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Chen, S. P.; Ferry, J. D. The Diffusion of Radioactively Tagged n-Hexadecane and n-Dodecane through Rubbery Polymers. Effect of Temperature, Cross-Linking, and Chemical Structure. Macromolecules 1968, 1, 270. Ehlich, D.; Sillescu, H. Tracer Diffusion at the Glass Transition. Macromolecules 1990,23, 1600. Ferguson, R. D.; von Meerwd, E. Free-Volume Interpretation of Self-Diffusion in Ternary Solutions: n-Paraffin-Hexafluorobenzene-cis-4-Polybutadiene.J. Polym. Sci., Polym. Phys. Ed. 1980,18, 1285. Fujita, H. Diffusion in Polymer-Diluent Systems. Fortschr. Hochpo1ym.-Forsch. 1961, 3, 1. Fujita, H. Diffusion in Polymers. In Diffusion in Polymers; Crank, J. C., Park, G. S., Eds.; Academic Press: New York, 1968. Haward, R. N. Occupied Volume of Liquids and Polymers. J. Macromol. Sci., Rev. Macromol. Chem. C 1970,4, 191. Ju, S.T.; Duda, J. L.; Vrentas, J. S. Influence of Temperature on the Diffusion of Solvents in Polymers above the Glass Transition Temperature. Znd. Eng. Chem. Prod. Res. Deu. 1981, 20, 330. Kishimoto, A.; Maekawa, E.; Fujita, H. Diffusion Coefficient for Jpn. Amorphous Polymer and Water Systems. Bull. Chem. SOC. 1960, 33, 988. Kokes, R. J.; Long, F. A. Diffusion of Organic Vapors into Polyvinyl 1953, 75,6142. Acetate. J. Am. Chem. SOC. Liu, H. T.; Duda, J. L.; Vrentas, J. S. Influence of Solvent Size on the Concentration Dependence of Polymer-Solvent Diffusion Coefficients. Macromolecules 1980, 13, 1587. Mauritz, K. A.; Storey, R. F. A General Free Volume Based Theory for the Diffusion of Large Molecules in Amorphous Polymers Above Tg. 2. Molecular Shape Dependence. Macromolecules 1990,23,2033. Mauritz, K. A.; Storey, R. F.; George, S. E. A General Free Volume Based Theory for the Diffusion of Large Molecules in Amorphous Polymers above Tg. 1. Application to Di-n-alkyl Phthalates in PVC. Macromolecules 1990,23, 441. Mearea, P. Polymers: Structure and Bulk Properties; Van Noatrand Reinhold London, 1965. Pawlisch, C. A. Measurement of the Diffusivity and Thermodynamic Interaction Parameters of a Solute in a Polymer Melt Using Capillary Column Inverse Gas Chromatography. Ph.D. thesis, University of Massachusetts, Amherst, MA, 1985. Pawlisch, C. A.; Macris, A.; Laurence, R. L. Solute Diffusion in
Polymers. 1. The Use of Capillary Column Inverse Gas Chromatography. Macromolecules 1987,20, 1564. Pawlisch, C. A.; Bric, J. R.; Laurence, R. L. Solute Diffusion in Polymers. 2. Fourier Estimation of Capillary Column Inverse Gas Chromatography Data. Macromolecules 1988,21, 1685. Prager, S.;Long,F. A. Diffusion of Hydrocarbons in Polyiaobutylene. J. Am. Chem. SOC. 1951, 73,4012. Prager, S.; Bagley, E.; Long, F. A. Diffusion of Hydrocarbon Vapors 1953, 75, 1255. into Polyisobutylene. 11. J. Am. Chem. SOC. Rhee, C. K.; Ferry, J. D.; Fetters, L. J. Diffusion of Radioactively Tagged Penetrants Through Rubbery Polymers. 11. Dependence on Molecular Length of Penetrant. J. Appl. Polym. Sci. 1977,21, 783. Van Amerongen, G. J. The Permeability of Different Rubbers to Gases and Its Relation to Diffusivity and Solubility. J. Appl. Phys. 1946,17,972. Vrentas, J. S.; Duda, J. L. Diffusion in Polymer-Solvent Systems. I. Reexamination of the Free-Volume Theory. J. Polym. Sci., Polym. Phys. Ed. 1977a,15,403. Vrentas, J. S.; Duda, J. L. Diffusion in Polymer-Solvent System. 11. A Predictive Theory for the Dependence of Diffusion Coefficient on Temperature, Concentration, and Molecular Weight. J. Polym. Sci., Polym. Phys. Ed. 1977b,15, 411. Vrentas, J. S.; Duda, J. L. A Free-Volume Interpretation of the Influence of the Glass Transition on Diffusion in Amorphous Polymers. J. Appl. Polym. Sci. 1978, 22, 2325. Vrentas, J. S.; Duda, J. L. Diffusion of Large Penetrant Molecules in Amorphous Polymers. J. Polym. Sci., Polym. Phys. Ed. 1979, 17, 1085. Vrentas, J. S.; Duda, J. L.; Liu, H. T. Effect of Solvent Size on Diffusion in Polymer-Solvent Systems. J. Appl. Polym. Sci. 1980, 25,1793. Vrentas, J. S.; Duda, J. L.; Hou, A X . ; Segmentwise Diffusion in Molten Polystyrene. J. Appl. Polym. Sci. 1986, 31, 739. Wong, C. P.; Schrag, J. L.; Ferry, J. D. Diffusion of Radioactively Tagged 1,l-Diphenylethane and n-Hexadecane through Rubbery Polymers: Dependence on Temperature and Dilution with Solvent. J. Polym. Sci. A 1970, 2, 991. Received for review February 6, 1991 Revised manuscript received July 29, 1991 Accepted August 13, 1991
PROCESS ENGINEERING AND DESIGN Knowledge Representation and Reasoning in the Presence of Uncertainty in an Expert System for Laboratory Reactor Selection Peter J. Hanratty, Babu Joseph,* a n d Milorad P. Dudukovic Chemical Reaction Engineering Laboratory, Washington University, St. Louis, Missouri 63130
This paper is concerned with modeling and computer implementation of the process of selecting multiphase reactors for a given application. The qualitative reasoning process is modeled using an expert system architecture. Uncertainty in the input data is handled using the theory of fuzzy sets. Uncertainty in the decision-making process is modeled using the analytic hierarchy process (AHP) adapted from the field of economics. The system is implemented using a commercial expert system shell. The work demonstrates the feasibility and utility of creating expert systems to encapsulate knowledge used by experts in chemical process and reaction engineering. Introduction This paper is concerned with the process of selecting an appropriate laboratory reador for collecting experimental data needed for such diverse purposes as catalyst screening,
