Identification of Multistep Reaction Stoichiometries: CAMD Problem Formulation

Computer Aided MolecularDesign: Theoryand Practice L.E.K. Achenie, R. Gani and V. Venkatasubramanian(Editors) 92003 Elsevier ScienceB.V. All fights reserved.

167

C h a p t e r 7: I d e n t i f i c a t i o n of M u l t i s t e p R e a c t i o n S t o i c h i o m e t r i e s : CAMD P r o b l e m F o r m u l a t i o n A. Buxton, A. Hugo, A.G. Livingston & E.N. Pistikopoulos

Reaction path synthesis and the selection of an optimal route for the manufacturing of a desired product provide the earliest opportunities for waste reduction when designing environmentally sound processes. In the work presented here, a systematic procedure for the rapid identification of alternative multi-step stoichiometries is described in which minimum environmental impact considerations are incorporated. Both the size and complexity of the reaction path synthesis problem are reduced by decomposing it into a series of steps. First, a new group based co-material enumeration algorithm, introduces material design principles through structural and chemical feasibility constraints to rapidly generate a manageable set of raw materials and co-products. Next, stoichiometries are extracted from the co-material set using a two step optimisation procedure, including whole number stoichiometric coefficient constraints, carbon structure constraints and case specific constraints based on chemical knowledge. Thermodynamic, economic and environmental impact criteria are employed in the evaluation of feasible stoichiometries, with aspects of the Methodology for Environmental Impact Minimisation (Pistikopoulos et al., 1994) providing the framework for the environmental evaluation of alternatives.

7.1 INTRODUCTION In the synthesis of a facility to manufacture a given desired product, the selection of an appropriate chemistry provides the earliest opportunity to influence the environmental and economic performance of the process. However, reaction route design and selection is a large and difficult problem. The major difficulty is attaching enough information to a particular reaction route alternative to make an informed choice about the potential of the route to be developed in to a promising process. When only chemistry is known, it is difficult to quantify the costs and wastes associated with the eventual process in which the chemistry will be carried out, because of the large number of sources of expenses and waste which are not directly related to chemistry, and the range of different process topologies and equipment which may be associated with alternative

168 chemistries. This problem is compounded by the fact that the vast majority of reaction schemes of industrial interest are of a multi-step nature (Rotstein et al., 1982). Recognising these problems, it seems more sensible to identify candidate multistep reaction routes rapidly according to some simple criteria using limited information, t h a n to devote time and resources to developing detailed reaction schemes which may be rejected later due to poor process performance. However, the synthesis of alternative reaction paths leading to a desired product was initiated by organic chemists who were interested in synthesising large, complex molecules, albeit in more efficient ways. Consequently, their approaches tended to concentrate on the generation of chemistries, rather t h a n on the selection of promising routes. Agnihotri and Motard (1980)categorised these tools as information based systems and logic based systems, according to the reaction representation technique employed. Information-based systems have their roots in real chemistry. Molecules are represented in terms of their atomic or group constituents and reactions, known as transforms, are based on real, known chemical transformations (Corey et al., 1969, 1972, 1976; Gelernter et al., 1973; Wipke et al., 1976; Govind and Powers, 1981; Kaufmann, 1977; Knight, 1995; Mavrovouniotis and Bonvin, 1995). The development of appropriate transforms relies heavily on chemical knowledge while each transform may carry with it information relating to the molecular substructures to which it can be applied and the structural alterations it brings about - requiring details of any by-products which are produced or reagents which are required as well as typical operating conditions for the reaction and kinetic information. Consequently, according to Govind and Powers (1981), information based systems offer good predictive power, in that they are able to represent specific distinct reactions in detail. However, they suffer poor generality, since their ability to represent different reactions is limited to the available transforms. Furthermore, a large data base of information or a set of predictive techniques is required to implement such approaches. Information based systems most commonly build synthesis trees, usually working ~backwards (retrosynthesis) from the product. Retrosynthesis is an open ended problem which may lead to the development of a large network of reaction schemes and corresponding materials, even with a small number of transforms. Accordingly, the screening requirements which go along with information based systems are typically large. By comparison, logic based systems are much easier to handle and control. These methods employ purely mathematical representations for molecules and

169 their reactions (Ugi and Gillespie, 1971; Hendrickson, 1976). The most widely studied logic-based approach is centred around an atom balance, a matrix equation which describes the chemistry of a particular set of predetermined species, and from which stoichiometries leading to a particular product can be extracted (Rotstein et al., 1982; Fornari et al. 1989, 1994a, 1994b; Crabtree and E1Halwagi, 1994; Holiastos and Manousiouthakis, 1998). In this approach, only chemical formula information is required to generate stoichiometries, so that this approach provides a much more direct route to alternative multi-step reaction schemes. However, in order to apply this approach, all candidate raw materials and stoichiometric co-products (which will henceforth be referred to collectively as com a t e r i a l s ) must be known in advance and included in the matrix. While the careful pre-selection of these materials provides an early opportunity to limit the size of the problem and to screen out poor materials, no systematic method has been proposed to generate these materials. While Fornari et al. (1989, 1994a, 1994b) and Crabtree and E1-Halwagi (1994) limited themselves to single step reactions, Rotstein et al. (1982) and Holiastos and Manousiouthakis (1998) demonstrated the potential of the approach to develop multi-step reactions by considering closed cycle sequences of reactions known as clusters. A cluster of reactions is a sequence of thermodynamically feasible reactions in which the intermediates produced by the reactions in the cluster must also be consumed by other reactions in the cluster, with the net result being an overall main reaction which is thermodynamically infeasible, and therefore not directly achievable (Rotstein et al., 1982). In cluster synthesis, this main reaction must be specified in advance. Rotstein et al. (1982) also applied their approach to open cycle sequences of reactions, in which the intermediates produced within the sequence are not completely consumed. However, although they introduced unspecified raw materials and co-products, they limited themselves to overall reactions in which the desired product and certain of the raw materials were specified in advance. Without careful consideration, stoichiometries generated by the matrix based approach may involve any number of apparently simultaneous reactants and co-products (so that a single stoichiometry may in fact be decomposable in to several sequential steps) with stoichiometric coefficients that may take any values. Buxton et al. (1997) were the first to tackle these problems directly, introducing linear whole number stoichiometries constraints together with limitations on the numbers of reactant and product species. Recently, Holiastos and Manousiouthakis (1998) introduced non-linear integer constraints to perform the same functions in the context of reaction cluster synthesis. They defined allowable chemical reactions according to the general characteristics of elementary reactions, which depict chemical transformations as they truly happen at

170 the atomic scale, and applied their constraints accordingly. Using a modified branch and bound solution procedure they circumvented the non-linearity of their integer constraints. Extensions have predominantly concentrated on the application of integer programming techniques to the design of simplified reaction mechanisms for improved computational efficiency (Androulakis, 2000; Edwards et al., 2000; Sirdeshpande et al., 2001). The key advantage of such information based systems is that they can provide kinetic information for the preliminary screening of reaction routes. Knight (1995) employed computational chemistry involving statistical mechanics and probability theory to determine products, their distribution and the reaction rates, while Mavrovouniotis and Bonvin (1995) used c h e m o m e t r i c s - the simulation of reaction systems with kinetic models and principal factor analysis to identify the major pathways. Consequently, the information and computational requirements of these approaches are large. Although the predictive power of the matrix based approach is poor, since it provides much less information, much simpler criteria can be applied to identify promising candidate stoichiometries, or at least to eliminate poor alternatives. Simple economic criteria, based only on the values of products and reactants have been employed by Fornari and Stephanopoulos (1994b). Gibbs free energy of reaction has been used to provide an initial indication of the cost feasibility of a process: conversion, yield, recycle flows, difficulty of separation etc. (Fornari and Stephanopoulos, 1994b), to indicate the directionality and reversibility of reaction steps (Mavrovouniotis and Bonvin, 1995), to determine equilibrium concentrations among reacting species (Crabtree and E1-Halwagi, 1994) and to provide an upper limit for thermodynamic feasibility (Agnihotri and Motard, 1980; Fornari et al., 1994a, b, 1989; May and Rudd, 1976; Rotstein et al., 1982)a Gibbs free energy change of reaction of 10 kcal/gmol has long been accepted to provide an upper bound for the thermodynamic feasibility of reactions (Rotstein et al., 1982). Rotstein uses this criterion to determine the temperature range over which reactions are thermodynamically feasible. The only documented reaction route design technique to take explicit account of environmental issues is that of Crabtree and E1-Halwagi, (1994). In order to select an i n n o c u o u s stoichiometry, they imposed simple concentration limits on certain compounds in the reactor effluent stream. However, this approach does not provide a consistent method of assessing the environmental impact of alternative reaction routes since only the effluent concentrations of certain compounds were considered (not the i m p a c t s of all compounds). Furthermore, it is unlikely that the reactor effluent, or even the by-products or co-products would be emitted directly to the environment. Moreover, the input wastes associated with the raw materials and the impacts of downstream processing are not included.

171 In the work presented here, a procedure for the rapid identification of alternative multi-step stoichiometries is developed. Material design principles are introduced to formalise the development of a set of co-materials and an optimisation procedure, based around the matrix representation, is employed to extract stoichiometries from this set. Linear constraints are developed to limit the number of reactant and product species and to ensure that each stoichiometric step involves whole number stoichiometric coefficients. Thermodynamic, economic and environmental impact criteria are employed in the evaluation of the stoichiometries, while aspects of the Methodology for Environmental Impact Minimisation (MEIM) of Pistikopoulos et al. (1994) provide the framework for the environmental evaluation of alternatives. The application of the method is illustrated in this chapter through an example; the synthesis of production routes for the pesticide 1-naphthalenyl-N-methyl carbamate also known as carbaryl. While in Chapter 14, the main features of the methodology is further highlighted through a second case study; the production of acetic acid, an important alipahtic intermediate.

