ARTICLE pubs.acs.org/IECR
Kinetic Modeling of Coal Swelling in Solvent Lei Chen,†,‡ Jianli Yang,*,† and Muxin Liu†,‡ † ‡
State Key Laboratory of Coal Conversion, Institute of Coal Chemistry, Chinese Academy of Sciences, Taiyuan 030001 Graduate University of Chinese Academy of Sciences, Beijing 100039, PR China ABSTRACT: To better understand the coal swelling kinetics in solvent, a kinetic model based on a pseudopolymolecular reaction is proposed to model the swelling data up to the quasi-equilibrium stage. The swelling isotherms of a Chinese sub-bituminous coal, named Coal-1, in carbon disulfide (CS2), N-methyl-2-pyrrolidinone (NMP), and CS2/NMP mixtures with the different volumetric mixing ratios at various temperatures were obtained by a so-called linear variable differential transformer (LVDT) deformation transducer, continually. The corresponding kinetic parameters, including the rate constants, order of the pseudopolymolecular reaction, apparent activation energy, and pre-exponential factor, were obtained with the coefficients of determination, R2, range between 0.851 and 0.999. The kinetic parameters obtained with obvious meanings which are useful for better understanding the mechanism of the coal swelling in solvent as well as the structure of coal. The apparent activation energy for Coal-1 swelling in CS2 is 8.9 kJ/mol, which corresponds to the dissociation energy barrier of van der Waals forces. It is less than that for Coal-1 swelling in NMP, 40.9 kJ/mol, which corresponds to the dissociation energy barrier of hydrogen bonds. It implies that the dissociation of the noncovalent bonds in coal is crucially important during coal swelling in solvent. The CS2 in the test system appeared as “catalyst”, accelerating the swelling rate by lowering the energy barrier.
1. INTRODUCTION Coal is an important energy resource with immense reserves in many parts of the world. As one of the clean coal technologies, solvent pretreatment of coal to alter coal properties and to produce low-ash/ash-free fuels and high value materials has been attracting attention in the past and present.1-4 Chemically, coal can be described as polyaromatic hydrocarbons with a macromolecular network structure in which some of the hetero atoms (such as O, S and N), inorganic components (such as pyrite and silicon aluminates), and small free molecules are dispersed. When coal is treated with solvents, especially organic solvents, it may swell and some portion of it may be dissolved. Consequently, the properties of coal may be altered. The swelling of coal can be used to increase its combustion rate due to the increase of surface area.5 Solvent extraction processes (such as HyperCoal) were developed to produce low ash content hydrocarbons that may be used as clean fuel or directly inject into turbines.4 However, the swelling of coal in solvent may cause serious problems. During the direct coal liquefaction process, coal is mixed with the recycle solvent to form slurry first and then preheated to the desired temperature before being fed into the reactor. The swelling of coal may be accompanied with the increase of temperature, which may cause a sharp increase in the slurry viscosity and result in the fluid and heat transfer difficulties. Understanding the swelling behavior of coal under slurry preparation conditions is desired and crucially important to prevent the pipeline plugging and temperature runaway. Solvent swelling has been used to study the mechanisms of the interaction of solvent with coal and to investigate the macromolecular network structure of coal, extensively. For these purposes, the continuous measure of the coal swelling in situ is essential but has not been well developed. r 2010 American Chemical Society
There are several methods to measure the coal swelling in solvent discontinuously. The pack-bed method is the most commonly used approach.6-8 In this method, the coal bed is packed by centrifugation. The change of the coal bed’s height is measured manually. The measure of the changes of particle size distribution by laser diffraction is another method being developed to measure the coal swelling.9,10 However, there is a major problem involved, although the size of the coal particles can be measured directly. The measurement only can be operated in certain solvents, such as water and ethanol. The coal particles usually have to be removed from the original swelling solvent and put into a measuring solvent for analysis. The difference caused by changing the solvent is assumed to be negligible although it is not the case in most of the situations. A method by microscopy coupled with an image analyzer is developed to study solvent swelling continually and observe the structural changes of the coal particles during solvent imbibition and removal.11,12 To obtain reasonable statistical results, however, analyzing the images is time-consuming. The drawback of the coal swelling measurement is one of the problems to halt the development on the theory related to the coal swelling. Carbon disulfide (CS2), N-methyl-2-pyrrolidinone (NMP), and their mixture (CS2/NMP) are commonly used solvents for extracting and swelling of coal to study the mechanisms of coal and solvent interactions and the coal structure. The CS2/NMP mixture appears with high extraction ability to coals. The role of
Special Issue: IMCCRE 2010 Received: March 15, 2010 Accepted: August 25, 2010 Revised: August 16, 2010 Published: November 5, 2010 2562
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Table 1. Proximate and Ultimate Analyses of Coal-1 Proximate analysis, wt %
Ultimate analysis, daf wt %
Mas
Ad
Vdaf
C
H
O*
N
S
0.68
6.62
32.68
77.51
4.75
16.78
0.76
0.20
M: moisture; A: ash; V: volatile; as: as received; d: dry; daf: dry-ash-free; *: By difference.
