicated kinetic experiments. If the kinetic data is determined from a life test, it is preferable to have one type of catalyst loaded in each reactor of a multiple fixed-bed reactor unit.23 Moreover, the kinetic data obtained should be from the actual feedstock as the catalyst is assigned to hydrotreat. In order to reduce the burden of having a dedicated experimental program in conducting a kinetic study, it will be useful to have a simple means to interpret results from a life test or from a reduced kinetic study without going through several levels of temperature and space velocity. 2. Proposed Kinetic Data Analysis 2.1. Model Formulation. From the previous discussion, the hydrotreating reactions mostly have a reaction order, n, greater than unity, and the following development will assume n > 1. Taking the mass conservation equation of a simple integral order with respect to the reactant concentration and with the initial conditions as described by eqs 4 and 5, respectively, and substituting the rate expression with eq 5, the following equation can be obtained:
[ ( )]
kTo exp
(5)
∴
The initial conditions are at t ) 0 c ) cf ;
T ) To
()
cf ) (LHSV) ln cp
(7)
And, for n * 1, the expression becomes kTo )
[
1 LHSV 1 - (n - 1) (n - 1) c (n - 1) c p f
)
]
and
[ (
dc cn
(
)
)]
1
)
(n-1)
1
-
cp
(n-1)
cf
(11) Take the logarithm on both sides of eq 10 and rearrange the terms to get
(
)
n-1 1 1 ) ln(kTo) + - (n-1 - ln LHSV cp(n-1) cf
(
)
1000 1 - )(12) ( -∆E 1000 )( R T )( T To
g o
Let
(
y ) ln
1 cp
(n-1)
1
-
(n-1
cf
)
n-1 ( LHSV ) ) ln(k ) + T 1000 1 - )(13) ( ( -∆E ) ( ) 1000 R T T
- ln
To
o
cp )
g o
1
[( ) 1
n-1
cp
1 1 1 - n-1 n - 1 c n-1 cf p
To -∆E (n - 1) (kTo) exp 1 LHSV RgTo T
23
More recently, Marafi et al. have proposed an alternative procedure to determine the hydrotreating kinetics of residual oils by substituting eq 5 into eq 4 and integrating with respect to the initial conditions of eq 6, a quantitative relationship between the product concentration and process conditions can be approximated as
∫
(10)
ln (8)
)
cf
(6)
where cf and cp are the concentration in the feed and product, respectively; kTo is the apparent rate constant at a reference temperature, To; -∆E is the activation energy; and Rg is the gas constant. Equation 4 can be integrated with the initial conditions of eq 6. Two expressions for the apparent rate constant, kTo, can be obtained. For a first order reaction, n ) 1, kTo
To -∆E 1RgTo T LHSV
1 cf
n-1
+
{
(
1 b1 + [b2 ln(n - 1)] + b3 ln LHSV
) [( +
b4 1 -
To T
)] } ] (9)
where b1, b2, b3, and b4 are the coefficients of the above equation. The kinetic data of kTo, n, and -∆E are obtained by comparing the measured product concentration to that predicted
y can also be expressed in the form of a linear algebraic equation as y ) a1x1 + a2x2
(14)
Equate the right-hand side of eqs 13 and 14 to get x1 ) 1, and
kTo ) exp(a1)
(15)
8596 Ind. Eng. Chem. Res., Vol. 47, No. 22, 2008
x2 )
[( )( )]
To 1000 1, RgTo T
- ∆E ) 1000a2
(16)
Substitute eqs 15 and 16 to eq 13 to obtain
(
y ) ln
1 cp(n-1)
-
1 cf(n-1
)
(
-ln
n - 1 ) a1 + a2x2 (17) LHSV
)
After solving eq 17 for the optimum n, values of kTo and -∆E can be determined directly from eqs 15 and 16. 2.2. Method of Solution. Due to the nature of experimentation and the requirement of data quality and data assurance, experiments using the same feed stocks, hydrotreating under the same process conditions and over the same type of catalyst will be conducted and occasionally repeated. Moreover, experiments are normally undertaken at several levels of temperature and space velocity, as well as using different feed stocks. These lead to a situation that the information available is more than the parameters to be evaluated, and constitute an overdetermined problem as expressed by eq 17. Due to the elusive characteristics arisen from uncertainties and random errors of measurements and observations, normal equations used in data analysis would be extremely illconditioned. Usually, there is no exact solution to an overdetermined system of algebraic equations. Two conventional approaches are commonly employed to solve overdetermined systems, namely, the least-squares solution24 and Chebychev’s “minmax” solution.25 In some cases, however, no convergence can be found, especially when the coefficient matrix of the overdetermined system is large and/or sparse. According to Buyukkoca,26 an overdetermined problem can be solved without using linear least-squares and total deviations, but by transforming the original overdetermined linear matrix into an auxiliary matrix, which is always symmetric and singular. To apply the Buyukkoca’s algorithm26 to solve the overdetermined system of linear algebraic equations, the following procedures are adopted: 1. Construct the overdetermined algebraic equations system (eq 17) by assuming a value for the apparent order of reaction, n, which should be greater than unity. 2. Solve the overdetermined system of algebraic equations for a1 (kTo) and a2 (-∆E) by Buyukkoca’s algorithm.26 3. Calculate the product concentrations according to the following equation: cp )
