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Object-oriented integration of macroscopic and microscopic characterization of matter
8)
Computers Md Chemical Engineering Supplement (1999) S731-S734 0 1999 Elsevier Science Ltd. All rights reserved PIl: S0098-13541991OO192-1
Pergamon
Object-oriented Integration of Macroscopic and Microscopic Characterization of Matter Pohjola, V.I., Ahola, J.L. & Pulkkinen, U. University of Oulu, Department of Process Engineering, FIN-90570 Oulu, Finland Abstract Molecular simulation is of growing importance in chemical engineering. The gap usually present in knowledge representations between disciplines is, however, a serious obstacle for efficient utilization of knowledge. The way of bridging the gap between macroscopic and microscopic characterization of matter presented in this paper is based on the view that the solution for integrating knowledge and for enhancing communication, in general, is possible by developing and adopting a unified concept system (PSSP language). The advantage of this system is that the same concepts can be used both in macroscopic and microscopic worlds, whereby the presentational gap is eliminated. Knowledge integration by the formal approach is illustrated by an example starting from an informal description of the example process which is represented as an object with its purpose and some features of its structure and state as specified. The structure of the process is then detailed hierarchically down to the molecular level. It is emphasized that structural detailing should be done in a manner which supports the subsequent state aggregation. The PSSP language can not eliminate discontinuities, which are in knowledge itself but precise location of the knowledge gap and its nature become more detectable by this kind of formal presentation
Keywords: knowledge integration, process design, molecular modeling Introduction The increasing flux of relevant knowledge of interdisciplinary nature has made knowledge integration a major challenge for chemical process engineers. For instance, more and more information is obtained by advanced experimental andv computational methods about relationships prevailing at the molecular level of matter. Statistical mechanics allows an effective theoretical tool for predicting, properties, such as activity coefficients, reaction selectivity and relative reaction rate. The most potential areas for molecular simulations are those in which experimental methods are difficult or even impossible to use (Siepmann, 1993) and empirical prediction methods show poor reliability (Sheehan, 1998). Molecular simulation is of growing importance in process engineering (Froment, 1998). It utilizes computational techniques that explicitly use a molecular-based approach to the problems important in the field of chemical engineering. Areas in which molecular simulations, such as molecular dynamics, Monte Carlo calculations and related techniques, offer possibilities for the prediction of physical and chemical properties are e.g. thermodynamics, transport phenomena, separation processes and chemical reaction kinetics. Molecular simulation has gained a status which "implies that all chemical engineers will require familiarity with it, just as industry assumes chemical engineers will be familiar with process flowsheeting packages today" (Cummings, 1997). The gap usually present in knowledge representations between disciplines is, however, a serious obstacle for efficient utilization of knowledge.
Formal approach to integration The way of bridging the gap between macroscopic and microscopic characterization of matter presented in this paper is based on the view that the solution for integrating knowledge and for enhancing communication, in general, is possible by developing and adopting a unified concept system leading - when formalized - to a formal language. The general requirements for such a formal language are domain independence, a highly unified format, and power of expression. An object-oriented formal language (called PSSP language) has been developed for forming the basis of the phenomenon driven process design methodology (called PDPD methodology) (pohjola, 1998). In PSSP the world is viewed as being composed of objects each being a descendant of the generic real thing and, thus, each having the same list of attributes: Purpose, Structure, State, and Performance (PSSP). As the result a unified representation of all the knowledge from molecular level characterization of matter up to managing a design project is obtained. The PDPD methodology based on PSSP was developed with an aim to invite to view conceptual process design from a new perspective and to open chances for more creative design solutions, more effective activity management, and more responsible decision making. The principles inherent to the methodology offer guidance for how to manage modelling even when utilization of knowledge from microscopic level is aimed.
