Innovative Approach to Improving Gas-to-Liquid Fuel Catalysis via

Mar 7, 2014 - School of Computer Science and Engineering, University of New South Wales, Sydney, ... Nano Communication Networks 2016 9, 43-57 ...
0 downloads 7 Views 3MB Size
Download PDF
Article pubs.acs.org/IECR

Innovative Approach to Improving Gas-to-Liquid Fuel Catalysis via Nanosensor Network Modulation Eisa Zarepour,*,† Adesoji A. Adesina,*,‡ Mahbub Hassan,† and Chun Tung Chou† †

School of Computer Science and Engineering, University of New South Wales, Sydney, Australia 2052 ATODATECH LLC, Brentwood, California 94513, United States

‡

S Supporting Information *

ABSTRACT: Fischer−Tropsch synthesis, a major process for converting natural gas to liquid hydrocarbons (GTL), suffers from selectivity limitations that refer to the ratio of highly useful hydrocarbons to the total product output. Existing strategies for selectivity improvement, such as manipulation of reactor operating conditions (temperature, pressure, etc.) and catalyst design variables may be classified as top-down approaches. In this work, a bottom-up approach is proposed in which surface processes can be controlled via a nanosensor network (NSN) involving the turning on or off of elementary steps creating undesired species and redirection of surface efforts to step(s) leading to the desired products. The overall effect of these nanolevel communications offers superior selectivity to that hitherto possible by reducing the rate of hydrogenation of surface unsaturated species to paraffin (HTP) reactions. Our numerical and simulation results confirm substantial improvement of overall selectivity in a catalyst that is equipped with a highly reliable NSN.

■

INTRODUCTION Fischer−Tropsch synthesis (FTS) is the main process for converting natural gas to the liquid hydrocarbons1 which are useful both as clean fuels and intermediates for the manufacture of other petrochemicals. However, the reaction is a complex network of other steps and the requirement for efficient use of the reactants (H2 and CO) to yield the specified product spectrum (e.g olefins of a particular narrow product weight distribution) is critical and measured in terms of selectivity, S, defined as S=

total olefins total olefins + total paraffins

control over the sequence of elementary chemical reactions. This bottom-up approach is evident in many biological processes and responsible for the high selectivity and specificity accompanying these reactions (e.g., ATP hydrolysis, photosynthesis, etc). As a result, an analytical model for the FTS reactor based on discrete time Markov chain (DTMC) was used to capture the effect of proposed NSN in small-scale scenarios followed by extensive simulations via stochastic simulation algorithm (SSA) for large-scale experiments. Recent advancements in the development of nanomaterials such as carbon nanotubes and graphene have paved the way for the new generation of electronic nanocomponents like nanosensor, nanomemories, nanobatteries, and even nanoprocessors.5 Although nanodevices are not yet available commercially, current efforts point to a future when such devices could be produced in bulk. For example, a miniature hydrogen sensor consisting of a nanotaper coated with an ultrathin palladium film was reported by Villatoro and MonźonHerńandez,6 where the optical properties of the palladium layer changes when exposed to hydrogen. Yonzon et al.7 have also surveyed many other types of nanosensors that may be used for chemical and biological sensing. Similarly, progress has been recorded in production of chemical and biological nanoactuators in order to perform basic tasks at molecular level by harnessing the interactions between nanoparticles, electromagnetic field, and heat.8 Technically, an NSN is a network of nanoscale devices capable of some basic computing, sensing, actuation, and communication tasks. The seminal papers by Akyildiz et al.5,9 show that conceptually it is possible to achieve communication

(1)

