Predici 11 Quick Overview - cit-wulkow.de · Over 100 modules for kinetics phase changes mass...
Transcript of Predici 11 Quick Overview - cit-wulkow.de · Over 100 modules for kinetics phase changes mass...
Introduction to Predici
Dr. Michael Wulkow, CiT GmbH, Rastede, Germany
PREDICI is the leading simulation package for kinetic, process and property modeling with amajor emphasis on macromolecular systems. It has been successfully utilized to model radical
copolymerization, living polymerizations (RAFT, NMP, ATRP), emulsion and suspensionpolymerizations and various Ziegler-Natta catalyzed systems.
Introduction to Predici 1 / 48
Company
CiT GmbH
• Founded in 1992, M. Wulkow is a mathematician
• Software for modeling and simulation in chemistry, mainly• Predici - polymer kinetics• Parsival - crystallization, particle systems• Presto-Kinetics - chemical and bio kinetics, spatial distributions
Contact us for more informationDr. M. Wulkow Computing in Technology GmbH (CiT)Harry-Wilters-Ring 2726180 RastedeGermany
Email: [email protected]: +49 4402 84248www.cit-wulkow.de
Introduction to Predici 2 / 48
New book about polymer kinetics
Klaus-Dieter Hungenberg, Michael Wulkow: Modeling and Simulation inPolymer Reaction Engineering - A Modular Approach
Introduction to Predici 3 / 48
Predici: Open and modular modeling system
• Polymerization of all types
• Basic chemical kinetics
• Biokinetics and systems biology
• Reactor models (batch, semi-batch, continuous, plug-flow, cascades)
• More than 100 modules for• kinetics• phase changes• mass transfers• particle growth• reactor flows
Introduction to Predici 4 / 48
The Predici 11 user interface
Introduction to Predici 5 / 48
Predici 11 : Selected new features
• Sophisticated ”all-in-one” model and project administrationincluding handling of alternative models and parameters, recipe lists,reaction groups, model comparison and much more
• Newly-developed dynamic outputs that reflect all structures of amodel by a configurable chart administration
• Efficient hybrid Monte-Carlo solver can be applied withoutadditional programming and extends the results of the deterministicsimulation
• New recipe modules control the full setup of a simulation and caneasily be organized, selected, edited and copied
• Recipe variation tool to compare process strategies
• Cape-Open interface to access thermodynamic data
• User database for parameters and substance data to organize modelinputs
Introduction to Predici 6 / 48
Predici 11: Selected new features
• New parameter estimation with numerous features, algorithms andoutputs
• Efficient sensitivity analysis based on parameter variation
• Optimization and Optimal Control module
• Improved script interpreter with powerful commands foruser-defined outputs, reaction rates and equations
• OLE/COM interface to control Predici from other software
• Script export of core model equations (moment-based) toMatlabTM or C
• PDE-solver for spatial profiles, e.g. instationary tubular reactors orconcentrations in films or particles
• Integration of Parsival models for particle size distributions
Introduction to Predici 7 / 48
Predici: Inputs and results
Inputs
• arbitrary kinetic schemes
• parameters and rate expressions
• additional differential equations
• reactor operation (recipes)
• experimental data
Outputs
• molecular weight distributions
• concentrations of species and reactor variables
• any other output based on state variables of the model
• deterministic and stochastic results
• parameters
• optimal controls
Introduction to Predici 8 / 48
Common Framework
CODEs - Countable systemspolymers, chemical master equations
ODEs - Differential equationschemical kinetics, biokinetics, catalysts
PDEs, PSDs - Partial differential equationsparticles, spatial concentration (temperature) profiles
Combined and augmented by algebraic conditionsNow: one source code (C++) for all tools → all modeling features havework for all structures. All type of modules can be combined in onemodel.
Introduction to Predici 9 / 48
Polymer kinetics
Polymer distributionPs(t): concentration of chains of length s of polymer P at time t.Distributions are functions of a discrete variable 1, 2, . . . , s.
Other representations
WPs (t) = Ps(t) · s ·MP
M̄
WPlog M (t) = Ps(t) · s2 ·
(MP
M̄
)2
Introduction to Predici 10 / 48
Polymer example
Module: INITIATION
R+Mki−→ P1
Module: PROPAGATION
Ps +Mkp−→ Ps+1
Introduction to Predici 11 / 48
Polymer example
Set of differential equations
dR
dt= −kiMR
dM
dt= −kiMR−kpM
∞∑s=1
Ps
dP1
dt= kiMR−kpMP1
dPs
dt= −kpM(Ps − Ps−1)
Predici
• all balances automatically derived and solved by special Galerkinh-p-FEM.