7.2 I D E N T I F I C A T I O N OF E N V I R O N M E N T A L L Y B E N I G N STOICHIOMETRIES

The problem addressed here may be stated as follows: Given a desired organic product Identify a set of candidate multi-step organic reaction stoichiometries for the production of the desired product which are both economically and environmentally promising. A three step procedure is applied, involving: (i) selection of co-material groups, (ii) determination of a set of candidate co-materials using group based molecular design techniques and (iii) identification of a set of promising candidate multi-step stoichiometries using the matrix based representation system and an optimisation procedure incorporating aspects of the MEIM. The use of such a structured, stepwise procedure reduces the multi-step stoichiometry identification problem to a manageable size. The key to the procedure is the introduction of co-material design (steps (i) and (ii)). With the product and stoichiometric co-materials known, the identification of feasible reaction stoichiometries is no longer an open ended problem. The steps of the procedure are described in the following sections.

172 7.3 CO-MATERIAL D E S I G N 7.3.1 I n t r o d u c t i o n

Co-material design is based on the observation that much organic chemistry essentially consists of reorganising functional groups, through additions, substitutions and eliminations, so that co-materials are expected to contain (at least) the chemical groups present in the desired product. According to this observation, a group based computer aided design approach is adopted for comaterial design. The aim of this approach is to systematically enumerate a set of alternative stoichiometric co-material candidates from a group set selected according to the groups present in the product, those present in any existing industrial co-materials, the types of chemistries to be considered (e.g. aromatic or aliphatic) and other considerations such as property constraints. Groups are employed as the molecular building blocks rather than atoms for several reasons. First of all, this considerably reduces the combinatorial size of the molecular generation problem without much loss of g e n e r a l i t y - very many organic compounds can be constructed using only a small number of groups. Secondly, a suitable choice of groups (e.g. UNIFAC groups) gives direct access to physio-chemical, thermodynamic and environmental properties through group contribution methods. Finally, with appropriate group bonding restrictions, such a method provides a short cut to structurally and chemically feasible molecules, hence significantly reducing molecular screening requirements. Any of the molecular design techniques reviewed by Buxton (2002) may be applied to generate sets of candidate materials. However, of the variety of available techniques, only the enumeration and knowledge based approaches are specifically designed to explicitly enumerate molecules from a pre-selected set of groups. All other approaches can be viewed as implicit enumeration strategies, in which the aim is to identify optimal structures through evolution or optimisation without explicitly constructing all alternatives. Thus, the knowledge based and enumeration approaches represent the best candidates for use in co-material design. Of these, the most general approach is that of Gani and coworkers, as reported by Constantinou et al. (1996). This procedure is UNIFAC group based, and includes in the enumeration algorithm rules designed to ensure that only structurally and chemically feasible molecules result from the molecular design exercise. These two features make this approach the most attractive starting point for co-material design. Although structural and chemical feasibility rules feature in the other group based techniques, Derringer and Markham (1985) focussed only on polymers, Joback, Stephanopoulos and coworkers (1984, 1989,

173 1995) employed a generate and test paradigm, applying their rules only after generating all possible combinations of groups, and Porter et al. (1991) considered only certain homologous series. The computer aided product design (CAPD) approach reported by Constantinou et al. (1994, 1996), is based on a system of group classification and categorisa-

tion. A total of one hundred and eight unique UNI FAC groups are featured in the technique, including nine aromatic groups. These groups are divided into nine classes and five categories. The class of the group (0 - 4) represents the number of free attachments of the group (i.e. the group valency) and the category signifies the level of restriction for bonding with other groups - the higher the category the tighter the restrictions. The aromatic groups are placed in classes 5 - 8, class zero consists of some simple complete molecules. The molecular design algorithm is based on a set of primary and secondary conditions. The primary conditions ensure structural and chemical feasibility, firstly by guaranteeing that the complete compound has zero valency and secondly t h a t it obeys the principles of chemistry. These principles have been embodied in a set of rules which determine the maximum permissible number of groups from any category which can be present in a molecule and the permissible combinations of groups from the different categories. The secondary conditions are related to restrictions arising from the limited validity of the group contribution properties prediction methods. The rules based on the primary conditions are divided into three sets; a set each for acyclic, cyclic and aromatic molecules, and the UNIFAC groups have been divided in to three sets (which share many common groups) according to the desired molecular structure. From these group sets, the rules allow for the design of cyclic and acyclic molecules of up to twelve groups and of aromatic molecules of up to eighteen groups with a maximum of three aromatic rings. The molecular design algorithm has been developed to systematically generate all molecules which satisfy these conditions. However, some feasible structures are rejected because of doubtful stability or because group parameters are not available. Nevertheless, despite this conservatism, this technique can potentially generate thousands of molecules (Constantinou et al., 1996), which is more t h a n adequate for co-material design. Furthermore, the approach provides very well for the inclusion of the additional structural restrictions which may be necessary in co-material design. Full details of group classification, categorisation and division, and of the primary chemical feasibility rules are provided in Constantinou et al. (1996), and a description of the enumeration algorithm is presented in Gani et al. (1991). It is these rules which form the basis of the co-material design procedure presented in the following sections. In addition to these rules, the co-material design procedure features other rules based on engineering and

174 chemical insight, which are designed to reduce the size of the enumeration problem.

7.3.2 Co-Material Design Procedure GROUP PRE-SELECTION Group pre-selection is the first step towards designing co-material molecules and has the most direct effect on the number of molecules generated. To restrict the size of the enumeration problem, the following simple rules are employed to guide group pre-selection: (i) select the groups present in the product, (ii) select the groups present in any existing industrial raw materials, co-products or by-products, (iii) add groups which provide the basic building blocks for the functionalities of the product or of similar functionalities, (iv) add groups from the group sets for the desired chemistry (cyclic, acyclic or aromatic) and (v) reject groups which violate property restrictions (e.g. chloro groups may violate environmental r e s t r i c t i o n s - Gani et al., 1991). CO-MATERIAL ENUMERATION FORMULATION The co-material enumeration formulation consists of four sets of equations; chemical feasibility rule equations (based on the rules provided by Constantinou et al., 1996), the octet rule for structural feasibility, additional problem specific structural restrictions and the objective function. It is assumed t h a t this approach provides all interesting organic co-materials and that all generated molecules are chemically feasible. The existence of generated molecules may be verified from chemistry literature (Compounds, 1996), although such sources tend to include rare compounds which may be unlikely co-materials. The sets employed in the algorithm are shown in Table 1. Table 1: Co-Material Enumeration Model Sets J CL CT R

chemical groups group class group category chemical feasibility rules

Chemical Feasibility Rules In Constantinou et al. (1996), the chemical feasibility rules are given according to the categories of groups. Category one groups have no bonding restrictions. According to Gani et al. (1991) category two groups of classes 1 - 4 are special groups which can appear more than once but cannot be connected with each other or with another group from the same or higher category. Since there are only six category two groups in classes 1 - 4 , only one of which (the chloro group) is included in the example problems considered here, no general rules reflecting

175 these restrictions were included in the co-material e n u m e r a t i o n formulation. To avoid violation of these restrictions, integer constraints are instead included on a case by case basis. For categories 3 - 5, the chemical feasibility rules are presented in t a b u l a r form, with a s e p a r a t e table for acyclic, cyclic and aromatic molecules in Constantinou et al. (1996). In each table the columns are: the total n u m b e r of groups in a molecule, the largest class of group present, the n u m b e r of groups from this largest class, the m a x i m u m allowable n u m b e r of groups from category 3, the m a x i m u m allowable n u m b e r of groups from category 4, the m a x i m u m allowable n u m b e r of groups from category 5, the total n u m b e r of groups allowed from categories 3, 4 and 5 together, and the total n u m b e r of groups allowed from categories 4 and 5 together. Thus, each row in the tables represents a unique set of rules for the allowable n u m b e r s and combinations of groups from categories 3, 4 and 5 according to the total n u m b e r of groups, the largest class of group present in the molecule and the n u m b e r of groups from this largest class. Above a certain total n u m b e r of groups, it is possible to construct molecules with the same total n u m b e r of groups in which the largest class of group is different, and in which the n u m b e r of groups from this largest class is different. Thus, there can be several rows in the table and therefore several rule sets, for a particular total n u m b e r of groups. In order to e n u m e r a t e co-materials, each table c o l u m n is first w r i t t e n as an R x 1 vector, where R is the n u m b e r of rule sets (i.e. the n u m b e r of rows in the rule table). However, the t r e a t m e n t of classes is somewhat different t h a n in the tables. I n s t e a d of writing a largest class vector, and a n u m b e r of groups from this largest class vector, two vectors are written for each class, one which gives a lower bound, and a second which gives an upper bound on the allowable n u m b e r of groups from each class. For classes above the m a x i m u m for the particular rule set, both lower and upper bounds are set to zero. For the largest class, both lower and upper bounds are given the appropriate value for the rule set, and for classes below the m a x i m u m , the lower bound is set to zero and the upper bound is given the value of the total n u m b e r of groups m i n u s the n u m b e r of groups from the largest class. The rules can then be w r i t t e n as the following equations. F i r s t of all, an R z 1 vector of binary variables d~ is introduced such that:

~dr- 1

(1)

/,

This vector is used throughout the equations to ensure t h a t only one rule set r is active at any one time. The total n u m b e r of groups in a molecule is then given by:

Z: j

,:2)

=

cl

ct

r

176 where nj,cZ,ct is defined as a positive integer variable which represents the number of groups j which appear in a molecule, and n rt is the total n u m b e r of groups in the rule set r. cl and ct are the class and category of group j respectively, each group is given a unique class and category a s s i g n m e n t by the following equation:

cl

ct

This equation allows nj,d,a to be non-zero only for cl = cl' a n d ct = ct' while for all other combinations of cl and ct, nj,cl,c t must be zero. The allowable n u m b e r of groups from each class is given by:

j

ct

r

j

ct

r

ar%'

,

Vcl c C L

(4)

a~n~'

,

Vcl E C L

(5)

where /~r _d,,~n and "lbr _~l,max are the m i n i m u m and m a x i m u m n u m b e r s of groups allowed from class cl in rule set r. The numbers of groups from categories 3, 4 and 5 are limited by: E j

(6)

Z nj'cl'3 ~-~ Z drT~Crt3 cl r

j

cI

r

j

cl

r

(8)

a~n~

where n~ta, n ct4 and n~t5 are the m a x i m u m group numbers allowed from categories 3, 4 and 5 respectively in rule set r. The numbers of groups from categories 3, 4 and 5 s u m m e d together, and from categories 4 and 5 s u m m e d together, are similarly limited: E j

Z (TtJ'cl'3 .at-TLJ'eI'4 @ TtJ'c/'5) --~ E drTt~t345 cl r

E j

Z el

(nj,cl,4 + nj,d,5) < Z

drn~t45

(9) (10)

r

where n~t345 and n ct45 are the m a x i m u m total group n u m b e r s allowed from categories 3,4 and 5 s u m m e d together, and from categories 4 and 5 s u m m e d together, respectively.

