Process Model for Styrene and n-Butyl Acrylate Emulsion Copolymerization in Smart-Scale Tubular Reactor

Abstract

Real-time optimization-based control methodologies in emulsion (co)­polymerization allow achievement of a significant intensification of the process and increase of the product quality. This paper describes the development of the fast and computationally simple process model of continuous styrene and n-butyl acrylate emulsion copolymerization for use in nonlinear model predictive control (NMPC) of a smart-scale tubular reactor. The model predictions agree well with experimental data for monomer conversion, copolymer composition, temperature profile, average particle size, and number-average molecular weight. To account for the slower reaction rate at the beginning of the reaction, the model incorporates a thermodynamic description of comonomer partitioning between particle, water, and droplet phases based on Morton equations. For the purpose of the process model, a simple empirical function representing the solution of Morton partitioning was implemented. The number concentration of particles was estimated from measured monomer conversion profiles, as the predictions by first-principle nucleation models generally provide values substantially different from experiments. After the model incorporation into a framework for online state estimation and control, it will be used for open- and closed-loop control of the smart-scale tubular reactor.

Low-Dispersity Polymers in Ab Initio Emulsion Polymerization: Improved MacroRAFT Agent Performance in Heterogeneous Media

“…Although [M] sat is generally considered constant during interval II, the extent of swelling of polymer particles with the monomer does depend on particle size for sufficiently small particles; this effect is particularly strong for diameters less than 60 nm (Figure SI11). The pressure arising from the surface tension causes a decrease in the monomer concentration and this effect is more significant for small particles , as initially proposed by Morton et al The Morton equation (eq ) provides a theoretical basis for the prediction of [M] sat where Γ is the interfacial tension between the latex particle and the aqueous phase, φ p is the volume fraction of the polymer in the latex particle, V sM is the partial molar volume of the monomer, χ is the Flory–Huggins interaction parameter, and r u is the radius of the unswollen particle. However, estimation of [M] sat as a function of particle size based on the Morton equation can be a laborious task.…”

“…SI 10). [54][55] The pressure arising from the surface tension causes a decrease in the monomer concentration and this effect is more significant for small particles 54 as initially proposed by…”

Transfer of Emulsion Polymerization of Styrene and n‐Butyl Acrylate from Semi‐Batch to a Continuous Tubular Reactor

“…Model predictive control (MPC) may serve to be a suitable option to control such processes and implementation of MPC schemes for tubular reactor systems needs to be investigated. A mathematical model, describing the copolymerization of styrene and n ‐butyl acrylate in the investigated tubular reactor, has already been developed …”

Solution of population balance equations by logarithmic shape preserving interpolation on finite elements

“…For this reason, the differential equation set, known as population balance equations (PBE), has been used extensively since its formal introduction. [7,8] PBE have been employed to rationalize polymerization reactions [9,10,11,12,13,14,15,16,17,18,19,20,21], colloid aggregation, [22,23,3,24,25,26,27,28] and crystallization processes [29,30,31,32,33]. This short list proves the versatility of the PBE, that enable the description of virtually any type of population, focusing on some key property such as the number of monomeric units in polymer chains, or the size of crystals.…”