(722aa) Rigorous Dynamic Model of the High-Pressure Polymerization of Ethylene in Tubular Reactors Able to Predict the Full Molecular Weight Distribution

High-pressure polymerization of ethylene in tubular reactors is a widely employed industrial process. It allows obtaining branched low density polyethylene with characteristics that have not been reproduced by the more modern low or medium pressure polymerizations. The process is carried out under rigorous conditions. For instance, the reactor is operated at very high pressure, between 1300 to 3000 bar at the inlet. The temperature rises from about 50 º C at the reactor inlet to 330 º C at the hottest points due to the exothermic polymerization. Axial velocities are also high, usually around 10 m/s. Besides, the reactor configuration is complex. The main feed usually consists of ethylene and inerts, transfer agents to control the molecular weight, and eventually oxygen as initiator. Most of the polymerization reaction, however, is initiated by peroxides that are fed to the reactor through lateral injections. Monomer and/or transfer agents can also be fed through side injections. The polymerization takes place in short reaction zones following the peroxides injections, exhibiting high heat generation. The rest of the reactor is mainly used as a heat exchanger, in order to reach appropriate temperatures for peroxides addition or for downstream units. The control of the reaction mixture temperature is achieved by circulating vapor or liquid water through different jacket zones, which may be interconnected or not. Moreover, some of these reactors are provided with a let-down valve located at the reactor exit that is periodically opened to produce a pressure pulse which sweeps out the polymer from the walls. Besides, the interaction between the different reacting species is very complex, and there is an intricate connection between polymer quality and process conditions.

In this context, a mathematical model is fundamental tool to study safely and economically the influence of the different design and operative variables on production performance and product quality, and for process optimization. In order to achieve high-quality results that could be useful for actual plants, comprehensive models with accurate predictive capabilities are required. However, mathematical modeling of industrial low-density polyethylene tubular reactors is a complex task that has motivated a considerable amount of research work. Rigorous steady state models of this process have been reported in the literature [1-3]. In general, these models consider realistic reactor configurations and include detailed predictions of physical and transport properties along the axial distance. Most of these models have focused on the polymer average molecular properties, like the average molecular weights or average degrees of branching. Nevertheless, the prediction of their distributions, such as the full molecular weight distribution (MWD) or two-dimensional distributions in molecular weight and branching frequency have also been reported [4-6].

However, less attention has been devoted to the dynamic operation of these reactors. Although it has been stated that dynamics are negligible and quasi-steady state can be assumed in this process [7], it has been shown that under certain conditions dynamics cannot be ignored, specially when material recycle is involved because in this case time constants may change from minutes to hours [8]. This becomes extremely important in start up, shut down and grade transition studies. There are few dynamic models of this process available in the literature. In these works, usually very simplified and small models have been used [9,10]. A few dynamic models involving a more detailed description of the process have been reported [8,11] but they have not included prediction of distributions of molecular properties.

In previous works we developed a rigorous steady state model of the process [6,12]. This model was validated against experimental data from an actual industrial reactor. In this work, we present an extension of that model consisting in the incorporation of the process dynamics. Comprehensiveness of the former model was kept. This involves employing rigorous correlations for the calculation of physical and transport properties, such as density, viscosity and heat capacity of the reaction mixture and coolant, and heat-transfer coefficient along the axial distance and time. Realistic reactor configuration is also considered. The resulting model is capable of predicting the full MWD, as well as average branching indexes, monomer conversion and average molecular weights along time and reactor length. The method of moments was employed for calculating the average molecular weights, and the probability generating function (pgf) technique [13,14] developed by the authors for calculating the full MWD. This technique allowed modeling the MWD easily and efficiently, in spite of the reactor model complexity.

Model implementation was carried out in the commercial software gPROMS (Process Systems Enterprise, Ltd.). The dynamic model consists of a system of partial differential (with respect to time and axial length) algebraic equations involving mass balances, MWD moments and pgf equations. Partial differential equations were discretized with respect to the axial length using backwards finite differences of order 1. The influence of the number of discretization points was analyzed by comparison with the predictions of the former steady state model, for which the ODE solver provides with sophisticated control of the integration error in the axial distance. Simulations with the dynamic model were performed for different sets of initial conditions. It was observed that, in all cases, model outputs evolved towards the expected values of steady state. The model was then employed for studying the influence of different dynamic scenarios on process and product quality variables. In particular, grade transition policies were analyzed. The model capability of predicting the full MWD allowed following the time evolution of this fundamental polymer property from initial to final grades in detail, which is very useful for a careful analysis of transition policies.

The results obtained show that the model has great potential for performing comprehensive analysis of the process dynamics, as well as for the determination of optimal policies for grade transition, start up and shut down operations.

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