scale-up, troubleshooting, and kinetic modeling. The accuracy and the reliability of the data must be matched with the time and cost constraints to arrive at a “best” choice for a particular application. Usually,this task is delegated
Q888-5885/92/2631-Q228$03.oo/O Q 1992 American Chemical Society
Ind. Eng. Chem. Res., Vol. 31, No. 1, 1992 229 to a chemical reaction engineering “expert”. The expert makes the decision based on the data available, the functional requirements, the constraints imposed, and finally his or her own past experience in the field. Unfortunately, one reactor type will not produce the desired data for all situations. Each reactor type has its own strengths and weaknesses which change with a change in the reacting system. Thus a reactor that produced good data for one system will not needy produce reasonable data for another system. Therefore, for each new reacting system, the best laboratory reactor should be chosen based upon the strengths and weaknesses for each of the reactors for that particular reacting system. To quote V. W. Weekman (1974) “To those fortunate enough to work in academic laboratories, it is possible to first choose a reactor type and then find a suitable reacting system to study in it. In the industrial sphere, alas, the specific reacting system is imposed on us and the problem is to search for a suitable reactor type ....” The procedure for selecting an appropriate reactor for an application is an involved process. There are presently over 18 different types of laboratory reactors. A wrong choice can lead to improper data which in turn will lead to errors in scale-up and design. Improper selection also can lead to lost time if the experiments have to be repeated. The knowledge needed to make the selection is not trivial. For someone not familiar with the field, there is a significant amount of information that must be digested. If it is possible to capture the essential knowledge needed for the selection process into an expert system, it would enhance the chemist’s or chemical engineer’s productivity. An expert system also would have the advantage of giving consistent and quick answers to a complicated problem. The expert system can be viewed as a model of the selection process. The model would provide the engineer or chemist who has limited experience in reaction engineering with choices similar to those which would have been selected by a knowledgeable expert. To construct such a model, one first needs to understand how and on what basis the laboratory reactors are chosen by the experts. The selection is based predominantly on qualitative reasoning backed by a few quantitative calculations. Qualitative reasoning appears to be essential because most of the input information about the reacting system (the system for which the reactor studies are needed) usually is known qualitative (i.e., the heat of reaction is known to be low or as about 1-5 kcal/mol) and a large part of the resoning used to manipulate this information is also qualitative (even when the input information is known quantitatively). The selection of laboratory reactors involves both qualitative reasoning and quantitative analysis. Traditional engineering computing techniques utilize predominantly quantitative methods so that they cannot adequately model this problem domain by themselves. However, artificial intelligence, in particular expert systems, offer the methodologies and techniques for modeling the problem domain both qualitatively and quantitatively. Expert systems also offer the advantages that they provide the user with a convenient way to interact with the system and obtain explanations of the selection process imbedded in the system. The objective of this paper is to show how the selection of laboratory reactors was modeled utilizing expert system techniques. This is accomplished by modeling the problem domain both qualitatively (usually in the form of rules) and quantitatively (usually in the form of equations). Specific issues addressed in this paper are (i) the model
