Three-Dimensional Molecules to Two-Dimensional Lattices

Apr 18, 2013 - The Applied Research Laboratory, The Pennsylvania State University, ... University of Delaware, Newark, Delaware 19716, United States...
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Novel Simplification Approach for Large-Scale Structural Models of Coal: Three-Dimensional Molecules to Two-Dimensional Lattices. Part 3: Reactive Lattice Simulations Yesica E. Alvarez,† Brian M. Moreno,‡ Michael T. Klein,‡ Justin K. Watson,§ Fidel Castro-Marcano,† and Jonathan P. Mathews*,† †

John and Willie Leone Family Department of Energy and Mineral Engineering and the Earth and Mineral Sciences (EMS) Energy Institute, and §The Applied Research Laboratory, The Pennsylvania State University, University Park, Pennsylvania 16802, United States ‡ Department of Chemical and Biomolecular Engineering, University of Delaware, Newark, Delaware 19716, United States ABSTRACT: Various studies have used lattice structures combined with simplistic kinetics to explore the devolatilization of coal with the goal of predicting yields of gas, tar, and char. In our previous work, we have demonstrated the ability to reduce a three-dimensional (3D) large-scale (>50 000 atoms) atomistic representation of Illinois no. 6 bituminous coal to a coal-specific two-dimensional (2D) lattice with cross-links being depicted as linkage lines and aromatic clusters being depicted as nodes. Because there is a direct link between the full complexity of the atomistic representation and the 2D lattice, the cross-links within the coal topography can be identified. Using this structural information, a statistical simulation of the kinetically controlled liquefaction reactions of an Illinois no. 6 coal lattice was performed. The Illinois no. 6 coal lattice was composed of a distribution of singular nodes, dimers, and multi-linkage molecules that ranged from 3 nodes (or clusters) to a 16-node entity. Probabilities for the cleavage of coal interunit links were calculated on the basis of the mixture of 10 model compounds comprised of two benzene rings connected by a cross-link (e.g., diphenyl sulfide, benzyl phenyl ether, diphenyl ether, etc.) equivalent to those found in the Illinois no. 6 model. The mixture of model compounds was based on the concentrations of cross-links representative of the model (and, thus, the coal analysis). Cross-link-specific kinetic parameters (Arrhenius preexponential factor and activation energy) for each pyrolysis reaction were obtained from literature sources or tuned from composition data using the Kinetic Modeling Editor, a software tool used to generate and solve the balance equations in a kinetic model. At a heating rate of 5 °C/min, thermolysis calculations from 360 to 490 °C showed that the 2D lattice structure broke down extensively, generating mainly monomer cluster molecules. At 400 °C with residence times of 600 and 1600 s, the number of cross-links between aromatic units was reduced by 40 and 60%, respectively, from the original population. At higher temperatures, the breakdown of the weaker and more kinetically favored cross-links (−CH2S− and −OCH2−) occurred rapidly at the earlier stages of heating. The absolute probability of cleavage (Pi) of certain cross-links (−CH2CH2−, −CH2OCH2−, etc.) increased at longer residence times. Cross-links such as phenyl and doubly aromatic bound (−S− and −O−) remained essentially unreactive at the conditions explored.

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INTRODUCTION

and manipulating kinetic data for more realistic coal representations has been difficult and cost-prohibitive because of the structural complexity of the coal models and the cost associated with identifying, organizing, and manipulating large kinetic data sets. Ideal lattice models (such as chains and Bethe lattices) have been used to represent the macromolecular structure of coal and to describe thermal network decomposition through inexpensive statistical approaches.1−4 Solomon et al. developed the functional group depolymerization vaporization cross-linking devolatilization model (FG/DVC) that is based on a simplified representation of the coal structure comprised of a twodimensional (2D) network of linear oligomers of N clusters linked by labile and non-labile bridges. In their approach, Monte Carlo and statistical methods are used to simulate random