CS2 is believed to reduce the viscosity of NMP and help the larger partner (NMP) enter the molecular structure of coal and break the stronger bond.13-15 It is interesting that a strong interaction between CS2 and NMP and the highest extraction ability were reported for a CS2/NMP mixed solvent with 1:1 volumetric ratio.16 A detailed study is desired to verify and understand the mechanisms. In this study, a method for continuous measure of the coal swelling in solvent was developed. The swelling isotherms can be obtained through a so-called linear variable differential transformer (LVDT) deformation transducer. The method gives a continuous measurement of the deformation of the coal bed versus time with a resolution of 0.2 μm, which allows studying the kinetics of the coal swelling with lower swelling ratios. As an example, the swelling behaviors of a Chinese sub-bituminous coal in CS2, NMP, and a CS2/NMP mixture were investigated. A pseudopolymolecular reaction was proposed to modeling the kinetics of the coal swelling in solvents. A mathematical model was developed to fit the observed swelling data up to a quasiequilibrium stage.
Figure 1. Schematic view of the apparatus for coal swelling measurement.
screen for positioning the tip of the LVDT. The whole sample cell was placed into the thermostat. The test sample in the sample cell and the designated solvent were preconditioned in the thermostat. At the designated temperature, about 3 mL of the preconditioned solvent was injected into the sample cell through the injection port. The change of the coal bed height with time was monitored by the LVDT and recorded by a computer. Swelling ratio Qt is used to characterize the deformation of the coal bed and is defined as Qt ¼ ht =h0
ð1Þ
where ht and h0 are the height of the coal bed at time t and time zero (at which the notable swelling is about to start).
2. EXPERIMENTAL SECTION 2.1. Coal and Solvents. A Chinese sub-bituminous coal, named
Coal-1, was used in this study. It was grinded, sieved, and dried in a vacuum oven at 110 C overnight under N2 and stored in a desiccator. Depending on the property of coal and requirement of the measurement, the specified coal particle size may be selected to balance the solvent diffusion rates in both the coal particles and the coal bed and to maintain the constant coal bed density, since a packed coal bed was used for measuring the deformation of the coal particles (see Apparatus and Procedure).17 The particle size fraction of 250-350 μm (60-40 mesh) was selected based on the above principle. The properties of Coal-1 were listed in Table 1. Commercially available solvents carbon disulfide (CS2) and N-methyl-2-pyrrolidinone (NMP) were used without further purification. 2.2. Apparatus and Procedure. A schematic view of the apparatus used for solvent swelling experiments was shown in Figure 1. It consists of a stainless steel sample cell (Φ17 mm 80 mm) with a solvent injection port on the top, thermostat with a precision of (0.5 C to control the experimental temperature, a linear variable differential transformer (LVDT) deformation transducer with a resolution of 0.2 μm to monitor the deformation of the coal bed, and an A/D converter connected with a computer to record the signals from the LVDT. About 0.6 g of coal was placed in the sample cell, which led to a coal bed with about 4 mm in height. The less amount of the sample was used to limit the diffusion effect of the solvent through the coal bed. The coal bed was packed and leveled off by gently shaking the sample cell. A stainless steel screen of 74 μm (200 mesh) was placed on the top of the coal bed as a solvent distributor. A stainless steel disk was placed on the top of the
3. RESULTS AND DISCUSSION 3.1. Swelling Isotherms of Coal-1 in CS2, NMP, and CS2/ NMP. The swelling isotherms of Coal-1 in CS2, NMP, and CS2/