Importantly, the reaction follows a polymerization scheme in which surface monomeric species stepwisely combine to form growing unsaturated hydrocarbons which are the precursors to olefins and paraffins via desorption and hydrogenation, respectively. In conventional operations, product selectivity is determined by catalyst type and composition as well as process conditions such as pressure and temperature.2,3 In spite of decades of research and industrial practice, it seems evident that selectivity modulation via catalyst formulation and process variables only permit modest improvements.2−4 However, an alternative strategy to overcome the constraints of macroscopic manipulation is to engage the reaction steps at the nanoscale level. In this work, we propose a new approach to improve selectivity using nanosensor networks (NSNs) which are formed by establishing communication between devices made from nanomaterials. Specifically, we introduce a network of nanomachines which may be used to turn off pathways leading to unwanted productse.g termination to paraffin and/or amplify the desorption of olefinic surface species. Unlike the conventional manipulation of H2:CO ratio in the reactor feed, the NSN will have to work at atomic or molecular level to exert © 2014 American Chemical Society

Received: Revised: Accepted: Published: 5728

November 19, 2013 February 11, 2014 March 7, 2014 March 7, 2014 dx.doi.org/10.1021/ie403931x | Ind. Eng. Chem. Res. 2014, 53, 5728−5736

Industrial & Engineering Chemistry Research

Article

surface C and O adspecies. Similarly, the dissociative chemisorption of H2 produces two hydrogen adatoms. CH2 surface species is formed when adsorbed C reacts with two neighboring H adatoms and in the presence of an adjacent Hs, the surface CH2 in turn may further react to form a CH3 surface group. The latter may either react with another H atom to form a CH4 (methane), or it may kick start a chain growth by reacting with an adjacent CH2, forming intermediate alkyl species CnH2n+1. The surface CnH2n+1 may be further hydrogenated to paraffins or suffer desorptive dehydrogenation to yield gas phase olefin, CnH2n. In order to improve the FTS selectivity, our NSN aims to reduce the occurrence of the surface alkyl hydrogenation reaction while enhancing the desorption to olefins. Each surface site on the catalyst would be equipped with a nanomachine to control operations on that site and also is able to communicate with its neighbor’s sites. For this reason, a clear understanding of the catalyst surface is necessary. In recent years, there has been significant progress in the production of nanostructured catalysts where the surface may be fashioned according to a predefined morphology at the micro- or nanoscale.17−19 The precision with which such nanoengineering can be achieved has been confirmed through various surface characterization methods such as high resolution scanning tunneling microscopy (STM),20 transmission electron microscopy (TEM), scanning electron microscopy (SEM), and X-ray absorption near-edge spectroscopy (XANES).21 Van Santen et al.22 have employed a 2D triangular surface configuration to perform KMC simulation of the FTS (cf. Figure 1). In this work, a 2D grid geometry has

at nanoscale either using electromagnetic or some form of molecular-based transceivers. This has sparked a flurry of new research activities in a bid to understand the unique properties of nanomaterials that could be utilized for communication between nanodevices.10−13 Since an NSN can work at the atomic level, it may be used for totally new kind of nanotechnology applications which cannot be realized with conventional sensor networks. Akyildiz and Jornet5 have outlined a number of interesting new applications of NSNs in biomedical, environmental, industrial, and military domains. In all these applications, distributed communication between nanomachines is envisaged to accomplish the application goal. In this paper, our goal is to explore the potential of NSN in improving product selectivity of FTS. An NSN deployed on the catalyst surface would be able to monitor all elementary reactions. This makes it possible to intervene the FTS process and divert the product path from paraffin to olefin in a more direct and efficient way. The overall hydrocarbon synthesis via FTS may be written as follows: Paraffin nCO + (2n + 1)H 2 ⇄ CnH 2n + 2 + nH 2O

Olefin nCO + (2n)H 2 ⇄ CnH 2n + nH 2O

The two inputs, H2 and CO are fed to the FTS at a predetermined ratio. Table 1 shows a general FTS mechanism3 leading to two main products: olefin (CnH2n) and paraffin (CnH2n+2). Olefins Table 1. Hydrocarbon Synthesis via Fischer−Tropsch3 Adsorption Sequence CO + s ⇄ COs COs + s ⇄ Cs + Os H2 + 2s ⇄ 2Hs Surface Reactions water formation chain initiation

chain growth Hydrogenation to Paraffin (HTP) β-dehydrogenation to olefin (BTO)

