Article pubs.acs.org/EF
A Delayed Coking Model Built Using the Structure-Oriented Lumping Method Lida Tian, Benxian Shen,* and Jichang Liu State Key Laboratory of Chemical Engineering, East China University of Science and Technology, Shanghai 200237, People’s Republic of China ABSTRACT: A total of 7004 types of molecular lumps and 92 types of reaction rules were proposed to characterize the feedstock and describe the reaction behaviors of delayed coking. The reaction rate constants were estimated as equations of structure vectors. A reaction kinetic model has been built to predict the products distribution of delayed coking. The good prediction accuracy of the model has been proven by the comparison of calculation results and experimental results of delayed coking.
1. INTRODUCTION In 1992, Quann and Jaffe proposed the concept of structureoriented lumping (SOL).1,2 This concept made the kinetic lumping method extend to the molecular level and made it possible to describe the reaction behaviors of complex reaction systems. In recent decades, the SOL method has been applied in some fields. In addition, some SOL models have been built continually.3,4 In 2005, Jaffe extended this concept to residue describing.5 However, building kinetic models of delayed coking still had two problems: the feedstock residue is difficult to characterize, and the reaction rate constants are difficult to calculate. This paper solved the two problems and built a kinetic model of delayed coking using the SOL method.
3. SIMULATE THE MOLECULAR REACTION BEHAVIORS 3.1. Reaction Rules. Reaction rules were used to describe the molecular behaviors. They were the standard to judge that how the material molecular matrix turned to a product molecular matrix. Each reaction rule included reactant selection rule and product generation rule. 6 Reactant selection rule selected the molecules (structure vector groups), whether this type of reaction will occur. Product generation rule generated the product molecules (structure vector groups) from reactant molecules of this type of reaction. Delayed coking is a thermal cracking process that obeys the free-radical mechanism.7 The reactions of delayed coking are complex. But overall, all the reactions could be divided into cracking and condensation. According to the reaction types in delayed coking, 92 types of reaction rules were established to describe the reaction behaviors of heavy oil delayed coking. Some typical reaction rules are as follows: (1) Side Chain Breaking of Single-Core Molecules (All)
2. CHARACTERIZATION OF THE FEEDSTOCK 2.1. Structure Vectors To Characterize Feedstock. In SOL, 22 structure vectors were proposed to characterize the feedstock.1,2 To characterize the residue, Jaffe proposed two more structure vectors to represent nickel and vanadium.5 For the specific delayed coking process, this work changed some structure vectors slightly. The RS, RN, and NO vectors were neglected and a vector called “cc” was considered to represent the strength and carbon numbers between cores and cores. The 22 new structure vectors and their stoichiometric matrices are shown in Table 1. 2.2. Molecular Lumps and Their Contents Calculation. According to the SOL method, this paper proposed 92 types of single-core seed molecules and 46 types of multicore seed molecules to characterize the residue. After adding different numbers of −CH2− to seed molecules, a total of 7004 types of molecular lumps were generated to characterize the molecular composition of residues. Figures 1 and 2 show single-core seed molecules and metal compound multicore seed molecules, respectively. To calculate the contents of the proposed molecular lumps, a cut of feedstock, such as that described in Figure 3, is needed. After doing this, a simulated annealing algorithm (SA) could be used to search the suitable contents. © 2011 American Chemical Society
Reactant selection rule: [(A6 > 0) ∨ (N6 > 0) ∨ (N5 > 0)] ∧ (R > me + KO) ∧ (A6 < 10) ∧ (N6 < 10)
Product 1:
R1 = R − me − KO, br1 = (br − 1) × (br > 0);
the rest: 0
Product 2:
R2 = me + KO,
br2 = 0;
the rest: invariant
Received: October 14, 2011 Revised: November 21, 2011 Published: December 16, 2011 1715
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e.g.,
Reactant: A6 1 Product 1: A6 0 Product 2: A6 1
A4 A2 N6 N5 N4 N3 N2 N1 R br me IH AA NS AN NN RO KO Ni V cc 0 0 0 0 1 0 0 0 6 1 1 0 0 0 0 0 0 0 0 0 0 A4 A2 N6 N5 N4 N3 N2 N1 R br me IH AA NS AN NN RO KO Ni V cc 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 A4 A2 N6 N5 N4 N3 N2 N1 R br me IH AA NS AN NN RO KO Ni V cc 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0
Table 1. Structure Vectors and Stoichiometric Matricesa A6
a
A4
A2
N6
N5
N4
N3
N2
N1
R
br
me
IH
AA
NS
AN
NN
RO
KO
Ni
V
cc
C
6
4
2
6
5
4
3
2
1
1
0
0
0
0
−1
−1
−1
0
0
0
0
0
H
6
2
0
12
10
6
4
2
0
2
0
0
2
−2
−2
−1
−1
0
−2
−2
0
0
S
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
N
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
O
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
Ni
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
V
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
The meanings of the 22 structure vectors are as defined in Chart 1.
