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.

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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: m.wulkow@cit-wulkow.dePhone: +49 4402 84248www.cit-wulkow.de

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New book about polymer kinetics

Klaus-Dieter Hungenberg, Michael Wulkow: Modeling and Simulation inPolymer Reaction Engineering - A Modular Approach

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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

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The Predici 11 user interface

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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

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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

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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

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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.

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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

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Polymer example

Module: INITIATION

R+Mki−→ P1

Module: PROPAGATION

Ps +Mkp−→ Ps+1

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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

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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

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Modules - Overview

Important patterns

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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

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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

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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

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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

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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

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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

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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.

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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

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Dynamic output of results

Configuration of chart tabs

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Dynamic output of results

Chart administration with many options

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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

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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

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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

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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

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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

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Hybrid Monte-Carlo topology

• Supported by LCB, crosslinking and beta-scission and some specialsteps

• Can be processed and analyzed even during simulation

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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

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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

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Cape-Open interface

Configuration

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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

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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.

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Sensitivity analysis

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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

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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

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Parameter estimation - Overview

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Parameter estimation - Configuration

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Parameter estimation - Handling of experimental data

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Parameter estimation - Analysis of results

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Parameter estimation - Detailed report on residuals

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Parameter estimation - Bayesian statistics

Example: Probability distribution of parameter f based on SimulatedAnnealing and Kernel Density Estimation

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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

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Optimization

Typical ControlsFeed profiles of monomers and initiators

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Optimization

Setup of objectivesBased on all outputs of the model, intermediate points are possible,weightings may be applied

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Optimization

Output of objectives

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