The complexity and variability of the structure of coal continue to challenge the understanding of the mechanisms that govern the most important reactions of coal: pyrolysis, combustion, liquefaction, and carbonization. As a result, the study of coal reactivity through molecular models or simplified lattice structures has been a historic (and recent) approach to provide a fundamental view into the behavior of coal. Bethe and other generic lattice arrangements have been used for the statistical representation of bond cleavage events to simulate coal pyrolysis and liquefaction.1−4 While this mathematical modeling has enabled tools that impressively allow for the prediction of yields, the kinetic data and the lattice representing the coal structure are highly simplistic. The use of lattices in thermolysis studies would have greater utility if these simplified representations could capture the key structural and chemical parameters (Arrhenius pre-exponential factors and activation energies) that drive the kinetics and science of the network breakup for each individual cross-link type within the coal network. Until now, identifying © XXXX American Chemical Society

Received: January 20, 2013 Revised: April 17, 2013

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cross-linking in the coal network. Only limited work with variable coordination numbers has been performed.4 Many of the chemical and structural differences between coal ranks, such as chemical functionalities, molecular weight distribution, heterogeneous cross-linking between clusters, composition of clusters and cross-links, etc., some of which play important roles in the kinetics of pyrolysis and devolatization, are rarely captured by these general lattices. Hence, there are improvement opportunities for these lattices to better represent the intricate structure of coal, which would ultimately provide a pathway for exploring the reactive behavior of coal and similar carbonaceous systems, such as biomass, with a more fundamental approach. The challenge then lies in the capturing of the molecular structure of coal and the application of the kinetic parameters to coal-derived lattice representations. Capturing the complexity, chemical diversity, and molecular weight distribution of coal requires large-scale representations. While the construction of large-scale representations is timeconsuming and requires considerable expertise, improvements have been made toward the speed and accuracy of their construction methods.16−18 Visualizing the structural information and using these structures of scale, however, remains challenging. Earlier papers in this series demonstrated the effectiveness of reducing the complexity of these large-scale atomistic representations by identifying rings and cross-links and portraying them in a 2D lattice arrangement.19 The visualization of the chemical data for the atomistic structure was demonstrated with coloring of the nodes (to communicate the size of chemical structures, such as benzene and conjugated polyaromatic rings) and linkage lines (representing crosslinks) in the 2D lattice.20 Thus, the lattice is specific to the atomistic representation of the coal (capturing rank, compositional, and possibly maceral influences). The ability to simplify large-scale molecular representations is enabled through the Col2D and Molecwalk approach, capable of generating equivalent three-dimensional (3D) coarse-grained and 2D lattice molecular models from the original atomic structure.19 The methodology applies pattern recognition of hydroaromatic/ aromatic (and heteroatom-containing) clusters and cross-links to identify unique moieties that are reduced into nodes and linkage lines, as shown for the simplification of the Illinois no. 6 bituminous coal structure18 (Figure 1). The approach was tested

