Molecular Analysis for Process Synthesis - Industrial & Engineering

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Molecular Analysis for Process Synthesis Frank X. Zhu Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b01919 • Publication Date (Web): 25 Sep 2018 Downloaded from http://pubs.acs.org on September 29, 2018

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Industrial & Engineering Chemistry Research

Molecular Analysis for Process Synthesis Frank (Xin X.) Zhu* Honeywell UOP 25 E. Algonquin Road, Des Plaines, Illinois, USA * corresponding author: [email protected]

Abstract

Process synthesis is about finding the appropriate processing routes with selection of catalyst, reaction and separation technologies followed by flowsheeting (connection of selected technologies) and equipment design at the least capital and operating cost. The common feature of current process synthesis methods is that they are mainly based on macroscopic parameters but do not exploit microscopic effects at molecular level. As a result, the fundamental aspects cannot be fully exploited to discover novel ideas. However, the essence of process synthesis is about maximizing the production of desirable chemical species via optimizing the routing of key species to their most appropriate destinations. To achieve this goal, a molecular analysis methodology for process synthesis is proposed in this article. Several industrial case studies are provided to prove the concept and demonstrate the value. Key words: molecular feed characterization, catalyst, reaction pathway, molecular modeling, hybrid separation, process optimization, process synthesis.

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1. Introduction Process synthesis is about finding the most appropriate processing routes with optimal selection of catalyst, reaction and separation technologies and system design for obtaining desirable product yields with the least capital and operating costs. In general, process synthesis is very complex progressing from chemistry and catalyst development, to reaction system, product separation, heat recovery, to equipment and utility system design, the sequence of which can be depicted by the onion diagram as shown in Figure 1. Complexity in design grows exponentially when one wants to explore interactions among catalyst, reaction system and separation system designs. Since there is no systematic methodology available, the industrial practice still heavily relies on practical experience and judgement. Due to the trial-and-error nature of this work process, process synthesis is still regarded as a form of art instead of science, which cannot guarantee the best performance for the overall system design. Much effort has been dedicated to developing systematical methods for process synthesis and numerous work has been published in the past, which is too many to cite. However, these works can be broadly grouped into three major camps of research. Firstly, Process Integration [3] adopts thermodynamic principles to provide insights for achieving higher energy efficiency at low capital costs. Secondly, Process System Engineering [4] relies on the power of mathematical optimization to derive ‘optimized’ process design based on a superstructure consisting of alternative design options. Thirdly, heuristic rules [5] rely on rules of thumbs and experience to guide process design. The common feature is that these methods mainly evaluate macroscopic parameters at bulk property levels during process design but do not investigate microscopic effects such as reaction pathways, catalyst selectivity and activity, limiting conditions for reaction and separation at the molecular level. Thus, these methods cannot exploit fundamental aspects of the process synthesis and thus incapable of identifying breakthrough ideas. Deviating from the above-mentioned methods, a novel method with a new way of thinking for process synthesis is proposed here with the focus on establishing molecular analysis as the foundation for process synthesis. This method is developed based on the fundamental understanding that the essence of process design is to find the best ways of converting feedstock molecules to produce molecules with desired compositions and properties. Therefore, process synthesis should be about finding ways for optimizing molecular transformations in a process. In this article, the methodology of molecular analysis will be introduced first and then application examples are discussed in this paper, which demonstrate the value of applying this methodology for catalyst and process development. In the case of catalyst development, molecular information can reveal new directions of improving catalyst selectivity and activity. For process development, reaction design, separation (including hybrid system) design and new process concepts can be generated based on molecular information so that important molecules will be allocated via adding/removing processing steps.


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Figure 1. Sequence of process synthesis 2. Review of previous work The molecular analysis method was originally proposed in [1,2] with the focus on operational optimization. The method consists of four pillars, namely a) molecular feed characterization and representation; b) molecular kinetic modeling; c) molecular property transformation and d) molecular simulation and optimization as shown in Figure 2.

Feed molecular characterization

Molecular modeling

Molecular based process simulation & optimization

Molecular transformation to bulk properties for products

Improved operation

Figure 2. Molecular analysis for operation optimization 2.1 Pillar 1 -- Molecular characterization and representation The molecular analysis method starts with molecular characterization of the feed chemical composition. Modern analytic technologies can provide measurement of composition of refining streams to support molecular modeling. For example, gas chromatography (GC) can be used to provide sufficient composition information for naphtha range materials. For heavier streams, such as distillate, vacuum gas oil (VGO) and vacuum residue, GC cannot provide enough molecular details due to their compositional complexity. Advanced analytical tools are available for measuring compositions for heavier streams, which include comprehensive two-dimensional gas chromatography (GC×GC) and mass spectrometry (MS).



The composition details measured via analytical tools can be repressed in an appropriate structure suitable for molecular modeling. For example, we can represent a gasoline fraction based on molecular type and carbon number. Figure 3 describes a naphtha stream based on five different types of homologous series including normal paraffins (NP), isoparaffins (IP), olefins (O), naphthenes (N), and aromatics (A) respectively together with different carbon numbers. The molecules that belong to a homologous series with the same carbon number have similar physical properties, and thus, they are lumped into a single component as an element in the matrix. The homologous series also form the basis for developing reaction pathways and then reaction kinetic modeling. This representation can capture much rich information than that by the tradition method based on lumping and pseudo-components.

Figure 3. A MTHS matrix for gasoline stream

2.2 Pillar 2 - Molecular kinetic modeling Once chemical composition is generated from molecular characterization for process streams, the next step is to develop molecular kinetic models in order to predict product molecular matrices and properties. Basically, a kinetic model is a set of rate expressions. To conduct a molecular based kinetic model, firstly reaction families must be generated to construct an extensive reaction network. Then kinetic parameters are determined for each reaction type. The objective of kinetic modeling is to predict product yield, conversion and process conditions when feed composition changes. Basically, there are three kinetic modeling approaches, namely lumping approach [7], pathways approach [8] and mechanistic approach [9]. The common practice for describing hydrocarbon streams is based on lumped compounds where individual molecules in a hydrocarbon feedstock are lumped into a small number of pseudocomponents measured based on narrow boiling range. The lumping method has been applied to


