Polymerization computation fluid dynamics

Computational fluid dynamics (CFD) approaches are emerging as alternative detailed tools for examining polymerization systems with complex mixing and reactor components. Recent examples on LDPE cases include Kolhapure and Fox [118], micromixing effects in tubular reactors Zhou etal. [119], tubular (and autoclave) reactors Wells and Ray [120], analysis of imperfect mixing effects applicable to many reactive flow systems, including LDPE autoclaves and Buchelli etal. [121], fouling effects. 

Instead of using compartment models, the flow pattern in the reactor also can be calculated via computational fluid dynamics (CFD). However, when using CFD, relatively small reaction networks are often used to reduce the computational cost. An exception is gas-phase polymerization, such as the production of low-density polyethylene). For more details on the application of CFD calculations for polymerization processes, the reader is referred to Asua and De La Cal (1991), Fox (1996), Kolhapure and Fox (1999), and Pope (2000). 

Itis worth mentioning that there is a fair amount of information on computer simulation to achieve steady-state reaction conditions [39]. These simulations use artificial neural networks, [40] advances in computational fluid dynamics (CFD) [41], as well as combination of new experimental and modeling techniques, whence the apphcation of these techniques can lead to improved models of polymerization systems as well as the discovery of new kinetic mechanisms that control polymerization rate and properties. 

Figure 10.1 Schematic representation of length and time scales involved in various types of physical models of polymeric and biological systems. CFD = computational fluid dynamics CG-MD = coarse-grained molecular dynamics DPD = dissipative particle dynamics FEA = finite element analysis SCMFT = self-consistent mean field theory ...

Computer modelling provides powerful and convenient tools for the quantitative analysis of fluid dynamics and heat transfer in non-Newtonian polymer flow systems. Therefore these techniques arc routmely used in the modern polymer industry to design and develop better and more efficient process equipment and operations. The main steps in the development of a computer model for a physical process, such as the flow and deformation of polymeric materials, can be summarized as ... 

These models require information about mean velocity and the turbulence field within the stirred vessels. Computational flow models can be developed to provide such fluid dynamic information required by the reactor models. Although in principle, it is possible to solve the population balance model equations within the CFM framework, a simplified compartment-mixing model may be adequate to simulate an industrial reactor. In this approach, a CFD model is developed to establish the relationship between reactor hardware and the resulting fluid dynamics. This information is used by a relatively simple, compartment-mixing model coupled with a population balance model (Vivaldo-Lima et al., 1998). The approach is shown schematically in Fig. 9.2. Detailed polymerization kinetics can be included. Vivaldo-Lima et a/. (1998) have successfully used such an approach to predict particle size distribution (PSD) of the product polymer. Their two-compartment model was able to capture the bi-modal behavior observed in the experimental PSD data. After adequate validation, such a computational model can be used to optimize reactor configuration and operation to enhance reactor performance. 

William Russel May I follow up on that and sharpen the issue a bit In the complex fluids that we have talked about, three types of nonequilibrium phenomena are important. First, phase transitions may have dynamics on the time scale of the process, as mentioned by Matt Tirrell. Second, a fluid may be at equilibrium at rest but is displaced from equilibrium by flow, which is the origin of non-Newtonian behavior in polymeric and colloidal fluids. And third, the resting state itself may be far from equilibrium, as for a glass or a gel. At present, computer simulations can address all three, but only partially. Statistical mechanical or kinetic theories have something to say about the first two, but the dynamics and the structure and transport properties of the nonequilibrium states remain poorly understood, except for the polymeric fluids. 

Smith, S.W., Hall, C.K., Freeman, B.D. Molecular dynamics for polymeric fluids using discontinuous potentials. J. Comput. Phys. 134, 16-30 (1997)... 

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