[( ) 1 cf
n-1
{ [(
- 1) [ (nLHSV ]+
+ exp ln(kTo) + ln
)(
To 1000(-∆E) 1RgTO T
) ]} ]
-(1/(n-1))
(18)
4. Estimate the absolute relative deviation (ARD) and absolute average deviation (AAD) based on the simulated and measured product values through eqs 19 and 20.
ARDi% ) 100
(cp - c/p)2 (c/p)2
i%
(19)
N
∑ ARD % i
AAD% )
i)1
N
(20)
where i is the index of product measurement and N is the total number of measured product concentrations, cp/.
5. Once the least value of the AAD for n is obtained, the corresponding kTo and -∆E values are determined from eqs 15 and 16. 3. Application and Comparison To demonstrate the application of the proposed procedure, the experimental data published by Ozaki et al.15 is used, in which the product sulfur was expressed in terms of the fractional conversion, c, that must be converted to cp/ in weight percent through eq 21. c/p ) cf(1 - c)
(21)
where cf ) 3.77 wt %. Table 1 presented the data reported by Ozaki et al.15 on their kinetic study of hydrodesulfurisation of Kuwait atmospheric residue. There are originally 62 records. Since the temperature for the last three records (60-62) have been taken at 713 K, which is too severe for residue hydrotreating, these are discarded and only the first 59 records are used in the present analysis. The last three columns in Table 1 constituting the overdetermined system of a set of 59 linear algebraic equations at n ) 2.5. This system is solved for the optimum reaction order, n, at which the least AAD% value should be obtained as shown in Figure 1. The data plotting the AAD% from the 59 records of Ozaki et al.15 against n are represented by the [ symbols and a thick line. The apparent reaction order is 2 at the least AAD% value of 6.12%. Figure 2 presents a comparison of the measured cp/ and the simulated cp obtained from eq 19. The data of 59 records15 is represented by the [ symbols and the straight line is a 45° line. The majority of these values are compared very well. Oyekunle and Kalajaiye16 selected a number of kinetic data reported by Ozaki et al.15 as presented in the first 25 records of Table 1 to facilitate their kinetic analysis. When using our developed simple procedure to analyze these data, a value of n at 2 is obtained but with an improved AAD% value of 4.67%, which is represented by the O symbols and a thin line in Figure 1. The simulated sulfur contents compared equally well with the measured cp/ values, as represented by the O symbols in Figure 2. A summary of the reaction order, apparent rate constant, and activation energy values reported by Ozaki et al.15 and Oyekunle and Kalajaiye16 and obtained from this work is depicted in Table 2. Some differences are shown between the kinetic quantities of kTo and -∆E obtained from the 5915 and 25 records of data.16 However, the kTo values are very close at around 6 × 109 in terms of weight percent and negligible deviation in -∆E at 30 kcal/mol is also found in this work when 59 or 25 records of data are used. In contrast, instead of a range of reaction order values obtained by the other two research groups, only a single value of n at 2 is determined from this study. The magnitude of second-order reaction is in good agreement reported by a number of researchers.7,10,27 From the above demonstration, the developed procedure is very simple to apply while the kinetic parameter values are reliable and readily to be determined. It will be useful to test our simple procedure to determine kinetic data from different workers from different residue hydrotreating catalysts. Table 3 presents a comparison of the kinetic data published by Marafi et al.3 for a catalyst system consisting of three hydrotreating catalysts, namely, the catalyst A for hydrodemetalation (HDM), catalyst B for hydrodesulfurisation (HDS), and catalyst C for both HDS and hydrodenotogenation (HDN) reactions. Since the catalyst system can also hydrocrack asphaltenes (HDAsph) and conradson carbon residue
Ind. Eng. Chem. Res., Vol. 47, No. 22, 2008 8597 Table 1. Data from Ozaki et al.
