STUDIES ON MODELLING OF HIGH PRESSURE POLYETHYLENE REACTOR

Abstract

Polyethylene is one of (he major plastics, used nowadays, in the variety of fields - from domestic to industrial purposes due to various advantages. Polyethylene is classified as high density (HDPE), medium density (MDPE), low density (LDPE) and linear low density (LLDPE). LDPE has registered spectacular growth throughout the world, with countless uses in electronics, power transmission, packaging, moulding and film. LDPE is produced by three processes: low pressure, high pressure tubular and high pressure stirred autoclave polymerization. Out of these three, high pressure process is most advantageous and employed commercially. In the past three decades, various researchers have attempted to study the behaviour and performance of the LDPE tubular reactor by using simulation and modelling, to predict the quality and quantity ofthe polyethylene and also to develop its control system. Several mathematical models with varying degree of complexity have been developed and analysed. These are critically reviewed in the Chapter II on literature review. Accordingly, the objectives of present research work on modelling of high pressure tubular reactor, used to produce LDPE, have been formulated. In this thesis, a comprehensive mathematical model of high pressure tubular reactor for producing LDPE has been derived and studied. The model uses twelve steps reaction mechanism for polymerization of ethylene. Initiation involves two steps, dccomposilion of initiator and the initiation of polymer chain, while termination by chain transfer occurs due to seven constituents/steps, namely initiator, solvent, monomer, polymer (LCB), backbiting (SCB), p-scission of secondary and tertiary radicals. Other steps are propagation, and termination by combination and disproportionation. The reaction mechanism includes all aspects of the formation of short chain branching (SCB), which is supposed to be the main characteristic of LDPE. Besides, initiator efficiency (f) has been considered to be a variable instead of unity unlike earlier research workers. Model assumes plug flow conditions, homogeneous reaction system and constant velocity in the reactor. It consists of fifteen nonlinear ordinary differential equations, and two algebraic equations. These can be solved to compute all the variables/parameters, which arc necessary for analysing the reactor performance, and also for the characterization of polymer produced. For polymerization of ethylene, large number of correlations are available in the literature, which provide dependency of rate constants of reaction steps on temperature in terms of Arrhenius equation. Frequency factor and activation energy of the rate constant for a particular reaction step differ very widely. It is also reported in the literature that the model predictions are highly sensitive to rate constants. Therefore, in the thesis, all the available correlations/expressions have been critically analysed, and the selection of best possible values/expressions for the model based upon appropriate criteria has been made. These values/expressions have been once again evaluated on the basis of accuracy of model predictions for a reference reactor, adopted from the literature, and are found to be suitable for the model. Correlations for other parameters have been taken from the literature. It is important to mention that these take into account the variation of constitutive variable along the length of reactor. Model differential equations are highly stiff in nature, and constitute an Initial Value Problem (IVP). A combination of fourth and fifth order Rungc-Kulta-Fchlbcrg formulas with variable step size was used to solve the IVP. Execution of the computer program, developed in C++ to solve the IVP, on a PC took long time. Due to this reason, steady state hypothesis was also used for [P,]. This reduced the execution time significantly without the loss of accuracy of results. Use of steady slate hypothesis was also attempted for p0\ Pi* and p2*- This yielded further reduction in execution time without sacrificing the accuracy of results of computation. However, results computed and reported in the thesis have been obtained without using the steady state hypothesis for p0*, a/ and u2*. For simulation, operating conditions and physical dimensions of a reactor were taken from the literature (table 5.1). Three models, namely PM8, PM9, and PM10, were formulated from the comprehensive model by considering fewer reaction steps (table 5.4). Solution of these models resulted similar shape of profiles for all the variables, studied by us, as obtained by previous research workers. Analysis of simulation results of models PM9 and PM10 have further confirmed our earlier conclusion of using rate constant for termination by disproportionation step due to Lee and Marino (1979) instead of the same due to Feucht et al. (1985), which resulted in higher value of peak temperature. Besides, overall predictions of model PMIO arc in accordance with the literature, and this further justifies the selection of constitutive correlations/relationships, made by us for the model. Effect of variation in initiator efficiency on the prediction of present model (PMI 2), and reduced model (PMI I), obtained without the consideration of the step of termination by chain transfer due to monomer, was studied. It has been observed that optimum value of f for reference reactor is 0.8 . Predictions of process variables by comprehensive present model (PMI 2) for the reference reactor are in acceptable range, and all profiles are similar in shape to those reported in the literature. For model validation, an industrial tubular reactor, producing LDPE in a Petrochemical Plant was also chosen. Model predictions were obtained for this reactor with variable initiator efficiency. The computed results for f = 0.8 are close to those obtained on the industrial reactor (table 5.10), and show a very good agreement. Thereafter, effect of change in operating variables (Initiator concentration, solvent concentration, feed temperature, wall temperature, feed velocity) and tube diameter on the performance of industrial reactor was also studied by using the present model. The conclusions, thus drawn, are in accordance with those reported in the literature/observed in industrial practice. It is our view that the model developed in the thesis represents a comprehensive model of a high pressure tubular reactor, producing LDPE in a Petrochemical plant. Initiator efficiency, in general, is not equal to unity as used by most of the earlier research workers in their models. It is recommended that f may be estimated with the help of present model by using the actual plant data. The model may be satisfactorily used for optimizing the performance of an industrial reactor, for conducting sensitivity and stability analyses, and also for the design of a new reactor.