of the selection process, (ii) the organization of the knowledge and data needed for decision-making, and (iii) the methodology for handling uncertainty in the input data as well as the uncertainty in the knowledge (manifested by differences among experts on critical decision points). This paper first will give a short background on the selection of laboratory reactors and then discussed how it was implemented into an expert system. The discussion of the implementation will include how the decisionmaking process was modeled, system was structured, uncertainty in the input and reasoning process was handled, and knowledge was acquired. The system capabilities are illustrated using an example. We conclude with a discussion of the system’s capabilities. Background In order to model the laboratory reactor selection process, a firm understanding of the strategies used and the significance of various choices are needed. This section will address these issues; in particular, it will cover (i) the performance factors upon which the selection process is based, (ii) the reactor types and configurations considered, and (iii) the rating methodology for each of the performance factors and for the reactor as a whole. Also, an example of how the reactors currently are chosen by an expert will be illustrated. This discussion will be limited to kinetic studies for multiphase systems. Extensions to other types of applications, i.e., catalyst screening, are possible. It is felt that items i-iii above encompass the major components of the reactor selection process. Based on consultation with experts, insight from the literature (Weekman, 19741, and engineering common sense the following procedure to select multiphase reactors was formulated Step 1. Select the desired reactor application (i.e., kinetic studies or catalyst screening). Step 2. Determine the performance factors (see below) which are important to the selected reactor application. Step 3. Determine which reactor types should be considered for the selection process. Step 4. Rate each of the performance factors listed in step 2 for each of the reactors to be considered for selection. Step 5. On the basis of the ratings of the performance factors rank the choices available. For this paper, the desired reactor application (step 1) is kinetic studies. Steps 2 and 3 correspond to items i and ii above, and steps 4 and 5 correspond to item iii above. Performance Factors. For laboratory reactor selection, an important first step is to identify the critical performance factors (attributes) upon which the selection is to be based (Weekman, 1974). In order to identify these performance factors, it is important to consider the objectives of the experiments to be conducted using the reactor and the nature of the data needed. This clearly depends on the specific application. Consider for example the requirements of a multiphase reactor system for the evaluation of reaction kinetics. For kinetics studies, the main requirement of the experimental data is that meaningful kinetic rate data can be obtained from it. Two factors could affect the data: masking of the actual kinetic rate by some other mechanism (i.e., transport effects) and experimental difficulties in getting good representative data. The data can be masked by mass-transfer limitations (the rate of reaction is limited by the rate at which the reactanta reach the reacting surface or zone), catalyst deactivation, and nonisothermal conditions. Experimental difficulties can be
230 Ind. Eng. Chem. Res., Vol. 31, No. 1, 1992
caused by problems associated with sampling and analysis of the product composition. Other practical considerations include the cost (initial and operational), the time to get the data, and the ease of data analysis. Based on the above considerations and consultation of the literature (Hill, 1977; Levenspiel, 1984 Ramachandran and Chaudhari, 1983; Shah, 1979; Weekman, 1974; Berty, 1984; Robinson and Mahoney, 1977; etc.) and experts in the field, the following attributes were defined most important in selecting the best multiphase laboratory reactor for kinetic studies: (1)isothermality; (2) mass-transfer limitations; (3) data analysis and sampling; (4) catalyst deactivation; (5) construction difficulty and cost; (6) operational cost. The first performance factor, isothermality, rates the uniformity of the temperature within the reactor. For kinetic studies, it is necessary to maintain as constant a temperature as possible both in time and in position within the reactor because temperature variations can greatly affect the rates of competing reaction paths. The more constant the temperature (isothermal) of the system is, the higher the performance rating. Factors which could affect the isothermality of the reactor include heat of reaction, mixing pattern within the reactor, and intrinsic reaction rate. The rating of the mass-transfer limitations performance factor depends on the extent to which the measured reaction rate is affected by the mass-transfer rate of the reactants or products. If the mass-transfer rate is slower than the intrinsic reaction rate, then the measured rate data represent the mass-transfer rate and not the intrinsic reaction rate. The smaller the mass-transfer rate effects on the measured reaction rate are, the higher the performance rating for this attribute. Factors which can affect the --transfer limitation attribute include the intrinsic reaction rate, mass-transfer coefficients (governed by the flow field in the reactor), effective diffusivity, and particle size. The data analysis and sampling performance factor rates the ease of sampling and accuracy of analysis of the reaction mixture at the reactor inlet and outlet. The ability to get representative samples of the reactor product and then to analyze the composition