bond-breaking (along with hydrogen capping) and bondforming reactions by applying pre-determined first-order kinetic rules and rates.3,4 The simulations were performed on various coals showing sensitivity to starting configuration (functional group contribution) but were otherwise insensitive to rank.5,6 Niksa and Kerstein used a linear chain representation (a lattice with a coordination number of two) within their distributed energy chain model (DISCHAIN) to evaluate four chemical reactions: bridge breaking, peripheral group elimination, tar formation, and char formation.7 Later work included Bethe lattice structures.2 A subsequent model of this group, FLASHCHAIN, improved upon DISCHAIN by including a flash distillation approach for tar/metaplast distribution, although it returned to the simplistic lattice chain configuration.8 The use of ultimate analysis, carbon and proton aromaticity values, pyridine extract yield, and average aromatic cluster size enabled yield predictions for a variety of conditions and coals.9,10 Ultimately, predictions could be made with the elemental analysis alone without the incorporation of structural characteristics in the calculations.11 Grant et al. developed the chemical percolation devolatilization (CPD) model to explore the generation of tar precursors through the breakup of Bethe pseudo-lattices (tree structures) that included nuclear magnetic resonance (NMR) data in the starting configuration of clusters.1 This statistical model achieved a lower simulation time by incorporating a lattice of constant coordination number.1 A single Arrhenius pre-exponential factor for the bridge breaking and gas stripping were used with a distributed activation energy function,4,7 ignoring mass transport issues. Good agreement with tar, char, and gas yields were obtained for Illinois no. 6, Beulah-Zap, and Rosebud coals from the experimental work by Serio et al.12 Fletcher et al. expanded upon this work to distinguish escaping tar and metaplast formation.13 Previous studies have focused on pyrolysis; however, direct liquefaction can also be evaluated, because there are similarities between the early stages of pyrolysis and liquefaction.14,15 The mostly generic lattices used in these studies were limited in their inclusion of chemical data.1,3,4,7 Typical lattices in these studies are characterized by a homogeneous connectedness among all aromatic units (through a constant coordination number), a lack of chemical differentiation between cross-links, and the coarse lumping of all aromatic units as a single species, thus compromising the representativeness of aromaticity and

Figure 1. Simplification for an Illinois no. 6 bituminous coal large-scale structural model performed by Col2D and Molecwalk: (a) original atomic model, (b) 3D skeletal structure or clusters and cross-links, and (c) 2D lattice model. B

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a temperature range of 360−490 °C. The ultimate purpose is to demonstrate the applicability of complex large-scale coal molecular models for reaction studies and maintain a low computational cost while using the molecular complexity. The kinetic simulation consists of random sampling of cross-links based on their kinetically derived cleavage probabilities. It is expected that the lattice visualization of the structural transformation will ultimately enable the exploration of functional-based decomposition and allow for pre-screening of experimental conditions for a wide range of applications from maturation to pyrolysis.

in various available large-scale models,19 and a reduction of scale to 3−5% of the original number of atoms was achieved without the loss of the original atomic/structural information. While the 2D lattice view is simplistic, the coarse-graining process is able to collect and retain all of the structural and chemical information (atoms, connectivity, atomic location, molecular weight, etc.) of the reduced units, clusters, and cross-links, making each reduced model (3D coarse-grained and 2D lattice model) equivalent to its original structure and facilitating their manipulation for visualization20 and simulation. The constraints considered during the construction of this model included a molecular weight distribution (ranging from 100 to 2850 Da).18 The range was determined from laser desorption ionization mass spectroscopy. There is a sharp peak at ∼230−400 Da, consistent with other approaches. It was also expected that, for this rank coal, some of the structure would be soluble in a good solvent. Using the Painter et al.21 approach, the solubility can be estimated for each molecule with dissolution occurring when solvent and solute have similar solubility parameters. The predicted solubility value of 22% by mass is somewhat lower than the 28% reported for pyridine.22 Thus, a portion of the structure is extractable. A meaningful, lattice-based kinetics model of coal reactions requires the kinetics (or breakage probabilities) of cross-links to be known. Improvements in computational approaches have yielded the Kinetic Modeling Toolkit and associated Kinetic Modeling Editor (KME).23 This end-to-end solution allows for the generation of reaction balance equations, kinetic rate estimation, and numerical solution of the complete kinetic model that have proven useful for analyzing pyrolysis kinetics in macromolecular structures of limited chemical diversity, such as lignin. The connection between the complexity of the full-scale atomistic representation and the 2D lattice view enables the measurable chemical information to provide the starting configuration (type and frequency) of the cross-links for latticebased kinetic studies. Individual Arrhenius pre-exponential factors and activation energies used in these studies are dependent upon the cross-link type. Here, the approach is demonstrated by coupling the 2D lattice and cross-link-dependent kinetics to simulate liquefaction for a coal-specific (Illinois no. 6 bituminous coal) 2D lattice model derived from a complex ∼50 000 atom large-scale molecular structure.18 The statistical simulation portrays an ideal, limiting-case description of the kinetically controlled cleavage of cross-links across the network during liquefaction over