Chart 1. Structures and Definitions Used in Table 1
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Figure 2. Metal compounds multicore seed molecules.
Figure 1. Single-core seed molecules.
(2) Multicore Molecules Cracking (First Joint) Reactant selection rule:
[fix(rem(cc, 100)/10) = 3] ∨ [fix(rem(cc, 100)/10) = 2]
Product 1:
R1 = rem(R, 100) + rem(cc, 10), me1 = rem(me, 10) + 1,
cc = 0;
the rest: X1 = rem(X , 10)
Product 2:
R2 = fix(R/100), IH2 = fix(IH/10) + 1,
cc 2 = fix(cc/100);
the rest: X2 = fix(X /10)
e.g.,
Reactant: A6 101 Product 1: A6 1 Product 2: A6 10
A4 A2 N6 N5 N4 N3 N2 N1 R br me IH AA NS AN NN RO KO Ni V cc 100 0 10 0 243 0 0 0 10301 0 101 0 0 0 0 0 0 0 0 0 2231 A4 A2 N6 N5 N4 N3 N2 N1 R 0 0 0 0 3 0 0 0 2
br me IH AA NS AN NN RO KO Ni V cc 0 2 0 0 0 0 0 0 0 0 0 0
A4 A2 N6 N5 N4 N3 N2 N1 R 10 0 1 0 24 0 0 0 103
br me IH AA NS AN NN RO KO Ni V cc 0 10 1 0 0 0 0 0 0 0 0 22
Here, the symbol “∨” means “or”; the symbol “∧” means “and”; the subscript “1” means “product 1”; the subscript “2” means “product 2”; without subscript means “reactant”; “invariant” means equal to reactant; “rem” means “remainder” and “f ix” means “eliminate the decimal to recent integer”. According to the method proposed by the authors’ previous paper,4 simultaneous differential equations could be generated. In addition, the product molecular matrix could be calculated from the reactant molecular matrix, using the fourth- and fifth-order Runge−Kutta methods. 3.2. Estimate of Reaction Rate Constants. To solve the above differential equations, the reaction rate constant of each reaction should be known. However, the number of equations would
be huge. Some reaction rate constants could be obtained from the literature,8,9 but far from the standard to solve such differential equations. It is also inappropriate to obtain these rate constants by experiment. Based on transition-state theory, rate constants could be calculated by formula. Molecular simulating software was used to search the transition state and calculate some kinetic parameters. However, for delayed coking, this method was limited by two factors: (1) There are so many reactions in delayed coking, it is very time-consuming to calculate the rate constant one by one with this method; and (2) Only simple molecules with a small number of atoms were available for the transition-state search. For the reactions involving complex molecules, it is difficult to 1717
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Figure 3. Method of the residue feedstock cutting.
Figure 4 shows the residual error distributions of these equations for extrapolated prediction. It could be found that the residual errors were slightly far from the zero point. To revise them, the reaction rate constants should be treated as follows:
search its transition state with molecular simulated software such as Materials Studio. Since it is hard to calculate every reaction rate constant exactly, it is necessary to estimate the value of rate constants. The concept that molecular kinetic properties and structure vectors could be associated with molecular structure provides the basis for estimating a large number of reaction rate constants. The first approximation to estimate the rate constants was that all reactions in a class had the same reaction rate constant, because they underwent the same reaction pathway. However, this approximation was insufficient, because, within each reaction class, the molecular structure of reactant and product could influence the rate constants. So the second approximation was that a perturbation to the reaction rate constants arose, considering the influence of different molecular structures on the reaction rate constants. The structure−activity relationship in kinetics was not a new concept. Such studies were done by Hammet, Taft, and Swain.10,11 Structure vectors were used to describe the molecular structure in the SOL method. Therefore, this perturbation could be associated with structure vectors. In transition-state theory, eq 1 could be used to calculate the reaction rate constant:4
⎛ T ΔS − ΔE ⎞ k T ⎟ k(T ) = B exp⎜ ⎝ ⎠ h RT
k′ = k(1 + δ)
Here, k′ represents the reaction rate constant after revision, k is the reaction rate constant before revision, and δ denotes the rate revision index. The influence of each reaction class on product distribution of delayed coking is considered to be the same. Therefore, each reaction class has the same δ value. Sixteen groups of results from delayed coking experiments of different feedstock under different operating conditions were taken as objectives. Moreover, these δ values could also be calculated using the SA method. One thing we want to explain is that these functions are only valid for the temperature range of 460−500 °C. Table 4 includes these δ values.