of the sample is essential to get accurate and useful data. Sampling is especially difficult for multiphase systems because of the need to separate different phases. Also, the accuracy and ease with which the data can be manipulated are important considerations. The more accurate the sampling and data analysis is, the higher the performance rating. Factors which affect this attribute include the product composition (gas-liquid-solid), intrinsic reaction rate, and state of mixing in the reactor. The rating for the catalyst deactivation performance factor depends on the extent to which catalyst deactivation masks the measured reaction rate in a chosen reactor and on the ease of decoupling the two effects. Many catalyst surfaces are fouled or deactivated during reactor operation (during the course of a reaction experiment). The deactivation of the catalyst reduces the overall reaction rate sometimes preferentially toward one reaction pathway over another. The lower the effect of catalyst deactivation is, the higher the performance rating. Reactors for which the catalyst mean residence time is large relative to the mean residence time for the reactants and products will be more a f f d by catalyst deactivation. Factors which affect this performance factor are the catalyst deactivation rate, reaction rate, mode of reactor operation, and catalyst residence time.
Table I. Characteristics of System for Example Problem (Adapted from Weekman, 1974) reaction type three phase (solid catalyzed) heat of reaction highly endothermic reaction catalyst activity highly active catalyst catalyst decay rapid catalyst decay reaction mechanism complex reaction mechanism type of catalyst powdered catalyst
The construction difficulty and cost performance factor is used to weight the economical considerations of the selected reactor. The easier and cheaper it is to construct the reactor, the higher the performance rating of this attribute. Some factors which affect the attribute rating are reaction rate, heat of reaction, reactor type, catalyst available, etc. The operational cost performance factor rates the cost it takes to operate the reactor. The operational cost includes the cost of the feed, the cost to maintainthe reactor, and the cost to operate the reactor. The lower the operational cost is, the higher the performance rating of this attribute. Reactor Types. Concurrently with the identification of the performance factors, it is necessary to decide which reactor typea and/or confiiations are appropriate for the given situation. For three phase catalytic systems, the following reactor types were considered (Shah, 1979; Chaudhari et al., 1986; Christoffel, 1982; Doraiswamy and Tajbl, 1974): micro reactor fixed-bed reactor: recycle, integral conversion, differential conversion stationary basket reactor: batch, semibatch, continuous spinning basket reactor: batch, semibatch, continuous mechanically agitated slurry: batch, semibatch, continuous transport slurry reactor: recycle, integral conversion, differential conversion wiper blade wetted wall Overall, there are 18 different reactor configurations listed above. A detailed description of the above reactor types will not be included here. For a good description and a general overview of these reactor types see Chaudhari et al. (1986), Christoffel (1982), Doraiswamy and Tajbl(19741, Shah (1979), and Weekman (1974). For more general-purpose multiphase reactor information see Mills et al. (1989) and Ramachandran and Chaudhari (1983). Example Problem: Laboratory Reactor Selection. An example of the reactor selection process is shown below in order to illustrate the reasoning process for reactor selection and demonstrate the usefulness of expert systems for this problem. This example is an illustration of how the reactor selection problem currently is solved by an expert. It should be noted that the objective of this work is to implement the reactor selection procedure into an expert system and make it available to both experts and nonexperte. The system studied was adapted from a paper on reactor selection by Weekman (1974). Table I gives a description of the reacting system to be studied. For this example, the reador application is taken to be kinetic studies. After establishment of the application, the important performance factors (attributes) need to be chosen. Weekman (1974) selected the following attributes: sampling and analysis of the product composition; isothermality; residence contact time; selectivity time averaging disguise; construction cost and difficulty. Note that these attributes are similar to the attributes listed earlier, but there are
Ind. Eng. Chem. Res., Vol. 31, No. 1, 1992 231 Table 11. Reactor h t i n p for Given Example sampling residence selectivity and isotherm- contact diaguke- construction reactor type analysis ality time decay problems F-G F P G differential P-F P-F F P G fixed bed G stirred batch F G G P G stirred G G F-G P F-G contained solids ontinuous F G F-G G P-F stirred tank straightF-G P-F F-G G F-G through transport P-F G G G ecirculating F-G transport G pulse G F-G P F-G “ G = good; F = fair; P = poor.
