Dynamic Optimization of Molecular Weight Distribution Using Orthogonal Collocation on Finite Elements and Fixed Pivot Methods: An Experimental and Theoretical Investigation

Abstract

In the present study, two numerical methods, namely the orthogonal collocation on finite elements and the fixed pivot technique, are employed to calculate the MWD in an MMA free‐radical batch suspension polymerization reactor operating up to very high conversions (e.g., ≥95%). The theoretical MWD predictions are directly compared with experimentally measured MWDs, obtained from a pilot‐scale batch MMA suspension polymerization reactor. It is shown that there is a very good agreement between model predictions and experimental measurements on both monomer conversion and MWD. Subsequently, two different time‐optimal temperature trajectories are calculated to obtain a polymer having either a narrow or a bimodal MWD in minimum batch time. The calculated time optimal trajectories are then applied, as set point temperature changes, to a pilot plant batch polymerization reactor. It is shown that the measured MWDs are in very good agreement with the off‐line calculated optimal MWDs.

From Molecular to Plant‐Scale Modeling of Polymerization Processes: A Digital High‐Pressure Low‐Density Polyethylene Production Paradigm

“…To deal with the above high-dimensionality problem, several numerical methods have been proposed in the literature to reduce the infinite system of differential equations into a loworder system. These can be broadly classified into kinetic lumping methods [19,20], global orthogonal collocation [21,22], method of moments [23][24][25][26][27][28], numerical fractionation methods [29][30][31], discrete weighted Galerkin [32][33][34], orthogonal collocation on finite elements [35,36], and sectional grid methods [15,18,37,38]. The above numerical methods are computationally complex and require special mathematical skills.…”

“…Based on the original work of Kumar and Ramkrishna [37], the fixed pivot technique (FPT) was applied to linear and nonlinear polymerization systems to predict the MWD [36,38] and joint MW-LCB [15] and MW-CC [18] distributions in batch and continuous reactors. According to the FPT, the different polymer chain populations are assigned to selected discrete points that are called grid points.…”

Prediction of the molecular and polymer solution properties of LDPE in a high-pressure tubular reactor using a novel Monte Carlo approach

“…Based on the general framework of molecular species population balances in a polymerization system, a number of deterministic and probabilistic models have been developed dealing with the prediction of molecular properties of linear and branched polymers. The various modeling approaches have been presented and reviewed in a series of recent publications by Kiparissides and his co-workers (Kiparissides, 2006;Meimaroglou et al, 2007Meimaroglou et al, , 2008Saliakas et al, 2007;Krallis et al, 2008).…”

Methodology for Kinetic Modeling of Atom Transfer Radical Polymerization

“…Furthermore, an extension of the method of moments is presented that allows an accurate description of the contribution of the polymer molecules with a high molar mass to the MMD of the polymer. It should be noted that the calculation of the full MMD of the polymer allows a more detailed link with polymer properties and especially for broad MMDs the calculation of the full MMD can be more appropriate 47…”

“…Only a few authors reported the calculation of the full MMD of the polymer for radical polymerizations 19, 47–53. Four important methods for the calculation of the MMD of a polymer in radical polymerizations are: the method of finite molar mass moments,48, 49 the global orthogonal collocation method,50 the Monte Carlo method,19 and the fixed pivot method 47, 51–53. The former two methods are based on the QSSA for intermediate reactive species and are related to the methodology presented in this work to calculate the full MMD of the dormant polymer in ATRP.…”