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Computers and Chemical Engineering Supplement (1999) S7JI-S7J4
Application to domain knowledge The value of the state attribute of any object follows from what has been specified under the structure attribute. Structure exhibits a parts/topology dualism. i.e. it is specified in two dimensions. In the unitstructural dimension an object decomposes to parts which are subobjects having ancestor classes different from that of the original object (except the generic real thing class). In the topological dimension an object and the subobjects it disaggregates into are descendants of the same class. The value of the state attribute of an object is obtained via aggregating the relations between all the subobjects instantiated in either dimension. Detailing the structure of a thing can in principle be done arbitrarily. However. knowing that aggregation of the state relations depends on how the structural disaggregation/decomposition was done. the latter should be carried out keeping the aggregation in mind. This leads to the following modelling principle inherent to the PDPD methodology: Describe the structure of a thing in such a way that it is beneficial to its state description. Explication of the central domain concepts Process. Material. Energy. and Phenomenon in terms of the PSSP language leads to an object hierarchy expanding via the structure attributes. The domain knowledge - in the form of relations - is embedded in the specifications of how each object disaggregates andlor decomposes into lower level objects. Knowledge integration - in the sense of this paper - takes place when the value of the state attribute of a macroscopic object is solved from an aggregate of relationships including links to microscopic objects.
(2) In object (enna . m:
L..=.:~~~--'(3)Graphically
1
Process object Attribute Purpose Structure State Performance Method
Consider. for illustration. a simple chemical process in terms of the generic representation depicted in Fig.I. Assume that interaction through process boundary between process interior and exterior is such that the process is characterized as an isothermal batch process. Let the conceptual modelling task be to specify the process interior state by utilizing microscopic data of interior material. energy and phenomenon. This task specification implies that the process interior structure has to be detailed down to the molecular level. The process interior state . by definition. is obtained from an aggregate of state relationships of its parts. i.e. relationships involving state variables of interior material. energy and phenomenon. Constitutive equations of thermodynamics and phenomenological rate and extent equations are typical relationships at this level of structural description. The aggregation operator is just a list. Material can be disaggregated into submaterials like phases or pure components. Either the original material or its submaterials can be decomposed to parts like molecules which. by definition. are objects not representing continuous material. These parts represent what is called the micro scopic characterization of matter. and decompose further to subparts like atoms. The choice whether to disaggregate the interior material before decomposing to microscopic parts depends on the method of state aggregation to be applied. For an ideal homogeneous mixture disaggregation may be unnecessary.
Valli
j
Why and how we want to take the pheno mena under controt How well we manage in making phenomena ~_ ....... _ - - - advance as desired
(structure only):
Boundary Interior
Exterior -~
Interaction
Fig . 1. Definition of chemical process. Energy can be detailed in the topological dimension. but it is assumed to have no structure in terms of unitstructural parts. Energy can be disaggregated into subenergies according to energy type or following the structural detailing of the material. Again the way of structural detailing should depend on what is the method of state aggregation available or to be applied . Statistical mechanics use partition functions as aggregation operators and imply that energy of the
process interior material is disaggregated into ensemble member energies or to molecul ar energies of each species repr esenting the most probable state of the population. Molecular dynamics simulation uses the relationships between energy and location of individual molecules in the phase space. Macroscopic phenomenon may disaggregate to subphenomena and further to mechanistic steps. which can further disaggregate down to. molecular level
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Computers and Chemical Engineering Supplement (1999) S731-S734
phenomena. Each phenomenon has a unit structure composed of cause, effect and preconditions. It is clear that while it is justified for practical reasons to keep material, energy and phenomenon as separate real things at the macroscopic level, there is the more overlapping between the three objects the deeper into structural detailing one advances. If, for instance, there is a chemical reaction taking place in the process interior, but the reaction has advanced to equilibrium, its state (rate and extent) is obtained from microscopic characterization of material and energy without the need to disaggregate the reaction to molecular phenomena. Example In the following an example taken from literature (Rowley, 1994) concerning dissociation equilibrium of chlorine gas, and translated to the PSSP language, will be reworked in terms of the PDPD methodology. Consider an isothermal