Octet Rule In order to ensure t h a t complete molecules have zero valency, the octet rule is

177 introduced: E

E

j

E (2 -

cl

vj)nj,d,~t =

2m

(11)

ct

where vj is the valency of group j (equal to class for classes 0 - 4) and m is 1, 0, -1 or -2 for acyclic, monocyclic, bicyclic and tricyclic compounds respectively.

Additional Structural Restrictions In addition to the above rules, other restrictions may be introduced on a case by case basis to limit the numbers of co-materials designed. To prevent chemistries in which the co-materials are much simpler or much more complicated t h a n the product, the m a x i m u m and m i n i m u m number of groups in each co-material can be bounded:

E E E nj,d,ct >_nmin j

cl

EEE j

cl

(12)

ct l'l'max

(13)

ct

where nmin and nmax are the m i n i m u m and m a x i m u m allowable numbers of groups. These constraints indirectly restrict chain length in homologous series. More direct constraints can be written by bounding the sums of the numbers of group types in any series. Since the formation and cleavage of carbon-carbon bonds often requires extreme operating conditions which are likely to disrupt the chemistry of interest, it m a y be desirable to avoid co-materials which m u s t undergo changes in carbon skeletal structure in order to arrive at the product. In general this is difficult to achieve, since co-material design focuses on types and numbers of groups, r a t h e r t h a n on the connections between them. However, m a n y undesirable materials can be avoided by imposing restrictions on the allowable types and numbers of groups. The numbers of branches, substituents, substituted sites and functional groups may also be limited in this way to avoid co-materials which are significantly more or less structurally complicated t h a n the product. For example, if only monosubstituted benzenes are required, the following equations are introduced: EETtACH, cl ct EEnAC,cl,ct cl ct

and m tures. cation which

cl,ct = 5 -1

is set to zero in the octet rule (equation 11) to allow only monocyclic strucAdditional restrictions can be incorporated in the stoichiometry identifiexercise to avoid, or at least further reduce, the generation of chemistries alter carbon skeletal structures, if required.

178

Objective Function The objective is set as the minimisation of the total number of groups in a molecule:

MinimiseEEEnj,d,ct j

cl

(14)

ct

In this way, co-materials are enumerated subject to the above rules, starting with the simplest first. Solution Procedure The above formulation consists entirely of binary and integer variables in linear equations and is therefore an mixed integer linear programming (MILP) problem. In order to generate a set of co-materials, the problem is solved repeatedly with an integer cut written after each iteration to exclude the current optimal group combination from future iterations. However, it is the precise combination of numbers of groups which must be eliminated, not just the combination of group types (excluding group type combinations would eliminate homologous series). In order to do this the binary variable CUTj,t is introduced, which is related to nj,cl,ct as follows:

(15) t

cl

ct

CUTj,t

-

1

(16)

t

According to these equations, CUTj,t is non-zero only for t = t' where t' is the n u m b e r of times group j occurs in a molecule. CUTj,t is zero for all other values of t # t'. The integer cuts are written in terms of CUTj,t. Note t h a t linear group contribution property prediction equations and bounds may be included in the above formulation without affecting the solution procedure. For example, to exclude co-materials with high toxicity, the following equation could be introduced based upon the lethal concentration (molfl) causing 50% mortality in fathead minnow (LC50):

where dl/j is the toxicity contribution of group j from Gao et al. (1992), and LC5Omin is the lowest permitted LC50. Since LV5Omin is fixed, this equation is linear. ADDITIONAL MOLECULES To complete any stoichiometry, it may be necessary to include some simple additional molecules, which cannot be systematically designed using the above

179 procedure. A set of simple complete molecules appears as class zero in Constantinou et al. (1996). However, further molecules may be required on a case by case basis according to any existing industrial stoichiometries and the type of chemistries to be considered. Examples of such molecules include oxygen, hydrogen, hydrogen chloride or other hydrogen halides, chlorine or other halogen molecules, carbon monoxide and carbon dioxide. A subset of these, or a larger set, may be selected as required as the final step of co-material design.

7.4 S T O I C H I O M E T R Y I D E N T I F I C A T I O N F O R M U L A T I O N

The multistep reaction stoichiometry identification problem can be defined as follows. Given, (i) a desired product and desired production rate, (ii) a set of stoichiometric co-materials, (iii) cost information for each material and group contribution parameters for the corresponding group set (iv) a set of role specification and chemistry constraints and (v) a range of reactor operating conditions, then the objective is to determine a set of candidate multi-step reaction stoichiometries which are promising in terms of both economics and environmental impact. The model for the identification and economic and environmental evaluation of a single step reaction stoichiometry is presented below, followed by a description of the solution algorithm in which this model is used to develop multistep stoichiometries. The model consists of seven sets of equations; an atom balance, whole number stoichiometries constraints, role specification constraints, chemistry constraints, carbon structure constraints, pure component property prediction equations and a reactor process model. The sets employed in the model are shown in Table 2. Table 2: Stoichiometry Identification Model Sets E S C S ( c S) J

elements species carbon containing species chemical groups

The formulation is based on the assumption that chemical species undergo reactions either singly (e.g. thermal decomposition or isomerisation, ignoring any reagent, catalyst or solvent effects) or at most in pairs, so that the number of reactants is limited to at most two. An upper limit is applied on the total number of materials in each stoichiometry (since the number of reactants is limited

180 this effectively limits the number of co-products) and no competing reactions are considered (stoichiometry determination can only develop stoichiometric coproducts not side products). The following additional assumptions are made in the analysis: isobaric reactor operation at known pressure Ptot, gas phase reaction and perfect gas behaviour. Only the products and the reactants are costed, no process equipment or operating costs are considered and the inherent inaccuracies in the property prediction techniques and thermodynamic models employed are accepted. Clearly, incorporating side reactions will add to the impacts so t h a t the present results are lower bounds in this respect. The limits and cuts employed here are practical constraints which can be tightened or relaxed as desired. In principle, the thermodynamic model permits consideration of operation at any pressure. More detailed costing depends on more sophisticated process models. 7.4.1 A t o m B a l a n c e The starting point for this work is an atom balance equation which describes the chemistry of a particular set of S species composed of E elements (Rotstein et al., 1982). The atom balance is written as follows" c~E = 0

(18)

where c~ is the E - S atomic matrix and V~ is the S. 1 column vector of stoichiometric coefficients v~. It is a s s u m e d t h a t the r a n k of the matrix c~ is E. In general, S = E + m, so t h a t m represents the degrees of freedom (DOF's) in the system. These DOF's represent stoichiometric coefficients which m u s t be specified in order for the atom balance to be solved. The remaining S - m coefficients are then determined as functions of these. Clearly when m = 0, a unique solution exists, and when m >_ 1, there is an infinity of solutions, corresponding to an infinity of possible stoichiometries. 7.4.2 W h o l e N u m b e r S t o i c h i o m e t r i e s C o n s t r a i n t s At the atomic level, chemical species react in whole number ratios so t h a t in general, meaningful chemical reactions are written in terms of stoichiometric coefficients which are rational numbers (i.e. whole numbers or numbers which can be expressed as ratios of whole numbers) so t h a t through multiplication by appropriate factors, stoichiometries involving only whole n u m b e r coefficients can be obtained. In such stoichiometries the product coefficient is a whole number which may be greater t h a n or equal to unity. In their atom balances, Rotstein et al. (1982), and later Crabtree and E1-Halwagi

181 (1994), assigned the value unity to the product stoichiometric coefficient with no restrictions on the co-material coefficients. While this does not lead to any loss of generality, it potentially allows the development of an infinity of meaningless solutions in which the co-material coefficients are not rational numbers. In order to ensure t h a t only solutions involving whole n u m b e r stoichiometric coefficients are obtained, the following linear equations are introduced where vp is the stoichiometric coefficient of the desired product. vp _> 1

(19)

Vs c S

(20)

N

Xs -- ~

2(n-1)bns,

n=l

Assigning 89>_ 1 allows the necessary flexibility in the value of the product stoichiometric coefficient so t h a t there is no loss of generality, x~ is a d u m m y coefficient which is defined as a positive, continuous variable. For each species s, this variable is expressed as a linear combination of binary (i.e. 0 - 1 ) variables bn~. In this way, the continuous coefficients x~ are constrained to take positive whole n u m b e r values in the range from zero to an upper limit d e t e r m i n e d by the value of N. The real stoichiometric coefficients v~ are related to the d u m m y coefficients x~ as follows: vs = xs - 2x~ii~,

Vs C S

The b i n a r y variable ii~ is necessary since the coefficients v~ m a y take positive or negative values. The variables ii~ take the value zero if species s is a product (v~ positive) and u n i t y if species s is a r e a c t a n t (v~ negative) so t h a t ii~ is the r e a c t a n t flag. This equation m a y be linearised using the Glover (1975) transformation, yielding: vs=xs-2.y~,

VscS

(21)

y~ - ?)max iis 9 < 0,

Vs C S

(22)

xs § Vmax(ii~ -- 1) -- ys _ 0,

Vs E S VscS

(23)

y~-x~_0,

(24)

where y~ is a d u m m y variable for the product x~ii~ and Vmax is the m a x i m u m p e r m i t t e d m a g n i t u d e for any stoichiometric coefficient. The variables y~ are defined as positive continuous variables. To ensure t h a t t h e y t a k e non-zero values only w h e n species s is a reactant, the following additional constraint is applied: ys >_ iis,

Vs c S

(25)

182 Note t h a t for any particular stoichiometry, xs and vs are non-zero only for the species involved and zero for all other species, while ys is non-zero only for the reactants involved and zero for all other species (including products and coproducts).