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major reaction processes [10-16]. These lumping methods are implemented in commercial software including Hysys, Unisim, Aspen Plus and Pro II. The lumping based kinetic modeling is simple and estimation of kinetic parameters is a relatively straightforward. However, the major shortcoming for lumping models is that it does not address chemical reactions in details and does not capture catalyst details and individual molecule conversions; thus opportunities for optimizing selectivity for these molecules get lost. Furthermore, the lumping based models have limited prediction power as they are developed based on experiments for a limited feedstock. When a feed is outside of experimental data, the kinetic parameters must be re-estimated based on new experiments. Quann and Jaffee [17] addressed this problem by introducing structural oriented lumping (SOL), which is a pathway approach. A large number of key molecules are modeled by assembling 25 structural groups in various ways so that the SOL synthetic feed could satisfy the observable characteristics, both chemical and physical. In other words, the SOL approach uses structural or functional groups to characterize the composition of complex feed stock and generates kinetic models with details at reaction pathway level. In this manner, the SOL method can track molecules in the feed based on the composition and structure in terms of number of aromatic rings, number of nitrogen and sulfur substituents, etc. Furthermore, Klein and co-workers [18,19] simplified the process of estimating kinetic parameters by applying free energy relationships. As the result, a computation platform is developed for generating the reaction network of this synthetic feed resulting in automation of molecular kinetic model construction, execution and editing. Another pathway approach [20] is based on molecular type homologous series (MTHS) matrix (e.g. Figure 3 for a naphtha stream). A MTHS is used to represent molecular compositions of a petroleum mixture to describe different homologous series corresponding to functional groups such as normal paraffins (nP), iso-paraffins (iP), olefins (O), naphthenes (N) and aromatics (A) respectively. Different sulfur and nitrogen compounds are also shown in this matrix. A homologous series has the same base structure but with varying carbon number, for example, through the addition of alkyl chains of increasing length. With this MTHS representation, the important assumption is that the molecules that belong to a homologous series with the same carbon number have the same reactivity and similar physical and chemical properties, and thus, they are lumped into a single component as one element of the matrix. Thus a MTHS defines a stream in functional molecular types and carbon number, which can be used as the basis for developing reaction pathways and reaction kinetic model. Recent advances in kinetic modeling has already made a paradigm shift towards more detailed molecular modeling in which the micro-kinetics approach [9, 21] is the most well-known. This approach can explore fundamental chemistry of the conversion of each individual hydrocarbon molecules, which is achieved by modeling elementary reactions and use molecules and intermediates explicitly. With this micro-kinetics approach, the kinetic models are independent of feed type and compositions as few assumptions are required and more accurate prediction can be obtained.



Due to the nature of the micro-kinetics approach, the modeling involves a reaction network of as many as O(1015) species and reactions and thus requires estimation of many kinetic parameters, which is beyond manual capability. To reduce the number of kinetic parameters to be estimated, the single event concept [9, 22] is applied to formulate their rates using only a reasonable number of independent kinetic parameters based on structural relationships. For example, use of structural relationships reduces the number of parameters required significantly. Experimental data may be used to fit the remaining parameters. This single event approach has been successfully applied to a variety of processes The prediction capability for the above three kinetic modeling methods and their comparison is shown in Figure 4. The comparison is based on the complexity of the methods and model fidelity. The traditional lumping method is the simplest since fewer lumps are used and thus it is to obtain kinetic parameters by fitting experimental data. However, the models derived have the lowest prediction capability as it is strongly dependent of feedstocks. When feed type changes, the kinetic parameters must be re-estimated based on new experiments. The pathways method requires more detailed feed data to develop molecular representation and estimate numerous kinetic parameters. Thus, the models can be extrapolated for a range of feedstocks and process conditions. Although the pathways models have much better prediction power than that of the traditional lumping models, the pathways models are still not completely independent of feedstock because fundamentally the method is still based on function lumps. In contrast, the mechanistic method such as single event approach is feed independent because it is based on fundamental chemistry of transformation of each individual hydrocarbon. As the result, the kinetic parameters are truly invariant with feedstock and prediction capability is much more accurate for a wide range of feed compositions and operating conditions.

Prediction capability

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Mechanistic (e.g. single-event approach)

Pathways (e.g. SOL, MTHS approaches)

Chemical lumping approach

Complexity

Figure 4. Comparison of perdition power for different kinetic modeling methods


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2.3 Pillar 3 – Molecular transformation to bulk properties for products The third task is the molecular transformation to convert molecular compositions to bulk properties because products are valued based on bulk properties in the market. After obtaining a molecular matrix for a process stream, we know molecule structure parameters, such as molecular type and carbon number, from which we can derive bulk properties for the products. The calculation procedure by Zhang and Towler [23] is given in Figure 5. First, using the molecular structure-property correlations of fundamental molecular properties (e.g., molecular weight, density, and boiling point) can be calculated. These molecules are mixed according to compositions and accumulated by volume percent to generate a true boiling point (TBP) distillation curve of the stream. The TBP curve is then converted into an ASTM (American Society for Testing and Materials) D86 distillation curve using existing correlations. Following this step, bulk properties of a stream, including density; molecular weight; viscosity; refractive index; flash point; pour point; cetane number; and contents of paraffins, naphthenes and aromatics, can be estimated. The research octane number (RON), motor octane number (MON), and Reid vapor pressure (RVP) of the stream can be calculated by molecular-composition-based correlations with the given values of the RONs, MONs, and RVPs of all molecules [24-27]. The molecular approach for RON and MON enables a proper accounting of nonlinear and composition-dependent blending phenomena.

Figure 5. Calculation procedure for translating molecular composition to bulk properties

2.4 Pillar 4 -- Process molecular simulation and optimization Simulation and optimization based on molecular information is the holy grail of molecular management for process optimization. The key is to integrate molecular based process models into the site-wide optimization with existing non-molecular based process models with the purpose to optimize process conditions [2].