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METHODOLOGY

The present idealized reaction scenario involves bond cleavage reactions in an ideal hydrogen donor to provide for any hydrogen deficiency in the cleavage stoichiometry. To illustrate the applicability of coal-specific lattices to kinetically limited thermolysis simulations, a statistical calculation of the thermal breakup of the network structure was undertaken. Specifically, the statistical simulation is intended to portray covalent bond cleavage (of cross-links) during liquefaction over a temperature range of 360−490 °C at a slow heating rate (∼5 °C/s). The central idealization is that thermolysis is the sole mechanism responsible for cleavage with instantaneous hydrogen capping from a liquefaction solvent where the reaction kinetics probabilities of cleavage are dependent upon the cross-link type. The extent of thermolysis is thus directly bound to the coal structure, i.e., the distribution of the cross-link population as well as the time/temperature history captured for the network. Derivation of Equivalent Lattice Model from Complex 3D Structure. The simulation presented here consists of sampling crosslinks from the Illinois no. 6 lattice model (Figure 1c) and breaking those cross-links based on the cleavage probability of each cross-link type. This lattice version of the Illinois no. 6 model was derived through a simplification process of the original atomistic coal model with the tool Col2D,19 which enables the identification and classification of cross-links20 through scripting. The lattice model files generated from Col2D were scanned by Visual Basic scripts to identify each type of cross-link by their chemical group constitution. During the construction of the original 3D atomistic model for Illinois no. 6 coal,18 the model undergoes a structural optimization that assigns an atomic force field to each atom in its makeup. The Col2D simplification method identifies the chemical groups in each cross-link based on a force-field designation of atoms in the cross-link, achieved through scripted scanning of the 3D model files. A total of 8 general classifications were used to organize prominent chemical groups (methylene, ether, sulfur, etc.), and 10 further subcategories were selected once unique main groups of crosslinks were identified (Table 1). Some cross-links may be composed of

Table 1. Composition and Kinetic Parameters of Cross-Links in Illinois No. 6 Coal Model main group number 1 2 3 4 5 6

7 8

subcategories in model

1 2 3 4 5 6 7 8 9

10

cross-link (CL) type carboxyl plus carbonyl plus sulfur bridges ether bridges sulfur-plus bridges ether and methylene

methylene

composition (CO)−O−CH2 CH2−(CO)−CH2 S O CH2−S−CH2 CH2−S O−CH2 O−CH2−CH2 CH2−O−CH2 CH2 CH2−CH2 CH2−CH2−CH2 CH2−CH2−CH2−CH2

phenyl (covalent bond)

A0 (%)a

2.2 14.9 5.4 4.3 33.1 0.2 26.8 6.5 0.8

5.9

log[A (s−1)]

E* (kcal/gmol)

data sourceb

46.58 64.5 0 72.11 23.46 41.7 50.19 45 28.7 80.7 56.4 62.57 70.53 113

14.53 16.62 0 14.8 5.66 13.4 15.15 11.1 6.16 14.3 13.9 16.62 18.2 15

24 25 assumed 26 27 28 29 26 29 30 30 31 31 32

a

Cross-links types that are not present in the Illinois no. 6 structure (A0 = 0%) but could potentially be found in other types of coal were included for illustration of the chemical diversity in cross-links. bData were obtained or tuned from the reference indicated. C

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Figure 2. Fractional link cleavage versus time at various temperatures: (a) 360 °C, (b) 400 °C, and (c) 490 °C. a mix of functionalities; hence, their type is termed “plus” to indicate the possible presence of other groups. In most cases this “mix” is

composed of the principal group plus methylene groups, for example, −CH2−S−CH2− for “sulfur-plus” bridges. The cross-link population D

