Prokopis Pladis

A comprehensive model for the calculation of molecular weight–long-chain branching distribution in free-radical polymerizations

Abstract A new method for the calculation of the joint molecular weight–long-chain branching distribution in free-radical highly branched polymerizations is developed. The method is based on the numerical fractionation of the total polymer population into a series of ‘classes’, each one representing a population of polymer chains with the same long chain branching content (e.g., linear chains, chains with one long–chain branch, etc.). Accordingly, dynamic molar balance equations are derived for the leading moments of the molecular weight distribution (MWD) of each polymer class as well as for the moments of the overall ‘live’ and ‘dead’ polymer chain distributions. A two-parameter Wesslau distribution is employed to reconstruct the MWD of each class in terms of its leading moments. The overall distribution is then calculated by the weighted sum of all class distributions. Simulation results are presented for a high-pressure ethylene continuous stirred tank reactor (CSTR) and a series of two CSTRs with or without a recycle stream. The effect of process parameters (e.g. temperature, chain transfer agent concentration and reactor residence time) on the MWD of low-density polyethylene (LDPE) is analyzed. It is shown that under typical operating conditions the calculated MWD exhibits a bimodal character in agreement with experimental measurements on MWD of LDPE produced in industrial autoclaves.

Dynamic modelling and steady-state multiplicity in high pressure multizone LDPE autoclaves

Abstract A comprehensive mathematical model is developed to simulate the ethylene polymerization in high-pressure autoclave reactors. Two generalised macromixing models, namely the external recycle and the backflow model are established to describe the complex mixing patterns occurring in multizone, multifeed low density polyethylene (LDPE) autoclaves. According to these models, each zone in the reactor is divided into a sequence of perfectly mixed vessels, called segments. To represent the kinetics of ethylene polymerization a general reaction mechanism is considered and the method of moments is employed to calculate the molecular weight developments. A new technique the so-called ‘numerical fractionation’ is applied to predict the formation of gel and the number chain length distribution in LDPE autoclaves. Finally, a detailed stability analysis is carried out for an LDPE autoclave to identify the number of multiple steady-states.

Design, Simulation and Optimization of Polymerization Processes Using Advanced Open Architecture Software Tools

Abstract As the polymer industry becomes more global and competitive pressures are intensifying, polymer manufacturers recognize the need for the development of advanced process simulators for polymer plants. The overall goal is to utilize powerful, flexible, adaptive design and predictive simulation tools that can follow and predict the behaviour of polymer production processes in an accurate, prompt and comprehensive way. In response to the current needs, a new generation of software packages has been developed for the simulation, design, parameter and state estimation, optimization and control of specific polymerization processes aiming at increasing plant efficiency, improving product quality and reducing the impact to environment. The new software tools provide a user-friendly interface, including an object-oriented design environment that can be accessed from the engineers windows-based desktop environment and provide full graphical interaction and expert system guidance on how to use the program or making engineering decisions (such as selection of unit operation or physical property method). Moreover, an open-system architecture is adopted and applied to the process modeling components (PMCs) in order to be transparent to any other compatible process modeling environment (PME). Finally, recent advances regarding the development of software applications for specific polymerization systems (i.e., an LDPE high-pressure tubular reactor process and a PVC batch suspension process) are presented.

Modelling of vinylidene fluoride emulsion polymerization

Abstract In the present study, a comprehensive mathematical model for the emulsion polymerization of vinylidene fluoride (VDF) in a semi-batch reactor is developed. The predictive capabilities of the model are demonstrated by a direct comparison of model predictions with experimental data on the monomer feed rate, monomer conversion, molecular weight averages and molecular weight distribution, mean particle size and particle size distribution, for a batch VDF emulsion polymerization reactor. It is shown that there is a good agreement between model predictions and experimental data.

A comprehensive investigation on high-pressure LDPE manufacturing: Dynamic modelling of compressor, reactor and separation units

Abstract A comprehensive mathematical model is developed for the simulation of high-pressure Low Density Polyethylene (LDPE) plants. Correlations describing the thermodynamic, physical and transport properties of the ethylene-polyethylene mixture are presented and compared with experimental data. Energy balances around the compression units are derived to calculate the energy requirements. A detailed kinetic mechanism is proposed to describe the molecular and structural developments of the free-radical polymerization of ethylene. Based on the postulated kinetic mechanism, a system of differential mass balance equations are derived for the various molecular species, total mass, energy and momentum in the polymerization system. Simulation results show that the proposed mathematical model can be successfully applied to the real-time prediction of reactor temperature profile and polymer melt index. Moreover, model predictions are compared with industrial measurements on reactor and coolant temperature profiles, reactor pressure, conversion, and final molecular properties for different polyethylene grades. Finally, various equations of state (e.g., Sako-Wu-Prausnitz, SAFT, PC-SAFT) are employed to simulate the operation and phase equilibrium in the flash separation units.