batch process like in the previous section. Let the purpose of the process be simply to act as a storage tank for chlorine gas in which Ch may freely dissociate to Cl at constant temperature. Let the modelling task be to check the effect of the extent of dissociation on the pressure of the process interior. There are data available on the dissociation energy and the characteristic vibration and rotation temperatures of Cl 2 molecule. For obtaining pressure one needs the state of the process interior. The state is obtained by solving an aggregate of the relationships between the three structural parts of the interior: material, energy and phenomenon. At the highest level of abstraction it is the tradition from classical thermodynamics to specify the material state by {p, T, n}. If ideal gas behavior is assumed, pressure (p) is obtained immediately when the number of moles (n) is known. The state of the interior phenomenon (dissociation) can be described by [r, ~}, i.e. its rate and extent. The relationship between material state and ~ implies disaggregation of the interior material into two pure components and their decomposition further to their parts. The unit-structural specifications of the two submaterials remain open as for the number of Ch and Cl molecules (moles) in each.These numbers (n CI, and nCl) are state variables of the two submaterials and are constrained by stoichiometry through their relation to ~. If the reaction is assumed to have reached equilibrium, ~=~* (the equilibrium extent) and r=O. The equilibrium extent is related to the state of interior energy at equilibrium, i.e. to the free enthalpy of the reaction and to the interior temperature. The former is an aggregate of free energies of the pure components at 1 atm. Thus, it is the equilibrium constant which needs to be obtained and there is no need to specify the reaction further. The (states of) molar free enthalpies of the two components at 1 atm (G CI" GCI) are obtained from (states of) molecular energies by statistical mechanics. Hence, the interior energy needs to be disaggregated to molecular energies of the two species and these further to energy types as depicted in Fig.2. Each of the
molecular energy types have a relation to' the process interior temperature. The states of individual molecular energies of each type are aggregated by the corresponding partition functions the mutual product of which is then the aggregate of all the molecular energies. For example, relation for electronic partition function can be written
q, = \YoefJDo
n e"'XT + L \V;e"'iT j
(1)
I
where \VO is ground-state degeneracy, \Vi is degeneracy of ith state, f3 is lIkT, Do is dissosiation energy, O,j is characteristic vibrational temperature and eti is characteristic electronic excitation temperature. The process model was implemented as an object in Mathematica environment. Mathematica permits carrying' out aggregation operations the state aggregations symbolically before solving the state model numerically.
Fig. 2. Energy classes and their semantic links to other objects in the case of chlorine dissociation example. An alternative way to catch the equilibrium composition would be to disaggregate material energy via the energies of ensemble members to molecule energies and to aggregate them to the minimum Gibbs free energy, for instance by Monte Carlo simulation.
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Computers and Chemical Engineering Supplement (1999) S731-S734
Discussion The example illustrates the use of the PSSP language in a situation where thermodynamic equilibrium is implied. The aggregation operators evolve in a fairly straight-forward manner from statistical mechanics. Specification of the link between material and phenomenon in a process interior not in thermodynamic equilibrium, in terms of the states of their microscopic subobjects, for obtaining the corresponding aggregation operator for molecular phenomena, cannot be done analytically. However, some parameters needed in rate relations can be related to the states of microscopic objects in the same kind of manner as when calculating the thermodynamic equilibrium. For instance, by applying transition state theory the frequency factor in a kinetic rate equation can be calculated from partition functions of reacting molecules and the activated complex. When the aggregation, for characterizing a macroscopic phenomenon advancing at a nonzero rate, is done by molecular simulation, computer capacity rather than conceptual mismatch in knowledge representation may become a limiting factor. Despite making it easier for the chemical engineer to see the potential of the available microscopic knowledge, a unified concept system, like the PSSP language, helps to pinpoint what specific microscopic knowledge should be generated for supporting decision making in conceptual process design: Also those working in the field of molecular level characterization of matter become more conscious of the needs of the chemical engineer. Microscopic and macroscopic characterization of matter cart be linked together by an unified concept system. The advantage of this system is that same concepts can be used both in macroscopic and microscopic worlds, whereby the presentational gap does not exist. All remaining discontinuity is caused by the gap in knowledge concerning behaviour, e.g. pressure gap, material gap and so on. Material, energy and phenomenon are disaggregated either in the unitstructural or topological dimension. The purpose of disaggregation is to facilitate describing the behavior of the target.
