(235h) Prediction of Ldpe Molecular Weight Distribution in CSTR Reactor Via Computationally Effective Kinetic Monte Carlo

LDPE(Low density polyethylene) has the characteristic of having high-density of long chain branches. This allows the polymer to have a low tensile strength and a high ductility. Due to their properties, LDPE is used to produce most of plastic bags and films. MWD(Molecular weight distribution) plays an important role in tailoring polymer product for different usage. Shapes of MWD largely effects on essential polymer properties. In case of the high density of long chain branches of LDPE, it revealed as a shoulder in MWD graph. The correlation between viscosity and shear rate is determined by the broadness of MWD. Therefore, prediction of MWD is essential in order to control and design polymer reaction system and improve the process productivity.

Numerous researches have been conducted on predicting MWD. There are two types of models to simulate MWD. One is deterministic model and the other is stochastic model. The most commonly used deterministic model is MoM(method of moment) which is simple and powerful tool for calculating average molecular weight. However, MoM is not suitable to simulate distribution of molecular weight. In order to calculate fraction along chain length, lots of moments are needed while making problem difficult to solve. Furthermore, additional moments are required to simulate branch density and scission point increasing the number of moments exponentially. For this reason, most of MoM technique take some assumption to simplify the problem while making results inaccurate. In contrast to MoM method, MC(Monte Carlo) technique can accurately implement the reaction algorithm especially the scission reaction based on polymer topological information. However, MC algorithm has a computationally intensive problem. It makes the industrial application of the MC algorithm impossible.

In this research, we propose the combined model of deterministic method and stochastic algorithm for CSTR reactor. In a deterministic part, model calculates bulk polymer properties such as live polymer, dead polymer and secondary radical polymer concentration. Detail distribution of polymer will then be simulated in stochastic part. We introduce a new concept of ‘Block’ which is a group of repeating reaction series. Model effectively reduces the calculation time by Blocking the reaction series. There are two reasons that the model is computationally efficient. First, the total number of each Block follow binomial distribution. It is because the probability of each reactions is constant at a steady state where the concentration of each polymer species is constant along time. Second, the propagation reaction is much faster than the other reactions. Due to the characteristic, model can effectively reduce the calculation time in ordering each Block. Therefore, the model is at least 10 times faster than conventional method for calculating the MWD of LDPE and this effect becomes much greater on longer polymer chain.

There are several opinions about the reason of shouldering in MWD. Some research has insisted that the shouldering results from the back mixing in reactor. On the other hand, some claims that shouldering can occur from the reaction itself. We examine the effects of each reaction on shouldering by simulating MWD in various cases. As a result, the faster the termination and chain transfer to polymer reaction and the slower the beta scission reaction, the higher the probability that the shoulder is observed. We suggest the numerical guideline that MWD has shoulder with 89% of accuracy in the range of temperature as 480K~520K, initiator concentration as 5*10^-9 mol/L ~10^-6mol/L and average residence time as 10sec~60sec.

In this research, we suggest new algorithm of kinetic Monte Carlo which can effectively reduce the calculation time while maintaining the accuracy. It can be universally applied on steady state polymer reactor not only the LDPE reactor. In an actual plant, reactor is an inhomogeneous system and has a complex mixing. Conventional MC algorithm is computationally intensive to simulate the complex flow of reactor, so it is hard to simulate the MWD in real plant. However, suggested model is fast enough to couple with flow data so that can practically possible to simulate a non-ideal reactor.