15
and Parameters for Constituting Equation 17 temperature
data no.
LHSV (1/h)
°C
K
c
cp/ (wt %)
a1
a2
y (n ) 2.5)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62
0.3430532 0.3850597 0.6788866 1.4005602 0.9699321 1.3351135 1.9607843 3.9840637 1.0266940 1.3175231 2.0120724 2.6737968 3.8759690 6.9930070 0.5149331 0.6788866 0.9980040 2.0366599 2.6954178 4.0322581 8.1300813 0.7183908 1.0460251 1.5698587 3.0674847 1.0111223 1.3586957 2.0120724 2.6525199 3.9840637 6.9444444 0.4070004 0.6858711 1.0101010 2.0491803 0.6238303 0.8467401 1.5290520 2.4875622 0.6835270 0.9832842 1.5772871 2.8490028 0.7479432 1.0298661 1.5698587 2.8571429 0.6662225 1.0460251 1.4662757 2.9498525 0.7147963 1.0460251 1.5974441 2.8571429 0.7047216 1.0298661 1.5479876 2.9498525 0.5230126 0.7917656 2.0408163
320 320 320 320 340 340 340 340 360 360 360 360 360 360 380 380 380 380 380 380 380 400 400 400 400 320 320 320 320 320 320 335 335 335 335 350 350 350 350 380 380 380 380 380 380 380 380 390 390 390 390 395 395 395 395 410 410 410 410 440 440 440
593 593 593 593 613 613 613 613 633 633 633 633 633 633 653 653 653 653 653 653 653 673 673 673 673 593 593 593 593 593 593 608 608 608 608 623 623 623 623 653 653 653 653 653 653 653 653 663 663 663 663 668 668 668 668 683 683 683 683 713 713 713
0.4421 0.4089 0.3438 0.2318 0.4545 0.3907 0.3219 0.1966 0.6216 0.5799 0.4939 0.4226 0.3489 0.2482 0.8639 0.8441 0.802 0.6609 0.604 0.5322 0.3936 0.9204 0.8806 0.8107 0.6897 0.2629 0.2383 0.1818 0.145 0.1032 0.0639 0.5158 0.4688 0.4167 0.2813 0.634 0.5651 0.4497 0.3724 0.8382 0.8011 0.7109 0.5862 0.8211 0.7344 0.6719 0.5495 0.8966 0.8568 0.7905 0.6419 0.9019 0.8594 0.8037 0.6764 0.9523 0.9151 0.8541 0.7533 0.9963 0.9899 0.9549
2.103283 2.228447 2.473874 2.896114 2.056535 2.297061 2.556437 3.028818 1.426568 1.583777 1.907997 2.176798 2.454647 2.834286 0.513097 0.587743 0.74646 1.278407 1.49292 1.763606 2.286128 0.300092 0.450138 0.713661 1.169831 2.778867 2.871609 3.084614 3.22335 3.380936 3.529172 1.825434 2.002624 2.199041 2.709499 1.37982 1.639573 2.074631 2.366052 0.609986 0.749853 1.089907 1.560026 0.674453 1.001312 1.236937 1.698385 0.389818 0.539864 0.789815 1.350037 0.369837 0.530062 0.740051 1.219972 0.179829 0.320073 0.550043 0.930059 0.013949 0.038077 0.170027
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
-0.0783 -0.0783 -0.0783 -0.0783 -0.0505 -0.0505 -0.0505 -0.0505 -0.0244 -0.0244 -0.0244 -0.0244 -0.0244 -0.0244 0 0 0 0 0 0 0 0.0230 0.0230 0.0230 0.0230 -0.0783 -0.0783 -0.0783 -0.0783 -0.0783 -0.0783 -0.0572 -0.0572 -0.0572 -0.0572 -0.0372 -0.0372 -0.0372 -0.0372 0 0 0 0 0 0 0 0 0.0117 0.0117 0.0117 0.0117 0.0174 0.0174 0.0174 0.0174 0.0340 0.0340 0.0340 0.0340 0.0651 0.0651 0.0651
-3.1297 -3.1678 -2.9098 -2.7824 -2.9294 -2.7742 -2.7434 -2.7490 -2.7426 -2.7207 -2.6180 -2.3139 -2.1671 -2.1230 -2.0332 -2.0094 -1.9574 -1.9588 -1.6106 -1.6515 -1.6001 -1.4735 -1.1770 -1.1373 -1.1217 -1.1663 -1.1429 -1.0784 -0.1118 -0.0834 -0.2478 -0.3350 -0.1198 -0.0591 -0.0611 -0.2826 -0.3016 -0.2478 -0.1892 -0.1838 -0.5252 -0.4816 -0.5102 0.5677 0.5085 0.2304 -0.0151 0.7196 0.5375 0.4235 0.1427 1.0466 0.7947 0.4656 0.2903 1.8077 1.3077 0.8708 0.6543 5.3547 4.2622 2.9560