7.4.3 Role Specification Constraints Role specification constraints (Fornari et al., 1994a, 1989) are used to restrict the participation of molecules in the stoichiometries; for example, to avoid certain stoichiometric co-products or to define a species as a raw material only. In order to apply such constraints the raw materials and products in any stoichiometry must be identified. Raw material identification is taken care of by the binary reactant flag iis, from the whole number stoichiometry constraints. Products are identified using the following equations: xs -- ys -- Vmax " Is <_ O, xs--ys--(Vmax+l)'Is+Vmax>_O,

Vs C S VscS

(26) (27)

where Is is a vector of binary elements is. Together with equations 20 and 21-24, these relationships assign the value zero or unity to is when the stoichiometric coefficient vs is negative or positive, respectively. Thus, is is the p r o d u c t flag. In order to relate the raw material and product flags, a third flag iiis is introduced which takes the value zero if species s is a raw material o r a product, and unity if species s is not involved in the stoichiometry. The three flags are related as follows: is § iis + iiis = l,

Vs C S

(28)

The role specification constraints are then posed simply by specifying the values of the flags in advance. For example, to define species s as a raw material only, it is excluded from being a co-product by setting is = 0. The role specification constraints may be written differently for different stoichiometry steps. The full list of the constraints used in the example presented later in this chapter is presented in Appendix A.

7.4.4 Chemistry Constraints In addition to the role specifications, the binary flags are employed to develop knowledge based chemistry constraints. These are used to restrict the number of reactants and products involved in any stoichiometry, and to eliminate certain chemistries. According to Holiastos and Manousiouthakis (1998) an elementary reaction can involve up to three reacting molecules and, if the reaction is to be reversible,

183 up to three product molecules. Furthermore, since the formation or cleavage chemical bonds which occurs during an elementary reaction requires the orbitals of reacting molecules to come sufficiently close together and be correctly oriented, elementary reactions involving two reacting molecules are more likely t h a n those involving three purely on statistical grounds. According to the same ideas, the number of different reacting species in any stoichiometry is here limited by the following:

E

iis _< _,.Nma~

(29)

8

where Nrmax is a problem specific maximum number of reactants. In the example presented in this chapter, N ~ ax is assigned the value two, which effectively eliminates side reactions except in the unlikely event of a simultaneous isomerisation. A problem specific upper limit on the total number of species N~ ax involved in any stoichiometry is also imposed according to the number of different species involved in the most complex step of the existing industrial routes to the product of interest.

~ ( i ~ + ii~) < N'~pm~~

(30)

8

Since there must be at least one reactant, this constraint limits the number of products to at most N~ a~ - 1. Note t h a t these constraints limit only the numbers of different species involved in any stoichiometry, not their stoichiometric coefficients. However, all stoichiometric coefficients are constrained to be less than ~a~, and can be further constrained by introducing the following equation if required: Ms ~ l/y ax,

(31)

VS C S

where u y ~ is the maximum permitted stoichiometric coefficient of species s. Other knowledge based chemistry constraints may be imposed directly on certain species. The following examples are provided for illustration, the full list of the chemistry constraints employed in the illustrative example problem are presented in Appendix A. 9s p e c i e s a a n d b

must not react together

iia + iib <_ 1 9s p e c i e s a

may only react with species b or species

i i a - (iib + iic) <_ 0

c

(32)

184 9species c may only be produced by reacting species a and b 2ic - (iia + iib) < 0

(33)

In order to identify a set of candidate stoichiometries, the stoichiometry selection problem must be solved iteratively, with integer cuts to exclude previous solutions. The binary flags provide the mechanism for this. Since the same combination of reactants may be involved in several stoichiometries in which the product is derived from the same underlying reaction but with redistribution of the co-products, the integer cuts are written to exclude only the combinations of raw materials observed in the solutions. In this way, such r e d u n d a n t solutions are avoided. 7.4.5 C a r b o n S t r u c t u r e C o n s t r a i n t s

According to section 3.2, constraints may be needed to prevent chemistries in which carbon-carbon bonds are broken or formed. However, since the atom balance contains no structural information it is not possible to write such constraints directly. Furthermore, since the need to break or form carbon-carbon bonds depends on the set of co-materials and the nature of the chemistry to be considered, carbon structure constraints can only be developed on a case by case basis. Moreover, the development of general constraints is hampered by the fact t h a t only the final product is known in advance (it is not known which co-materials will be reactants or co-products). Despite these difficulties, general constraints which infer certain restrictions on carbon structural changes are possible, and under certain special circumstances, carbon structure changes can be eliminated. Noting t h a t ys is non-zero only for reactants and xs - y~ is non-zero only for products, the following constraint may be used to prevent a n e t change in the number of carbon-carbon bonds in a stoichiometry: ~ - y~ Ncb ~ = ~(x~8

ys)g: b

(34)

8

where N2b is the number of carbon-carbon bonds in species s. The n e t gain or loss of carbon-carbon bonds may be allowed by writing this constraint as an inequality. For stoichiometries involving straight chain acyclic molecules in which the carbon skeleton is uninterrupted, the following prevents any change in the carbon skeleton (and permits only one carbon containing reactant and no carbon containing co-products): ~c~N~ = Npb , 9

9

cb

Vcs C C S

(35)

185 where N~b is the n u m b e r of carbon bonds in the product. Clearly, this is a n ext r e m e l y restrictive constraint. Less restrictive constraints can be w r i t t e n for the same type of chemistry. For example, the f o r m a t i o n of carbon-carbon bonds for stoichiometries involving straight chain acyclic molecules with u n i n t e r r u p t e d carbon chains can be prevented by considering the relationship between the stoichiometric coefficients of the reactants and the product, if only one carbon containing r e a c t a n t is allowed. Consider the production of a product with a single carbon-carbon bond from reactants containing up to six such bonds. Allowing only a single carbon containing r e a c t a n t and disallowing the formation of carbon-carbon bonds, the following reaction schemes are permitted: C-C C-C-C C-C-C-C C-C-C-C-C C-C-C-C-C-C C-C-C-C-C-C-C

--+ --+ ~ ~ ~ -+

C-C C-C+C 2(C-C) 2(C-C) + C 3(C-C) 3(C-C) + C

while schemes such as: 2(C) 2(C-C-C) 2(C-C-C-C-C) 2(C-C-C-C-C-C-C)

-~ -~ -~ -~

C-C 3(C-C) 5(C-C) 7(C-C)

are not. These reaction schemes imply t h a t in an allowable stoichiometry, the following relationships between vp and yes m u s t be obeyed if species cs is selected as a reactant, according to the ratio of the n u m b e r of carbon-carbon bonds in the r e a c t a n t to t h a t in the product: If 0 <_ ~N2
~

_

Pb

--

--Vcs

If

3
then

vp

-2v~s

If

5<~--~ <6 N~9 b - -

then

vp --- - 3 v ~

Since the n a t u r e of the relationship between vp and v~s depends on the bond ratio, the relationships are in fact quite general and can be applied to acyclic products with u n i n t e r r u p t e d carbon chains featuring any n u m b e r of carboncarbon bonds. In addition, they can be extended for r e a c t a n t s with any n u m b e r of such bonds. Clearly, a problem arises if N~b = 0, however this can be overcome by introducing the binary variable p which takes the value of zero w h e n N~b > 1 and u n i t y w h e n N~b = 0 according to:

1 - p < N~b <__( 1 - p ) N mcba x

(36)

186 a n d N~a cb ~ is the m a x i m u m n u m b e r of carbon-carbon bonds f e a t u r e d in the species from the set CS. Incorporating p, the vp to vc~ relationships are embodied in the following g e n e r a l constraints"

E(2t-1)qt,c~ < [

N~b

Vp(1 -- p) -- (1 -- iics)Vma x ~ (Zcs --~ E

] < 2 E tqt,cs + O.99Zcs, Vcs c CS

tqt'cs)Ycs ~-

(1 --

Zcs)V p -~- pVmax,

VC8 e C S

(37)

(38)

t

w h e r e qt,c~ a n d z~ are integer variables such that:

Z~s + E

qt,~ = 1,

Vcs c C S

(39)

t

so t h a t for each species cs only one of z~ and the vector of qt,~ b i n a r y variables can t a k e the value unity. Note t h a t ycs is used in equation 38 so t h a t the cons t r a i n t s affect only reacting species. To u n d e r s t a n d how these c o n s t r a i n t s function, consider the following: 9W h e n N~ b - 0 and N ~ = 0, p - 1 from equation 36, and in order t h a t e q u a t i o n 37 be obeyed z~ = 1 and all qt,c~ = 0. Thus since y~ is a positive variable, w h e t h e r ii~ is zero or one, 0 <_ y~ < Vmax from equation 38, which imposes no additional restriction on y~s. 9W h e n N~b = 0 and N~C~ _ 1, p = 1 from equation 36, a n d in order t h a t e q u a t i o n 37 be obeyed zcs = 0 and qt,,cs - 1 (and all qt#t,,~ = 0). Thus, w h e t h e r iic~ is zero or one, 0 __ t'yc~ <_ v, + Vma~. This potentially r e s t r i c t s y~s, b u t since chemistries in which products with no carbon-carbon bonds are developed by b r e a k i n g up r e a c t a n t s with such bonds are not of i n t e r e s t here, this limitation is acceptable. 9W h e n N~b _ 1 and N~C~ < N~b, p = 0 from equation 36, a n d in order t h a t e q u a t i o n 37 be obeyed Zcs = 1 and all qt,~s = 0. Thus, y~ _< 0 from the u p p e r bound in equation 38 so t h a t ii~s m u s t equal zero for the lower bound to be feasible. This m e a n s t h a t all species with fewer carbon-carbon bonds t h a n the product are not p e r m i t t e d as reactants. 9W h e n N~b >_ 1 a n d N~C~ >_ N~b, p = 0 from equation 36, a n d in order t h a t e q u a t i o n 37 be obeyed zcs = 0 and qt,,cs = 1 (and all qt#t,,~ = 0). T h u s if ii~ = 0, 0 < t'y~ <_ 89or if iic~ = 1, vp <_ t'ycs <_ vp. This m e a n s t h a t if species iic~ is not a r e a c t a n t , t h e r e is no additional limitation on y~, b u t if species cs is a r e a c t a n t , yc~ and therefore V~s m u s t be r e l a t e d to vp in one of the w a y s prescribed above, depending on the bond ratio.

