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From Macroscopic World to Microscopic World through Mazes of Process Graphs and from Microscopic World to Mesoscopic World through Drunkards’ Paths

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Title: From Macroscopic World to Microscopic World through Mazes of Process Graphs and from Microscopic World to Mesoscopic World through Drunkards’ Paths


1
From Macroscopic World to Microscopic World
through Mazes of Process Graphs and from
Microscopic World to Mesoscopic World through
Drunkards Paths
Computing in Chemical Engineering Award Lecture
By L. T. Fan Department of Chemical
Engineering Kansas State University Computing
and Systems Technology (CAST) Banquet November
18, 2003 AIChE Annual Meeting San Francisco, CA,
November 16 21, 2003
G1
2
From Macroscopic World to Microscopic World
through Mazes of Process Graphs
P1
3
  • Pre- Process-graph days early 1950s late
    1980s
  • Heuristics
  • Dynamic programming
  • Structural parameter
  • Super-structure with structural parameters
    conventional search techniques random search
    adaptive random search
  • Conventional graphs
  • Successes only with small problems
  • Computational complication
  • Local optima nonlinearity
  • Combinatorial complexity exponential
  • (2n 1) or (3n 1)

P2
4
  • Meeting of minds 1989 90
  • Fan Friedler at the North American-German
    Workshop on Chemical Engineering Mathematics and
    Computation, Göttingen, West Germany, July 18
    23, 1989
  • Fans struggle to overcome combinatorial
    complexity in process synthesis without
    approximation
  • Friedlers struggle to overcome the difficulty in
    establishing a formal framework for combinatorial
    process synthesis on the basis of process graphs
  • 1-year stint by Friedler and Tarjan with Fan in
    1990

P3
5
  • First Milestone early 1990s
  • Presentations of a series of papers at major
    technical conferences
  • Review of the 1st major manuscript for journal
    publication by late Professor Rippin and his
    daughter, a mathematician
  • Publications of the first 2 refereed journal
    papers
  • Friedler, F., K. Tarjan, Y. W. Huang, and
    L. T. Fan,
  • Combinatorial Algorithms for Process
    Synthesis, Computers
  • Chem. Eng., 16, S313-320 (1992).
  • Friedler, F., K. Tarjan, Y. W. Huang, and
    L. T. Fan, Graph-
  • Theoretic Approach to Process Synthesis
    Axioms and
  • Theorems, Chem. Eng. Sci., 47, 1973-1988
    (1992).

P4
6
  • Graphs
  • Natural Language or logical tool for describing
    and representing networks
  • Examples of networks gas or oil pipelines
    waterways or irrigation channels process
    flowsheets highways railroads telephone lines
    family trees social relationships structures of
    any organizations, etc., etc., etc., some
    visible and some invisible
  • Structures of graphs nodes arcs ,
  • Types of graphs monopartite bipartite

P5
7
  • Process graphs (P-graphs)
  • What? unique bipartite graphs
  • P-graphs of some operating units and their
    concomitant material streams
  • Materials A, B, and C, and operating unit (A,
    B, C)
  • Material C, D, and E, and operating unit (C,
    D, E)

P6
8
  • Why?
  • Syntactically and semantically rich
  • Unique representation possible
  • Special classes of graphs, e.g., call graphs,
    social graphs and highway graphs, needed for
    different fields according to Hayes (Graph
    Theory in Practice Part I, American Scientist,
    January- February, 2000), The next step is to
    develop a mathematical model of the structure,
    which typically takes the form of an algorithm
    for generating graphs with the same statistical
    properties. Such models of very large graphs will
    be the subject of

P7
9
  • How?
  • Recognition of the nature of the networks
    involved materials transfer and transformation
    networks
  • Identification of statistical properties of the
    graphs to represent the networks perfect
    statistics representing mass conservation and
    stoichiometry
  • Axioms based on perfect statistics
  • Algorithms derived from the axioms MSG for
    maximal structure generation SSG for solution
    structure generation and ABB for accelerated
    branch-and-bound for generating the optimal and
    near-optimal solutions