some differences which can be attributed to differences in opinion and/or priority. Next, the suitable reactor types are listed. Also, the ratings for the performance factors for each of the established reactor c o n f i a t i o n s need to be determined. The results of both of these steps are illustrated in Table 11. The ratings in Table I1 are taken directly from the paper of Weekman (1974), and these attribute ratings apply only to the example cited. The ratings given to each performance factor reflect the expertise and knowledge of the expert involved. From Table 11, it can be seen that each reactor type has its own advantages and disadvantages. From the ratings, Weekman chose the recirculating transport reactor and the continuous stirred tank reactor (CSTR) as the best two alternatives. Going through the example above, a number of points should be clarified. First, the attribute ratings in Table I1 are valid only for the example given. A change in the system conditions (the properties of the reacting system, such as the heat of reaction) will change the attribute ratings. The modeling of how the attribute ratings change with the system conditions is one of the keys to modeling the selection process. This entails determining which system conditions and/or combination of conditions affect the attribute rating and how they affect the overall rating. Information to model attribute ratings comes in the form of heuristics, rule-of-thumb, design equations, reactor specific information, etc. From the example, it can be seen that qualitative information is used throughout the selection process. The input information about the process is not always known exactly but as approximate values such as high or low. The input information is known approximately because the systems are not well understood. (That is why the experiments are being conducted-to learn more about the system!) The output ratings for the attributes are hard to quantify because the input information is qualitative and the knowledge about the reactor type is not precise (in other words, qualitative). Finally, from this example it can be seen that there are no clear-cut answers to which reactor is the best. Each reactor type has its own advantages and disadvantages, but while some lead to useful data others may lead to significant problems in data interpretation. The above observations illustrate why an expert system is a good tool for modeling the laboratory reactor selection process. To model the changing attribute ratings, tools which can incorporate a combination of qualitative, quantitative, and heuristic information are needed. Since there is no clear-cut “best”reactor, an explanation of the selection process is important to strengthen the answers.
Expert systems give the capability of explaining how and why the modeling process progressed toward a particular selection.
Expert System Implementation An expert system, named LARS (LAboratory Reactor Selection system) was designed to capture the reasoning illustrated by the example in the previous section. The expert system for laboratory reactor selection is intended to give both the expert and nonexpert quick answers to the problem of reactor selection. Knowledge Acquisition. The acquisition, organization and representation of the knowledge required to model the laboratory reactor selection process was conducted in two parts: (i) general knowledge acquisition in order to obtain an understanding of the problem domain and (ii) specific knowledge acquisition to obtain detailed knowledge about each reactor. The objective of the general knowledge acquisition was to obtain an overview of the problem domain. With this understanding, a model of the selection process was developed leading to the five-step reactor selection procedure outlined in the Background section. While this five-step procedure is not enough to solve the selection problem, it does represent an understanding of the problem domain and it does help to direct and focus the knowledge acquisition of more detailed and specific information. The scope and magnitude of the project was also reassessed and redefined at the end of this phase. The scope of this implementation was limited to the selection of multiphase reactors for kinetic studies and catalyst screening. The information for the general knowledge acquisition phase was obtained mainly from the literature (textbooks and publications) and through discussions with experta in the field. For the most general information about chemical reactors, textbooks such as those by Hill (1977) and Levenspiel(1984) were found to be useful. Discussion and interaction with the experts in the field also was useful. Review papers on the available laboratory reactora (such as Chaudhari et al. (19861, Shah (1979), Christoffel(1982), and Doraiswamy and Tajbl (1974)) were used to obtain information more specific to the laboratory reactors. A paper by Weekman (1974) was found to be especially useful for obtaining information about the reactor selection process. The second phase of the knowledge acquisition gathered the specific information needed for the reactor selection problem. The objective was to obtain the knowledge necessary to build and complete the expert system model and structure. This phase was guided by the knowledge gathered and the model developed in the first phase of knowledge acquisition. The critical performance factors and the feasible reactor configurations were determined, and the knowledge necessary to model the performance factors for each of reactor configurations was acquired. The knowledge for this phase was obtained from interviews with experta in the field and from papers specific to a single reactor type,such as Berty (1984) for basket-type reactors, Abichandani et al. (1984) for slurry reactors, or Harrison et al. (1965) for recirculating transport reactors. Structure. When designing the structure of the expert system, the goal is to mimic as much as possible the problem-solving strategy of the expert. Other strategies are possible. Experts employ many different strategies and/or variations in problem-solving. Even when the problem-solving strategy is decided upon, there are still many different ways to approach the design of the struc-
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232 Ind. Eng. Chem. Res., Vol. 31, No. 1, 1992
Select Application
&' - I 1
Ab-7 1
Figure 1. Structure of expert system for laboratory reactor selection.