Summary Knowledge integration by the proposed formal approach is illustrated by an example taken from the literature. Starting from an informal description of the example process, the process is represented as an object with its purpose and some features of its structure and state as specified. The structure of the process is then detailed hierarchically down to the molecular level. It is shown how the state of the process interior (composition and pressure) is obtained as a series of nested aggregations starting from the state specifications of the molecular level energy types (translational, rotational, vibrational and electronic) of each molecule. It is especially shown that when applying the PSSP language there is no discontinuity in knowledge representation between the macroscopic and microscopic worlds. The PSSP language cannot eliminate discontinuities, which are in the knowledge itself but precise location of the knowledge gap and its nature become more detectable by this kind of formal presentation. Acknowledgements The authors acknowledge Dr. Tapio Rantala for clarifying the relations between physical quantities and concepts at the molecular level. References Cummings, P.T. (1997) The CACHE molecular modeling task force. CACHE News (44), 2-4. Froment, G.F. and Kalitventzeff, B. (1998) Computers chem. Engng., 22(Suppl.), xvii. Pohjola, V.J. and Tanskanen, J. (1998) Phenomenon driven process design methodology: Formal representation. Paper presented at the CHISA'98 Conference, Prague, Aug. 23-28, 1998. Rowley, R.L. (1994) Statistical mechanics for thermophysical property calculations, Prentice Hall, New Jersey. Sheehan, M.E. and Sharratt, P.N. (1998) Computers chem. Engng., 22(Suppl.), S27-S33. Siepmann, J.I., Karaborni, S. and Smit, B. (1993) Nature, 365, 330-332.
Computers Md Chemical Engineering Supplement (1999) S731-S734 0 1999 Elsevier Science Ltd. All rights reserved PIl: S0098-13541991OO192-1
Pergamon
Object-oriented Integration of Macroscopic and Microscopic Characterization of Matter Pohjola, V.I., Ahola, J.L. & Pulkkinen, U. University of Oulu, Department of Process Engineering, FIN-90570 Oulu, Finland Abstract Molecular simulation is of growing importance in chemical engineering. The gap usually present in knowledge representations between disciplines is, however, a serious obstacle for efficient utilization of knowledge. The way of bridging the gap between macroscopic and microscopic characterization of matter presented in this paper is based on the view that the solution for integrating knowledge and for enhancing communication, in general, is possible by developing and adopting a unified concept system (PSSP language). The advantage of this system is that the same concepts can be used both in macroscopic and microscopic worlds, whereby the presentational gap is eliminated. Knowledge integration by the formal approach is illustrated by an example starting from an informal description of the example process which is represented as an object with its purpose and some features of its structure and state as specified. The structure of the process is then detailed hierarchically down to the molecular level. It is emphasized that structural detailing should be done in a manner which supports the subsequent state aggregation. The PSSP language can not eliminate discontinuities, which are in knowledge itself but precise location of the knowledge gap and its nature become more detectable by this kind of formal presentation
Keywords: knowledge integration, process design, molecular modeling Introduction The increasing flux of relevant knowledge of interdisciplinary nature has made knowledge integration a major challenge for chemical process engineers. For instance, more and more information is obtained by advanced experimental andv computational methods about relationships prevailing at the molecular level of matter. Statistical mechanics allows an effective theoretical tool for predicting, properties, such as activity coefficients, reaction selectivity and relative reaction rate. The most potential areas for molecular simulations are those in which experimental methods are difficult or even impossible to use (Siepmann, 1993) and empirical prediction methods show poor reliability (Sheehan, 1998). Molecular simulation is of growing importance in process engineering (Froment, 1998). It utilizes computational techniques that explicitly use a molecular-based approach to the problems important in the field of chemical engineering. Areas in which molecular simulations, such as molecular dynamics, Monte Carlo calculations and related techniques, offer possibilities for the prediction of physical and chemical properties are e.g. thermodynamics, transport phenomena, separation processes and chemical reaction kinetics. Molecular simulation has gained a status which "implies that all chemical engineers will require familiarity with it, just as industry assumes chemical engineers will be familiar with process flowsheeting packages today" (Cummings, 1997). The gap usually present in knowledge representations between disciplines is, however, a serious obstacle for efficient utilization of knowledge.