• additional moment equations also internally processed and solved
Introduction to Predici 12 / 48
Example from living polymerization
P (s) for fast initiator - narrow distribution
(Monte-Carlo chains line-by-line in red)
P (s) for slow initiator - broader distribution
Introduction to Predici 13 / 48
Modules - Overview
Important patterns
Introduction to Predici 14 / 48
Modular approach
• Single reactions derive their own differential equations internally
• All terms are superposed, even kinetic steps and abstract ODEs
• All further terms are added automatically
• Once a kinetic step pattern is implemented and validated, it can beused again and again.
• Reaction rates can be arbitrarily complex and entered usinguser-scripts
Introduction to Predici 15 / 48
Predici: Modular kinetics
• Select reaction step from comprehensive list• Assign species w.r.t modeling context• Add Monte-Carlo settings, user scripts and options• Define new model components if required
Introduction to Predici 16 / 48
Predici: Modular kinetics
• Create any kind of kinetic system
• Link parameters and user-defined rate expressions (optional)
• Define parameter and module sets to study model alternatives
Introduction to Predici 17 / 48
Example: Module of type Change
Pattern
Ps +Ak−→ Qs +B
Versatile usage dependent on context
• Elimination (LiH in anionic polymerization)
• Ring closure (eg. in PA6), may be dependent on some function ofchain length
Introduction to Predici 18 / 48
Copolymerization
• Use two or more monomers for polymerization
• Often a certain “co-monomer” has a special feed strategy
• Leads to a mixture of blocks inside chain
• Additional model results• average fraction of co-monomers in chains• detailed composition of co-monomers in chains• sequence length distribution• gradient of fraction along chains
• Meta tasks: optimize feed and temperature in order to get requiredcomposition
Introduction to Predici 19 / 48
Copolymerization - Terminal model
General description for n = 1, 2, ..., N monomersInitiator decay:
Ikd,f−−−→ 2R
Chain start:R+Mn
kin−−→ Pn1
, n = 1, . . . , N
Propagation:
Pms +Mn
kp,m,n−−−−→ Pns+1 , m, n = 1, . . . , N
Transfer:
Pns + S
ktr,S,n−−−−→ Ds +R , n = 1, . . . , N
Pms +Mn
ktr,m,n−−−−−→ Ds + Pn1 , m, n = 1, . . . , N
Termination:
Pns +Pm
r
ktc,m,n−−−−−→ Ds+r, m, n = 1, . . . , N
Pns +Pm
r
ktd,m,n−−−−−→ Ds +Dr, m, n = 1, . . . , N
Introduction to Predici 20 / 48
Copolymerization - Analysis
Counter species
Pms +Mn
kp,m,n−−−−→ Pns+1 + Cn , m, n = 1, . . . , N
Mass balanceThe average molecular weight MM̄ of all polymer species P involved in acopolymerization is given by:
MPM̄ =
N∑m=1
Ci∑k Ck
Mi
applying the molecular weights Mi of the single monomers.
Introduction to Predici 21 / 48
Dynamic output of results
• Create own chart collections by drag and drop, even during asimulation
• Choose from comprehensive list of graphical representations
• Combine different graphics in one chart
• Export all or selected data as required for postprocessing
• Store the complete setup in the project
• By one click compare to reference results from other simulations,e.g. based on different parameters or recipes
Introduction to Predici 22 / 48
Dynamic output of results
Configuration of chart tabs
Introduction to Predici 23 / 48
Dynamic output of results
Chart administration with many options
Introduction to Predici 24 / 48
Reactor operation: Recipes
• Recipes provide reactor operation and model scenarios• All inputs of all species entered in recipes• Project contains list of recipes, one set to be active• Various feed strategies are possible - from simple feed to control of
properties
Introduction to Predici 25 / 48
Recipe input options
• Direct conversion of various input types• Input can also be entered for polymer species, particles or profiles,
e.g, GPC or PSD data• Temperature and pressure control possible• Open number of feed tanks with individual composition
Introduction to Predici 26 / 48
Scripts
• Add own code for• additional output• rate expressions• additional equations
• Simple script language, access to all system variables by high-levelscript commands
• Easy online check of all intermediate script results
Introduction to Predici 27 / 48
Hybrid Monte-Carlo algorithm
• Predici performs deterministic simulation based on h-p-method.