Os + Hs ⇄ HOs + s HOs + Hs ⇄ H2O + 2s Cs + Hs ⇄ CHs + s CHs + Hs ⇄ CH2s + s CH2s + Hs ⇄ CH3s + s CnH2n+1s + CH2s ⇄ CmH2m+1s + s (m = n + 1), r = kp CnH2n+1s + Hs ⇄ CnH2n+2 + 2s, r = ktp

Figure 1. Schematic used to model surface of the catalyst with reaction sites as triangular grids.22

CnH2n+1s ⇄ CnH2n + Hs, r = kto

also been adopted with the assumption that a site is either vacant or occupied by only one adsorbed species. Moreover, the concentration of surface reactant is deemed proportional to its gas phase partial pressure and the number of vacant sites.

are unsaturated hydrocarbons used as “building blocks” for making other petrochemicals and polymers in a wide variety of industrial and consumer markets such as packaging, transportation, electronics, textiles, and construction.14−16 However, paraffins are saturated hydrocarbons that are not readily usable for further product development and therefore have low commercial value. Thus, the olefin−paraffin ratio is an important reaction performance index. The typical FTS mechanism illustrated in Table 1 assumes that the catalyst surface contains sites suitable for the adsorption of reactants and subsequent reaction between sorbed species. Upon adsorption, CO may dissociate into

■

COMPUTATIONAL DETAILS In this section, a novel approach is proposed in which surface processes can be controlled via nanomachines involving the turning on or off of elementary steps (at periodic/aperiodic intervals) involving undesired species and redirection of surface efforts to step(s) leading to the wanted products. First, a general architecture for NSN will be provided and then selectivity control via this NSN will be explained. As catalysts may now be routinely prepared using nanoscale methods,17−19 deployment of a nanomachine at each site of the 5729

dx.doi.org/10.1021/ie403931x | Ind. Eng. Chem. Res. 2014, 53, 5728−5736

Industrial & Engineering Chemistry Research

Article

Figure 2. Network of nanomachines (NSN) on the catalytic surface. (A) Schematic snapshot of the surface of the catalyst as a 2D grid. (B) Conceptual architecture of a nanomachine equipped with four operational units, namely: nanosensor, nanoactuator, nanoprocessor, and a nanotransmitter.

surface may be considered as part of catalyst preparation. Each nanomachine contains four main components, namely: nanosensor, nanoactuator, nanotransceiver, and nanoprocessor. The nanosensor can identify the adsorbed species associated with its site. Nanoactuator can deactivate (desorb) hydrogen adatom from the site while the nanoprocessor can run a simple algorithm to decide whether the H adatom should be desorbed by the nanoactuator or not. This decision-making process also relies on a specific type of information which the nanotransceiver receives from the neighboring sites. The nanotransceiver is also responsible for sending an acknowledgment to any direct neighbor if CnH2n+1 formation occurs on its site. A schematic of such nanomachine is depicted in Figure 2. With these simple capabilities, the mechanism of selectivity control via NSN will be described. The main goal of the proposed NSN is to cut off the path to the production of paraffin and redirect surface effort to increase olefin productivity. From Table 1, it may be seen that H plays a key role in the product selectivity. Paraffin is produced only when a H reacts with a surface CnH2n+1, which is the elementary reaction termed hydrogenation to paraffin (HTP). Therefore, the aim of NSN communication would be to prevent H from reacting with CnH2n+1 as much as possible. Assuming that a H and CnH2n+1 would react only if these two species are on adjacent sites (the possibility of surface species migration may, however, be admissible in some catalytic systems but has been excluded in this initial modeling exercise to aid conceptual clarity in the NSN proposal), then one way to reduce reaction rate of HTP would be to control the location of H adsorption on the catalyst surface based on the knowledge of current content of each site. For example, Figure 3 shows the content of a number of sites (represented by circles) on the catalyst surface. There are two unoccupied sites, marked as 1 and 2. If an H is adsorbed at site 1, then it could lead to paraffin due to presence of CnH2n+1 (C3H7) in the neighborhood, but an adsorption of an H at site 2 cannot lead to the production of paraffin. Therefore, the NSN should allow H adsorption for site 2 but prevent it for site 1. Such spatial control of H adsorption on a catalyst surface could be achieved with an NSN in the following way. Each nanosensor is capable of sensing two