P8
10
  • Illustration

Reduction in the search space of (2n 1)
P9
11
  • Second Milestone mid 1990s
  • Favorable comments by Prof. Sargent in a report
    of Center for Process Systems Engineering of
    Imperial College
  • Citation by Prof. Sargent in the Rippin memorial
    issue of Computers Chem. Eng. (Vol. 22, No. 12,
    1998), The task performance models also set
    conditions (both qualitative and
    quantitative)......, as considered by Friedler et
    al. (1992)...... . Armed with these rules and
    conditions we can devize an algorithm which
    sistematically generates all feasible
    state-task-networks

P10
12
  • Third Milestone mid 1990s late 1990s
  • Realization for potential adaptation of P-graphs
    for mesoscopic-level process synthesis and
    identification of molecular-level networks
  • Publication of a series of papers on azeotropic
    distillation for example
  • Feng, G., L. T. Fan, F. Friedler, and P. A.
    Seib, Identifying
  • Operating Units for the Design and
    Synthesis of Azeotropic-
  • Distillation Systems, Ind. Eng. Chem.
    Res., 39, 175-184 (2000).
  • Publication of a series of papers on
    catalytic-reaction and metabolic pathways
    combinatorial complexity, (3n 1) for example
  • Fan, L. T., B. Bertok, and F. Friedler,
    Combinatorial Framework for
  • the Systematic Generation of Reaction
    Pathways, presented at the
  • AIChE Annual Meeting, Dallas, TX,
    U.S.A., October 31
  • November 5, 1999, ISBN 0-8169-0805-2

P11
13
  • Fourth Milestone late 1990s early 2000
  • Endorsement by Dr. Keller Institute Lecture at
    the 1999 AIChE annual meeting CEP Vol. 96, No.
    1, ... the P-graph may be the fastest
    computationally, as well as the method most
    likely to find a truly optimal solution.
  • Accelerated pace of adoption of P-graphs by other
    researchers and citation in their presentations
    and publications including books, monographs and
    journal articles none reviewed by us

P12
14
  • Fifth Milestone early 2000
  • Selection by Prof. Timmerhaus as the method of
    choice for algorithmic flowsheeting
  • Inclusion of a 30-page section entitled
    ALGORITHMIC FLOWSHEET GENERATION in the 5-th
    edition of Plant Design and Economics for
    Chemical Engineers by Peters, Timmerhaus, and
    West
  • Publication of a landmark paper by Brendel,
    Friedler and Fan, Computers Chem. Eng., Vol. 24,
    2000 an additional proof for the rigorousness
    and superiority of the P-graph-based method for
    process synthesis

P13
15
  • Current status and future prospect of P-graphs
  • Downstream processing in biochemical production
  • Identification of catalytic pathways
  • Metabolic flux analysis
  • Molecular design (conventional bipartite graph)
  • Azeotropic-distillation system synthesis
  • Design of alternative synthetic routes
    profit-potential estimation
  • Further generalization, automation, computational
    acceleration through parallel and grid computing

P14
16
Algorithmic Identification of Stoichiometrically
Exact, Plausible Mechanisms of the Catalytic
Ethylene Hydrogenation Reactionby Fan, Shafie,
Khaitan, More, Bertok, and Friedler (AIChE
Annual Meeting, Nov. 18, 2003)
  • A graph- theoretic algorithmic method
  • Process graphs (P-graphs)
  • Axioms
  • Feasible reaction pathways
  • Combinatorially feasible reaction networks
  • Algorithms
  • RPIMSG
  • PBT
  • Input
  • Overall reaction 1
  • Elementary reactions 7
  • Combinatorial complexity
  • (3n 1) 37 1 2,186
  • Overall reaction S
  • C2H4 H2 ? C2H6
  • Elementary reactionsproposed mechanism for two
    active sites
  • H2 2l1 ? 2Hl1
  • H2 2l2 ? 2Hl2
  • C2H4 2l1 ? l1C2H4l1
  • l1C2H4l1 Hl1 ? l1C2H5 2l1
  • l1C2H4l1 Hl2 ? l1C2H5 l1 l2
  • l1C2H5 Hl1 ? C2H6 2l1
  • l1C2H5 Hl2 ? C2H6 l1 l2