The objective function for the site-level optimization model is to maximize overall profit at the site level by determining the optimal feed conditions in terms of feed composition, bulk properties and flow rates for the processes. At the process level, operating conditions (such as temperature and pressure) and product conditions (flow rates, composition) are optimized while major operating constraints (such as column flooding, compressor capacity) are observed. The molecular and non-molecular models are interfaced using the transformation methods. Ideally, we would like to build molecular models for all processes and then conduct optimization based purely on molecular information. However, this requires too much time and might also be unnecessary. To reduce the overall complexity and the effort for obtaining molecular information, the optimization methodology [2] allows co-existence of molecular and non-molecular based models. With molecular based process models into the overall optimization model, this would lead to an optimization problem with a prohibitively large size. To solve such a complex problem, the decomposition optimization strategy proposed by Zhang and Zhu [28] is adopted. The optimization method decomposes the overall plant optimization into two levels: a site level (master model) and a process level (submodels), as shown in Figure 6. The master model determines common issues among processes, such as selection of feeds, allocation of utilities and marginal values (or transfer values) of intermediate products with the objective function of maximizing the total plant profit subject to major process constraints. With these common issues determined, submodels then optimize process conditions for individual processes. The limiting constraints from sub-model optimization are then fed back to the master model for further optimization. This procedure terminates when convergence criteria are met (Figure 6). In this way, individual process optimizations are effectively coordinated by the central master model. The details for the structure of total optimization can be seen in [29]. In overall, this molecular based optimization approach can be the enabler for operation optimization for selection of raw feed and intermediate feeds as well as conditions so that the plant can maximize selectivity to make more valuable products while routing all species to their most appropriate destinations to achieve maximal profit. The molecular management platform is a powerful platform for operation and control optimization.


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Process superstructure Update linear yield

Yield

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Y K-1 Yk Yk

Linear yield correlation

YK-1

Yk

Site level optimization

Feed rate

Process connections Process optimization Limiting constraints

No

Yk Process conditions Yk – Yk < Ɛ ? Yes Optimal solution

Figure 6. Overall optimization procedure 3. Molecular analysis for process synthesis In this section, the major limitation associated with the current process synthesis methods is defined first and then the molecular analysis method for process synthesis is proposed supported by several industrial case studies to demonstrate the value created by applying this new approach for guiding process synthesis. 3.1 Problem statement and the new approach The goal of process synthesis is to determine optimal processing routes to make on-spec products by selecting the cheapest feedstock possible with lowest capital and operating costs as well as minimum environmental impact. The major shortcoming associated with current process synthesis methods is that it does not investigate microscopic influences at molecular level on reaction pathways, catalyst recipe development and selection of reaction and separation technologies. Thus, interaction between chemistry, catalyst and process development cannot be fully exploited to maximize yields and improve processing efficiency. The proposed molecular based process synthesis approach, as shown in Figure 7, aims to address this shortcoming by applying molecular analysis to provide guiding principles for process synthesis in terms of optimizing molecular flows and conversion with efficient technologies, configurational changes and optimal flowsheeting.



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The molecular analysis approach consists of four steps (Figure 7), namely molecular feed characterization, molecular modeling, limiting condition analysis and molecular process simulation/optimization. The approach starts with molecular characterization of the feed chemical composition. The molecular information from the feed characterization is organized to form a molecular matrix representation, which becomes the basis for molecular modeling. The second step is building molecular models for the reaction and separation processes to predict molecular information and physical properties for products. The third task is limiting condition analysis for catalyst, reaction and separation systems, from which new ideas for improvements can be identified. Limiting conditions analysis covers catalyst selectivity/activity, rate limiting, separation efficiency limiting as well as capital and operating cost restriction, etc. To overcome the limitations, improvement ideas are generated via exploring interactions between chemistry, catalyst, reaction and separation considering hybrid system. Given improvement ideas identified from step 3, in the fourth step, molecular based simulation and optimization will assess the technology feasibility and eventually determine the best technology improvements. The key difference between this molecular based process synthesis approach (Figure 7) comparing with molecular based operation optimization (Figure 2) lies in the focus on technology improvements and process configuration changes while the latter focuses on changes in operating conditions only while treating technology and process configurations as it is.

Feed molecular characterization

Molecular modeling

Limiting condition analysis for idea discovery for catalyst and process improvement

Molecular based process simulation & optimization

Improved design

Figure 7. Molecular analysis for process synthesis

3.2 Molecular analysis enabling novel hydrodesulfurization system design Molecular characterization and modeling can obtain good understanding of characteristics of individual molecules, and this understanding could help identify the best pathway for individual molecules from chemistry point of view and then determine efficient process design to achieve the chemistry target. This case study focuses on individual sulfur species. The existing reaction modeling for FCC gasoline hydrodesulfurization is mainly based on lumping methods. With this lumping approach, sulfur species are lumped into one compound and thus the lumping model loses sight of the individual sulfur species. Although the sulfur is reduced to meet the sulfur specification, gasoline octane is reduced through desulfurization. However,


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molecular characterization indicates that the FCC naphtha contains different sulfur species including mercaptans, thiols, sulfides, alkyl-thiophenes and alkyl-benzothiophenes. Effectively, the molecular analysis groups sulfur compounds into two classes, namely SI and SII [6]. SI includes mercaptan only while SII consists of other types of sulfur species. SI is much easier to remove than SII. The segregation of sulfur species based on chemical properties was proved to be very insightful in deriving a novel and efficient naphtha hydrotreating process design, which is discussed below. The problem of interest is related to the selective hydrodesulfurization of the gasoline portion of the fluid catalytic cracking process, otherwise known as FCC gasoline. This stream is comprised principally of normal/iso-/cyclo-alkanes and mono-alkenes, aromatics, organo-sulfur, and organo-nitrogen species in the C5-220 °C boiling range. The octane number of this stream is often in the range of 90-95, due for the most part to the significant octane contribution from monoalkenes and aromatics. FCC gasoline comprises up to 50 vol% of a refinery’s motor gasoline pool, and up to 90% of the motor gasoline pool’s sulfur content, so it is imperative that the hydrodesulfurization of this stream, required to meet US Tier 2 (30 wt ppm S, now) and US Tier 3 (10 wt ppm S, 2017) federal fuel specifications, should not significantly reduce its octane contribution to the pool. Currently, FCC gasoline is treated through hydrodesulfurization with a supported CoMo catalyst, under typical processing conditions: 17-26 bar(g), 250-315 °C. It was found that hydrodesulfurization can reduce the sulfur content for FCC gasoline, it also reduces gasoline octane significantly, which is a big loss to the market value. Therefore, the objective for this case study was to satisfy overall sulfur limit while minimizing the octane loss over the course of hydrodesulfurization. Detailed characterization and molecular modeling of FCC gasoline reveals that different fractions of this gasoline stream consist of different sulfur species and molecular components contributing to octane number (Figure 8). Figure 8 indicates that the highest octane mono-alkenes and most reactive sulfur species (mercaptans, sulfides) in FCC gasoline can be found in the light fraction (light cat naphtha, or LCN) and the lowest octane alkenes/least reactive sulfur species (alkyl-thiophenes, alkyl-benzothiophenes) can be found in the heavy fraction (heavy cat naphtha, or HCN). Understanding of these sulfur species and properties at molecular level sheds insights and directions for determining the best way for sulfur management. The new idea identified from the insight above is: hydrotreating LCN in a different process from ICN/HCN. In this case, converting the sulfur species in the light fraction to heavier sulfur species, such as disulfides, should be accomplished in UOP Merox™ process for oxidative sweetening for two purposes: sulfur removal and retention of gasoline octane. The Merox™ process is nearly 100% efficient sweetening the light fraction of the FCC gasoline. In other words, the Merox™ process avoids octane loss via retention of mono-alkenes. Thus, thiophene (boils at 65 °C as an azeotrope) becomes the lightest boiling sulfur species. So the sweetened FCC gasoline



