Numerical Simulation And Optimization Of Reactive Extrusion Processes For Free Radical Reaction

The reactive extrusion (REX) process is a new kind of polymer processing technology that integrates the chemical reaction and extrusion processing. Using twin-screw extruders as reactors, the reactants and other essential additives such as initiators and catalysts react to synthesize the expected polymers during the continuous extrusion process, and then products can be directly formed via the extrusion die. It has great prospects and has drawn wide attentions at home and abroad in its advantages such as the short periods, continuous production, low energy consumption and little environmental pollution.In REX processes, the fluid flow, chemical reaction, heat transfer and mass transfer coexist and interact with each other. The physical and chemical changes are usually performed under nonisothermal, non-constant pressure and high shear rate conditions. In addition, there exist some special technological requirements such as the high reaction rate, good heat transfer ability and high conversion ratio. So it is difficult to carry out quantitative and in-situ investigations by means of the classical reactor theory. Researches involving the numerical simulation and optimization design can be used as one of the effective methods to solve the aforementioned problems, on the basis of which the effects of the chemical reaction on the material structures and physicochemical properties can be quantitatively studied, the reactor structure, material compositions and reactive processing conditions can be optimized, and then the application range of REX can be enlarged. To sum up, this project has an important scientific meaning and a good prospect of engineering application.The existing theoretical investigations have been mainly confined to one-dimensional (1D) models and have generally simplified the intercoupling relations among variables involved in fluid flow, chemical reaction, material structures, physicochemical properties. And the optimization design of material composition and processing conditions are seldom studied. In this paper, using such disciplines as mechanical science, polymer chemistry, polymer physics, statistical theory of polymeric reactions, computational fluid dynamics, engineering optimization and software engineering, the chemorheological behaviors of REX processes for the free radical polymerization and free radical grafting modification were simulated in a macroscale. The functional relationships among the material compositions, reactive processing conditions, material microstructure and macroscopic properties were constructed. The intercoupling relations among the considerable field variables were solved by an uncoupled semi-implicit iterative algorithm. At the aim of making REX process controllable and optimal, the core programs for systems of numerical simulation and optimization design were developed to predict the evolution of field variables and select the optimum reactor structure and processing conditions.The main contents and conclusions were as follows:The configuration of the twin screw extruder is complex and the fluid undergoes complicated physical and chemical changes, which make it very difficult to perform the rheological simulation based on real reactor configurations and working conditions. According to the geometrical structure and movement characteristics of closely intermeshing co-rotating twin screw extruders, the flow space of each fluid were unfolded along the axial direction of the screw channel, and then the expressions involving characteristic parameters such as the unfold length, the width, depth and area of the cross section were derived. Neglecting the non-mainstream flow from one screw to the other and simplifying the shape of the cross section, an equivalent axisymmetric reactor model was established. The reactor model is assumed to be fully filled and its wall moves along the axial direction at a velocity equivalent to the comprehensive effect of the rotary screws and the static barrel on the fluid flow. Thus, the space model for the numerical simulation was constructed.Combining with the aforementioned space model, the basic governing equations describing fields of chemical reaction, material structure and chemorheology were constructed. Based on the free radical reaction kinetics, kinetic models of the free radical polymerization and grafting were constructed, and expressions of reaction rate, monomer concentration, monomer conversion and initiator concentration were deduced. According to the statistical theory of polymeric reactions, the average molecular weight can be divided in three hierarchies: the first is that of polymer chains instantaneously produced, the second is that of polymer chains considering the cumulative effect and the third is that of the fluid with both the reactant and the production taken into account. Expressions of the number-average molecular weight and weight-average molecular weight for each hierarchy were constructed. The continuity equation, the momentum equation as well as the initial and bondary conditions were derived to describe the viscous incompressible fluid flow process. On the basis of polymer physics, expressions of zero shear viscosity and apparent viscosity related to processing conditions and material structures were built.The control volume integration was applied to deduce the discrete expressions of the convection-diffusion equations. The staggered grid and SIMPLE algorithm were introduced to deal with coupling between pressure and velocity, and then the numerical computation expressions of such variables as fluid flow velocity and pressure were deduced. Using the backward difference method and incremental theory to discretize the governing equations for fields of chemical reaction, material structure and chemorheology, the numerical computation expressions of variables such as the monomer conversion, average molecular weight and fluid viscosity were constructed.An uncoupled semi-implicit iterative algorithm was proposed to deal with the complicated relationships among the considerable field variables. Core programs for the numerical simulations of REX processes for the free radical polymerization and free radical grafting were developed. The continuity equation, the momentum equation, the chemical reaction kinetic equation, the average molecular weight and the constitutive equation can be solved numerically under the given initial and boundary conditions.Runing the program for the numerical simulation of REX processes for the free radical polymerization, the evolutions of field variables such as monomer conversion, average molecular weight and apparent viscosity were predicted for the example of butyl methacrylate. The simulated result of the monomer conversion is in agreement with the experimental result. The influences of the gel effect and throughput on field variables were discussed. The analyses give laws controlling the materical structure and rheological properties and offer reliance to choose screw configuration and processing conditions.Runing the program for the numerical simulation of REX processes for the free radical grafting, the evolutions of field variables such as grafting degree, mass fraction of homopolymer, average molecular weight and apparent viscosity were predicted for examples of polyethylene grafting with vinylsilicane, acrylic acid and methyl methacrylate. The simulated results are in agreement with the experimental results. The influences of the material compostion and processing conditions on grafting behaviors were discussed to search effective methods to increase the grafting degree and grafting efficiency.The optimization design was carried out on the basis of the numerical simulation. The finite volume simulation of REX processes was used to solve objective functions, and the genetic algorithm was introduced to search optimum parameters, on the basis of which a new optimization system of REX processes was established. The single object and multi-object optimization models faced to the restriction of monomer conversion and the reaction efficiency for REX processes of the free radical polymerization were constructed respectivelly. The optimum screw geometric parameters and operating parameters can be obtained according to the pre-specified objectives.