Formal approach to integration The way of bridging the gap between macroscopic and microscopic characterization of matter presented in this paper is based on the view that the solution for integrating knowledge and for enhancing communication, in general, is possible by developing and adopting a unified concept system leading - when formalized - to a formal language. The general requirements for such a formal language are domain independence, a highly unified format, and power of expression. An object-oriented formal language (called PSSP language) has been developed for forming the basis of the phenomenon driven process design methodology (called PDPD methodology) (pohjola, 1998). In PSSP the world is viewed as being composed of objects each being a descendant of the generic real thing and, thus, each having the same list of attributes: Purpose, Structure, State, and Performance (PSSP). As the result a unified representation of all the knowledge from molecular level characterization of matter up to managing a design project is obtained. The PDPD methodology based on PSSP was developed with an aim to invite to view conceptual process design from a new perspective and to open chances for more creative design solutions, more effective activity management, and more responsible decision making. The principles inherent to the methodology offer guidance for how to manage modelling even when utilization of knowledge from microscopic level is aimed.
5732
Computers and Chemical Engineering Supplement (1999) S7JI-S7J4
Application to domain knowledge The value of the state attribute of any object follows from what has been specified under the structure attribute. Structure exhibits a parts/topology dualism. i.e. it is specified in two dimensions. In the unitstructural dimension an object decomposes to parts which are subobjects having ancestor classes different from that of the original object (except the generic real thing class). In the topological dimension an object and the subobjects it disaggregates into are descendants of the same class. The value of the state attribute of an object is obtained via aggregating the relations between all the subobjects instantiated in either dimension. Detailing the structure of a thing can in principle be done arbitrarily. However. knowing that aggregation of the state relations depends on how the structural disaggregation/decomposition was done. the latter should be carried out keeping the aggregation in mind. This leads to the following modelling principle inherent to the PDPD methodology: Describe the structure of a thing in such a way that it is beneficial to its state description. Explication of the central domain concepts Process. Material. Energy. and Phenomenon in terms of the PSSP language leads to an object hierarchy expanding via the structure attributes. The domain knowledge - in the form of relations - is embedded in the specifications of how each object disaggregates andlor decomposes into lower level objects. Knowledge integration - in the sense of this paper - takes place when the value of the state attribute of a macroscopic object is solved from an aggregate of relationships including links to microscopic objects.
(2) In object (enna . m:
L..=.:~~~--'(3)Graphically
1
Process object Attribute Purpose Structure State Performance Method
Consider. for illustration. a simple chemical process in terms of the generic representation depicted in Fig.I. Assume that interaction through process boundary between process interior and exterior is such that the process is characterized as an isothermal batch process. Let the conceptual modelling task be to specify the process interior state by utilizing microscopic data of interior material. energy and phenomenon. This task specification implies that the process interior structure has to be detailed down to the molecular level. The process interior state . by definition. is obtained from an aggregate of state relationships of its parts. i.e. relationships involving state variables of interior material. energy and phenomenon. Constitutive equations of thermodynamics and phenomenological rate and extent equations are typical relationships at this level of structural description. The aggregation operator is just a list. Material can be disaggregated into submaterials like phases or pure components. Either the original material or its submaterials can be decomposed to parts like molecules which. by definition. are objects not representing continuous material. These parts represent what is called the micro scopic characterization of matter. and decompose further to subparts like atoms. The choice whether to disaggregate the interior material before decomposing to microscopic parts depends on the method of state aggregation to be applied. For an ideal homogeneous mixture disaggregation may be unnecessary.