NMP with 1/1 volumetric ratio are presented in Figures 2-4. The lower temperatures were selected for CS2 and CS2/NMP cases to keep CS2 in the liquid phase. The swelling ratios at the quasi-equilibrium state are defined as the equilibrium swelling ratios, Qe, and are tabulated in Table 2. Under the test conditions, the swelling of Coal-1 in NMP is more significant than that in CS2. At the quasi-equilibrium state, the increase of the coal bed’s height is about 109% by NMP and about 13% by CS2. It is a common understanding that the coal swelling in solvent mainly involves weakening the intermolecular attraction related to noncovalent bond and relaxing the coal structure. The difference in the swelling ratios caused by the different solvents may be attributed to the difference in the influence on the intermolecular attractions. The swelling rate in NMP is slower than that in CS2. It is understandable that NMP may diffuse into the coal particles with less diffusion rate than CS2 does if the difference of the viscosity and molecular size of the two solvents is compared. The extent of the swelling, however, should mainly depend on the activity of the solvent to the noncovalent bond in coal. Nevertheless, it takes more time to reach the equilibrium in NMP than in CS2. Generally, the swelling rates decreases with the increase of time and increases with the increase of temperature, which can be see clearly from Figures 2b, 3b, and 4b. Figure 5 compares the swelling isotherms of Coal-1 in CS2/ NMP with different mixing ratios and two pure solvents at 35 C. The corresponding equilibrium swelling ratios are also 2563
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Figure 2. Swelling isotherms of Coal-1 in CS2: (a) 0-1440 min; (b) 0-10 min.
Figure 3. Swelling isotherms of Coal-1 in NMP: (a) 0-1440 min; (b) 0-60 min.
Figure 4. Swelling isotherms of Coal-1 in CS2/NMP (1:1 by volume): (a) 0-1440 min; (b) 0-60 min.
listed in Table 2. In comparison of the results obtained from the mixed solvents with that from pure NMP, it seems that by addition of CS2 in NMP the swelling rate is significantly increased. The swelling rate of coal in the mixed solvent may be higher than that in CS2 when the proper mixing ratio is used. 3.2. Kinetic Analysis. The swelling kinetics of coal in solvents was studied by many researchers.12,18-21 eq 2 is the simplified kinetic model mostly used. It was adopted from a simplified kinetic model, eq 3, through the relationship expressed as eq 4. eq 3 is originally developed for studying the rubber swelling
in solvents, in which the solvent diffusion should be mainly considered. ðQt - 1Þ=ðQe - 1Þ ¼ kt n
ð2Þ
Mt =Me ¼ kt n
ð3Þ
Mt =Me ¼ ðQt - 1Þ=ðQe - 1Þ
ð4Þ
where Qt and Qe denote the swelling ratios at time t and quasiequilibrium, Mt and Me denote the amounts of solvent imbibed in 2564
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sample at time t and quasi-equilibrium, and k and n are constants. k is used to describe the swelling rate, and n is named as diffusion exponent and is used to describe the nature of the diffusion process. Although the model can fit the first 30-60% of the swelling isotherms and classify the swelling process into detailed diffusion categories, the swelling mechanism cannot be clearly described. In fact, the transport mechanism of solvent in the main body of coal should be different with that in the main body of rubber. The porous nature and small particle size should assist the solvent diffusing into the coal particle and reaching the coal molecules. Possibly, the diffusion effect of solvent in the main body level is diminished to some extent, depending on the physical chemistry properties of coal and solvent. In the molecular level, however, it may be similar to rubber in that the main structure of coal consists of macromolecules or supermolecules that appear as associated structure and are bound together by the intermolecular attraction through a noncovalent bond. The intermolecular attraction refers to attractions between molecules and is described by terms of hydrogen bonds, ionic bonds, hydrophobic attractions, and intermolecular forces (those are usually referred as van der Waals forces and consist of dipole-dipole attraction and London forces.). Hydrogen bond is a stronger noncovalent bond due to its polar nature. Theoretically, the relaxation of the coal structure has to be based on the dissociation of the associated macromolecules. As the matter of fact, the dissociation of the noncovalent bonds in coal is crucially important during coal swelling in solvent. It may not be Table 2. Swelling Ratios at Quasi-Equilibrium State, Qe Qe CS2/NMP (V/V)
a
temp. (C)
CS2
NMP
10
1.09
25
1/1
3/1
1/3
--a
--
--
--
--
--
2.06
--
--
30
1.12
--
2.10
--
--