ture for the knowledge base. For instance, for the before-mentioned problem-solving strategy, the knowledge base could be designed with one module per reactor type with the module giving that particular reactor an overall rating, or the knowledge base could be designed in a different modular fashion with each module designed to handle one task toward the overall rating process. There are advantages and disadvantages to each scheme. For instance, comparing the two designs above: the first design has the advantage that it is easier to organize the reactor-specific knowledge but it has the disadvantages that it requires repetitive programming (at the cost of additional programming time and program size) of information which can be applied to all the reactor types or to a class of reactor types, it is harder to explain the differences between reactor types (i.e., why one reactor is rated higher than another), and it is harder to obtain consistent reactor ratings with which to compare the different reactors. Note that simplicity in structure and design is highly desirable but not easy to find or produce especially as the constraints on the system performance increase. For this system, the second scheme was utilized. This approach was chosen because it gives a structure which should be easy to maintain and update while modeling the domain well. The structure of this system was built in such a way as to incorporate the five-step procedure while keeping in mind that the system should be easily expandable, have the ability to explain its reasoning, be able to handle different types of reactor applications, and be interactive with the user. To accomplish this,a three-level system was implemented. Figure 1 illustrates the structure of the system. Note the multitier, modular structure. Each level is further broken down into modules. The multitier system is then paralleled by an explanation section. The multitier system separated the knowledge based on levels of abstraction-the top level incorporated the most general
information and the lower levels handled progressively more specific information. This modular form breaks down and organizes the knowledge on each level. The modular approach allows for easier understanding of the problem domain and easier system maintenance. The top tier, level 1,contains the most general knowledge. Problem-specific information is collected from the user. The reactor application (what the reactor will be used for, i.e., kinetic studies) is determined here. The problem-solving strategy is set up on the basis of the selected application. With this strategy and the reactor application level 1 directs level 2 to obtain the overall reactor ratings. On the basis of the overall reactor ratings, the reactor types are ranked and the highest rated reactor is recommended for use. After recommending a reactor type, the user may choose to obtain an explanation of the reasoning process. Level 1 also directs the explanation process. Therefore, level 1 conducts the overall system control. The next tier, level 2, gives each reactor type an overall rating for a chosen reactor application. This level is organized in a modular fashion, with one module for each different reactor application. Each module follow a similar procedure to get the overall reactor rating. First, the reactor types and configurations which are plausible choices for the chosen application are established. Then the performance factors which are important to the chosen reactor application are determined. Then these performance factors are ranked in importance and given a corresponding weight toward the overall rating. The ratings for the performance factors are obtained from level 3. On the basis of the performance factor ratings and weighting, an overall rating is assigned for the reactor type and passed back to level 1. The knowledge on level 2 is more specific than level 1, and it is related to information needed for the selection problem for a specific type of application. Level 3 gives a rating for the reactor performance factors needed by level 2. Every reactor type investigated on level 2 is given a rating for each of the performance factors. The level is built in a modular architecture with each module designed to rate one reactor performance factor. Each module is further broken down into three subsections or levels of abstraction: fust, conditions which affect all the reactors; second, conditions which are specific to a class of reactors; and finally, the conditions which are specific to a single reactor type. Each reactor type investigated in level 2 is given ratings for each of the performance factors. This level contains the bulk of the system knowledge and the most specific knowledge utilized for the selection problem. The knowledge is mainly stored in the form of rules (i.e., If A and B then C), facta, and assertions. The facta and assertions are stored and represented within a frame structure (Minsky, 1975; Firebaugh, 1988). After a performance factor is rated on level 3, the value is passed back to level 2. The explanation section of the program is similar in structure to the selection process. It has the ability to explain the final reador selection, illustrate the differences between two reactor types, and explain the reasoning that led to a performance factor rating. Prototype Coding of Expert System. To code this system, the commercial expert system shell CxPERT was utilized. This simplifies and greatly reduces the coding time for the implementation. The CxPERT shell was chosen because it possesses the necessary expert system tools (backward and forward chaining, and frames) and it allows for the incorporation of c (a programming language) code directly in the program. This allows the