(HDCCR), HDAsph and HDCCR are also included in their kinetic study. Table 3 consists the kinetic data of three catalysts (in rows) and five hydrotreating reactions (in columns). The reaction order, n, of the catalyst A between Marafi et al.3 and this work matches perfectly for all five hydrotreating reactions. The rate constants (kTo) are also very compatible for all the reactions. Although the activation energy (-∆E) values from HDS, HDAsph, and HDCCR agree well, they are quite different for the HDV and HDNi reactions. A single
-∆E value at 38.4 kcal/mol is obtained from this work for the HDV and it lies between the values reported by Marafi et al.3 at 27.7 and 62.2 kcal/mol for two temperature ranges of 633-673 K and above 673 K, respectively. This also reflects a higher value of AAD% for this reaction at 17%. Similar observation applies to HDNi, which has also two -∆E values of 12.5 and 28.9 kcal/mol for the same two temperature ranges. Again, only a single value of 19.3 kcal/ mol is obtained from this work.
8598 Ind. Eng. Chem. Res., Vol. 47, No. 22, 2008
Figure 1. Comparison of AAD% with reaction order.
Figure 2. Comparison of predicted and measured values at n ) 2. Table 2. Comparison of Frequency Factor, Activation Energy, and Reaction Order ref 15
Ozaki et al. this work Oyekunle and Kalajaiye16 this work a
frequency factor, Ao 3.35 5.84 3.42 6.08
× × × ×
7
10 109 108 109
(wt (wt (wt (wt
activation energy, -∆E (kcal/mol)
reaction order, n
remarks
22.1 29.1 29.7 30.9
1.42 - 5.42 2 1.42 - 4.33 2
59 records of dataa
fraction) %) fraction) %)
25 records of dataa
from the work of Ozaki et al.15
In the catalyst B, a second-order reaction is found for HDS, HDAsph, and HDCCR from Marafi et al.3 and this work. However, the n for the HDM reactions for both V and Ni is 1.5
from Marafi et al.3 but 2 from this work. Nevertheless, it is reasonable to assume that the HDM reactions obey second-order since several investigators20,29,30 have shown second-order
Ind. Eng. Chem. Res., Vol. 47, No. 22, 2008 8599 3
Table 3. Kinetic Data Comparison from Original KEC-AR Feedstocks HDS kinetic data
Marafi et al.3
HDV this work
Marafi et al.3
HDNi this work
Marafi et al.3
HDAsph
HDCCR
this work
Marafi et al.3
this work
Marafi et al.3
this work
1.5 0.1992 19315 8.55
2 0.3230 23600
2 0.2726 26277 9.73
2 0.0304 24500
2 0.0267 16983 4.01
2 0.1550 31500
2 0.1535 31258 3.66
2 0.0630 20100
2 0.0793 20110 7.99
2 0.2910 15100
2 0.1820 19960 4.63
2 0.0950 17100
2 0.0777 27600 2.17
catalyst A n kTo -∆E AAD%
2 0.1362 26200
2 0.1399 27038 3.50
1.5 0.1853 27700
1.5 0.1937 38410 16.94
n kTo -∆E AAD%
2 0.7110 25500
2 0.8726 25050 18.14
1.5 0.0310 29600
2 0.0456 27490 17.89
n kTo -∆E AAD%
2 1.0760 28500
2 0.7294 34192 15.44
1.5 0.0270 23400
2 0.0298 21760 10.68
1.5 0.2144 12500 catalyst B 1.5 0.0770 19500
0.0760 20578 12.60
catalyst C 1.5 0.0500 25300
2 0.0521 23647 8.21
Table 4. Kinetic Data Comparison from Treated KEC-AR Feedtocks22 HDS
HDV
HDNi
HDAsph
HDCCR
kinetic data Marafi et al.22 this work Marafi et al.22 this work Marafi et al.22 this work Marafi et al.22 this work Marafi et al.22 this work catalyst B n kTo -∆E AAD%
2 1.4200
2 1.1526 37006 18.01
2 0.0630
2 0.0496 35260 4.25
n kTo -∆E AAD%
1.5 2.2390
1.5 1.9887 33165 3.43
2 0.0480