Figure 3. Example snapshot from the surface of a catalyst. There are two unoccupied sites, each having four neighbors containing different species.

events: (1) a CnH2n+1 that has just been formed at the site from an elementary reaction and (2) an H that is attempting to adsorb on the currently unoccupied site. Upon detection of the first event, the nanomachine should update a local binary variable, which indicates whether the site currently contains a CnH2n+1 species. However, if the second event is detected, the nanomachine queries all the neighboring nanomachines via its transceiver to learn whether there exists a CnH2n+1 in the neighborhood (neighborhood search). If CnH2n+1 is present in the neighborhood, the nanomachine would prevent the H adsorption via its actuator (a basic actuation task) but allow the adsorption otherwise. This means that a nanomachine can process and decide whether the current adsorbed species should be desorbed or not. This decision making will be based on information obtained from neighboring sites and can be implemented by preprogramming each nanomachine with the following algorithm to be executed in a loop via its nanoprocessor:

5730

dx.doi.org/10.1021/ie403931x | Ind. Eng. Chem. Res. 2014, 53, 5728−5736

Industrial & Engineering Chemistry Research

Article

may terminate in many different absorbing states with different probabilities. Probability of eventually reaching each of these absorbing states may be extracted from the fundamental matrix obtained by performing some operations on the transition probability matrix.29 Figure 4 demonstrates a snapshot of a simple DTMC model of FTS with only 2 and 4 starting species of CO and H

Based on this algorithm, if a site forms Hs within another site in its neighborhood containing (CnH2n+1s), it will immediately deactivate the Hs to reduce the probability of forming paraffin. The overall impact of the NSN is reduction in the rate of HTP reactions. It is evident that the proposed NSN meets its target without requiring the physical movement of any of the nanomachines. Nanostructured catalysts may be prepared via any of the wellknown assembling techniques.23−26 The proposed nanomachine may separately fabricated using the nanodevice production methods (e.g., nanolithography) described by Alkyildiz and Jornet5 followed by integration on catalyst surface or incorporation of the nanosensor components along with metal oxide ingredients via molecular self-assembly during the catalyst preparation phase.5 As a result, the collection of individual nanomachines (each of the size of a few nanometers) associated with individual sites on the catalyst surface constitutes the NSN since there is communication (electromagnetic or molecular) between neighboring nanomachines in the network. It is evident that the size of the NSN is determined by the number of active sites and, thus, a typical NSN may consist of up to a few thousand nanosensors. The performance of such an NSN-enabled catalyst may then be compared with a conventional catalyst under the same FTS conditions. Nevertheless, as NSNs are in the early stages of development and deployment of a real NSN on the surface of the catalyst is not yet possible, an analytical model and extensive simulations have been carried out to evaluate the proposed framework.

■

RESULTS AND DISCUSSION A network of chemical reactions can be modeled by a continuous time Markov chain (CTMC) whose states are all the different possible chemical compositions during the reaction.27 However, a CTMC may be approximated by a discrete time Markov chain (DTMC) with a sufficiently small sampling time interval.28 In such a DTMC model, any consumption of input, intermediate, or production of output species resulting in changes in their population leads to change in the state of the system. For example, a simple reaction such as A + B → C with initial composition of A = 1, B = 1, and C = 0 can be considered as a DTMC with two different states, S0 (A = 1, B = 1, C = 0) and S1 (A = 0, B = 0, C = 1). In this instance, if any increase in the initial reactant population occurs, then the number of states will increase. For instance, if A = 2, B = 2, it leads to three different states of S0 (A = 2, B = 2, C = 0), S1 (A = 1, B = 1, C = 1), and S2 (A = 0, B = 0, C = 2). The probability of transition from one state to another state can be obtained from reaction rate, r (r = kXAXB, where XA or XB is the species population for A or B respectively in that specific state and k is a kinetic constant of the reaction). Thus, in a system with two possible reactions of R1 and R2 to move from S1 to S2 with rate of r1 = 66 and r2 = 33, the probability of transition from S1 to S2 via R1 is 66/99 (0.66) and via R2 is 33/99 (0.33). In the present study, the FTS is fed with a specified amount of CO and H2 and state changes based on the scheme shown in Table 1. In each state, all possible reactions, based on current composition, would be considered to generate the complete state space. When no further reaction is possible, the system is said to have attained the so-called absorbing state, in DTMC terminology. By definition, state i is absorbing when the probability, P(i, i) = 1 and, hence, P(i, j) = 0 for all j ≠ i. Absorbing state is not unique and in some scenarios system