4. SIMULATE THE DELAYED COKING PROCESS 4.1. Simplification and Assumption. The delayed coking process includes several components, such as coking, fractionation, gas recovery, coking processing, and venting system. The prediction of the SOL model is directed only at the reaction system. Therefore, the delayed coking process could be simplified similar to the process depicted in Figure 5. There were simplifications and assumptions for the model: (1) The delayed coking process was composed of many short batch processes. (2) The coking drum inlet amount and its molecular composition were unchanged every time. (3) All the reactions occurred in a coking drum. (4) The reactant molecules could be vaporized, immediately, in the coking drum. (5) There were no reactions during the input of materials and the output of products, and the output of products was completed immediately. (6) The molecular compositions of gas products leaving and remaining in the coking drum were the same. (7) The coking drum was an ideal reactor, and the gas in the coking drum behaved as an ideal gas.
(1)
Here, kB is the Boltzmann constant, h the Planck constant, T the temperature, R the ideal gas constant, ΔS the entropy changes before and after reaction, and ΔE the reaction energy barrier. Therefore, if ΔS and ΔE were known, the reaction rate constant under certain temperatures could be calculated. For simple reactions, ΔS and ΔE could be calculated using Materials Studio software directly. For complex reactions, ΔS and ΔE could be estimated by functions with structure vectors. A common function type was
y = a1 × x1b1 + a 2 × x2b2 + ··· + an × xnbn + c
(3)
(2)
After calculating ΔS and ΔE of simple reactions as a regression aggregate with Materials Studio software and using “lsqcurvefit” function and the Matlab optimization toolbox, equations to calculate ΔS and ΔE could be obtained. These equations are shown in Tables 2 and 3. 1718
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Table 2. Equations Used To Calculate ΔE reaction classes carbon chain cracking
equation
ΔE = − 0.3139R0.8043 − 0.2096br 0.5137 − 0.0845(R1 × R2)0.0197 − 0.0614IH + 95.8311
side chain breaking
( CoresA6−+NiA4− V ) − 0.334( CoresN6−+NiN4− V ) 0.3974 0.7023 R br + me − 0.1495( + 0.1199( Cores − Ni − V ) Cores − Ni − V ) |IH| + 0.0172( + 92.781 Cores − Ni − V )
ΔE = 0.2074
dehydrogenation
0.3977
( CoresN6−+NiN4− V ) − 0.2927( Cores −RNi − V ) 0.1599 IH br + 0.0072( − 0.3585 × ( Cores − Ni − V ) Cores − Ni − V ) 0.1039 me + 0.0018 × ( + 99.7853 ) Cores − Ni − V
ΔE = − 0.0774
molecular cracking
ΔE = − 0.5472cc11.5102 + 0.2772(Cores1 × Cores2)0.0039 + 0.0057
0.0081
( A2Cores+ A6− Ni+−A4V ) 1
1
1
0.0024
+ 0.0042
( Cores −RNi − V )
− 0.0027 × Cores0.0031 + 98.0873 ring opening 0.0649
( CoresA6−+NiA4− V ) + 0.0137( Cores −RNi − V ) |IH| + 0.3248( + 100.7336 Cores − Ni − V )
ΔE = 0.1742
polycondensation
⎛ ⎞0.4953 A62 + A4 2 ⎟ ΔE = − 0.1885(A61 + A41)0.5089 − 0.1876⎜ ⎝ Cores2 − Ni2 − V2 ⎠ ⎛ ⎞0.1833 R2 ⎟ + 0.0312R10.1719 + 0.0321⎜ + 106.4872 ⎝ Cores2 − Ni2 − V2 ⎠
Diels−Alder
⎛ N62 + N4 2 ⎞0.3113 ⎟ ΔE = 0.1737R10.2178 − 0.5179⎜ ⎝ Cores2 − Ni2 − V2 ⎠ ⎛ ⎞0.2106 R2 ⎟ + 0.2842⎜ + 95.7364 ⎝ Cores2 − Ni2 − V2 ⎠
desulfuration
0.7471
0.5244
0.8033
0.1386
N6 + N4 + N1 R + 0.4805( ( Cores − Ni − V ) Cores − Ni − V ) 0.0078 me + 0.0057( + 96.1871 Cores − Ni − V )
ΔE = 0.2284
decarboxylation
( CoresN6−+NiN4− V ) + 0.0099( CoresR−−Ni1 − V ) 0.0061 br + me + 0.0073( + 102.7983 ) Cores − Ni − V
ΔE = 0.0199
(9) Molecules of recycled oil were wax oil molecules, and the molecular compositions of each part of the recycled oil were the same.