Supervisory Control of High Pressure LDPE Reactors

Abstract A comprehensive mathematical model was employed to simulate the dynamic behaviour of ethylene polymerization in high-pressure autoclave reactors. The model was capable of describing the complex mixing patterns occurring in multizone, multifeed low density polyethylene (LDPE) autoclaves. To represent the kinetics of ethylene polymerization a general reaction mechanism was considered and the method of moments was used to calculate the molecular properties. A two-zone autoclave reactor model was considered for our control studies. The reactor opiated at an unstable steady-state, thus, the temperature in each zone was controlled by manipulating the corresponding initiator flow rate. A Quadratic Dynamic Matrix Controller (QDMC) was designed for controlling the polymerization temperature in a twozone autoclave and its performance was compared to that of two SISO PI controllers, usually employed to control the polymerization temperature. Finally, a supervisory QDMC controller was implemented to a simulated reactor model for the optimal control of polymer quality (e.g., melt index) during reactor start-up and grade transitions.

Modeling and Simulation of Particle Size Distribution in Slurry-Phase Olefin Catalytic Polymerization Industrial Loop Reactors

In the present study, a multi-scale, multi-phase, dynamic model is developed for the determination of the distributed properties (i.e., particle size distribution (PSD), molecular weight distribution (MWD)) of polyolefins produced in industrial catalytic gas and slurry phase olefin polymerization reactors (Scheme 1). The polymer MWD is determined by employing a generalized multi-site, Ziegler-Natta (Z-N) kinetic scheme (including site activation, propagation, site deactivation and site transfer reactions) in conjunction with the well-known method of moments. All the thermodynamic calculations are carried out using the Sanchez-Lacombe Equation of State (S-L EOS) (Kanellopoulos et al., 2006). A detailed population balance approach is employed to predict the PSD. The population balance model is combined with a single particle model and the comprehensive kinetic model to predict the properties of the final product in the reactors. Numerical simulations are carried out to investigate the effect of mass transfer limitations on the molecular and morphological properties of the produced polymer.

Dynamic Modeling and Optimization of Flash Separators for Highly-Viscous Polymerization Processes

In the present study, a multi-phase, multi-zone mathematical model is developed to describe the dynamic operation of industrial high-pressure separators (HPSs) for highlyviscous polymer systems. The proposed multi-phase, multi-zone description of the highpressure separator takes into account the complex gas carry-under and liquid droplets carryover phenomena. Moreover, the model takes into account the mass transfer rate from the liquid droplets to the gas phase as well as the bubble formation in the liquid zone. Extensive numerical simulations are carried out to determine the optimal operating conditions (i.e., temperature, pressure, feed composition and mass flowrate, etc.) on the dynamic performance and the separation efficiency of the HPS for highly-viscous fluids. It is shown that the proposed model is capable of simulating the dynamic operation of industrial-scale HPSs over a wide range of operating conditions (i.e., pressures 200-260 bar and temperatures 220-260 0C) and copolymers of different copolymer composition and viscoelastic properties (i.e., melt index in the range of 2-50 g/10min). Finally, it is shown that industrial HPSs do not operate near the thermodynamic equilibrium conditions. Therefore, their non-ideal behaviour should be taken into account when simulating their dynamic operation. Subsequently, model-based optimization and control studies are carried out to optimize the dynamic operation and performance of an industrial HPS.

Computer aided design of styrene batch suspension polymerization reactors

Abstract The present paper deals with the development of a comprehensive, CAD tool for a styrene free-radical batch suspension polymerization reactor. The gPROMS© simulation platform is employed for describing the dynamic behavior of the batch polymerization system. The kinetic model accounts for both thermal and chemical initiation mechanisms, thus, the model can be employed over an extended range of polymerization temperatures. A generalized free-volume model is derived to account for diffusion-controlled reactions (e.g., termination, propagation, and chemical initiation). The overall reactor model includes also appropriate dynamic energy balances for the reaction medium and the coolant in the reactor jacket. An equation of state model is employed to calculate the concentration of the various species (e.g., monomer, solvent, H2O) in the various phases present in the reactor. A WindowsTM user-friendly interface, based on DELPHI programming language, has been developed to link the gPROMS model with the input file containing the necessary design and reactor operating data. It is shown that the model can successfully simulate the operation of batch styrene suspension polymerization reactors, and predict the polymerization rate, temperature, pressure and molecular weight distribution of polystyrene.