35
1.15
2.09
2.07
1.83
2.00
40 50
1.17 --
2.08 2.05
2.13 --
---
---
60
--
2.11
--
--
--
70
--
2.10
--
--
--
appreciated if one considers the coal swelling in solvent mainly as a solvent diffusion problem although the solvent diffusion may occur inside the coal macromolecules. Furthermore, not all diffusion occurring in the coal molecules can cause swelling. It is known that helium can diffuse easily in the coal molecules, but no detectable swelling can be observed. Therefore, a proper kinetic model is desired for better understanding the coal swelling mechanism in solvent. The overall process of the coal swelling in solvent is extremely complex. It cannot be described by an individual process or chemical reaction. To establish a simple kinetic model for coal swelling in solvent, a pseudopolymolecular reaction or pseudoelementary reaction is proposed as follows
In this pseudoreaction scheme R[A--B] denotes a kind of macromolecule structure of coal hold by R specified noncovalent bond, A and B denote the unit macromolecules. Solvent, S, is absorbed by the macromolecule structure of coal, dissociates R noncovalent bonds and forms dissociated macromolecule, [A S B]. Then the dissociated macromolecule undergoes relaxation and forms the enlarged coal structure, [A S B]. In addition, the following assumptions are made. (1) The dissociation of the noncovalent bonds in coal is crucially important during coal swelling in solvent. (2) The concentration of the specified noncovalent bond that can be dissociated by the specified solvent, C[A--B], can be considered as the “reactant” concentration. Similar to that described in the molecular collision theory, to drive the original form [A--B] to the swollen form [A S B] not only “one” [A--B] bond is required to dissociate but “R” [A--B] bond. (3) The normalized difference of the swelling ratios at equilibrium and time t, (Qe - Qt)/(Qe - Q0), is related to and can be used to reflect C[A--B]. By adopting the law of the mass action for the elementary reaction, the rate equation for coal swelling in solvent can be defined as ð6Þ dC½A--B =dt ¼ - k1 CR½A--B or d½ðQe - Qt Þ=ðQe - Q0 Þ=dt ¼ - k2 ½ðQe - Qt Þ=ðQe - Q0 ÞR ð7Þ
--: not determined.
Figure 5. Swelling isotherms of Coal-1 in CS2/NMP mixed solvents at 35 C along with the corresponding swelling isotherms in pure solvent for comparison: (a) 0-2880 min; (b) 0-30 min. 2565
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where k1 and k2 are the rate constants and depend on the characteristic of solvent, temperature and the characteristics of other processes, which are considered as the minor processes during the coal swelling and not included in the proposed mechanism. The rest of the symbols are the same as defined previously. Power R represents the amount of specified noncovalent bonds dissociated to drive the pseudopolymolecular Table 3. Parameters Obtained from Modeling of Swelling Isotherms and Associated R2 solvent
temp. (C)
R
k2 100
reaction (eq 5). It relates to the properties of solvent and coal as well as the experimental conditions, such as temperature, in some extent. The boundary conditions are Qt ¼ 1
at
t ¼ 0
ð8Þ
Qt ¼ Qe
at
t ¼ ¥
ð9Þ
Integration of eq 7 yields ½ðQe - Qt Þ=ðQe - Q0 Þ1 - R
R2
¼ ðR - 1Þk2 t þ 1
CS2 10 30
2.42 2.26
33.2 40.7
0.990 0.996
35
2.40
40.4
0.995
40
2.34
45.8
0.998
35
1.44
0.7
0.996
40
1.23
0.9
0.999
50
1.38
2.1
0.999
60 70
1.21 1.00
2.5 2.7
0.999 0.999
25
2.08
4.3
0.996
30
2.60
5.7
0.991
35
2.16
6.4
0.997
40
2.02
7.6
0.996
35
2.98
12.0
0.973
35
1.40
6.5
0.998
NMP
CS2/NMP (1:1)
CS2/NMP (3:1) CS2/NMP (1:3)
for
ðQe - Qt Þ=ðQe - Q0 Þ ¼ expð - k2 tÞ
R>1 for
ð10Þ
R ¼ 1 ð11Þ
In order to maintain the validation of eq 9, R < 1 is excluded. Both integrated and differential models derived above can be used in regression of the observed data to obtain the parameters of R and k2. In this study, the differential model of equation 7 was used in modeling. The program of lsqnonlin in Matlab was used for nonlinear regression by adjusting R and k2 simultaneously to minimize the residual sum of squares (RSS). The modeling results for each isotherm are listed in Table 3 and plotted in Figure 6. The coefficient of determination, R2, is used as a measure of goodness-of-fit of the regression. The associated R2 values are also listed in Table 3. The reasonable high R2 values indicate the good fitting of the observed data to the model proposed. It can be noticed that the value of R varies with solvents and temperatures. It reflects the slight difference in the swelling mechanisms. It should be mentioned that the influence of the solvent diffusion may not be negligible in some cases, which many also cause the variation of the R value. Nevertheless, the R value is higher for the CS2 case than that for NMP case. The