can then be fractionated conventionally to retrieve the sulfur-free LCN, up to the maximum sulfur specification, which may account for 30-40% of the FCC gasoline. The combined ICN and HCN can then be hydrodesulfurized together or separately by applying catalysts with activity and selectivity appropriate for the mono-alkenes present in each fraction. The mono-alkenes present in the HCN have lower octane values and are fewer in proportion than the ICN, so a more active/less selective catalyst can be employed on the HCN without significant octane loss. This reasoning leads to a new process flowscheme for selective FCC gasoline hydrodesulfurization [30]. An additional opportunity for applying the principle of molecular management lies within the management of the hydrodesulfurization itself. One of the three chief reactions occurring in selective hydrodesulfurization is the so-called recombination of mono-alkenes and hydrogen sulfide, to produce thiols. This reaction occurs because the hydrogen sulfide liberated as a product of hydrodesulfurization combines with the mono-alkenes present in the feed. This reaction therefore represents another pathway, besides the hydrogenation of mono-alkenes, through which octane value may be lost. This molecular understanding can lead to a couple of improvement ideas for octane management. For example, to mitigate the recombination reaction, the hydrogen-rich gas that is recycled to the ICN/HCN feedstock is scrubbed first in an amine absorber to remove the hydrogen sulfide so that it does not re-enter the hydrodesulfurization reactor. Furthermore, dividing a single hydrodesulfurization stage into two stages can also applied to reduce octane loss. For refiners with high sulfur feedstocks, it may be necessary to conduct the hydrodesulfurization in two stages, where the hydrogen sulfide liberated in the first stage is removed before the effluent is hydrodesulfurized further in the second stage. These two ideas of molecular management can be applied to reduce the octane value lost in the process of hydrodesulfurization [30]. LCN Light Cat Naphtha

ICN Intermediate Cat Naphtha

HCN Heavy Cat Naphtha

70 Sul fur

Ol efins

5,000

Thiophenes & Benzothiophenes

4,000

40

20

2,000

0

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1,000

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Thiophenes

Mercaptans & Sulfides

25

10 90

155 Distillation Temp, o C

Note 1: Olefin content is critical to FCC gasoline octane. Note 2: Difficult sulfur species concentrate in the heavy portion of FCC naphtha.

Figure 8. Sulfur and olefin distributions in FCC gasoline


220

0

Olefins, vol-%

6,000

Sulfur, wt ppm

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3.3 Molecular analysis enabling catalyst and process improvements This case study demonstrates the value of molecular analysis in discovering of new catalyst and process improvement for maximizing diesel yield and cetane enhancement via aromatic saturation and enriching diesel with paraffins. . Many refineries have a fluid catalytic cracking unit (FCC) where vacuum gas oil (VGO) boiling-range streams are converted primarily into gasoline and light olefins. One of the products of an FCC is a highly aromatic diesel boiling-range material commonly referred to as light cycle oil (LCO). Inclusion of LCO as a diesel blend component is desirable based on increasing worldwide demand of diesel relative to gasoline or fuel oil. However, LCO cannot be directly blended into the diesel pool based on its typical properties because of high sulfur content, high density and very poor ignition delay in diesel engines as indicated by low cetane number or index. In Europe and the United States, diesel specifications call for sulfur concentration of less than 15 ppm and a cetane index greater than 40 [31]. The cetane index is a value calculated from a formula based on the specific gravity and the ASTM D86 distillation. Lower specific gravity and a higher distillation boiling curve directionally increase the diesel cetane index. Hydroprocessing options are commonly employed for the upgrading of LCO into a suitable diesel pool blend component. Based on the molecular composition of this LCO the strategy for creating a suitable diesel blend component is saturation of aromatics into naphthenes and enrichment of paraffins in the diesel relative to the dense rings such as naphthenes and aromatics [32,33]. Naphthenes, in general, have about 25 cetane number value higher than their aromatic analog. Paraffins, in general, have a 10 to 20 higher cetane number relative to naphthenes. In addition, paraffins have a lower specific gravity than naphthenes or aromatics. The chemical and physical properties of the LCO are shown in Table 1. The LCO is desired to be upgraded from a cetane index of 28 to greater than 40. In the study, the LCO was subjected to operating conditions conducive to meeting the processing objectives. For example, the pressure is approximately twice the hydrogen pressure used for more typical hydrotreating for ultra-low sulfur diesel production. The pressure and hydrotreating catalysts are selected for favorable aromatic saturation. The hydrocracking catalyst is a "maximum saturation" type with moderate hydrocracking activity. Two ideas for upgrading the LCO qualities are investigated. The first option makes between 10 to 30 mole% conversion of the LCO into naphtha [32]. The second option increases the pretreat catalyst temperature to further increase saturation of aromatics. The diesel quality as a function of molar conversion is shown in Figure 9. A substantial portion of the cetane index upgrading of the LCO already occurs at 13 mole percent diesel conversion. Further increasing the pretreat temperature increases the LCO cetane number another two numbers to 41, which then meets the cetane number target.