P15
17
  • Results
  • Feasible pathways independent 8 combined
    acyclic 17
  • Conventionally accepted mechanism for one active
    site
  • Pathway 3
  • Computational efficiency less than a second with
    a PC (Intel Pentium III, 533 MHz, 128 MB RAM)

P16
18
  • P-graph representation of independent pathway 7
  • H2 2l1 ? 2Hl1
  • H2 2l2 ? 2Hl2
  • 2C2H4 4l1 ? 2l1C2H4l1
  • 2l1C2H4l1 2Hl1 ? 2l1C2H5 4l1
  • 2l1C2H5 2Hl2 ? 2C2H6 2l1 2l2

P17
19
Feasible and Optimal Flowsheets for Downstream
Processing in Biochemical Production of Butanol,
Ethanol and Acetone Inclusion of Pervaporation
by Liu, Fan, Seib, Friedler, and Bertok (AIChE
Annual Meeting, Nov. 20, 2003)
  • A graph- theoretic approach
  • Process graphs (P-graphs)
  • Axioms
  • Feasible reaction pathways
  • Combinatorially feasible reaction networks
  • Algorithms
  • MSG
  • SSG
  • ABB
  • Input 25 operating units

Comprehensive flowsheet with inclusion of
pervaporation P-graph
P18
20
Comparison of the total costs of the 10-best
flowsheets generated
  • Combinatorial complexity
  • (2n 1) 225 1
  • 33.554 ? 106
  • Results
  • Optimal and near-optimal flowsheets 4 sets of 10
    each for parametric study with respect to the
    cost of pervaporation
  • Conclusion
  • Profound computational efficiency less than 5 s
    for each set with PC (Pentium 266 Mhz 65 MB RAM
    W95)
  • Novel paradigm for process design and development
  • Retrofitting vs new design
  1. Conventional operating units only
  1. Current best estimate
  1. 84 reduction
  1. 97 reduction

P19
21
The optimal flowsheet with pervaporating and
ultrafiltering units included
P20
22
Synergistic identification of multiple flux
distributions and multiple metabolic pathways
Application to the E. coli modelby Lee, Fan,
Park, Lee, Shafie, Bertok, and Friedler(AIChE
Annual meeting, Nov. 21, 2003)
  • Model
  • Metabolites 52
  • Reactions 48

P21
23
  • Algorithmic Method
  • P-graph Representation of the E. coli Model
    Input
  • Glycolytic pathway
  • PPP
  • TCA
  • Algorithm RPIMSG
  • Algorithm PBT

P22
24
  • Results
  • Normalized Multiple Flux Distributions for the
    Maximum Ethanol Production
  • Four different flux distributions leading to the
    same external state the net reaction balance,
    GLCxt ? 2 ETHxt 2 CO2xt
  • Pathway redundancy cell robustness which is a
    unique feature of complex systems
  • Computational efficacy less than 1 second with a
    PC (Intel Pentium IV, 1.8 GHz, 768 MB RAM)
    extension to the large-scale models (300 700
    metabolic reactions)

P23
25
From Microscopic World to Mesoscopic World
through Drunkards Paths
S1
26
  • Drunkards Paths, Random Walks and Stochastic
    Processes
  • Stochastic processes a rigorous branch of
    mathematics or mathematical statistics

Statistics ?? Stochastic Processes Statistics
gt Stochastic Processes random behavior evolving
with time or operation according to a certain
mathematical property defined by a distribution
of the random variable
S2
27
  • Awakening at Dawn 1950s
  • Residence-time distribution ? age distribution of
    molecules
  • Microscopic discrete
  • Continuum, statistical or stochastic?
  • Dancing particles, droplets and bubbles
    everywhere
  • Mesoscopic, finite discrete
  • Continuum, statistical or stochastic?
  • Stochastic processes population of discrete
    entities evolving with time
  • Natural logical language for the mean
    behavior
  • of microscopic entities
  • Natural logical language for the mean
    fluctuating
  • behavior of mesoscopic entities

