Model‐based design of experiments for polyether production from bio‐based 1,3‐propanediol

Abstract

Sequential model-based design of experiments (MDBOE) accounts for information from previous experiments when selecting conditions for new experiments. In the current study, sequential MBDOE is used to select operating conditions for experiments in a batch-reactor that produces bio-based polytrimethylene ether glycol (PO3G). These Bayesian A-optimal experiments are designed to obtain improved estimates of 70 fundamental-model parameters, while accounting for industrial data from eight previous runs. Settings are selected for three decision variables: reactor temperature, initial catalyst level, and initial water concentration. If only one new experiment is conducted, it should be run at high temperature, with relatively high concentrations of catalyst and initial water. When two new runs are conducted, one should use an intermediate catalyst concentration. The effectiveness of the proposed MBDOE approach is tested using Monte-Carlo simulations, revealing that the selected experiments are superior compared to experiments selected randomly from corners of the permissible design space. K E Y W O R D S model-based design of experiments, parameter estimation, PO3G, polymerization model, sequential experimental design | INTRODUCTIONCerenol ® is tradename for a bio-based polytrimethylene ether glycol (PO3G) that has been commercialized by Dupont. [1][2][3] The monomer used for producing Cerenol ® is corn-based 1,3-propanediol derived from a glucose fermentation process (Bio-PDO ® ), 4 so that Cerenol ® is renewably-sourced. Cerenol ® offers a variety of value-added properties (e.g., excellent biodegradability, high reactivity, high oxidative stability) and has a wide range of applications in automotives, cosmetics, and polymer specialties. [1][2][3]5 Cerenol ® is produced in batch, semi-continuous, and continuous reactors using super-acid catalyst. Operating conditions such as catalyst concentration and temperature vary depending on the desired molecular weight and the end-use properties of the final products. 3,[6][7][8][9][10][11][12][13][14] The influences of operating conditions on product properties and production rates have been studied via several fundamental PO3G models. [15][16][17][18][19][20][21][22] Recently, we developed a series of PO3G models that account for: (a) the effects of super-acid catalyst on polycondensation reactions and side reactions in the liquid phase, (b) liquid hold-up in the condenser system, (c) the inhibitory influence of water on polycondensation kinetics, (d) the generation, consumption, and evaporation of cyclic oligomers, and (e) the effects of temperature on polycondensation kinetics and on mass-transfer rates of volatile species. [20][21][22] Our most-recent PO3G model contains a total of 49 ordinary differential equations (ODEs) and 70 kinetic, transport and thermodynamic parameters. 22 A comprehensive industrial dataset obtained from 8 batch-reactor runs, 3 which were conducted at temperatures ranging from 160 to 180 C and using super-acid catalyst levels from 0.1 to 0.25 wt%, w...

Theory and simulation of ligand functionalized nanoparticles – a pedagogical overview

“…Unlike spherical cores, where separate discussions are used for each ligand type, we combine discussion across ligand lengths using a governing theoretical model capable of predicting a continuous transition from hard to soft to ultrasoft corona morphologies in the limit of polyhedral core geometry. 79,99 This theory additionally extends to the limit of low surface coverage 48 and branching 99 or block copolymeric 142 ligand architectures.…”

“…However, in the enthalpically dominated regime, ligand distributions are highly non-ideal and often breaks the underlying NP core symmetry. Corona morphologies in this regime are predicted using modifications of eqn (9) to account for weak attraction between ligands, 48 leveraging microphase separation between block copolymeric ligands to produce surface partitioning 142 (Fig. 7c), or assuming a complete ligand collapse in the limit of poor solvent.…”

Parameter estimation and estimability analysis in pharmaceutical models with uncertain inputs

“…In Equation (3.2), the subscript Kub in refers to an improved estimator developed by Kubokawa et al that Wu et al used in their calculations 47,61 . The parameter estimability ranking and MSE‐based parameter subset selection methods in Tables 2 and 3 have been used to aid WLS parameter estimation for models of a wide variety of chemical processes (e.g.,47,50,62–64) where all of the independent variables are assumed to be perfectly known. In the next section, these methodologies are extended for use in EVM parameter estimation.…”

“…Select the value of k corresponding to the lowest value of r CC,k as the appropriate number of parameters to estimate based parameter subset selection methods in Tables 2 and 3 have been used to aid WLS parameter estimation for models of a wide variety of chemical processes (e.g., 47,50,[62][63][64] where all of the independent variables are assumed to be perfectly known. In the next section, these methodologies are extended for use in EVM parameter estimation.…”

Parameter Estimation and Estimability Analysis in Pharmaceutical Models with Uncertain Inputs

“…where 47,61 The parameter estimability ranking and MSE-based parameter subset selection methods in Tables 2 and 3 have been used to aid WLS parameter estimation for models of a wide variety of chemical processes e.g., 47,50,[62][63][64] where all of the independent variables are assumed to be perfectly known. In the next section, these methodologies are extended for use in EVM parameter estimation.…”