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Molecular weight distribution modeling of LDPE in a continuous stirred-tank reactor using coupled deterministic and stochastic approach

  • Polymer, Industrial Chemistry
  • Published:
Korean Journal of Chemical Engineering Aims and scope Submit manuscript

Abstract

A hybrid approach that combines the method of moments and Monte Carlo simulation to predict the molecular weight distribution of low-density polyethylene for a continuous stirred tank reactor system is proposed. A ‘Block’, which is repeating reaction group, is introduced for the calculation cost-effective simulation. This model called the ‘block Kinetic Monte Carlo’ is ∼10 to 32 times faster than Neuhaus’s model. The model can be applied to any steady state system and provide a calculation cost reduction effect, where one reaction is much faster than others, for example, the propagation reaction. Furthermore, we performed a case study on the effects of the system temperature and initiator concentration on the MWD and reaction rate ratio. Based on the simulation results of 180 case studies, we determined a quantitative guideline for the appearance of shoulder, which is a function of the rate ratio of reactions to the propagation reaction.

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Abbreviations

Ca :

concentration of molecule a [mol/L]

Dn :

dead polymer chain of length n

f:

effectiveness factor for initiator decomposition [dimensionless]

Fsh :

shouldering measurement [dimensionless]

k:

kinetic constant

kb :

kinetic constant of beta scission reaction [s−1]

kcp :

kinetic constant of chain transfer to polymer reaction [L(mol· s)−1]

kcm :

kinetic constant of chain transfer to monomer reaction [L(mol· s)−1]

kd :

kinetic constant of initiator decomposition reaction [s−1]

kp :

kinetic constant of propagation reaction[L(mol·s)−1]

kt :

kinetic constant of termination by combination reaction [L(mol·s)−1]

Ln :

live polymer chain of length n

Ln, sec :

secondary radical polymer chain of length n

Llive :

chain length sampled from the live polymer chain length distribution

Lmat :

the matrix where chain length data is stored

M:

ethylene monomer

N:

number of simulated taget chain

Na :

number of molecules

N AVO :

Avogadro number

N B1 :

number of B1 blocks

NB2 :

number of B2-1 and B2-2 blocks

NB3 :

number of B3-1 and B3-2 blocks

NB4 :

number of B4-1 and B4-2 blocks

nrand :

random number between 0–1

Nsamp :

total number of taget chains to be simulated

Pp1, Pp2 :

Probabilities of propagation reaction

Pt :

Probabilities of termination by combination reaction

Pcp1, Pcp2 :

Probabilities of chain transfer to polymer reaction

Pcm :

Probabilities of chain transfer to monomer reaction

Pb1, Pb2 :

Probabilities of beta scission reaction

r:

stochastic reaction rate

Rj :

initiator decomposition reaction

Rp1, Rp2 :

propagation reaction

Rt :

termination by combination reaction

Rcp1, Rcp2 :

chain transfer to polymer reaction

Rcm :

chain transfer to monomer reaction

Rbeta1, Rbeta2 :

beta scission reaction

rp1, rp2 :

stochastic rate of propagation reaction [mol·s−1]

rt :

stochastic rate of termination by combination reaction [mol·s−1]

rcp1, rcp2 :

stochastic rate of chain transfer to polymer reaction [mol·s−1]

rcm :

stochastic rate of chain transfer to monomer reaction [mol·s−1]

rb1, rb2 :

stochastic rate of beta scission reaction [mol·s−1]

T:

average residence time in CSTR reactor [sec]

t:

current simulation time [sec]

tsamp :

residence time of target chain [sec]

V:

total volume of reactor system [L]

v:

volumetric flow rate of input flow [L/s]

[D]:

concentration of dead polymer [mol/L]

[Dn]:

concentration of the dead polymer of length n [mol/L]

[I]:

concentration of initiator [mol/L]

[L]:

concentration of live polymer [mol/L]

[Ln]:

concentration of the live polymer of length n [mol/L]

[Lsec]:

concentration of secondary radical polymer [mol/L]

[Lsec, n]:

concentration of the secondary radical polymer of length n [mol/L]

[M]:

concentration of monomer [mol/L]

λ k :

kth moment of live polymer chain

λ sec, k :

kth moment of secondary radical polymer chain

μ k :

kth moment of dead polymer chain

CSTR:

continuous stirred-tank reactor

CTA:

chain transfer agent

HDPE:

high density polyethylene

KMC:

kinetic monte carlo

LDPE:

low density polyethylene

MC:

monte carlo

MI:

melt index

MoM:

method of moment

MWD:

molecular weight distribution

PDI:

polydispersity index

SMMA:

single macromolecule approach

SVM:

support vector machine

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Acknowledgements

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1A2C1005503).

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Authors and Affiliations

  1. School of Chemical and Biological Engineering, Seoul National University, Seoul, 08826, Korea

    Solji Choi, Yongkyu Lee, Seongho Park & Jong Min Lee

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  1. Solji Choi
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  2. Yongkyu Lee
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  4. Jong Min Lee
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Correspondence to Jong Min Lee.

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Choi, S., Lee, Y., Park, S. et al. Molecular weight distribution modeling of LDPE in a continuous stirred-tank reactor using coupled deterministic and stochastic approach. Korean J. Chem. Eng. 39, 798–810 (2022). https://doi.org/10.1007/s11814-021-0943-9

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  • DOI: https://doi.org/10.1007/s11814-021-0943-9

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