Valli
j
Why and how we want to take the pheno mena under controt How well we manage in making phenomena ~_ ....... _ - - - advance as desired
(structure only):
Boundary Interior
Exterior -~
Interaction
Fig . 1. Definition of chemical process. Energy can be detailed in the topological dimension. but it is assumed to have no structure in terms of unitstructural parts. Energy can be disaggregated into subenergies according to energy type or following the structural detailing of the material. Again the way of structural detailing should depend on what is the method of state aggregation available or to be applied . Statistical mechanics use partition functions as aggregation operators and imply that energy of the
process interior material is disaggregated into ensemble member energies or to molecul ar energies of each species repr esenting the most probable state of the population. Molecular dynamics simulation uses the relationships between energy and location of individual molecules in the phase space. Macroscopic phenomenon may disaggregate to subphenomena and further to mechanistic steps. which can further disaggregate down to. molecular level
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Computers and Chemical Engineering Supplement (1999) S731-S734
phenomena. Each phenomenon has a unit structure composed of cause, effect and preconditions. It is clear that while it is justified for practical reasons to keep material, energy and phenomenon as separate real things at the macroscopic level, there is the more overlapping between the three objects the deeper into structural detailing one advances. If, for instance, there is a chemical reaction taking place in the process interior, but the reaction has advanced to equilibrium, its state (rate and extent) is obtained from microscopic characterization of material and energy without the need to disaggregate the reaction to molecular phenomena. Example In the following an example taken from literature (Rowley, 1994) concerning dissociation equilibrium of chlorine gas, and translated to the PSSP language, will be reworked in terms of the PDPD methodology. Consider an isothermal batch process like in the previous section. Let the purpose of the process be simply to act as a storage tank for chlorine gas in which Ch may freely dissociate to Cl at constant temperature. Let the modelling task be to check the effect of the extent of dissociation on the pressure of the process interior. There are data available on the dissociation energy and the characteristic vibration and rotation temperatures of Cl 2 molecule. For obtaining pressure one needs the state of the process interior. The state is obtained by solving an aggregate of the relationships between the three structural parts of the interior: material, energy and phenomenon. At the highest level of abstraction it is the tradition from classical thermodynamics to specify the material state by {p, T, n}. If ideal gas behavior is assumed, pressure (p) is obtained immediately when the number of moles (n) is known. The state of the interior phenomenon (dissociation) can be described by [r, ~}, i.e. its rate and extent. The relationship between material state and ~ implies disaggregation of the interior material into two pure components and their decomposition further to their parts. The unit-structural specifications of the two submaterials remain open as for the number of Ch and Cl molecules (moles) in each.These numbers (n CI, and nCl) are state variables of the two submaterials and are constrained by stoichiometry through their relation to ~. If the reaction is assumed to have reached equilibrium, ~=~* (the equilibrium extent) and r=O. The equilibrium extent is related to the state of interior energy at equilibrium, i.e. to the free enthalpy of the reaction and to the interior temperature. The former is an aggregate of free energies of the pure components at 1 atm. Thus, it is the equilibrium constant which needs to be obtained and there is no need to specify the reaction further. The (states of) molar free enthalpies of the two components at 1 atm (G CI" GCI) are obtained from (states of) molecular energies by statistical mechanics. Hence, the interior energy needs to be disaggregated to molecular energies of the two species and these further to energy types as depicted in Fig.2. Each of the
molecular energy types have a relation to' the process interior temperature. The states of individual molecular energies of each type are aggregated by the corresponding partition functions the mutual product of which is then the aggregate of all the molecular energies. For example, relation for electronic partition function can be written
q, = \YoefJDo
n e"'XT + L \V;e"'iT j
(1)
I
where \VO is ground-state degeneracy, \Vi is degeneracy of ith state, f3 is lIkT, Do is dissosiation energy, O,j is characteristic vibrational temperature and eti is characteristic electronic excitation temperature. The process model was implemented as an object in Mathematica environment. Mathematica permits carrying' out aggregation operations the state aggregations symbolically before solving the state model numerically.