Ind. Eng. Chem. Res., Vol. 31, No. 1, 1997 233 flexibility to incorporate both qualitative and quantitative reasoning in the selection process. The expert system shell also provided the necessary user interface capabilities to build a pleasant environment for the user (pop-up windows, help facilities, etc.). The model of the selection process was encoded using rules (i.e., If A then B) to represent the qualitative reasoning,frames to store the facts and assertions, and c and FORTRAN routines to represent the quantitative procedures and calculations. While the structure and knowledge are needed before the coding of the expert system can begin, the coding process identifies many of the structure deficiencies and the gaps in acquired knowledge. Therefore, during the coding of the expert system, the system structure eas refined and specialized knowledge was acquired as needed to fill in the missing pieces. The result of the coding phase is a prototype expert system for multiphase laboratory reactor selection. System Testing and Updating. After developing the prototype expert system for laboratory reactor selection, the system performa'nce, knowledge, and reasoning were tested and validated. On the basis of the results of the tests, the system was updated to create a more complete and powerful system. The system was tested not only for the validity of its reasoning and selections but also for its presentation format, ease of use, and understandability. The system was tested in two ways: first through distribution to potential users and experts for their use and comments and, second, through one-on-one consultation regarding the reasoning imbedded in the system with experts in the domain. The comments from the potential users in industry were found to be helpful mainly in improving the system on a more general level since most of the comments did not address the details of the implementation or validity of the knowledge base. It did show though that there is a need to have an expert system to assist in the selection of laboratory reactors. To validate and test the system in detail, the system model and knowledge was thoroughly covered in interviews with three experts in the domain (two from academia and one from industry). The consultation sessions were conducted by presenting the model and knowledge in a language (not computer code) that the experts could easily understand. The model was initially presented on the most general level, followed by discussion of the model details and how they fit into the overall model. Through oneon-one consultation the weaknesses and omissions of the model and knowledge were identified. Separate discussions with the three experts increased the individual expression of how the model needed to be updated; therefore it maximized the input of new information. If there were differences of opinion between the experts, compromises were made. The feedback obtained from both distributing the system to some of the potential users in industry and through in-depth model verification with domain experts was used to build an updated expert system. The system has the flexibility to be continuously updated and to grow as additional information becomes available. The updating of the prototype system demonstrated the ability of the system to be expanded and maintained. System Description. The above-described expert system for three-phase catalytic laboratory reactor selection, named LARS,has been completed, and currently it is operational. The system logic and reasoning has been tested in-depth and updated based upon the results of the testing. The system currently chooses the best reactor
Explain
Adiabatic Temperature Rise
Value
rise
1: Law
Law
45K
Medium
520K
Hbh
>20K
2: Medium
3: Hbh
4 Numeric value
What is the approximate adiabatic temperature ise for your system?
Figure 2. Sample query for input information for LARS expert system.
from 18 different reactor types and for two different types of reactor applications (kinetic studies and catalyst screening). The system knowledge and model is represented and stored with over 700 rules and within a frame structure. The system suggests to the user the best laboratory reactor(s) for a given chemical system and reactor application. The rating and ranking of the laboratory reactors is based upon the knowledge about the reactor, the chemical system, and the interaction between the two. The knowledge about the reactors and the interaction between the reactor and the chemical system is stored in the expert system. This knowledge makes up the system model. The knowledge about the reacting system is obtained for the user. If the system is thought of as a model, then the values obtained from the user about the reacting system are the input variables for the model and the ranking and rating of the reactors is the output from the model. When the system needs information about the chemical system, the system queries the user for the information. The system queries the user in a window format as illustrated in Figure 2 of the query for the adiabatic temperature rise. Note that the user has the option to enter either a qualitative (low, medium, or high) or numeric value. For all queries, the user has the option to ask for an explanation of the query and/or why the queried value is needed. An example of a simple explanation of a query is illustrated in Figure 2 by the window (box) with the dashed edge. More detailed explanations are available. All of the needed information about the system is queried from the user in a similar manner. After obtaining all the needed information, the system will recommend the best reactor, give two alternative reactors as choices, and give a listing of the top 10 ranked reactors for the chemical system and reactor application of the user. Along with results, an option for an explanation of the results is offered. The explanation facility includes the ability to explain why the recommended reactor is top rated, why one reactor is rated better than another, and why and how a reactor attribute for a given reactor got a particular rating.