187 Note t h a t once the product is known, equation 36 can be solved for p, so t h a t equations 37 and 39 can be solved for zcs and qt,cs, p, z~s and qt,cs can then be entered as parameters in equation 38 which becomes linear as a result.

7.4.6 Thermodynamic and Environmental Property Equations The enthalpy of formation and Gibbs Free Energy of formation of each species is required to estimate the enthalpy and Gibbs Free Energy of reaction in the process model. Pure component heat capacities are required for the energy balance and pure component toxicity is also needed. ENTHALPY OF FORMATION According to Perry and Green (1984), the enthalpy of formation at 298K AH}~s of species s in kJ/mol can be found using the group contribution scheme of Verma-Doraiswamy: AH}~S = 4.1868EnsjSH~'29s, J

Vs C S

(40)

where 5Hs'~"~ is the contribution of group j (in kcal/mol) from Perry and Green (1984). GIBBS FREE ENERGY OF FORMATION Also from Perry and Green (1984), the Gibbs Free Energy of formation AG/s(Tope~) of species s in kJ/mol can be estimated using the group contribution techniques of Van Krevelen and Chermin (1951) with accuracy of +21 kJ/mol:

Aa/s(Toper)=4.1868{ E nsj.a~r + [~nsy~S+ j

Rln (--)]Tope~}, as ?Ts

VsES

(41)

where Tope~.is the reactor operating temperature, a~F and ~ r are the group contributions of group j in kcal/mol (from Perry and Green, 1984), R is the gas constant, as is the symmetry number of the molecule (the number of independent orientations which appear identical to an observer) and ~s is the number of optical isomers. For molecules with no symmetrical orientations or optical isomers, as and ~s are assigned the value of unity to avoid numerical problems. ~ r a n d / ~ F are valid for temperatures between 300K and 1500K, so t h a t is bounded as follows" 300 _< Toper<_1500

Toper

(42)

HEAT CAPACITY AND TOXICITY The ideal gas molar heat capacity C yap(J/mole K) of species s is estimated using v p,i the following polynomial equations:

188

CpVap j 37.93)-~- ( ~ n,jAJb -~- 0.21)T -]-- ( ~ n ~ j A Jc ,s _ ( E TtsjnaJ

/

--3.91 • 10-4)T 2 + ( E J

(43)

J

nsJAJd+ 2.06 x 10-7)T 3, V8 C S

where the coefficients A {, A j, AJ and A ( are group contribution p a r a m e t e r s from Joback and Stephanopou~os (1989). ~ In order to m e a s u r e the short-term environmental impact of any m a t e r i a l rel e a s e d , the toxicity of each species s is estimated using the group contribution techniques of Gao et al. (1992): -logLC50~ = ~ oljnsj, J

V8 E S

(44)

7.4.7 R e a c t o r P r o c e s s Model E q u a t i o n s The process model is based on a single reactor in which chemical equilibrium is achieved. Unreacted raw materials are recycled a s s u m i n g t h a t they are separ a t e d cleanly from the products and ignoring, for the present, the necessary separation technology. The chemical equilibrium position is located by minimising s y s t e m Gibbs Free Energy, and since this position is independent of the reactor, it is not necessary to prepostulate the reactor type (e.g. PFR, CSTR etc.}). COMPONENT MASS BALANCES The m a s s balance around the reactor is written as follows for all species in the set S:

n~; - n~i = crv~,

Ys c S

(45)

where n~ is the total molar feed flow of component s to the reactor, nsy is the molar flow of component s in the reactor effluent and cr is the extent of reaction. Recalling t h a t x~ is non-zero for all species involved in the reaction and ys is nonzero only for the reactants and taking a flow basis of 10 kmol/hr, the following restrictions are written for n~ and nsy: nsi = 10y~, Vs c S

(46)

nss <__10x8, Vs E S

(47)

According to equation 46, nsi is non-zero only for the reactants in a particular stoichiometry, and according to equation 47, n8S can be non-zero only for the components involved in a particular stoichiometry. For all other components in the set S, both n~i and nss are zero. To ensure all reactions exhibit acceptable conversion, the extent is bounded as follows: ~r ~ Cr~o

(48)

189 For the reactants, the product -c~vs represents the consumption rate in the reactor and therefore the fresh feed demand. For the products, E~vs represents the production rate. Thus, the fresh feed demand and production rate in kmol/hr are given by:

F~ = -~rv~ii~, Vs E S P~ = G~v~i~, Vs C S

(49) (50)

ENERGY BALANCE It is assumed that the fresh feed enters the reaction block at 298K and the products leave the block at the reactor operating temperature Top~. The reactor energy demand therefore has two contributions, one from fresh feed pre-heat and one from the heat of reaction. The heat of reaction is estimated in three steps. First, the total feed (comprising fresh feed and recycled reactants) is cooled from the operating temperature to 298K, the reaction is then performed and finally the entire reactor effluent is reheated to the operating temperature. The reactor energy demand Qreactor, in kJ/hr per mole of product is given by:

QrcactorPp = E ( - crvsiis)

~[ov~

S

8

f29S

C'p,s dT +

s

§E

+1000r

Cp,sVapdT

J Toper ~ roper yap

Cp,s dT

nsf 98

8

where Pp is the production rate of desired product and C~,~p is the vapour heat capacity of component s. Substituting for n~f from equation 45, this reduces to:

= l{lo00r

"T~ Cp,svapdT}

(51)

98

The heat of reaction at 298K AH~98 in kJ/mol is estimated from: _

(52) 8

SYSTEM GIBBS FREE ENERGY

The Gibbs Free Energy of the reaction system G~y~(in kJ/hr since n~f is a molar flow) may be estimated from the following expression (for perfect gases or real gases at low pressure): Gsys

1000 = E nsfAGfs-4- RTo;cr E nfsln [ nfsPoper Differentiating this expression with respect to n~f at constant temperature and pressure leads to the condition for chemical equilibrium:

A G R = - RTope~lnK

(53)

190 where R is the gas constant, and the Gibbs Free Energy change of reaction per mole of product AGR in kJ/mol and the reaction equilibrium constant K are given by:

AGR : ~ v~AG y~

(54)

8

K-

IL

pe~

ns ~

In order t h a t the chemical equilibrium condition be obeyed, a reaction with a large positive or negative AGR must exhibit a very small or a very large K respectively. A very small K implies very small n~f values for the products, while a very large K implies very small nsf values for the reactants. In some cases, these nsf values are so close to zero that the optimisation problem becomes poorly scaled. Introducing an n~f lower bound does not solve the problem since any such bound may render the equilibrium condition infeasible. Thus, r a t h e r than imposing the chemical equilibrium condition, Gsy~ is minimised directly instead, with an n~f bound in place to prevent scaling problems. While this prevents reactions with large positive or negative AGR from achieving equilibrium, since the n~f lower bound is small, the solutions are barely affected. The nfs bound is written as follows, with the binary flag iiis introduced so t h a t nf~ takes the value zero for all species not involved in the stoichiometry of immediate interest:

ny~_> 1 x 10-4(1-iii~),

VsES

(55)

Since n~y is zero for some s, iiis must also be introduced in to the G~y~expression: Gsys

i000 : E

nsfAGfs

8

+RTop~r[~nfsln((ny~+iii~)Poper)-En~yln(En~yPe)]s

~

(56)

Crabtree and E1-Halwagi (1994) use a similar approach to deal with species not involved in a particular stoichiometry, although they reported using the reaction equilibrium condition to determine the reaction equilibrium position. Note t h a t the chemical equilibrium condition provides a unique relationship between n~f and Toper, whereas in the G~y~ expression they are independent variables. Thus an additional temperature bound is required to ensure t h a t t e m p e r a t u r e is consistent with the extent bound from equation 48. This bound is calculated by solving the following equation for T':

AGR(T') = -RT'lnK~o

(57)

191 where K~zo is the equilibrium constant evaluated at cr = ergo "

lnK~z~= E v~ln ((n~ + v~c~~+

- E vsln ( ~ (nSi + v ~ P e ) )

(58)

The reactor operating temperature must then satisfy:

Toper> r'

(59)

THERMODYNAMIC AND ECONOMIC CONSTRAINTS The Gibbs Free Energy of reaction per mole of product is employed to eliminate thermodynamically infeasible solutions, using a 10 kcal/mol (or 41.868 kJ/mol) upper limit as follows: AGR < 41.868 vp

(60)