(8) The temperature and pressure of the coking drum in the reaction process was kept constant, and cooling occurred when the reactions were totally finished. 1719
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Table 3. Equations Used To Calculate ΔS reaction classes
equation
carbon chain cracking ΔS = − 0.0369R0.8942 − 0.0087br 0.1394 − 0.6745(R1 × R2)0.0289 R
− 0.0049IH + 25.8387 side chain breaking ΔS A6 + A4 = 0.0218 R Cores − Ni − V
) − 0.0299( CoresN6−+NiN4− V ) 0.8072 0.4011 R br + me − 0.0151( + 0.0123 Cores − Ni − V ) Cores − Ni − V |IH| + 0.0018( + 24.5755 Cores − Ni − V ) (
dehydrogenation
0.4122
ΔS N6 + N4 = − 0.0164 R Cores − Ni − V
( ) − 0.0602( Cores −RNi − V ) 0.1604 IH br + 0.0019( − 0.0798( ) ) Cores − Ni − V Cores − Ni − V 0.1113 me + 0.0004( + 26.0377 Cores − Ni − V )
molecular cracking
A21 + A61 + A41 0.3917 ΔS = 0.0015Cores0.0019 − 0.1311 R Cores − Ni − V 0.2299 R − 0.0772 + 27.2086 Cores − Ni − V
(
(
)
)
ring opening ΔS A6 + A4 R = − 0.0369 − 0.0049 R Cores − Ni − V Cores − Ni − V |IH| − 0.0429 + 26.9285 Cores − Ni − V
( (
polycondensation
) )
(
0.0517
)
⎛ ⎞0.4873 ⎛ ⎞0.5015 A62 + A4 2 ΔS ⎟ = 0.0318⎜⎜A61 + A41⎟⎟ + 0.0303⎜ R ⎝ Cores2 − Ni2 − V2 ⎠ ⎝
⎠
⎛ ⎞0.1604 R2 ⎟ − 0.0052R10.1476 − 0.005⎜ + 29.1078 ⎝ Cores2 − Ni2 − V2 ⎠ Diels−Alder
⎛ N62 + N4 2 ⎞0.3075 ΔS ⎟ = − 0.0399R10.2977 + 0.1195⎜ R ⎝ Cores2 − Ni2 − V2 ⎠ ⎛ ⎞0.2073 R2 ⎟ − 0.0668⎜ + 25.3282 ⎝ Cores2 − Ni2 − V2 ⎠
desulfurization ΔS N6 + N4 + N1 = − 0.0459 R Cores − Ni − V
0.7713
0.5766
ΔS N6 + N4 = − 0.0424 R Cores − Ni − V
0.7979
0.1291
( ) − 0.1307( Cores −RNi − V ) 0.008 me − 0.0016( + 25.8764 ) Cores − Ni − V
decarboxylation
( ) − 0.0031( CoresR−−Ni1 − V ) 0.0011 br + me − 0.0009( + 25.7382 Cores − Ni − V )
4.2. Routinization of the Reaction Process. Only the batch process could be disposed with the SOL method; therefore, it was necessary to assume that the delayed coking process was composed
of many short batch processes. At the same time, an imaginary coking drum was needed. This coking drum was an operating unit that had two valves (for the inlet and outlet, respectively). 1720
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Figure 4. Residual error distributions of extrapolated prediction.
4.3. Product Division. The main products of delayed coking were gas, gasoline, diesel, wax oil, and coke; the results of the SOL model gave the molecular composition of the products. To compare the simulated results and experimental results efficiently, it is necessary to separate the molecules. The molecular carbon number, the boiling point, the carbon content, and the carbon residue value were the main factors that were used to separate the products. The molecules whose carbon numbers were