An inspection of the compositional changes of the diesel over this range of conversions indicate that di-, tri- and 4+ aromatics are completely saturated at 13 mole% conversion. Monoaromatics are only partially saturated over all the conversion range despite the relatively high hydrogen partial pressure. The incremental diesel cetane number increase from 13 to 27 mole% conversion is primarily due to enrichment of the diesel with higher cetane number paraffins. However, the conversion of the LCO directly leads to yield loss into naphtha. The maximum selectivity for diesel retention is observed when there is a minimization of secondary cracking. Ideally, as conversion is increased the desired number of formed molecules per cracked molecule would remain constant at two. Figure 10 shows for every molecule of diesel converted, three to five molecules of cracked product instead are formed. The molecules created from cracking the LCO are hydrocarbons with primarily carbon numbers of three to eight (Figure 11), which fall outside of the diesel boiling range. Thus, it is found that using the current hydrocracking catalyst to upgrade LCO is not selective for retaining diesel, which is a very important finding. As a conclusion, molecular considerations for improving LCO qualities lead to discovering of new ideas for maximizing diesel yield and cetane enhancement. Aromatic saturation is the key process variable for cetane improvement and diesel retention. Hydrocracking provides additional increase in cetane number by enriching the retained diesel with paraffins. The trade-off for this cetane enhancement through hydrocracking is lower diesel retention. This molecular analysis indicates the direction for catalyst developments, which should focus on catalysts that change the cracking pattern of the diesel for higher diesel retention. Table 1. LCO properties and compositions LCO Properties

Value

Specific Gravity (15.5/15.5C)

0.942

Organic Sulfur, wt.-ppm ASTM D86 Distillation, LV% off 5 50 95 Cetane Number D976 Cetane Index Composition, mole-% Paraffins Naphthenes Mono-aromatics Di-aromatics Tri+ -aromatics

10700 °C 221 283 371 23 27.8 12.1 13.9 21.1 43.7 9.2


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Diesel Quality

D4737 Cetane index

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Figure 9. Trend of diesel cetane number

Molar Conversion of Light Cycle Oil Moles Created, mole% feed

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Figure 10. LCO Conversion by mole percent

Molar Conversion of Light Cycle Oil by Carbon Number Moles Created, mole% feed

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20mole% Conversion

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Paraffins

Figure 11. LCO conversion by carbon number



3.4 Molecular analysis enhances selectivity/activity and overcomes limiting conditions Selectivity and activity are the two most important aspects for catalyst and reaction system development. The molecular kinetic modeling for naphtha reforming is used as an example to improve the catalyst performance. In reforming, catalyst selectivity is a relative measure of desired product yields (C5+ reformate, aromatics and hydrogen) made with a constant feed quantity and quality and a constant conversion level (reformate octane). A catalyst with high selectivity will produce a greater yield of desired products than a catalyst with low selectivity. Maximizing catalyst selectivity is critical for reforming operators, since high selectivity will lead to high yields of high-value desired products and low yields of low value undesired products (methane, ethane and LPG). The molecular modeling for naphtha reforming was conducted [20, 34] and the model treats the process as a bifunctional catalyst system containing a metal function and an acid function based on the fundamentals of reaction chemistry and kinetics. The metal function performs via platinum sites promotes only the dehydrogenation (desired), which converts naphthene to aromatics. On the other hand, the acid function is produced via chloride on the alumina base, which contributes to hydrocracking reactions in making light end products such as LPG and fuel gas (undesired). The molecular model identified what acid sites could drive hydrocracking and how a specific metal of interest modifies the acidity of the chlorided alumina. Experiments were conducted to determine a specific metal to be added to reduce the acidity and the increase in selectivity in optimizing the ratio [35]. Firstly, the catalyst alumna base was improved via new manufacturing technique. Furthermore, acid function was modified via addition of tin (Sn) which decreases the amount of strong acid sites of chlorided alumina and thus results in lower cracking activity. As the result, acid-catalyzed cracking reactions decreased due to lower catalyst chloride levels. Thus, C5+ yield was increased by 0.6% wt% and undesired coke generation reduced by 30%. Finally, the improvements are added to the kinetic model which indicates that the value of the rate parameters of dehydrogenation on the metal function with tin added are very large compared with those of cracking reactions on the acid function, a situation preferred for high selectivity of aromatics in catalytic reforming. However, there is a limit of adding tin because lower acid level reduces catalyst activity. Then the question arises: how can the selectivity be increased further? In order to answer such a question, it is critical to have deep understanding of how a metal modulates the acidity of chlorided alumina, in particular the reaction mechanisms and active sites at the atomic level. Molecular modeling can bring new mechanism or elementary steps into kinetic modeling and helps identify the correlation between distribution of the metal of interest, promoter and acid sites, and the catalytic performance of the system. As the result, several metal promotors for yieldenhancing were identified. Selection of a promoter for a commercial CCR reforming unit is


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dependent on selectivity, activity, stability and coke make as well as its ability to maintain other catalyst properties such as chloride retention. The improved catalyst consists of a new alumina base, Pt attenuated by tin and the new promoter as well as re-optimized metal/acid ratio, which helped to increase selectivity by 2 wt% higher C5+ yield and 0.2 wt% higher H2 yield [36, 37]. Improving activity is another important aspect. The molecular modeling work for the base case catalyst shows very low effectiveness factors caused by very low internal diffusion within catalyst pellets. Low catalyst effectiveness implies that a large fraction of the catalyst surface (i.e., internal surface) does not effectively participate in the reactions due to too slow diffusion compared with relative fast reactions. This question led to development of a new catalyst with better diffusion performance, which is achieved via a high-density alumina base with a tailored pore structure to minimize already very small pores to enhance diffusion. This implies that making the pellets smaller in size and the pores short in length and straight in passage so that more particles are present at the surface and reactants can reach these surfaces faster. These properties result in increased reaction rates and higher activity. High activity catalyst enables refiners to process high throughputs [35, 38]. Thirdly, what about the rector type and what is the best reaction system design? The reaction chemistry indicates the need of avoiding back mixing as it leads to undesired products. Thus, the plug flow reactor is the choice. At the same time, the reaction energy balance shows a large temperature drop if a single reactor was used, which could have significant negative impact on yields. Thus, three or four reactors in sequence with intermediate heating was designed to mitigate the issue. It was also found that the first reactor experiences a steep temperature drop because of the rapid naphthene dehydrogenations, which are very endothermic. The effective remedy is to reduce the flow length for the first reactor to reduce the temperature drop. The reactor design eventually evolved to moving bed design as it enabled the continuous catalyst regeneration (CCR) which features high catalyst activity, more reformate with higher aromatic content, and high hydrogen purity. The CCR design can satisfy the increased reforming severities due to a continuous catalyst regeneration system. Since reaction rates for different reactions are so different, some reaction(s) may be dominant in a certain reactor and the design of a reaction system involving different catalyst formula, WHSV’s and temperature for different reactors can achieve higher selectivity and activity. 3.5 Molecular modeling enabling catalyst selection and process condition optimization This case shows the power of integrating molecular modeling with mathematical optimization to explore synergy of optimizing catalyst selection (via integer variable) and operating conditions (via continuous variables). The reactions involved in the reforming process include hydrogenation and dehydrogenation, isomerization, paraffin cracking, naphthene and aromatic side-chain cracking, ring opening, and