The profit associated with each reaction is calculated as follows, assuming t h a t any stoichiometric co-products are sold at their market value: Profit = ~ s

vsCs

vp

(61)

where C8 is the market value of species s using Chemical Prices (1998). Note t h a t individual reaction steps cannot be rejected on the basis of profit since the profit of any one step is not representative of the profit of the entire chemistry. ENVIRONMENTAL CONSIDERATIONS The environmental impact directly associated with carrying out each stoichiometry is assumed to arise only from the energy consumption necessary to maintain reactor temperature. By-products are not considered and it is assumed that there are no material emissions of the co-products of any stoichiometry. In addition, the impacts associated with separating the products from the recycle, and with all other downstream processing are ignored for the present. In these respects, the impact figures calculated here are very much lower bounds for the eventual process impacts. This simplistic treatment of environmental impact assessment reflects the level of information available at stoichiometry selection. In principle, the full range of life cycle assessment (LCA) based metrics available within the MEIM could be used to develop a full impact vector for each stoichiometry. However, since air emissions are the dominant form of energy associated waste, the critical air mass (CTAM) metric is chosen. According to Stefanis (1996), the critical air mass associated with energy production is 1.629 • l0 s kg air/MWh. Assuming that the environmental impact per unit energy of maintaining reactor temperature is the same as that of burning fossil

192 fuels to produce electricity, the environmental impact arising from the reactor energy demand per mole of desired product is:

CTAME(kgair/hr)=l'629•

V/(Qr~act~ )3600

(62)

Note t h a t it is assumed here for simplicity that the impact of cooling the reactor (which is necessary for negative is the same as that of heating it. This is a simplistic assumption, however, in this way reactions which require withdrawal of energy are equally penalised in environmental terms as those which require energy supply.

Qr~actor)

This assumption is made on the basis that reactions which require energy withdrawal are likely to be exothermic reactions occurring at moderate temperatures, so t h a t the heat of reaction term dominates the energy balance (equation 51). This is only likely to occur towards the reaction temperature lower bound (i.e. 300K) at which the reactor temperature is too low to use cooling water at ambient temperature. Thus, some kind of refrigeration would be required which carries with it a high energy demand and therefore a high impact, associated with compression requirements. In order to complete the impact assessment, the input wastes associated with the materials consumed in any stoichiometry must be included. However, the quantification of the input waste of any material can be a lengthy exercise, since all processing steps necessary to produce the material from naturally occurring substances must be considered in accordance with the principles of LCA (Heijungs 1992; ISO 14040, 1997; SETAC, 1993). Thus, r a t h e r t h a n performing this exercise for all co-materials, it is more efficient to assess the input wastes only of those materials which are identified as raw materials by the multi-step stoichiometry identification formulation (i.e. those materials with no precursors). Since these materials are not known at the outset, input waste assessment can only be performed after stoichiometry identification.

et al.,

Provided input wastes are included in this way, consistent impact figures can be obtained for multi-step stoichiometries involving branches of different lengths, and different stoichiometries can be compared on a consistent basis.

7.5 SOLVING THE M U L T I S T E P S T O I C H I O M E T R Y I D E N T I F I C A T I O N PROBLEM 7.5.1 O v e r v i e w

It is desirable to use the above model to enumerate and evaluate multistep stoichiometries simultaneously and within a framework of constrained

implicitly

193 optimisation. However, the optimisation objective (minimise Gsus) is not suitable for a such an approach since it must be applied to each individual stoichiometric step and furthermore, even for a single step stoichiometry, the model is a large mixed integer nonlinear programming (MINLP) problem. It involves a large number of optimisation variables, including for each species s: the binary variables is, iis, iiis, bns (Vrt) and also the binaries qt,es (Vt), Zcs and p if the carbon structure constraints are employed, and the continuous variables vs, xs, ys, n4, nsi, Fs, Ps and AGfs. Furthermore, the relationships between these variables are not trivial, including many instances of products between binary and continuous variables. Thus, in order to solve the multistep stoichiometry identification problem, a decomposition based approach is adopted in which the single step problem is solved by explicit enumeration and subsequent evaluation of stoichiometries in two sequential steps. This procedure is then applied successively in an algor i t h m designed to build up multistep reaction stoichiometries. The enumeration and evaluation of single step stoichiometries are discussed below, followed by a description of the multistep stoichiometry identification solution algorithm. SINGLE STEP STOICHIOMETRY ENUMERATION The basic single step stoichiometry enumeration formulation consists of equations 18 - 33. Carbon structure constraints (equations 3 4 - 39) are optional and are included on a case by case basis. With the exception of the more complicated carbon structure constraints (equations 37 and 38) all equations are linear. However, as discussed above, provided equations 36, 37 and 39 are solved in advance, equation 38 becomes linear. Thus, with or without carbon structure constraints, the single step stoichiometry enumeration problem can be formulated as an mixed integer linear programming (MILP) problem so t h a t optimal solutions can be guaranteed. Recognising t h a t simple stoichiometries with few reactants and co-products are more attractive t h a n complex ones (which in general require more complex reaction and separation technologies) a new objective function is introduced in order to extract stoichiometries systematically from the matrix _%starting with the simplest first. The number of materials involved in any stoichiometry Nspe is obtained by summing the reactant and co-product flag values, so t h a t this objective is written as follows: minimise E{(i~

+ ii~)

= N~p~}

(63)

8

In order to identify a set of candidate stoichiometries this problem must be solved repeatedly, with integer cuts introduced at each iteration to exclude previous solutions. Accordingly, the simplest stoichiometries are enumerated first

194 and as cuts are added the solutions become progressively more complicated. SINGLE STEP STOICHIOMETRY EVALUATION The single step stoichiometry evaluation problem consists of the property prediction and reactor process model, equations 40 - 62. For each stoichiometry, this model is solved immediately after the stoichiometry enumeration model. Thus, vs, xs, ys, is, iis and iiis are known and are treated as parameters in the stoichiometry evaluation problem which is then reduced to an nonlinear prog r a m m i n g (NLP) problem. The optimisation objective is to minimise Gsy~ and the main optimisation variables are Top~, ~ and n/s.

7.5.2 Multistep Stoichiometry Identification Algorithm OVERVIEW OF ALGORITHM In order to generate multistep stoichiometries the single step stoichiometry enumeration and evaluation problems are solved successively using a depth first enumeration strategy, in which the desired maximum number of reaction steps is specified in advance. The operation of the algorithm is schematically depicted in Figure 1 for the case where at most three reaction steps are allowed.

: ~ / s t e = 0 - - 1 ~"

]

-- . . . . . .

l o-,

.......... t~? ......

....

- Eva

"1

don ~A,SaBUE

,

[ Eva

'

~A~a~

tion

r

. . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

System 2B

~'~sm,,

System 214

,

iion l"~

.....

Evaluation I .....................

'System 2C ' ~ [ E. . . . . . tion I

/

'System 2D

~B"

,

..... ,

:

........

|

', , .

.

.

.

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Figure 1: Multistep Stoichiometry Identification Algorithm At the first level, system zero, the final desired product is the target molecule, and a single stoichiometry involving up to two first generation precursor reactants is extracted from the matrix es. One of these first generation precursors is then arbitrarily selected as the target molecule for system 1A and a single sto-

195 ichiometry involving up to two second generation precursor reactants is identified which leads to this compound. One of these second generation precursors is then selected as the target molecule for system 2A. Since system 2A completes this branch of the enumeration exercise, it is solved iteratively until all stoichiometries leading to this second generation precursor target molecule have been enumerated. Once this has been achieved, system 2B is solved iteratively for all stoichiometries leading to the other second generation precursor. With this pair of second generation precursors completely fathomed, System 1A is run again to generate two more, which are then treated as the target molecules for system 2A and system 2B. This process is repeated until all stoichiometries leading to the first generation precursor target molecule have been enumerated. Once this has been achieved, systems 1B, 2C and 2D are employed to enumerate all stoichiometries leading to the other first generation precursor. System zero is then solved again to generate two more first generation precursors, and the whole procedure is repeated until all stoichiometries leading to the final desired product have been enumerated. In this way, multistep reaction stoichiometries are developed in which a family tree of precursors are linked to each other by individual reaction stoichiometries which lead eventually to the desired product. In principle, this approach may be applied to generate any number of successive reaction steps. Each system comprises of both stoichiometry enumeration and evaluation, so t h a t for each stoichiometry, the evaluation problem is solved immediately after the stoichiometry is generated. Infeasibility in the linear stoichiometry enumeration problem implies that no stoichiometries exist which lead to the particular target molecule, while infeasibility in the non-linear stoichiometry evaluation model implies violation of the thermodynamic constraints (ignoring numerical problems) for a particular stoichiometry. Thus, if the stoichiometry enumeration model is initially infeasible or becomes infeasible after all possible stoichiometries in a particular system have been enumerated, the algorithm immediately moves onto the next system. If however, the stoichiometry evaluation model is infeasible for a particular stoichiometry, the algorithm continues to enumerate stoichiometries within the same system. The results of the system are stored only if both problems are feasible. The same occurrence matrix _%and variables are used throughout all systems, so t h a t each time a system is solved all variables are over written. Thus, parameters are employed to store results and to communicate variable values between stoichiometry enumeration and evaluation problems within each system. Different role specification constraints, chemistry or carbon structure constraints may be included in different systems, if required, simply by including different equations in the model definitions. Otherwise, the same equations and models are also employed throughout all systems.