2 0.0676 20141 10.19
2 0.0760
2 0.0642 36399 6.26
2 0.7630
2 0.8015 28170 8.48
2 0.0790
2 0.0739 32680 1.79
2 0.0545 28650 5.01
2 1.2500
2 1.2792 3251 2.06
2 0.0750
2 0.0641 31027 2.14
catalyst C 2 0.0570
Table 5. Comparison of Kinetic Data in Thermal Cracking Reactions23 analysis 23
Marafi et al.
this work
n b1 (kTo @ 633 K) b2 b3 b4 (-∆E in kcal/mol) AAD % n kTo @ 633 K -∆E (kcal/mol) AAD %
HDS
HDV
HDNi
HDAsph
HDCCR
1.74 0.01162 1.34144 0.61379 25.4200 4.76 1.74 0.00826 25.3420 2.77
1.79 0.00454 1.2718 1.507 43.8343 5.00 1.79 0.00632 45.9097 4.76
1.38 0.05824 2.751 1.77769 50.6459 6.44 1.38 0.0173 50.6459 5.59
1.76 0.007 1.38119 0.57231 35.2734 12.50 1.76 0.0048 38.2825 6.26
1.85 0.00131 1.079 0.77869 31.4425 1.20 1.85 0.00113 31.4425 1.01
kinetic behavior for metal removal from residue oils. The kTo and -∆E values from Marafi et al.3 and this work are very compatible. Similar observation is found in catalyst C for the reaction order. The 1.5th reaction order is reported by Marafi et al.3 but second-order is found in this work. The kTo and -∆E values from both findings are very compatible for HDS, HDV, HVNi, and HDAsph reactions. Nevertheless, the -∆E of the HDCCR from this work at 27.6 kcal/g-mol is higher than that of Marafi et al.3 of 17.1 kcal/mol, but it is well below the value of 66.09 kcal/mol reported by Trasobares et al.31 Moreover, the AAD% from the HDCCR reaction over catalyst C is 2.17%, which is the lowest in Table 3 and reflects the quality of this set of kinetic data as well as the reliability of this simple procedure. The overall ADD% of Table 3 for the three catalysts and five hydrotreating reactions reaches 8.55%. To examine the reliability of this simple procedure further, it is applied to determine the kinetic data for hydrotreated feed stocks reported by Marafi et al.22 and a summary of comparison is given in Table 4. Since catalyst A is used to hydroprocess
the original KEC-AR and has been reported in Table 3, only the kinetic data generated by hydrotreating the demetallized residue oils over catalyst B and hydrotreating the demetallized/ desulfurized residual oils over catalyst C is presented. Second-order kinetics which is determined in this work for HDS, HDV, HDNi, HDAsph, and HDCCR reactions over catalyst B, matches exactly the results published by Marafi et al.22 Moreover, the apparent rate constants of HDNi, HDAsph, and HDCCR are very compatible, while that of HDS and HDV are slightly different than the published data. No activation energy values have been reported by Marafi et al.22 However, from this simple analysis, the activation energy values are obtained at 37.0, 35.3, 36.4, 28.2, and 32.7 kcal/mol for the HDS, HDV, HDNi, HDAsph, and HDCCR, respectively. Similar observation is made for catalyst C, in which a 1.5thorder is obtained for HDS reaction while a second-order reaction is found for HDV, HDNi, HDAsph, and HDCCR reactions from both procedures. Again, the apparent rate constants of HDNi, HDAsph, and HDCCR are very close, while slightly difference is found in HDS and HDV reactions. Furthermore, the activation
8600 Ind. Eng. Chem. Res., Vol. 47, No. 22, 2008