Figure 6. Comparisons of the swelling isotherms (dotted line) and the modeling results (solid line). 2566
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Table 4. Recalculated k2 According to Assumed Constant R Values (Average Value of Similar R) and Associated R2 solvent
temp. (C)
R
k2 100
R2
Table 5. Calculated Apparent Activation Energies, Ea, and Pre-Exponential Factor, A, for Coal-1 Swelling in CS2, NMP, and CS2/NMP with 1/1 Volumetric Mixing Ratio solvent
CS2
temp. (C)
R2
0.987 0.996
14.0
10-40
0.851
NMP
40.9
6.2 104
35-70
0.933
35
38.9
0.995
CS2/NMP (1/1)
30.4
1.4 104
25-40
0.984
40
46.0
0.998
0.6
0.996
40
0.9
0.999
50
2.0
0.999
60 70
2.6 3.1
0.999 0.997
2.35
NMP 35
1.32
CS2/NMP (1:1) 25
6.4
0.996
30
2.22
8.1
0.986
35
10.0
0.997
40
11.4
0.995
Figure 7. Arrhenius plot for determining apparent activation energy Ea.
R value for the mixture cases increases as the CS2 concentration increases. The rate constant, k2, of the pseudoreaction can be related to the apparent activation energy, Ea, and pre-exponential factor, A, by the Arrhenius expression k2 ¼ A expð - Ea =RTÞ
ð12Þ
An attempt was made to obtain the apparent activation energies and pre-exponential factors for Coal-1 swelling in CS2, NMP, and CS2/NMP mixture with 1/1 volumetric ratio under the conditions with the similar R values. A new set of k2 values were calculated according to the assumed constant R values (the average value of the similar R) and listed in Table 4 along with the associated R2. The corresponding Arrhenius plots are given in Figure 7. The calculated apparent activation energies and pre-exponential factors are listed in Table 5 along with the associated R2. It is generally believed that hydrogen bond strengths in coal vary from 20 to 70 kJ/mol,12,19-21 and van der Waals forces in
8.9
A
30.9 43.1
10 30
CS2
Ea (kJ/mol)
coal are lower by 1 order of magnitude than that. The calculated apparent activation energy of Coal-1 swelling in CS2 is 8.9 kJ/ mol (10-40 C) and that in NMP is 40.9 kJ/mol (35-70 C), which suggests that the main energy barrier of Coal-1 swelling in CS2 mainly is the dissociation of van der Waals forces and that in NMP mainly is the dissociation of hydrogen bonds. Indeed, NMP is a hydrogen-bond accepting solvent. It is likely that the swelling by specific solvents involves the disruptions of specific intermolecular attractions such as van der Waals forces and hydrogen bonds. The calculated apparent activation energy for swelling of Coal1 in CS2/NMP (1:1 by volume) mixture is 30.4 kJ/mol (25-40 C), that is lower than that in NMP and higher than that in CS2. Considering the fact that the equilibrium swelling ratio of Coal-1 in this mixture (2.09 in average) is close to that in pure NMP (2.08 in average), it seems that CS2 functions as a “catalyst” and accelerates the coal swelling process without altering the “product” (equilibrium swelling ratio) by lowering the energy barrier, at least for this case. It is an interesting finding and may agree or disagree with the findings published. There is some confusion related to coal swelling in the CS2/NMP system although the role of CS2 has been studied and several mechanisms have been proposed. The detailed study is on the way in our laboratory. It is understandable that the pre-exponential factor is considerably lower for Coal-1 swelling in CS2 than that in NMP or mixed solvent. According to the interpretation of the Arrhenius expression, [which states that, in eq 12, k2 is the number of collisions that result in a reaction per second, A is the total number of collisions (leading to a reaction or not) per second, and exp(-Ea/RT) is the probability that any given collision will result in a reaction], the higher k2 and Ea should be accompanied by the lower A and vice versa. It may imply that the proposed mechanism and model are reasonable.