Figure 4. Modeling of a FTS via a Markov chain for an initial reactants of CO = 2 and H = 4. S6 and S8 are absorbing states. The blue number in the parentheses is probability of transition from one state to another state.

respectively. For simplification, water formation reactions and absorption sequence may be ignored although in the analytical model and the numerical simulations, all FTS reaction steps were considered. In this example, due to the small number of initial molecules, the system has only five reactions as outlined in Table 2. The system starts from initial state (S0) with C = 2 Table 2. . Reactions of Figure 4 R1 R2 R3 R4 R5

chain initiation

hydrogenation to paraffin (HTP) β-dehydrogenation to olefin (BTO)

Cs + Hs ⇄ CHs + s CHs + Hs ⇄ CH2s + s CH2s + Hs ⇄ CH3s + s CH3s + Hs ⇄ CH4 + 2s CH3s ⇄ CH2 + Hs

and H = 4. The only possible reaction based on composition of S0 is R1 (C + H → CH) that leads to state 1 with probability of 1 via R1. Then the system can move via two different paths: to S3 via R1 (C + H → CH) or S2 via R2 (CH + H → CH2). When the rate of R1 and R2 are equal then these two transitions have equal probabilities of 0.5. The rest of the probable states and possible transitions are depicted in Figure 4. There are nine different compositions in this illustration, and states S6 and S8 5731

dx.doi.org/10.1021/ie403931x | Ind. Eng. Chem. Res. 2014, 53, 5728−5736

Industrial & Engineering Chemistry Research

Article

are absorbing states and also final states since there is no further possible reaction based on composition of these two states. As NSN aims to reduce HTP reactions rates, S4 should be considered as that is a potential state for HTP reactions. S4 has three different options, viz: back to S2 with 33% probability, move to S7 with the same probability, or transit to S6 with a probability of 33% via a HTP reaction (CH3 + H → CH4). In order to capture the effect of NSN in the DTMC model it will be assumed NSN would be able to reduce rate of all HTP reactions by δ percentage. For example, in case of δ = 20, Figure 4 shows that the probability of going from state 4 to state 6 via R6 will decrease by 20% and drops from 0.33 to around 0.266. In modeling FTS as a DTMC, the composition of absorbing states may be taken as the final probable compositions to calculate selectivity and product distribution. All olefin and paraffin species in all possible absorbing states will be considered to extract overall selectivity. For example, in Figure 4 selectivity of S6 is 0 because there is no olefin in its composition. However, as there are two CH2 in S8 without any paraffin, selectivity of S8 is 1. In a real FTS, the system eventually converges to one of these absorbing states. Hence, it is necessary to involve the probability of reaching these absorbing states to calculate overall selectivity and obtain product distribution. The probability of eventually reaching a specific absorbing state m from initial state 0 can be extracted from the fundamental matrix29 of the DTMC model. The output of the computation gives B(0, j), which is the probability of eventually reaching absorbing state j from the initial state 0. Generally, to analyze the output of each experiment based on DTMC model, the composition of each absorbing state Sj gives the amount of olefin (CnH2n) as Olej and paraffin (CnH2n+2) as Parj, and the total olefins (or paraffins) may be calculated as follows: j=1

olefin =

∑ OlejB(0, j), m

Figure 5. Product distribution from the analytical model with initial CO = 5 and H = 15 for 10 different scenarios of HTP rate reduction (δ from 0 to 100%).

