A mathematical model of mixing and polymerization in a semibatch stirred‐tank reactor

Abstract

Effects of mixing on number-and weight-average degree of polymerization in free radical homopolymerization in solution in a semibatch stirred tank-reactor have been modeled by use of the "partially segregated feed" model of Villermaux (1989) and the lumped kinetic treatment of addition polymerization. Mixing conditions are described in terms of the dimensionless time constants OM and 0, for convective and diffusive mixing, respectively. Results show that DP,, is relatively insensitive, while DP, is highly sensitive to mixing conditions. Comparison with ideal mixing results shows thatpolydispersity (DPJDP,,) can rise greatly as mixing becomes increasingly nonideal, depending on the value of dimensionless flow rate and dimensionless initiator rate constant. Time constants of the mixing model need to be expressed as dimensional correlations before the proposedpolymerization model can be compared to experimental measurements. The model may be adapted to melt polymerization in nonideal CSTR such as LDPE.

Mixing Effects in Continuous Free‐Radical Solution Copolymerization Tank Reactors: I—Characterization of Residence Time Distributions

“…Viscosities of polystyrene solutions were characterized in many previously published works. [40][41][42] In order to describe the viscosity of the reacting system, the Harkness [43] correlation (Equation (19)) was used for monomer conversions smaller than 0.4, while the Mendelson [41,42] correlation (Equation (20)) was used for monomer conversions higher than 0.4. Particularly, these correlations have been used successfully to perform simulations in other works.…”

“…[15,16] Several other studies have investigated the influence of imperfect mixing on the dynamic behavior of polymerization reactors and polymer properties by assuming compartmental modeling. [17][18][19][20][21][22][23] These works showed that the bifurcation behavior of the polymerization systems can be very sensitive to compartmentalization, indicating that the dynamic behavior of the whole process can be affected by mixing effects.…”

Modeling of imperfect mixing and its effects on polymer properties

“…However, they can also represent some degree of micromixing if diffusion is allowed between different zones (Villermaux, 1989a). Compartmental models have been used to study imperfect mixing in continuous LDPE autoclave (Marini and Georgakis, 1984a;Chan et al, 1993) and a semibatch reactor (Tosun, 1992). They have also been used to study the influence of mixing on reactor stability and interaction of mixing and gelation (Kalbfleisch and Teymour, 1995).…”

“…1984a1, copolymer composition distribution (CCD) (Atiqullah and Nauman, 1990;Mecklenburgh, 1970;O'Driscoll and Knorr, 1969), and the molecular-weight distribution (MWD) (Tadmor and Biesenberger, 1966;Marini and Georgakis, 1984b;Tosun, 1992). The mean values of CCD and MWD are less affected than the breadth of the distributions, which often increases with poorer mixing.…”

Continuous polymerization in tubular reactors with prepolymerization: Analysis using two‐dimensional phenomenological model and hybrid model with neural networks

“…After radial derivative discretization, the nonlinear system of ordinary differential equations obtained was numerically integrated through an implicit integration method (the Adams–Moulton method). The most important characteristic of this implicit integration method is its capability to overcome stiffness problems, frequently reported in modeling and simulation studies on polymerization systems 27–29…”