4. CONCLUSIONS It is advantageous to use a linear variable differential transformer (LVDT) deformation transducer for obtaining the swelling isotherm of coal in solvent. On the basis of the concept that the disruption of the noncovalent bonds in the macromolecule structure of coal is crucially important during the coal swelling in solvent, the coal swelling process can be assumed as a pseudopolymolecular or pseudoelementary reaction. The concentration of the specified noncovalent bond that can be dissociated by the specified solvent, C[A--B], is considered as the “reactant” concentration. The normalized difference of the swelling ratios at equilibrium and time t, (Qe - Qt)/(Qe - Q0), is used to reflect C[A--B]. A power kinetic model related to (Qe - Qt)/(Qe - Q0) is proposed to describe the coal swelling process. The program of lsqnonlin in Matlab is used for regressions of the swelling isotherms. Arrhenius expression is used to correlate the relationship of the apparent activation energy and the swelling rate at the different temperature. The rate constants and the apparent activation energies are 2567
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Industrial & Engineering Chemistry Research obtained with the coefficients of determination, R2, range in 0.851-0.984. The calculated apparent activation energies for Coal-1 swelling in CS2, NMP, and CS2/NMP (1/1) mixture are 8.9 (10-40 C), 40.9 (35-70 C) and 30.4 (25-40 C) kJ/mol, respectively, which represent the energy barriers that can be overcome and specified associated macromolecules that can be dissociated by the specified solvents. It suggests that the main energy barrier of Coal-1 swelling in CS2 is the dissociation of van der Waals forces and that in NMP is the dissociation of hydrogen bonds. The apparent activation energy of Coal-1 swelling in CS2/ NMP (1/1) mixture is lower than that in NMP and the swelling rate in CS2/NMP (1/1) mixture is higher than that in NMP. The swelling induced by CS2 for Coal-1 is less significant and much less than that by NMP or CS2/NMP mixtures. The swelling ratio of Coal-1 in CS2/NMP (1/1) mixture at equilibrium (2.09 in average) is close to that in NMP (2.08 in average). It seems that CS2 is functions as a “catalyst” and accelerates the coal swelling process by lowering the energy barrier. A detailed study is necessary.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. Tel: þ86-351-404-8571.
’ ACKNOWLEDGMENT The authors gratefully acknowledge the financial support from Synfuels China Co., Ltd, the National Basic Research Program of China (2010CB227003), and State Key Laboratory of Coal Conversion research projects (09BWLD1941, 09-904). Prof. Yongwang Li, Dr. Yong Xiao, Mr. Zenghou Liu, Prof. Bijiang Zhang, Dr. Yong Yang, Dr. Baoshan Wu, Ms. Yunmei Li, and Ms. Fengshuang Han of Institute of Coal Chemistry, Chinese Academy of Sciences, are acknowledged for their valuable suggestions and help with experiments. Prof. Zhenyu Liu of Beijing University of Chemical Technology and Dr. Hong Cui of University of Hawaii are acknowledged for their valuable suggestions and comments.
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