energy values are 33.2, 20.1, 28.7, 32.5, and 31.0 kcal/mol for the HDS, HDV, HDNi, HDAsph, and HDCCR, respectively, but no -∆E value has been reported by Marafi et al.22 The overall AAD% estimated from the comparing the predicted cp and the measured c/p obtained from the two catalysts and five reactions is 6.16%. To demonstrate the flexibility of this procedure, it is applied to interpret the kinetic data from noncatalytic reactions, such as the thermal cracking kinetics reported by Marafi et al.23 The methodology from both approaches is similar but it is comparatively very simple in this work since there are no coefficients required to determine the contaminant concentrations in the product oil as expressed by eq 18. All the associated kinetic parameters are then determined, Table 5. The n and -∆E values obtained from both methods are very compatible. However, there are marked differences in the kTo values because the method based on eq 8 requires extra coefficients, b2 and b3, to determine cp, while eq 18 used in this work can determine cp readily. When comparing the AAD%, the cp values determined by eq 18 are more accurate then eq 8 for all five reactions. 4. Conclusion The simple procedure to determine the apparent rate constants, reaction orders and activation energies of various hydrotreating reactions developed in this work is derived from basic kinetic and engineering principles. Sulfur, vanadium, nickel, nitrogen, and asphaltene contents in the feedstock and products, reaction temperatures, and liquid hourly space velocity (LHSV) are the only required input parameters, which are normally available from laboratories performing the kinetic studies. The proposed procedure can interpret kinetic information from a catalyst performance test or a reduced kinetic experiment program. There is no requirement of an extensive work-plan or dedicated experimental design to undertake a kinetic study systematically at several levels of temperature or space velocity. The procedure has been extensively tested to determine the kinetic parameters from data published by various research organizations using different catalysts to hydrotreating a variety of feedstocks. Excellent agreements are obtained. In some cases, kinetic data that have not been reported can also be determined. The overall AAD is less than 10%. Notation a1, a2 ) parameters used in eqs 14 and 17 b1, b2, b3, b4 ) coefficients used in eq 8 AAD% ) absolute average deviation defined by eq 20 ARD% ) absolute relative deviation defined by eq 19 c ) fractional concentration cf, cp ) concentrations of feed and product, respectively (wt % or wtppm) ci, c/i ) concentrations from pilot plant and simulation, respectively (wt % or wtppm) -∆E ) activation energy (kcal/mol) i ) index kT ) reaction rate constant (wt %/h or wtppm/h) LHSV ) liquid hourly space velocity (1/h) n ) reaction order (-) N ) number of data in the overdetermined system or for comparison (-) r ) rate of reaction (conc(n-1)/h) Rg ) gas constant (kcal/(mol K)) t ) process time (h) T ) process temperature (K)
To ) reference reaction temperature (K) x, y ) variables for solving the overdetermined problem
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ReceiVed for reView February 17, 2008 Accepted March 10, 2008 IE8002705