196 INTEGER CUTS Within the algorithm, integer cuts are automatically written each time a syst e m is solved. The cuts are written in such a way t h a t they prevent the same stoichiometry from occurring again both within the current system and within all s u b s e q u e n t systems. Furthermore, they are written to prevent the reappearance of the stoichiometry in both forward and reverse directions. In this way, each m a t e r i a l which appears as a reactant in the entire multistep stoichiometry n e t w o r k is fathomed only once and circuits, in which a reaction appears in both forward and reverse directions within the same multi-step stoichiometry, are avoided. The integer cuts are written in t e r m s of the r e a c t a n t and co-product flags in m u c h the same way as the chemistry constraints, and since the same r e a c t a n t and co-product flag variables are used for each system, it is a simple m a t t e r to write these constraints in such a way t h a t once written, they are included in all s u b s e q u e n t systems. TARGET MOLECULE IDENTIFICATION At the outset, only the desired product is known so t h a t a m e a n s of communicating t a r g e t molecule identities between the subsequent systems is required. This is achieved by using the iis values from each system as lower bounds for the stoichiometric coefficients in the next. If species k and 1 are the precursor r e a c t a n t s generated by a certain system, iik and ii~ will take the value u n i t y for this system. These species m u s t then be identified as the products of the pair of subsequent systems. However, species k and 1 m u s t be considered independently, i.e. one in one system and one in the other. In order to do this, the vector IIs m u s t be split so t h a t in one system ik = 1 while iz (and all other product flags) are unconstrained, whereas in the other system il = 1 while ik (and all other product flags) are unconstrained. This is achieved by incorporating the following equations in all stoichiometry e n u m e r a t i o n formulations: iis = as + bs,

Vs C S

(64)

as -- 1

(65)

bs _< 1

(66)

s

s

E q u a t i o n 64 splits the vector IIs from each system into two vectors As and Bs, of which the elements as and bs are binary variables. According to equations 65 and 66, As and Bs m a y have only one non-zero entry each, so t h a t the nonzero entries in IIs are divided, one in to As and one in to Bs. The values of As and Bs are t h e n communicated to the subsequent pair of systems through the p a r a m e t e r vectors APs and B G respectively, by replacing equation 19 with one of the following equations in all systems subsequent to system zero: is >_ aps,

Vs c S

(67)

197 i~ > bp~, Vs c S

(68)

Note t h a t equation 66 is written as an inequality to permit stoichiometries in which there is only one reactant (e.g. isomerisation or thermal decomposition). In such cases, all elements of the vector B~ take the value zero and the algorithm omits the entire branch of corresponding subsequent systems. Note also t h a t %, the stoichiometric coefficient of the target molecule for each system subsequent to system zero, which is needed in the stoichiometry evaluation equations, is identified using one of the following equations: vp - E

ap~v~

(69)

bp~v~

(70)

8

vp = E 8

where ap~ and bp~ are the parameter values generated by the previous system, and v~ are the stoichiometric coefficients of the current system. For all systems, vp is included as a parameter in stoichiometry evaluation. CALCULATION OF FINAL RESULTS The profit and impact from each system are stored as parameters immediately after the system is solved. These figures are calculated per mole of the target molecule produced in the current system. The total profit and impact associated with the multistep stoichiometries are calculated per mole of the final product, by starting at the final systems and working forward towards the final product, adding the profits and impacts sequentially. However, the target molecule in a certain system may exhibit a stoichiometric coefficient with any value (subject to Vma~) in the previous system where it appears as a reactant, and the product of this previous system may also exhibit any such stoichiometric coefficient value. Thus, the profit and impact of each system m u s t be multiplied by the magnitude of the stoichiometric coefficient of its target molecule as it appears in the previous system, and divided by the magnitude of the stoichiometric coefficient of the product of this previous system, before being added to the profit or impact of the previous system. Since each system may have up to two immediate subsequent systems, the profits and impact of both subsequent systems must be treated in this way. In addition, each combination of subsequent system stoichiometries must be considered and a separate profit and impact figure calculated for each. Depending on whether ap~ or bp~ is used in a particular system, xp, kk-1 the magnitude of the stoichiometric coefficient which the target molecule of system k exhibits as a reactant in system k - 1 is given by one of: ap~k-1 x~k-1

k-1 XP, k --- E 8

(71)

198

k-1 ~ - E bPsk-l-k-1 :I; s

X p, k

(72)

8

where ap~ -1 and bp~-1 are parameter values from system k - 1 and x sk-1 are the stoichiometric coefficients of system k - 1. Thus, the profit and impact of system k are multiplied by xp, k and divided by xpk-1 before being added to the profit and k-1 impact of system k - 1. Using these parameters, profits and impacts are cascaded through the multistep stoichiometry network and a total profit and impact figure is arrived at for each set of stoichiometries which eventually leads to the final product. Note that each reactor is assumed to be fed at ambient conditions. It is assumed that any cooling which may be required between successive reaction steps to achieve this will be accommodated by energy integration at a later stage of the process design, with no environmental penalty.

7.6 A P P L I C A T I O N

7.6.1 Case Study: Production of 1-Naphthalenyl Methyl Carbamate 1-naphthalenyl methyl carbamate, also known as carbaryl was employed as a pesticide (Kalelkar, 1988; Shrivastava, 1987; Worthy, 1985). It was manufactured under the trade name SEVIN by Union Carbide India, Limited (UCIL) in Bhopal until December, 1984 when production was terminated following the Bhopal disaster. UCIL's process involved the raw materials 1-naphthol and methyl isocyanate, a toxic substance with a permissible exposure limit (PEL) of 0.02ppm (AGCIH, 1977; Dagani, 1985). Under disputed circumstances, 45 tons of methyl isocyanate underwent a chemical reaction and were released, killing approximately 2,500 people in the vicinity of the plant and resulting in some 300,000 additional casualties. Crabtree and E1-Halwagi (1994) considered this example with the objective of identifying stoichiometries with more innocuous raw materials, to reduce the potential impact of fugitive emissions. The approach employed here is somewhat different in that the objective is to identify stoichiometries which exhibit low environmental impact under normal operating conditions. While materials with high toxicity can be excluded at the co-material design stage by including equation 17 in the co-material design formulation, this potentially excludes stoichiometries which could be environmentally promising provided proper cont a i n m e n t were employed. Thus, no such limit was included in this example. In cases where fugitive emissions are of concern, the methodology for environmental risk assessment of non-routine industrial releases presented by Stefanis and Pistikopoulos (1997) could, in principle, be incorporated as part of stoichiometry

199 evaluation. GROUP PRE-SELECTION According to Worthy (1985), there are two accepted industrial routes to carbaryl, which can be produced with or without methyl isocyanate. The alternative chemistries are shown in Figure 2. Methyl IsocyanateRoute CH3NH 2

§

COCI 2

Methyl Amine

>

CH3--N--- ~

Phosgene

§

CH3mN-- ~

§

O

2 HCI

Methyl Isocyanate

O O - - C ~ N ~ CH 3

OmH

II

1-Naphthol

O

Carbaryl (1-NaphthalenylMethyl Carbamate)

Non-Methyl Isocyanate Route §

COCI 2

HCI

> .iCl

O--H

II

O

1-Naphthalenyl Chloroformate HC! CH3NH 2 iCl

II

O

> O---C I N ~ CH 3

II

O

Carbaryl

Figure 2: Carbaryl Production Routes

For simplicity, to limit the size of the co-material design problem in this illustrative example, the group set is restricted to the simplest set of groups which are required to form the product and industrial co-materials shown in Figure 2. The selected set of UNIFAC groups (eleven in all) then consists of the aromatic groups AC, ACH, ACC1 and ACOH, and the groups -CH3, CH3NH-, CH3NH2, -CO0-, -CHO, -OH and -C1. Note that methyl amine (CH3NH2) appears as a class zero group in Constantinou (1996), that is as a complete molecule, so that the NH2 group is not required. Note that the -C1 group is a category two group.

200 CO-MATERIAL DESIGN Using this group set, the co-materials were then constructed by solving the co-material e n u m e r a t i o n formulation once for acyclic molecules and once for aromatic molecules. Additional structural restrictions were included, according to the structures of the industrial co-materials: (i) for non-aromatic molecules an upper limit of two groups was imposed, (ii) for aromatic molecules an upper limit of twelve groups was imposed since it is unlikely t h a t carbaryl (which contains twelve groups) would be synthesised from a more complex molecule, (iii) only u n s u b s t i t u t e d or monosubstituted aromatics which contain the double ring (naphthyl group) aromatic structure were allowed (since the product contains the n a p h t h y l group is monosubstituted) by specifying a m i n i m u m of seven ACH groups, and a total of ten ACH and AC groups altogether, and (iv) only one s u b s t i t u e n t group with a carbon free a t t a c h m e n t was allowed in the aromatics. In addition, all non-aromatic molecules containing carbon bonds were screened out after enumeration. Thus, chemistries in which the n a p h t h y l group structure is constructed or decomposed, or in which any other carbon-carbon bonds are formed or broken, are avoided. For the acyclic molecules, constraints were included to prevent chlorine bonding with itself or with any groups of higher category. However, for the aromatic molecules, these constraints were removed, to allow the formation of 1n a p h t h a l e n y l chloroformate. The results of co-material e n u m e r a t i o n are shown in Figure 3.