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ring closure. Based on the MTHS pathway approach [20], the reforming reaction pathways can be represented as shown in Figure 12, which involves 21 components (or composition groups) and 51 reaction steps. The reaction kinetics can be modeled [39] with the effective reaction rate constant kj for the reaction j (j =1…51) in the network correlated with temperature (T) and pressure (P) as α  1 1   P  j  −    R  To T  Po 

E j k j = k 0j exp 

j = 1,⋅ ⋅ ⋅,51

(1)

where k 0j is the effective rate constant; Ej is the activation energy; αj the pressure effect parameter; To and Po are base reaction temperature and pressure respectively. P5 + P1 P6 + P1

P7 + P1 P8 + P1

.. . .. .

N6 + H2

P6 + P1

P7 + P2

A6 + H2

P9 + P1 A8 + P1

P6 + P4

P10

N10

P4 + P2

A9 + P1 A10

A7 + P1

A8 + P2 N9 + P1 N7 + P3

N8 + P1 N7 + P 1 A7 + H2

Figure 12. Reaction network of catalytic reforming For the reaction network of Figure 12 and based on the kinetic parameters, the rate equations are in the form of differential equations, which can be expressed as below

ri =

dci = f i (k1 ,..., k j ,..., k n r , c1 ,..., ci ,..., cn c ) × η dt

(2)

where ri is the reaction rate for component i in the reforming product; ci is the product mole fraction of component i (i=1…nc) and nc (= 21) is the number of reforming components modeled; fi is the reaction rate equation for component i; kj is the kinetic constant for reaction j (j=1…nr)


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defined in equation (1) and nr (= 51) is the number of reforming reactions; t is the time. η is the effectiveness of catalyst pore diffusion describing the effects of diffusion on the reaction rate. The kinetic model and reaction rate model expressed in equations (1) and (2) are applicable for the reaction network depicted in Figure 12 for a given catalyst. For different catalysts, the effective rate constant k 0j , activation energy Ej, pressure effect parameter αj and catalyst effectiveness η will be different. Thus, a new subscript l is introduced in the model while an integer variable zl is defined to represent different catalysts. nx is the number of catalysts available for selection. Thus, an optimization model can be expressed as equation set (3) with the objective to optimize molecular fractions in the product and thus maximize the profit for the process via catalyst selection and process conditions optimization. n x nc

Maximize

s.t.

∑ ∑ pi ⋅ (ci ,l ⋅ mi ,l ⋅ Fl ) ⋅ zl

l =1 i =1

z, T , P

(3)

nx

dci ,l

= ∑ zl × f i ,l (k1,l ,⋅ ⋅ ⋅, k n r ,l , c1,l ,⋅ ⋅ ⋅, cn c,l ) ×η l

dt

l =1

ci ,l (0) = ci0,l

k j ,l

E = k exp  j ,l  R 0 j ,l

ηl = g l ( M T ) nc n x

RON = ∑ ∑ zl × RON i ,l i l =1

nc n x

BEN = ∑ ∑ zl × BEN i , l i l =1

nx

∑z

l

α j ,l

1  P   1 −     766 T  300 

=1

l =1

T L ≤ T ≤ TU P L ≤ P ≤ PU

RON L ≤ RON ≤ RON U

BEN L ≤ BEN ≤ BEN U

i = 1,⋅ ⋅ ⋅, nc , j = 1,⋅ ⋅ ⋅, nr , l = 1,⋅ ⋅ ⋅, nx



where fil is the reaction rate equation for component i for given catalyst l while kjl is the kinetic constant for reaction j for given catalyst l as defined in equation (1). ci is the product mole fraction for component i. mi is the ratio of molar mass of component i and average molar mass of the product. F is the total mass rate of the product. pi is the price of component i. Thiele Modulus MT is a very important parameter for describing the effects of internal pore diffusion on reaction rate in the porous catalyst pellets with no mass transfer limitations. MT is a function of pore diffusion, pore geometry and concentration inside pore. Superscript L indicates the lower bound and superscript U the upper bound applied to temperature (T) and pressure (P), benzene content (BEN) and octane (RON). The type of the catalyst (zl), temperature (T) and pressure (P) are the independent variables while molecular fractions (ci) are dependent variables. Catalyst type, temperature and pressure influence the reaction kinetics and the molecular compositions while molecular flow rates and composition determine the profit of the process defined in the objective function. While temperature and pressure are treated as continuous variables, catalyst selection is modeled as the integral variable. With the sum of zl equal to one, it guarantees that only one catalyst is selected at one time from the given number of catalysts (nx). If considering the possibility that two catalysts could be selected at the same time for synergetic interaction, the sum of zl will equal to and less than two in equation set (3). If the optimization model selects the option of two catalysts in coexistence, it could lead to a novel catalyst bed design and one such an example is to stack these two catalysts in layers of packing, which features linear interaction of two catalysts. When two different catalysts are in mixture which are stacking in layers of packing, both the linear and the none-linear interactions between catalysts must be considered in the mathematical expressions. Two catalysts were considered for selection in this case, which have different yield performance in terms of C5+, aromatics and H2. Type B catalyst has relative lower C5+ yield but higher aromatics yield because of higher benzene content. On the other hand, Type A catalyst has relative high C5+ yield which is important for reformate production. For simplicity, it was assumed that the reaction system consists of four plug flow reactors. To model each reactor, it is divided into five continuous stirred-tank reactor (CSTR) zones and thus four reactors form 20 CSTR zones. The outlet of a previous reaction zone becomes the feed for the next zone. The optimization model is solved sequentially from zone 1 to zone 20. Through catalytic reforming, the naphtha feed is converted into three products, namely hydrogen, light hydrocarbon products and reformate for gasoline (main product). The optimization model expressed in equation set (3) will determine the optimal catalyst, temperature and pressure which will maximize the profit under constraints of process conditions (T, P), gasoline quality in terms of octane (RON) etc. If necessary, other specifications, such as MON, RVP, etc., can also be added to the model as constraints.