S3
28
  • Encounter with Markov mid 1960s early 1970s
  • Feller, Cox Miller, Chiang, etc.
  • Frequent consultations extensive collaboration
    with statisticians
  • Markovian Property
  • Classification
  • Markov chain (time discrete)
  • Markov process (time continuous)
  • Diffusion process (state and time
    continuous) Fokker-Planck
  • Strictly linear processes analytical solutions
    for moments of the evolving distribution of a
    random variable

S4
29
  • Encounter with Prigogine early 1980s
  • Nicolis, G., I. Prigogine Self-organization in
    Non-Equilibrium Systems, 1977
  • Non-linearity
  • Stochastic mechanics
  • Encounter with van Kampen mid 1980s
  • van Kampen, N. G., Stochastic Processes in
    Physics and Chemistry, 1982
  • Master equation probability balance
  • gain-loss equation
  • Non-linearity system-size expansion

S5
30
  • Publications of series of papers, each ranging
    two to more than a dozen, on various subjects
    such as chemically reacting systems, solids
    mixing, grinding, fluidization, crystallization,
    filtration, biochemical processes, mass transport
    and residence-time distribution
  • Noteworthy articles
  • Fan, L. T., B. C. Shen, and S. T. Chou, The
    Surface-Renewal Theory of Interphase Transport A
    Stochastic Treatment, Chem. Eng. Sci., 48,
    3971-3982 (1993).
  • Fan, L. T., B. C. Shen, and S. T. Chou,
    Stochastic Modeling of Transient Residence-Time
    Distributions during Start-Up, Chem. Eng. Sci.,
    50, 211-221 (1995).

S6
31
  • Current status and future prospect of stochastic
    analysis and modeling
  • Stochastic Modeling of Thermal Death Kinetics of
    a Cell Population Revisited
  • Stochastic Modeling and Simulation of the
    Formation of Carbon Molecular Sieves by Carbon
    Deposition
  • Nanoparticles formation
  • Tumor growth
  • Human neuron cells decay
  • Monographs on stochastic modeling of particulate
    systems chemical reacting systems biochemical
    systems

S7
32
Stochastic Modeling of Thermal Death Kinetics of
a Cell Population Revisited by Fan,
Argoti-Caicedo, Chou, and Chen (Chemical
Engineering Education, 37, 228-235)
  • Microorganisms Discrete and randomly behaving
  • Stochastic modeling Pure-death process
  • Mean and higher moments Variance, skewness, and
    kurtosis.
  • Comparison with experimental data Mean in accord
    with experimentally measured data

Electron microscopic image of S. aureus (From
http//www2.uol.com.br/cienciahoje/chdia/n468.htm)
S8
33
Normalized mean, m, and normalized standard
deviation, s, as functions of the dimensionless
time, ?, for the low-range of the number
concentration of live cells
S9
34
Stochastic Modeling and Simulation of the
Formation of Carbon Molecular Sieves by Carbon
Deposition by Fan, Argoti, Walawender, and
Chou (AIChE Annual Meeting, Nov. 20, 2003)
  • CMS Formation Complex and random
  • Stochastic modeling Pure-birth process
  • Mean and higher moments Variance, skewness,
    kurtosis, etc
  • Comparison with experimental data Mean in accord
    with experimentally measured data

Side view of the progression of CMS formation
Carbon source Fine carbon particle
Carbon packet
S10
35
Dimensionless mean, m, and dimensionless standard
deviation, s, for the pore-narrowing as functions
of the dimensionless time, ?
S11
36
Concluding Remarks       Obviously borrowing
heavily from General Douglas MacArthur, Old
professors never die they just (asymptotically)
fade away.
G2
37
Acknowledgement   Many thanks to   All my
current and former students, assistants,
associates, collaborators, and teachers   All my
current and former colleagues and staff in the
department   All organizations and agencies in
and out of the University which supported my
research   All attendants who suffered through my
random talks   All my family members,
especially my wife, Eva, who has accompanied me
for 45 years in the journey through the Mazes of
Process Graphs and Drunkards Paths
G3
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