Fig. 2. Energy classes and their semantic links to other objects in the case of chlorine dissociation example. An alternative way to catch the equilibrium composition would be to disaggregate material energy via the energies of ensemble members to molecule energies and to aggregate them to the minimum Gibbs free energy, for instance by Monte Carlo simulation.
5734
Computers and Chemical Engineering Supplement (1999) S731-S734
Discussion The example illustrates the use of the PSSP language in a situation where thermodynamic equilibrium is implied. The aggregation operators evolve in a fairly straight-forward manner from statistical mechanics. Specification of the link between material and phenomenon in a process interior not in thermodynamic equilibrium, in terms of the states of their microscopic subobjects, for obtaining the corresponding aggregation operator for molecular phenomena, cannot be done analytically. However, some parameters needed in rate relations can be related to the states of microscopic objects in the same kind of manner as when calculating the thermodynamic equilibrium. For instance, by applying transition state theory the frequency factor in a kinetic rate equation can be calculated from partition functions of reacting molecules and the activated complex. When the aggregation, for characterizing a macroscopic phenomenon advancing at a nonzero rate, is done by molecular simulation, computer capacity rather than conceptual mismatch in knowledge representation may become a limiting factor. Despite making it easier for the chemical engineer to see the potential of the available microscopic knowledge, a unified concept system, like the PSSP language, helps to pinpoint what specific microscopic knowledge should be generated for supporting decision making in conceptual process design: Also those working in the field of molecular level characterization of matter become more conscious of the needs of the chemical engineer. Microscopic and macroscopic characterization of matter cart be linked together by an unified concept system. The advantage of this system is that same concepts can be used both in macroscopic and microscopic worlds, whereby the presentational gap does not exist. All remaining discontinuity is caused by the gap in knowledge concerning behaviour, e.g. pressure gap, material gap and so on. Material, energy and phenomenon are disaggregated either in the unitstructural or topological dimension. The purpose of disaggregation is to facilitate describing the behavior of the target.
Summary Knowledge integration by the proposed formal approach is illustrated by an example taken from the literature. Starting from an informal description of the example process, the process is represented as an object with its purpose and some features of its structure and state as specified. The structure of the process is then detailed hierarchically down to the molecular level. It is shown how the state of the process interior (composition and pressure) is obtained as a series of nested aggregations starting from the state specifications of the molecular level energy types (translational, rotational, vibrational and electronic) of each molecule. It is especially shown that when applying the PSSP language there is no discontinuity in knowledge representation between the macroscopic and microscopic worlds. The PSSP language cannot eliminate discontinuities, which are in the knowledge itself but precise location of the knowledge gap and its nature become more detectable by this kind of formal presentation. Acknowledgements The authors acknowledge Dr. Tapio Rantala for clarifying the relations between physical quantities and concepts at the molecular level. References Cummings, P.T. (1997) The CACHE molecular modeling task force. CACHE News (44), 2-4. Froment, G.F. and Kalitventzeff, B. (1998) Computers chem. Engng., 22(Suppl.), xvii. Pohjola, V.J. and Tanskanen, J. (1998) Phenomenon driven process design methodology: Formal representation. Paper presented at the CHISA'98 Conference, Prague, Aug. 23-28, 1998. Rowley, R.L. (1994) Statistical mechanics for thermophysical property calculations, Prentice Hall, New Jersey. Sheehan, M.E. and Sharratt, P.N. (1998) Computers chem. Engng., 22(Suppl.), S27-S33. Siepmann, J.I., Karaborni, S. and Smit, B. (1993) Nature, 365, 330-332.