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In overall, the optimization determines the operation that can maximize stabilized gasoline rate while maintaining a sensible RON value. For the comparison purpose, two different objective functions are investigated under the same constraint RON ≥ 99 and within the temperature range 750-790 K and the pressure range 190-200 psia. Optimization results are given in Table 2. For the objective function of maximizing profit, the benzene content limit is provided in model (3) to reflect the market specification for gasoline. From optimization, Type A catalyst with the lower benzene yield but higher C5+ yield was selected in order to meet the market requirement for the benzene content in gasoline. From the optimization results, it is observed that raising the temperature can make the RON higher for the gasoline via increasing benzene and aromatics content. However, the yield of the stabilizing gasoline decreases significantly due to more hydrocracking of valuable components converting to light hydrocarbon products, which generally has a negative effect on the profit. On the other hand, reducing pressure promotes the production of reformate for the same RON. Assume the catalytic reforming process will be utilized to produce an intermediate product as the feed for aromatics production. To reflect this operation, a different objective function, e.g. maximizing RON, is used. In this case, the benzene limit is removed from the model as the operation mode is to produce feed for aromatics production. The optimization selected a different catalyst (Type B) with higher aromatic yield. At the same time, the reaction severity (e.g. temperature and pressure) is increased in order to increase the benzene and aromatics contents as much as possible. In this case, profit will be calculated based on the ultimate products (i.e. benzene, toluene and para-xylene) instead of the stabilized gasoline. It must be pointed out that the equation set (3) is not a complete model for reaction system optimization. A complete model should also include mass balances describing the relationship between catalyst, reaction conversion, and reactor volume ; as well as the energy balances describing the relationship between reaction equilibrium, heat of reaction and temperature profile inside reactors. Furthermore, a complete model should consist of detailed expressions on surface kinetics to define pore effectiveness η and Thiele Modulus MT. The details of the modeling aspects are not provided here as it is beyond the scope of the discussions here. Table 2. Optimization results for the Catalytic Reforming Process Catalyst (Type)

Profit ($/hr.) 79726

T (K) 765

P (psia) 206

Octane RON 99.6

Ga (wt%) 50.61

Gb (wt%) 5.66

Gc (wt%) 80.22

Catalyst B

72662*

790

204.2

103.5

57.75

5.68

62.73

Initial value Obj: maximize RON

Obj: maximize profit Catalyst A 80953 760 190.1 99.0 49.47 5.59 83.41 Ga (wt%) is the weight percentage of total aromatics in the stabilizing gasoline. Gb (wt%) is the weight percentage of total benzene in the stabilizing gasoline. Gc (wt%) is the weight percentage of stabilizing gasoline in the corresponding product. * The profit is calculated based on intermediate product. It would be higher if transfer price for aromatics production is applied.



3.6 Molecular analysis enabling novel process concepts Molecular analysis can reveal what are the desired molecular compositions in the feed needed to meet the composition requirement in the product for a process. This understanding can optimize molecular routes which lead to discover of new process technology. The following example is used to illustrate this opportunity. Growth of petrochemicals such as ethylene, propylene and BTX is expected to continue in the future. With relative low crude oil price in recent years, a significant opportunity exists to convert crude oil directly to petrochemicals. For most steam crackers (SC) producing ethylene and propylene, the main feeds are refinery LPG and light naphtha. The main source of light naphtha could be produced from refineries via CDU (crude distillation unit), FCC (fluidized catalytic cracking) and LCO HCU (hydrocracking) processes. Typically, refinery LPG and light naphtha are sent to the steam cracker directly. However, molecular analysis of compositions in FCC and LCO HCU products indicates that the LPG and naphtha produced from FCC and LCO HCU contain a large amount of isoparaffins (i.e., iC4, iC5 and iC6 etc.); while the steam cracker prefers feeds containing normal paraffins. If these isoparaffins can be converted to normal paraffins, the ethylene yield from the steam cracker will increase significantly. Otherwise, the steam cracker will make more cracked gas as by-product from the iso-components. The idea for new process concept was developed based on this molecular composition analysis: reverse the reaction direction in traditional isomerization processes. The current isomerization technology converts normal C4, C5 and C6 paraffins to iso C4, C5 and C6 paraffins for the production of isomerate as gasoline blending stock, because iso-paraffins has higher gasoline RON than normal paraffins. The reversed isomerization will convert C4, C5 and C6 iso-paraffins to C4, C5 and C6 normal paraffins making a much better feedstock for the steam cracker. This idea led to the birth of the reverse isomerization concept [40], which resulted in significant yield improvement for the petrochemical products. The conversion from iso’s to normal’s has been readily accomplished by transforming Honeywell UOP’s traditional ButamerTM Process (converting normal C4 to iso-C4) and PenexTM Process (converting normal C5 and C6 to iso-C5 and iso-C6) into the reverse isomerization technology. Conversion of naphtha from FCC and HCU based on LCO feed from iso-paraffins to normal paraffins via reverse isomerization technology will increase ethylene yield by 20-30% and propylene yield by 10%. The added value of the reversed Butamer TM and Penex TM Processes for one steam cracker process could be in hundreds of million dollars per year.


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3.7 Molecular property difference enabling hybrid separation The last case but not the least is to demonstrate that molecular analysis can determine property difference between key components to b separated, which can be used for selecting the appropriate separation technology and identify the need of hybrid separation system. It is common to apply distillation technology for most separation tasks in the process industries due to the maturity of technology and the reliability of column operation. However, distillation has its own limitations due to the nature of distillation. When boiling point temperature of two key components is close, the size of distillation column becomes very large and the cost becomes prohibitive. Thus, the question becomes: how to identify the most promising separation method as an alternative for the task in hand and why? Let us use the propane and propylene separation example to explain. Propylene and propane are among the light hydrocarbons produced by thermal and catalytic cracking of heavy petroleum fractions. They are traditionally separated by distillation. Because distillation requires more than 120 trays and high energy costs due to considerable reflux and boil up flow rates compared to the feed flow, great attention has been given to the possible replacement of distillation with a more economical and less energy-intensive separation alternative. To search for better separation technology for this separation problem, molecular analysis was conducted. First, molecular properties of these two components were obtained as shown in Table 3. The fact that the relative volatility between these two components is very close to 1 indicates that distillation is not effective fundamentally for this separation task and reveals the sole reason why the distillation requires a very tall and large column with lots of energy. However, dipole number stands out to differ between these two components. Propylene has the asymmetric location of the double bond leading to a higher dipole number than propane. Facilitated transport (FT) membrane could be the promising fit-in-purpose separation technology for this task. FT membrane separation is based on solution diffusion as well as facilitated transport, i.e. reversible olefin complexation through π bonds with metal cations in a polymer membrane where olefins can form reversible chemical bonds with transition metal ions incorporated in the membrane due to the specific interaction between the olefin’s hybrid molecular orbitals and the metal’s atomic orbitals. But the question remains: how to explore the dipole number different between propylene and propane? From the lab experiments searching for a material which can provide high affinity to propylene, it was found that impregnating silver nitrate onto FT membrane can achieve this [41,42]. Effective separation occurs: propylene can be easily adsorbed to membrane surface and permeate through it much better than propane. Thus, FT membrane using impregnated silver nitrate becomes the most promising separation technology for this task.