• For all distributions after each time step an ensemble of chains isupdated by SSA-type algorithm using the deterministic results.
• A number of property indexes and topology information is tracked.
• The most important steps are prepared for Monte-Carlo treatment.
• Output• Total and relative number of property indexes in chains• Mean values of chain ensemble from MC (compare to h-p-method)• Sequence of indexes in chains, sequence length analysis• Topology based on random walk
Introduction to Predici 28 / 48
Hybrid Monte-Carlo outputs
Script functionsMain usage: comparison with deterministic results for error control:getmcmn, getmcmw, getmcindex
Distribution outputAbsolute and relative values of indexes or fractions
Introduction to Predici 29 / 48
Hybrid Monte-Carlo topology
• Supported by LCB, crosslinking and beta-scission and some specialsteps
• Can be processed and analyzed even during simulation
Introduction to Predici 30 / 48
Hybrid Monte-Carlo full chain mode
• Supported by e.g. propagation, transfer, initiation, termination steps
• All events along a chain can be stored, e.g. incorporation of differentmonomers
• Built-in sequence length analysis of copolymers
• Analysis of any single event along all chains possible
Introduction to Predici 31 / 48
Cape-Open interface
• Access thermodynamic packages that are installed on yourcomputer, e.g. Multiflash by KBC (particularly suited forpolymerization) or COCO by AmsterCHEM
• Configure the thermodynamic computations required in your Predicimodel
• Use script commands to relate simulation results to thethermodynamic computations
Introduction to Predici 32 / 48
Cape-Open interface
Configuration
Introduction to Predici 33 / 48
User database
• Collect thermodynamic data or parameters in a separate XMLdatabase
• Assign values to scripts or directly to model components
• Model projects can be distributed by just including the required data
Introduction to Predici 34 / 48
Sensitivity analysis
• Parameters are distributed, e.g. n-dimensional normal distribution
• Vary parameters in certain ranges to get variance of the model
• Stochastic approach: select parameter combinations by aMC-algorithm, perform simulation, collect all results, computeprobability of states
• Efficient approximation: sigma-point method (Julier/Uhlmann1997) computing only only 2N + 1 parameter combinations andreconstruct normal distribution of state variables.
Introduction to Predici 35 / 48
Sensitivity analysis
Introduction to Predici 36 / 48
Parameter estimation - Basics
• Use all kind of data, time-dependent or GPC
• Relate experimental data to user-defined outputs in the model
• Configure parameter estimation by selecting parameters, data andadditional options
• Perform parameter estimation using special algorithms
• Analyze results and store obtained parameters as new parameter sets
• Run control simulations and export results
Introduction to Predici 37 / 48
Parameter estimation - Basics
Weighted least squares
SSE =
r∑j=1
nj∑i=1
ε2i,j =
r∑j=1
nj∑i=1
1
w2i,j
(mi,j − si,j)2
ResidualFor practical purposes we need the relative total residual rrel
rrel =1√N
√SSE
with N total number of single measurements.rrel(p): relative deviation between experiment and simulation per value,function of all parameters, leading to residual landscape
Introduction to Predici 38 / 48
Parameter estimation - Overview
Introduction to Predici 39 / 48
Parameter estimation - Configuration
Introduction to Predici 40 / 48
Parameter estimation - Handling of experimental data
Introduction to Predici 41 / 48
Parameter estimation - Analysis of results
Introduction to Predici 42 / 48
Parameter estimation - Detailed report on residuals
Introduction to Predici 43 / 48
Parameter estimation - Bayesian statistics
Example: Probability distribution of parameter f based on SimulatedAnnealing and Kernel Density Estimation
Introduction to Predici 44 / 48
Optimization and Optimal Control
Given a reliable and predictive model, tested for a range of reactionconditions and recipes.
Typical objectives
• conversion of monomer, rest monomer
• polymer properties like Mn,Mw, GPC
• fraction of co-monomer in polymer
• mass fraction of substance in reactor
Typical controls
• feed strategies for monomer and/or initiator
• temperature control
• initial load of reactor
• process time
Introduction to Predici 45 / 48
Optimization
Typical ControlsFeed profiles of monomers and initiators
Introduction to Predici 46 / 48
Optimization
Setup of objectivesBased on all outputs of the model, intermediate points are possible,weightings may be applied
Introduction to Predici 47 / 48
Optimization
Output of objectives
Introduction to Predici 48 / 48