in HTP and rises to 2.4 when all HTP reactions have been cut off via NSN. On the other hand, paraffin formation dropped from 2.1 molecules to 0 indicating that selectivity rose from 40.2% to 100% as depicted in Figure 6. The results revealed an exponential relationship between δ and selectivity.

j=1

paraffin =

∑ ParjB(0, j) m

(2)

Where, B(0, j) is probability of reaching absorbing state j from initial state and m is number of absorbing states in the model. After extracting total olefins and paraffins, the olefin product selectivity, Solefin (cf. eq 1). The DTMC model was evaluated using an initial feed containing of H:CO = 15:5. For computational purposes, only hydrocarbons with chain length, n, 1 ≤ n ≤ 5, was considered. Thus, based on Table 1 there is a total of 20 reactions (3 chain initiation steps, 5 chain growth steps, 2 water formation steps, 5 hydrogenation to paraffin, and 5 dehydrogenation to olefin steps). Similarly, a total of 22 species including CO, C, H, CH, O, OH, H2O, 5 intermediate species as (CnH2n+1), 5 final olefin products (CnH2n), and 5 final paraffin products (CnH2n+2) were involved. All 20 reactions steps were deemed to have equal kinetic constant (taken as 7 in this case although the trend in the computational results is inconsequential to the exact numerical value of the kinetic constant). The simulation was carried out in MATLAB and produced 3271 different states (distinct possible compositions) with 257 different absorbing states. Figure 5 shows the change in product distribution and selectivity for any value of δ. The direct implication of reduction in HTP rates is the increase in olefin production and decrease in amount of paraffin. In this experiment, the number of olefin molecules starts from 1.41 when there is no reduction

Figure 6. Selectivity for different successful reduction in HTP reaction rates based on results of model with initial molecules of CO:5 and H:15.

For large and complex systems, traditional Markov models may experience state explosion and quickly become intractable.30 In the present FTS with even 20 reactions, the DTMC model produced a huge state space matrix. For example, in case of CO = 10 and H = 20, there are more than 35 000 different states which makes it computationally demanding (in terms of power and memory) to solve the numerical problem. Indeed, to run the previous experiment with initial CO:5 and H:15 for 21 different values of δ (ranging from 0 to 100%), a cluster of 21 machines with 84 cores and a total of 168 GB RAM for 35 h has been used. Figure 7 shows how the state space grows exponentially with linear increase in the amounts of initial CO and H fed to the reactor. The result may be described by f(x) = 29.38exp(0.521x), with an R-square value of 0.9995, where f(x) is the number of states and x is the number of carbon monoxide molecules. However, the stochastic simulation algorithm (SSA) by Gillespie31 based on the generalized DTMC framework 5732

dx.doi.org/10.1021/ie403931x | Ind. Eng. Chem. Res. 2014, 53, 5728−5736

Industrial & Engineering Chemistry Research

Article

even insurmountable. In order to design a large scale experiment, an FTS with hydrocarbon length, n ≤ 10, has been considered that leads to a total of 37 probable species during the synthesis including CO, C, H, CH, O, OH, H2O, 10 intermediate species as (CnH2n+1), 10 final olefin products (CnH2n), and 10 final paraffin products (CnH2n+2) are implicated. The initial species counts (number of molecules) were set as CO = 10 000, H = 20 000, and zero for all other species. There are 34 reactions in 4 different categories (based on Table 1), and all the 34 kinetic constants were assumed equal (k = 7) for simulation purposes. Figure 9 shows how the states change for a given simulation. Effect of the NSN on the catalyst surface was investigated by varying δ in increments of 5% over the range 0−100%. This produced a total of 84 simulation configurations for the 4 sets of kinetic constants used. For each configuration, the simulation was repeated 10 times and the average results over 10 runs are presented. Figure 10 displays the SSA product distribution with respect to δ for the case of CO = 10 000 and H = 20000. It confirms that, by increasing δ (reduction in rate of HTP reactions), the number of olefin molecules (CnH2n) increases and the population of paraffin species (CnH2n+2) decreases. Olefins start from 1233.4 molecules in a conventional FTS (δ = 0) and rise to 2740.4 molecules when NSN is able to cutoff 100% of HTP reactions. On the other hand, paraffin drops from 1704 molecules to zero in the case of δ = 100%. Selectivity has been investigated in Figure 11 that indicates olefin selectivity increases from 42% to 100% when HTP reduction is 0 and 100 respectively. It also reveals the exponential relationship dependency of selectivity on δ. The behavior with 95% confidence bounds can be captured as f(x) = 0.3784exp(0.008877x) with an R2 value of 0.9655. FTS product distribution is frequently described by the Anderson−Schulz−Flory (ASF) polymerization model3,32 written as follows:

Figure 7. State space complexity of DTMC model that grows exponentially with increasing number of initial molecules.

produces a smaller and more manageable state space through optimization of possible reactions in each state. Subsequent numerical work was therefore performed via the SSA. The standard SSA algorithm takes three inputs: (1) a set of reactions, (2) a set of kinetic constants corresponding to each reaction, and (3) initial counts for each species, which define the initial state of the simulation. In general, the state in SSA is defined as the number of each chemical species in the system. At each state, the simulator determines a candidate reaction to take place from the set of all possible reactions and updates the state (species counts) accordingly. Simulation stops when there are no reactions to take place. The output of the algorithm is the number of each chemical species at the end of the simulation. The comparison between the numerical results of the DTMC model and the SSA simulation for previous experiment of CO:5, H:15 is shown in Figure 8 as a function of δ. The excellent agreement observed suggests that the optimized, smaller state space used by the stochastic approach did not have any significant effect on the quality of the results and justifies the use of the SSA for large complex systems like the FTS where the DTMC model is more computationally intensive or

mn = (1 − α)α n − 1

(3a)

ln(mn) = n ln(α) + ln[(1 − α)/α]

(3b)

or

Where, mn is the mole fraction of a hydrocarbon with chain length n and α is the chain growth probability factor. The linearized version of the ASF model (cf. eq 3b) yields the estimation of α from a plot of ln(mn) against n so that mn can be calculated from simulation results via eq 4. mn =

Cn H 2n + Cn H 2n + 2 10 ∑n = 1 (Cn H 2n + Cn H 2n + 2)

(4)

The slope of the ASF plot may be used for calculation of α. For the case with δ = 0 (conventional FTS with no NSN communication mediation), the chain growth factor, α, is 0.52 (nearly identical to experimental value for FTS on cobalt under similar conditions2) as seen in Figure 12. The chain growth factor for different values of δ ranging from 0 to 100% also have been calculated based on aforementioned method as depicted in Figure 13. α-Value starts from 0.52 when δ = 0 and rises to 0.76 when the NSN has suppressed all HTP reactions (δ = 100). It is clear that success of the proposed NSN in exerting spatial control over H adsorption would depend in turn on its sensing, actuation, and communication capabilities. While

Figure 8. Selectivity for different reduction in HTP rate (δ) for CO = 5, H = 15 based on numerical (solid line) vs simulation (squares) results. 5733

dx.doi.org/10.1021/ie403931x | Ind. Eng. Chem. Res. 2014, 53, 5728−5736

Industrial & Engineering Chemistry Research

Article

Figure 9. Snapshot of state changes during simulation (CO = 10 000, H = 20 000).

Figure 10. Product distribution for the simulation with initial molecules of CO:10 000 and H:20 000 for different values of δ.

Figure 11. Selectivity for different reduction in HTP rate based on large scale simulation (CO = 10 000, H = 20 000).

NSNs are in the embryonic stage of development, there would be issues with all three dimensions, sensing, actuation, and communication. In a previous aritcle,33 we have modeled the effect of the communication reliability on the selectivity assuming perfect sensing and actuation capabilities. In a multistep chemical system, changing the rate of any reaction step will affect other possible reactions if they have common reactants. In FTS, any reduction in rate of HTP reactions leads to some side-effects such as, providing more CnH2n+1 and hydrogen for other reactions which consume CnH2n+1 or H. As a result, three possibilities are conceivable:

(1) β-dehydrogenation to olefin (DTO) reactions would be more likely to happen as it can find more CnH2n+1; (2) increasing in the rate of chain growth as it consumes CnH2n+1; (3) raising in the rate of water formation reaction as it consumes H. In this work, the direct effect of reduction in HTP on the selectivity and product distribution is captured. While some of these effects such as increasing DTO rate has a positive impact on the product selectivity, a more comprehensive account of the NSN role would reveal benefits in other reaction indices such as catalyst stability, reduced carbon deposition and hence, deactivation. This is the subject of future investigation. 5734

dx.doi.org/10.1021/ie403931x | Ind. Eng. Chem. Res. 2014, 53, 5728−5736

Industrial & Engineering Chemistry Research

Article

steps involving hydrogenation to paraffin (HTP) and olefin production at the molecular-level. An NSN prevents adsorption of H on sites adjacent to those containing CnH2n+1 with the ultimate goal of improving olefin selectivity of FTS. An analytical model based on Markov chain has been developed to capture the effect of any reduction in rate of HTP reactions (δ). The numerical results revealed a decrease in the paraffin (CnH2n+2) formation with concomitant increase in olefin production. Indeed, there is an exponential relationship between δ and product selectivity. Complementary extensive simulations based on SSA for a large-scale FTS were also in agreement with the DTMC computational results.

■

ASSOCIATED CONTENT

* Supporting Information S

MATLAB codes for the simulation exercise, analytical model, and other related computations have been deposited. This information is available free of charge via the Internet at http:// pubs.acs.org/.

Figure 12. ASF plot.

■

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The numerical experiments reported in this work were performed on LEONARDI, the computing cluster of the University of New South Wales.

■

Figure 13. Chain growth probability (α) for different reductions in HTP rates based on large scale simulation (CO = 10 000, H = 20 000).

REFERENCES

(1) Dry, M. E. Commercial Conversion of Carbon Monoxide to Fuels and Chemicals. J. Organomet. Chem. 1989, 372, 117−127. (2) Adesina, A. A. Hydrocarbon Synthesis via Fischer−Tropsch Reaction: Travails and Triumphs. Appl. Catal., A 1996, 138 (2), 345− 367. (3) Van der Laan, G. P.; Beenackers, A. C. M. Kinetics and Selectivity of the Fischer−Tropsch synthesis: A Literature Review. Catal. Rev. Sci. Eng. 1999, 41, 255−318. (4) Zhang, Q.; Kang, J.; Wang, Y. Development of Novel Catalysts for Fischer−Tropsch Cynthesis: Tuning the Product Selectivity. Chem. Eng. Process. 2010, 2, 1030−1058. (5) Akyildiz, I. F.; Jornet, J. M. Electromagnetic Wireless Nanosensor Networks. Nano Commun. Networks 2010, 1 (1), 3−19. (6) Villatoro, J.; Monźon-Herńandez, D. Fast Detection of Hydrogen with Nano Fiber Tapers Coated with Ultra-thin Palladium Layers. Opt. Express. 2005, 13 (13), 5087−92. (7) Yonzon, C. R.; Stuart, D. a.; Zhang, X.; McFarland, A. D.; Haynes, C. L.; Van Duyne, R. P. Towards Advanced Chemical and Biological Nanosensors - An Overview. J. Talanta. 2005, 67 (3), 438− 48. (8) Falconi, C.; Damico, a.; Wang, Z. Wireless Joule Nanoheaters. Sens. Actuators, B. 2007, 127 (1), 54−62. (9) Akyildiz, I. F.; Brunetti, F.; Blazquez, C. Nanonetworks: A New Communication Paradigm. Comput. Networks 2008, 52 (12), 2260− 2279. (10) Atakan, B.; Akan, O. Carbon Nanotube-based Nanoscale Ad Hoc Networks. IEEE Commun. Mag. 2010, 48 (6), 129−135. (11) Chou, C. T. Molecular Circuits for Decoding Frequency Coded Signals in Nano-Communication Networks. Nano Commun. Networks 2012, 3 (1), 46−56.

In order to for the NSN to monitor the site occupancy, sensors on the scale of a few atoms,