H I N ~ CH 3 1) Naphthalene

2) 1-Chloronaphthalene

3) 1-Naphthol

OH

4) N-Methyl-l-Naphthylamine

.i CI

II

I N ~ CH 3

II

O

II

O

5) 1-Naphthalenyl Hydroxyformate

O

7) Carbaryl

6) 1-Naphthalenyl Chloroformate

CI 2

CH3C 1

CH30 H

CI----C~ H

I~

8) Chlorine

9) Chloromethane

10) Methanol

11) Chloromethanal

H'-'C I N~. CH 3

CH3NH 2 12) Methyl Amine

C! ~C'-~ O CI 13) Phosgene

CH3--N--- C-~ O 14) Methyl lsocyanate

II

O 15) Methyl Formamide

Figure 3" Co-Material Design R e s u l t s - Carbaryl Example

201

Note that species 8, 11, 13, 14 and 15 are included as additional molecules since none of these can be constructed according to the structural restrictions employed. Four further additional molecules were also included, as shown in Figure 4. H2

16) Hydrogen

02

17) Oxygen 18) Water 19) Hydrogen Chloride

a20

HCI

Figure 4" Additional Molecules MULTI-STEP STOICHIOMETRY IDENTIFICATION RESULTS The solutions of the stoichiometry identification program are presented in the form of a table of stoichiometric coefficients in Table 3, where blank spaces indicate zero coefficients and the species are numbered as above. According to the industrial routes, stoichiometries of up to two steps in length were allowed, with a m a x i m u m of four species permitted in any step. The role specification and chemistry constraints employed in this example are given in Appendix A. No carbon structure constraints were employed in this example. A production rate (c~vp) lower bound of 2.5 kmol/hr and an allowable reactor temperature range of 300-800K were imposed. Table 3" Multistep Stoichiometries- Carbaryl Example ]]

Index]Nsp~ A B C D

3 4 4 4

E F G H

3 4 4 4

I

I 4

K

4

L M N

4 4 ! 4

Species

]]

11 2[ 3]4151 6171819110111112113114115116117118119

System 0 - Producing Species 7

1 -1 1 1 -1 1 -2

2 -1 1 -1 1 -1 1

I I III

-1

1 -1

-1 -1

1

System 1 - ProducingSpecies 3 1 -1

System 1 - ProducingSpecies 14

IIII

-1 -1

I l-1[-11 11 1 1 1 1 2

System 1 - ProducingSpecies 15

1

I I I rSystem I I I 1-1111:II I I il ,11 11 Producing Species 1-

K [kmol/hr erVp I Profit Toper $/mol I

CTAM tnair/mol

300 300 300 300

9.99 5.51 10.00 3.17

0.4508 -2.9885 0.5026 -2.9485

19.57 22.22 16.63 16.08

300 300 300 300

20.00 9.34 10.00 10.00

0.5509 0.5013 0.5015 0.5249

6.90 18.23 17.85 13.44

s00 I lo.00 101ss71 300 I 2.7510.04001 736 2.50 0.0535

5~s 4.20 2050.78

6

300 300 300

10.00 10.00 10.00

3.95561 3.49111 3.5880

17.86 14.11 10.27

System zero produced four candidate stoichiometries that satisfy all constraints,

202 in which materials 3, 6, 12, 14 and 15 appear as first generation precursor reactants. Systems 1A and 1B produced a total of ten further stoichiometries leading to all of these materials except species 12, which is allowed only as a reactant in systems 1A and 1B since it could only be produced by decomposing more complex naphthyl molecules. All stoichiometries except I and K achieve acceptable conversion at 300K. For stoichiometry I, Gsys is minimised at 800K and high conversion since AGR for this reaction has a large negative temperature gradient, so that equation 56 is dominated by its first RHS term. For stoichiometry K however, reactor temperature has to be elevated to meet the production rate bound, so that this stoichiometry is the only one for which T' > 300K (from equations 57-59). The two industrial chemistries shown in Figure 2 were reproduced; stoichiometries A and I representing the methyl isocyante route, and stoichiometries D and N representing the non-methyl isocyanate route. Stoichiometries C and D represent the first and third of the three alternative single step routes put forward by Crabtree and E1-Halwagi (1994), their second alternative does not appear here since it involves three apparently simultaneous reactants. Table 4 shows the total profits and impacts for the individual solutions combined in to multi-step stoichiometries. For example, the index AEI denotes the combination of steps A, E and I. Note that the profits reflect only the values of the products minus the values of the reactants, assuming that stoichiometric co-products are sold at their market value, and that in this example, raw materials are assumed input waste free. Note also that stoichiometries with poor conversion are not penalised since the costs and impacts of separation are not included here, and it is assumed that unconsumed reactants are recycled with no loss of heat and no compression or pumping requirements. Only stoichiometries involving step K can justifiably be eliminated from further consideration on impact grounds, this step being penalised in impact terms by high reactor temperature, and only stoichiometries involving steps M or N can justifiably be eliminated on economic grounds. Despite the fact that these steps both exhibit high profits, species 6 is such a high value material that only step L generates sufficient profit to cover the cost of consuming species 6 in system zero. It is for this reason that stoichiometry DL remains competitive despite the poor economic performance of step D, which was rejected by Crabtree and E1-Halwagi (1994) on economic grounds. This clearly illustrates the advantages of considering multi-step production routes. Of the remaining ten stoichiometries, the original industrial chemistry (steps A and I) with the addition of step E, F, G or H to produce species 3, exhibits the

203 Table 4: Total Profits and Impacts Index A A A A

E F G H

I I I I

B B B

J J J

L M N

B B B

K K K E E F F G G H H L M N

L M N J K J K J K J K

D D D

Total Profit $/mol 1.1403 1.1408 1.1409 1.1644 1.0070 0.5426 0.6394 1.0205 0.5561 0.6529 1.0453 1.0570 1.0439 1.0574 1.0441 1.0576 1.0675 1.0810 1.0070 0.5426 0.6394

Total CTAM

tnair/mol 32.15 43.48 43.10 38.69 44.28 40.53 36.69 2090.86 2087.12 2083.27 27.72 2074.31 39.05 2085.64 38.68 2085.26 34.27 2O8O.85 33.93 30.19 26.34

most promising economics of all, which is probably why it was selected. Furthermore, the environmental impacts of the routes based on this chemistry are also among the most promising. Of these routes, stoichiometry AEI represents the best compromise solution. Only stoichiometry CEJ exhibits a significantly lower impact t h a n AEI, with only a marginally reduced profit, and so appears to r e p r e s e n t the best compromise solution of all. However, conversion is poor for step J so t h a t higher separation and recycle costs are anticipated. Issues such as this m u s t be explored in order to eliminate further alternatives.

7.7 C O N C L U S I O N S

In the work presented here, a procedure for the rapid identification of alternative multi-step stoichiometries has been described in which each stoichiometric step involves whole n u m b e r stoichiometric coefficients and a limited n u m b e r of species. The key to the procedure is the introduction of m a t e r i a l design principles to formalise the development of a set of co-materials from which stoichiome-

204 tries are then extracted using an optimisation procedure. The co-material enumeration procedure is based on a set of structural and chemical feasibility rules from Constantinou et al. (1996). However, r a t h e r t h a n employing their molecular generation algorithm, the rules are instead used to develop a set of linear integer constraints governing the numbers and combinations of particular structural groups in a molecule. Combining these rules with the octet rule, and additional structural restrictions to limit the total number of groups, and the numbers of branches, substituents, substituted sites and functional groups, results in the co-material enumeration MILP formulation. This problem is solved repeatedly, introducing integer cuts after each iteration to exclude previous solutions, to produce a set of co-materials. Stoichiometries are then extracted from this set of materials using an optimisation procedure, in which stoichiometries are explicitly enumerated and subsequently evaluated in two sequential steps. Stoichiometry enumeration includes whole number stoichiometric coefficients constraints, constraints to restrict changes to the carbon skeletons of the reacting species, and case specific constraints based on chemical knowledge. Thermodynamic, economic and environmental impact criteria are employed in the evaluation of the stoichiometries, with aspects of the MEIM (Pistikopoulos et al., 1994) providing the framework for the environmental evaluation of alternatives. The illustrative example has shown that the co-material design technique provides an interesting set of co-material molecules and that, with the inclusion of a few simple rules based on chemical knowledge, it is possible to limit the quantity of co-materials to a manageable number. Furthermore, by incorporating simple chemical rules along with thermodynamic, economic and environmental criteria in stoichiometry identification it is possible to identify a small number of alternative stoichiometries which are promising both in terms of economics and environmental impact. Moreover, it has been shown that developing multistep stoichiometries directly can lead to the acceptance of alternatives which would be rejected as single step syntheses. In the illustrative example, existing industrial chemistries were identified as the most promising compromise solutions, with several new and competitive alternatives. This suggests that the approach could lead to promising results in the search for production routes for new molecules. F u r t h e r reinforcement of this conclusion appears in a second application presented in Chapter 14.

7.8 R E F E R E N C E S

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208

A p p e n d i x A: Role S p e c i f i c a t i o n and C h e m i s t r y C o n s t r a i n t s for C a s e S t u d y - 1 M a n u f a c t u r e of Carbaryl A.1 R o l e S p e c i f i c a t i o n C o n s t r a i n t s Table 5 shows the knowledge based role specification constraints employed in the carbaryl example, where R denotes reactant only, P denotes the final product, C denotes product or co-product, N denotes the exclusion of a species from a system and a blank space denotes no restriction. Table 5: Role Specification C o n s t r a i n t s - Carbaryl Example Species System 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 RRRRRRP R R R C N C 0 1A & 1B CCCC R C C C R

These constraints were developed specifically for two step stoichiometries according to the following arguments, based on chemical knowledge and the existing industrial chemistries: 9The product (carbaryl, species 7) should appear only as the product in system zero, or as a product or co-product in systems 1A and 1B, never as a reactant. 9Other naphthyl group containing molecules should be reactants only in system zero (i.e. no naphthyl containing co-products should appear in system zero), and naphthyl containing compounds with complex substituents (i.e. species 4, 5, and 6) should be products or co-products only in systems 1A and lB. 9Methyl isocyanate and methyl formate (species 14 and 15) may be produced only in systems 1A and 1B and consumed only in system zero (i.e they may not be decomposed to produce simpler molecules). 9/-/2 (species 16) appears as a coproduct only in all systems since hydrogenation reactions are not required. 9H C I (species 19) appears as a co-product only in system zero, and as a reactant (Cl provider) or co-product (as in the industrial chemistries) in

systems 1A and lB. 9H 2 0 (species 18) appears as a possible O H group donor or recipient in all

systems.

209 902 (species 17) appears as an oxygen provider in systems 1A and 1B only.

A.2 Chemistry Constraints The following knowledge based chemistry constraints were employed: 9n a p h t h y l containing species with complex substitutions not allowed as reactants

ii4 + ii5 + ii6 = 0

(73)

9other n a p h t h y l group containing species may not react with each other

iil § ii2 § ii3 § ii7 _ 1

(74)