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and initial concentrations (A0) of each cross-link type in the Illinois no. 6 coal structure are shown along with the kinetic parameters used to develop the relative cleavage probabilities during the thermal breakdown. The Illinois no. 6 coal model is comprised of a molecular distribution that includes single-cluster molecules (single nodes, about 70% of all molecules), two-cluster molecules (dimers, about 8% of all molecules), and up to highly cross-linked molecules that range from 10 to 16 clusters in a single molecule. There are 10 generic cross-link types (subcategories in Table 1) within the model; within the mix, methylene ethers (−OCH2− and −CH2OCH2−) contribute 33 and 27%, respectively, ethers contribute 15%, and methylene and phenyl contributed 6% each. The majority of cross-links are a combination of ether and methylene groups. A Perl script was used to modify the lattice model to use a color scheme as a visual aid for each cross-link type. Statistical Kinetic-Based Simulation of Thermal Breakdown of Coal Lattice. Experimental data have suggested that rate constants for the release of tar and for the thermal decomposition of the various functional groups in coal pyrolysis, analogous to liquefaction chemistry, depend upon the nature of the bridging bond or the functional group.6 In our approach, the cleavage of a given cross-link connecting two clusters within the coal network is modeled kinetically as the decomposition of a representative aromatic molecule composed of two benzene rings (Ph) connected by the particular cross-link of interest. For example, the cleavage of an ether −OCH2CH2− cross-link is represented by the first-order, irreversible pyrolysis of phenethyl phenyl ether (Ph− OCH2CH2−Ph); because benzene rings (and most aromatic entities) are stabilized by resonance and, thus, more resistant to thermal cleavage, the decomposition of this representative molecule will come about basically thorough the cleavage of the cross-link. Thus, in our reactive simulation, we assume that the kinetic parameters characterizing the cleavage of these representative bicluster molecules will represent the thermolysis-driven breakdown of cross-links within the coal network. Kinetic parameters (Arrhenius pre-exponential factor and activation energy) for each pyrolysis reaction were obtained from various literature sources24−26,30,33−36 or tuned from composition data27,28,31,37 using KME.23 The chemical conversion of each linkage is calculated by KME at a given temperature via solution of the associated stoichiometric mass balances and kinetic differential equations. Cross-link cleavage probabilities were then calculated on the basis of a mixture of 10 model compounds comprised of cross-links equivalent to the Illinois no. 6 coal model and at initial compositions representative of the coal model. The reaction of this mixture of compounds was modeled for various residence times, and the concentration of each model compound was used to estimate the probability of cross-link cleavage, as follows. The relative probability of linkage breaking was modeled as the chemical conversion of that linkage (eqs 1−3). For a fast reaction, the rate constant k is large, resulting in a large conversion and relative probability.

Ai → Bi

(1)

⎡A ⎤ xi = 1 − ⎢ i ⎥ = 1 − exp[− kit ] ⎣ Ao ⎦

(2)

Pi = xi

(3)

Visualization of Statistical Thermal Breakdown in the Coal Lattice. To display simulation results in the lattice, each cross-link within a subcategory was assigned an index number, thus forming 10 pools (one for each population). A random number generator was used to sample cross-links by their index number selection from each pool according to the probabilities of cleavage of each cross-link. For example, for a particular time step of reaction (in seconds) and at a specific temperature within the studied reaction range of 360−490 °C, the population of each subcategory pool is reduced proportionally to their probability of cleavage, Pi. Thus, a number of cross-links from each pool are selected for cleavage based on the kinetically derived concentration, xi (T, t). The resulting “broken cross-links” within each pool, selected on the basis of the index sampler (random number generator) for the desired conditions of time and temperature, are recorded as a text output of the statistical calculation and sequentially exported in a table to Materials Studio 5.0 computational software, where a Perl script is used to delete linkages in the 2D lattice model according to the sampling results. The run time for this semi-automated statistical simulation, including required manual steps between Excel and Materials Studio 5.0, was ∼60 min on a standard desktop computer.