234 Ind. Eng. Chem. Res., Vol. 31, No. 1,1992
Handling of Uncertainty In this section we will address two difficulties that we ran into during the implementation phase: the handling of uncertainty in the input data and the handling of the decision-making process in the presence of multiple objectives. Uncertainty of the Input Data. A typical rule in the expert system looks like the following: IF adiabatic temperature rise is low THEN isothermality of system is good By utilizing the rule paradigm, the two qualitative quantities (low heat of reaction and good isothermality) can be related. Building a structure of rules will allow qualitative modeling of the domain. One problem that arises with this type of modeling is from the definition of the qualitative variables. For instance, if the adiabatic temperature rise is assigned the three possible qualitative ratings of low, medium, and high, then an assignment is needed to determine the range of values for the adiabatic temperature rise which corresponds to low, medium, and high. Now assume that low is assigned the range 0-5 "C, medium 5-20 "C, and high >20 "C. If a value for the adiabatic temperature rise is known to be 5 f 3 "C, then it becomes difficult to decide on a qualitative rating for the adiabatic temperature rise. Another difficulty arises when adiabatic temperature rise is not known. For example, let us assume the value for the adiabatic temperature rise is known to be low with 80% certainty. We would like the propagate this uncertainty to the final recommended selection. Note that the ranges assinged for the adiabatic temperature rise are dependent upon the chemical system (industry) investigated and the defined ranges should be assigned (using rules within the system) based upon this consideration. For example, the oil industry may consider the above assigned ranges to be low, while the biological industry may consider them to be high. The values listed above represent a generic system. Another problem encountered is that the rule shown above is written as if it were always true. However, what happens if the system isothermality is known to be good most of the time (not always) if the adiabatic temperature rise is low? This represents an uncertainty in the implemented qualitative logic. How is the uncertainty of relations propagated through the system and utilized for making decisions? Uncertainty occurs because of incomplete knowledge-and it is therefore unavoidable. In the system for the selection of laboratory reactors, the uncertainty in the system which represented the greatest concern was similar to the first example. The issue is how to represent as qualitative variables the input information, with ita inherent uncertainty, and the input information obtained from the user about the reacting system, and how to propagate this information through the system. Many different methods are utilized for expert systems to handle uncertainty such as probability theory (Duda, 1980), certainty factors (Rolston, 1988), Dempster-Shafter theory (Lee et al., 1987), and fuzzy logic (Zadeh, 1965). For this application, fuzzy logic was chosen to represent and handle the uncertainty of the system. Fuzzy logic was first proposed by Zadeh (1965) and since then it has been implemented and modified by many others, (Le., see Maiers and Sherif (1985) for extensive listing of over 500 applications of fuzzy logic in the literature). Fuzzy logic is an implementation of the fuzzy set theory which is an analogy to set theory where the *edgen of the set is fuzzy (Rolston, 1988). Values are assigned a membership value from 0 to 1, where 0 means no mem-
3
Figure 3. Fuzzy set membership function, m A ( x ) ,for adiabatic temperature rise.
bership in the set, 1means membership in the set, and 0.5 means equally likely to be in the set or out of the set. Fuzzy set theory lays out the means by which to relate fuzzy sets (assertions) and to manipulate fuzzy relations. To illustrate fuzzy logic and how it was implemented in this system, assume that we want to assign a qualitative value of low, medium, or high to represent the value for the adiabatic temperature rise (ATR). If the ATR is 0 "C, then low can be assigned. If the ATR is incrementally increased, then the question becomes a t what point does the qualitative value change from low to medium and then from medium to high. Should low be assigned when the ATR is 4.9 "C and medium assigned when the ATR is 5.1 "C? Fuzzy logic defines low, medium, and high as seta for which a membership from 0 to 1 can be assigned. The membership in each of these sets can be defined as a function of the magnitude of ATR, so that for an ATR of 5 "C a membership of 0.5 in low and 0.5 in medium is assigned, instead of just low or medium. If the ATR is reduced, then the membership in the set for low would increase and the membership in the set for medium would decrease. Fuzzy logic then gives the means to manipulate these fuzzy sets. Each of the qualitative values is assigned a membership mapping function, mA(x),which is a function of the input value. The function defines the membership of quantity x in the fuzzy set A. For example, the membership mapping function for the adiabatic temperature rise for each of the possible qualitative variables is described by eq 1 and illustrated in Figure 3 A low
medium
mA(4 1.0 1.5 - 0 . 2 ~ 0 0 0 . 2 ~- 0.5 1
2.5 - 0 . 1 ~ high
0 0
0 . 1 -~ 1.5 1
range 0 < x < 2.5 2.5 < x < 7.5 7.5 < x 0 < x < 2.5 2.5 < x < 7.5 7.5 < x < 1.5 15 < x < 25 25
(1)