However, FT membrane alone cannot accomplish this separation practically as it could require too big the membrane size resulting too large the plot space. Thus, a hybrid system consisting of FT membrane and a distillation tower was considered [43]. In this hybrid system, distillation does the rough separation while the membrane completes the separation for propylene to meet specification. The simulation result indicates the hybrid system with FT membrane and distillation can increase propylene recovery from 80% by distillation only to 95% by the hybrid system. Many million dollars in both capital and operating costs could be saved by using FT membrane to reduce the size of the distillation column and reboiling duty.

Table 3. Molecular properties for propylene and propane Molecular weight van der Waals volume, m3/mol Dipole moment, debyes Normal melting point, K Normal boiling point, K

Propylene 42.1 34.08 0.4 87.9

Propane 44.1 37.57 0.0 85.5

225.4

231.1

This example shows that understanding of molecular properties provides insights for the most promising separation methods to use for the task in hand. There are many potential hybrid systems that could achieve the separation objectives with lower capital and operating costs than distillation alone. When two or more separation techniques are integrated in a single operation, such operations are termed as hybrid separations. Such integration may lead to improved separation processes with reduced capital and operating costs. 4. Concluding remarks and future challenges In summary, it has been demonstrated above that the molecular analysis can provide strong insights for process synthesis. The discussions presented in this article provide a glimpse of the power of the molecular analysis for process synthesis in practical applications; but much more needs to be done. Research in molecular analysis for process synthesis will lead to breakthroughs in terms of science, engineering and applications. This is largely true because molecular models provide new insights into chemistry, materials and chemical engineering. Fully exploiting these new insights will lead to discovery of new opportunities for technology development and process optimization [6]. This molecular analysis method can be used to test new ideas and inspire new theories. Of course, much more research work needs to be done to make the molecular analysis more systematic for practical applications. The challenges could be daunting; but the reward will be huge as efficient design of chemical processes could play important roles in increasing economic margin while reducing environmental impact to achieve the sustainability of chemical production in the face of enormous economic growth worldwide. The research along the line should receive significant attention from research community and funding bodies.


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Several major challenges lay in front of research into developing the molecular analysis based process synthesis methodology. The primary challenge comes from molecular modeling. Currently, the reaction kinetic models are usually obtained via pilot plant tests, which are expensive and time consuming. Thus, the question is: how could reaction kinetic models be developed based on first principles using smart methods in a more automated manner to avoid extensive experiments? The solution to this challenge is possible due to advance in both theoretical and computational chemistry and computing technology such as big data analytics and cloud data storage. Nowadays, kinetic models can contain hundreds of molecular species and thousands of reactions. Models with over thousands of reactions are not unusual [44]. To avoid tedious manual handling, the kinetic community developed automation methods for generating reaction mechanism, the reaction network and then kinetic models using software tools [45,46]. The reaction constants in the kinetic models can be adjusted based on process conditions. The molecules of interest can be tracked throughout the reaction network via kinetic models [47]. Therefore, with advances in chemistry, big data analytics and computer hardware and software, automation is possible for kinetic modeling including automated feedstock modeling, reaction pathway construction, reaction type selection and kinetic rate estimation. The focus for meeting this challenge should be on practical application of this kind of automated kinetic modeling based on first principles. However, such an approach, which is quite popular at current stage of molecular kinetic modeling, is heavily dependent on known reaction mechanisms of relevant chemistry. In development of new catalysts, it is not unusual to see new chemistry processes at the atomic scale, mostly due to new active sites which have not been studies before, which defines the second major challenge. In this situation, estimate of kinetic constants or mechanistic details could be unreliable or even misleading, which causes great deviation of the overall kinetic model from reality. In order to improve understanding of chemistry on new materials, it is more reliable to carry out quantum chemistry based molecular modeling so that fundamental steps can be elucidated with both atomic scale mechanisms and estimates of kinetic constants. Therefore, it is critical to automate the generation of reaction mechanisms in molecular modeling so that the complicated reaction network can be mapped out [48]. Preliminary effort has been made by theoretical and computational chemists on addressing such challenge. For example, the adaptive kinetic Monte Carlo method integrated with DFT calculations has been demonstrated with the capability of identifying complex reaction networks without significant manual inputs by users [49,50]. Other challenges come from process design. For separation system design, the challenge is to develop technology selection methodology and hybrid separation design to accomplish difficult separation. Hybrid separation has the potential in reducing energy and capital costs because it combines different separation principles and constitute a promising design option for the separation of complex mixtures. For example, integration of distillation (based on boiling points)



with adsorption (based on selectivity) can significantly improve the separation of azeotrope mixtures. Similarly, the challenge for reaction system is to develop design methodology for reactive separation system which can enhance both reaction conversion and selectivity against a conventional reactor on stand-alone. For example, in membrane reactors, reaction and separation via the membranes are coupled. When the membrane is selective both conversion and selectivity can exceed those of a conventional reactor. Understanding of molecular information could lead to discovery of new catalysts/materials and new process concepts. R&D in obtaining molecular information, developing molecular models and optimizing molecular flows will enable technology companies to develop new process technology and improve existing technology, at the same time, help operating companies to enhance operating margin and achieve true potential.

Acknowledgements The author would like to specifically thank Haiyan Wang, John Petri, Steve Zink, Mark Lapinski and Selman Erisken for their contributions to the article. Furthermore, the author wishes to express sincere thanks to Rich Rossi, Jim Paschall and Mark James for company internal review.

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Molecular Analysis for Process Synthesis - Industrial & Engineering

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