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RESULTS AND DISCUSSION The changes in the concentration of each cross-link with time at various temperatures are shown in Figure 2. In accordance with the calculated probabilities, the figure shows how the crosslinks with the highest probabilities decompose rapidly at the beginning of the reaction as opposed to other cross-links that may require longer residence times and/or higher temperatures to cleave (sulfur, phenyl, and ether). With the combination of longer residence times and higher temperatures, the largest cleavage of the cross-link population is achieved, even those of relatively “medium strength” (−CH2CH2− and −OCH2CH2−); however, there are cross-links that will remain intact beyond these conditions (sulfur, phenyl, and ether). Figure 3 shows the estimated conversion of cross-link populations in the Illinois no. 6 bituminous coal model at different liquefaction temperatures within the selected range (360−490 °C) for 1600 s into the reaction. It is apparent that some cross-links (−CH2S−, −OCH2−, etc.) will break rapidly at the earlier stages of heating (while the temperature is rising), as indicated by the quick decrease in the cleavage probabilities as the temp-

Figure 3. Cross-links absolute probability of cleavage versus temperature during the first 1600 s of reaction. E

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Figure 4. Simulation of thermal network decomposition in Illinois no. 6 coal lattice during liquefaction: (a) lattice at the initial state, (b) breakdown at 400 °C and 600 s, and (c) breakdown at 400 °C and 1600 s. Clusters are represented by gray nodes. Cross-links are colored by type.

(mainly monomer) fragments. In the first time step shown (600 s at 400 °C), 40% of the initial population of cross-links has been broken, whereas at later time steps (1600 s), the reduction of cross-link connections has reduced 60% from original conditions. This set of lattices was representative of thermal breakdown data in Figure 2b. Various factors are not considered in this initial approach, such as mass transfer effects that influence tar formation, effects of hydrogen pressure, type of solvent, solvent/coal ratio, or catalytic activity. The central assumption is that thermolysis is the sole mechanism responsible for cleavage; hence, cross-link cleavage through the radical hydrogen transfer mechanism38,39 was not included nor were retrogressive reactions (i.e., reactions leading to the formation of cross-links), which are expected to be uncommon under the conditions studied.40−42 Instantaneous hydrogen capping from a liquefaction solvent was assumed for the cleavage products. Cleavage of attachments to the clusters, which is relevant for gas formation, was also ignored. Similar liquefaction conditions were used by Baldwin et al.43 They found that, for Illinois no. 6 liquefaction (tubing bomb, 1000 psi hydrogen pressure), at 350 °C, the extraction yield increased from ∼16 to ∼38% from 5 to 30 min of residence time. At 425 °C, a higher yield of ∼63% increased to ∼86% as determined by solubility in tetrahydrofuran (THF). Our observations are qualitatively consistent with this experimental work. It is desirable to account for retrogressive reactions (cross-link formation reactions) in view of producing a more realistic simulation of these processes. Therefore, the possibility of bond formation, in addition to cleavage, is contemplated in future work through a series of “hidden layer models” (Figure 5), which enable the cross-linking of clusters across the lattice without disrupting the view. Because the original location of moieties

erature increases and as fewer cross-links remain. Analogously, the probability of cleavage of certain cross-links (−CH2CH2−, −CH2OCH2−, etc.) increases with higher temperatures, while selected one-to-zero-atom cross-links (phenyl, −S−, and −O−) are essentially unreactive at the temperature range and residence time evaluated or under the chemical mechanisms considered. Figure 3 shows that, as the reaction proceeds for primary thermolysis and the total number of linkages decreases, the probabilities of cleavage for each cross-link type reach equilibrium, such that, for particularly weak cross-links like −OCH2−, −CH2OCH2−, and −OCH2CH2− at long reaction times (1600 s) and high temperatures (490 °C), cleavage becomes highly probable, close to 100%. For strong cross-links, such as singular sulfur bridges, ether bridges, and phenyl, the probability of cleavage does not show an increase within this temperature and reaction time range, suggesting that higher temperatures, longer reaction times, or other chemical mechanisms, such as radical hydrogen transfer, could be necessary to achieve the decomposition of such connections. The consequences of these link cleavages can be visualized with the current capabilities of the Col2D−Molecwalk approach, whereby calculations of this nature can be displayed in a coalspecific lattice obtained from the original atomistic model. These lattice models may use color schemes to show lattice component properties (for example, cross-link types), as shown in Figure 4a. A set of sequential time steps during the thermal breakdown of the lattice at 400 °C is also shown in Figure 4. A total of 10 variations of cross-links are present in the original Illinois no. 6 molecular model, which lead to the resulting lattice classification. A first set of results showing the decomposition at 400 °C and 600 s of reaction time is observed in panels b and c of Figure 4, where the reduction of lattice connectivity produced smaller F

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While the simulation assumptions currently applied are relatively simplistic, the ultimate goal of this approach is to improve the applicability of complex coal molecular models for reaction studies, decreasing the computational cost associated with using the full molecular complexity by combining lattice-statistical calculations with experimentally derived large-scale atomistic models. This approach will ultimately better enable exploration of functional-based decomposition and allow pre-screening of experimental conditions for a wide range of applications from maturation to pyrolysis.

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AUTHOR INFORMATION

Corresponding Author

*Telephone: 814-235-7359. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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Figure 5. Example of “hidden” layer visualization of the lattice to simulate bond formation.

ACKNOWLEDGMENTS We thank Michael Merves and Amy Quach at the University of Delaware for assistance in performing kinetic calculations and Josep Pou for assistance in lattice-coloring programming.

is known, the possibility of cross-linking components that are neighbors in the atomic space (original model) could be incorporated into the simulation approach when working with a comprehensive kinetic model. Moreover, the use of a comprehensive kinetic model would be an improved method to produce results that are predictive and representative of the radical chemistry in liquefaction. Examples that may be transferable to this technology are the mathematical models of those by Provine and Klein,42 Solomon et al.,3 and Grant et al.,1 with the latter being based on the use of lattice statistics. A desirable feature of this approach is a means to transfer the results of a simulation from the lattice view to the original structure, i.e., being able to translate to the atomic structure all of the structural changes to the network produced by a lattice-based statistical simulation. The current work sets the foundations for a new computationally inexpensive method of simulating bond-breaking and bond-forming reactions in complex network systems through the combination of existing approaches and large-scale molecular models. The work presented here, along with the development of the Col2D and Molecwalk modeling tools,19,20 are the initial steps taken toward this goal.

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REFERENCES

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CONCLUSION A novel coupling of lattice and kinetic models of coal liquefaction applicable to large-scale complex structures was demonstrated. The complex 3D large-scale atomistic representation of Illinois no. 6 coal was simplified using Col2D and Molecwalk scripts to generate a 2D lattice model that was specific to the original structure, capturing the typology, cross-link distribution, and chemical diversity, while presenting the data in a simplified view that can be manipulated (color-coded) to aid in communicating structural information or transformations. A kinetically controlled simulation under liquefaction conditions was performed with the cleavage probabilities for each cross-link type calculated on the basis of the mixture of 10 model compounds comprising cross-link populations determined from the original coal model. Kinetic parameters (Arrhenius pre-exponential factor and activation energy) for each cross-link thermolysis reaction allowed for predictions of the chemical conversion of each linkage to be calculated at a given temperature via solution of the associated stoichiometric mass balances and kinetic differential equations. G

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dx.doi.org/10.1021/ef4001105 | Energy Fuels XXXX, XXX, XXX−XXX