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Modeling and simulation of an industrial slurry phase ethylene polymerization reactor: effect of reactor operating variables

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Abstract

A hierarchical and computationally efficient mathematical model was developed to explain the polymerization of high-density polyethylene (HDPE) in an isothermal, industrial, continuous stirred tank slurry reactor (CSTR). A modified polymeric multi-grain model (PMGM) was used. Steady-state macroscopic mass balance equations were derived for all species (namely, monomer, solvent, catalyst and polymer) to obtain the final particle size and the required monomer and solvent input rates for a given catalyst input and the reactor residence time. The interphase mass transfer coefficients were calculated for the industrial CSTR using the operating data on the reactor. The present model was tuned with some data on an isothermal industrial reactor and the simulation results were compared with data on another set of industrial reactor. The comparison revealed that the present tuned model is capable of predicting the productivity and the polymer yield at various catalyst feed rates and the mean residence times. The effects of variation of two operating variables (catalyst feed rate and mean residence time) on the productivity, the polymer yield, the polydispersity index (PDI) and the operational safety were analyzed. The present study indicated that an optimal value of the reactor residence time (for maximum productivity per catalyst particle) exists at any catalyst feed rate.

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Abbreviations

a gl :

Interfacial area of gas/liquid interface (m2/m3)

a ls :

Interfacial area of liquid/solid interface (m2/m3)

C * :

Concentration of catalyst active site (kmol site/m3 of catalyst)

d a :

Diameter of the impeller (m)

d b :

Average diameter of gas bubbles (m)

D 1 :

Diffusivity of monomer in pure polymer (m2/s)

D cat :

Diameter of original catalyst particle (m)

D ef :

Effective diffusivity of monomer inside the macroparticle (m2/s)

D ef,i :

Effective diffusivity of monomer inside the macroparticle at the ith grid point (m2/s)

D L :

Diffusivity of monomer in the bulk liquid (m2/s)

D mp :

Diameter of macroparticle (m)

D n :

Concentration of dead polymer chains of n monomeric units (kmol/m3 catalyst)

\(D_{{{\text{mp}}}}^{{{\text{plant}}}}\) :

Diameter of macroparticle from industrial reactor data (m)

\(D_{{{\text{mp}}}}^{{{\text{ref}}}}\) :

Reference value of the diameter of macroparticle (m)

D R :

Diameter of the reactor (m)

F :

Volumetric fraction of solids in the slurry (m3 of solid/m3 of slurry)

f c :

Mass fraction of catalyst present in the solid (kg cat/kg solid)

H2 :

Hydrogen concentration (kmol/m3)

\({\text{H}}_{{\text{et-hex}}}\) :

Henry’s law constant of ethylene in n-hexane (Pa m3/kmol)

\({\text{H}}_{{{\text{H}}_{{2}} {\text{-hex}}}}\) :

Henry’s law constant of hydrogen in n-hexane (Pa m3/kmol)

\(I_{{\text{C,in}}}\) :

Rate of catalyst input (kg/s)

\(I_{{\text{M,in}}}\) :

Rate of monomer input (kg/s)

\(I_{{\text{M,in}}}^{{{\text{ref}}}}\) :

Reference value of the rate of monomer input from industrial reactor data (kg/s)

\(I_{{\text{S,in}}}\) :

Rate of the solvent input (kg/s)

\(I_{{\text{S,in}}}^{{{\text{ref}}}}\) :

Reference value of the rate of solvent input from industrial reactor data (kg/s)

k gl :

Mass transfer coefficient at gas/liquid interface (m/s)

\(k_{{{\text{ls}}}}\) :

Mass transfer coefficient at liquid/solid interface (m/s)

k P :

Rate constant for propagation (m3 kmol−1 s−1)

k tr :

Rate constant for chain transfer to H2 (m1.5 kmol−0.5 s−1)

M * :

Equilibrium monomer concentration (kmol/m3)

M L :

Molar concentration of monomer in the bulk of the reacting liquid (kmol/m3)

\(M_{{\text{n}}}\) :

Number average molecular weight (kg/kmol)

M P + 2 :

Monomer concentration at the outer surface of the macroparticle (kmol/m3)

\(\overline{M}_{n}\) :

Mean value of the number average molecular weight (kg/kmol)

\(M_{{\text{w}}}\) :

Weight average molecular weight (kg/kmol)

\(\overline{M}_{w}\) :

Mean value of the weight average molecular weight (kg/kmol)

MW:

Molecular weight of the monomer (kg/kmol)

N E :

Total number of catalyst particles entering the reactor per second (s−1)

N F :

Dimensionless flow number

N P :

Dimensionless power number

N S :

Speed of impeller (rps)

N i :

Number of sub-particles in the ith shell

P :

Number of computational shells

P 0 :

Concentration of empty sites (kmol/m3 catalyst)

\(P_{{\text{d}}}\) :

Power delivered to liquid (W)

p et :

Partial pressure of ethylene in the vapor phase (Pa)

p H 2 :

Partial pressure of hydrogen in the vapor phase (Pa)

p hex :

Partial pressure of n-hexane in the vapor phase (Pa)

\(P_{{\text{S}}}\) :

Power delivered to the impeller shaft (W)

P t :

Total pressure inside the reactor (Pa)

PDI:

Polydispersity index

\(\overline{\text{PDI}}\) :

Mean value of polydispersity index

Q T :

Rate of withdrawal of product (slurry) (m3/s)

R c,av :

Average radius of catalyst sub-particles (m)

R c, i :

Radius of catalyst sub-particle in the ith shell (m)

Re:

Reynolds number

R gl :

Rate of monomer transfer from the gas phase to the liquid phase (kmol/s)

R ls :

Rate of monomer transfer from the liquid phase to the solid phase (kmol/s)

R h, i :

Radius of macroparticle at the hypothetical grid point i (m)

R c,max :

Maximum radius of catalyst sub-particles (m)

R mp :

Polymer production rate of each catalyst particle (kmol/cat particle s)

R poly :

Rate of formation of polymer inside the reactor (kg/s)

R v :

Rate of reaction per unit volume (kmol/m3 s)

R v ,i :

Rate of reaction per unit volume at the ith grid point (kmol/m3 s)

Sc:

Schmidt number

Sh:

Sherwood number

u s :

Velocity of gas bubble (m/s)

\(v_{{\text{C}}}\) :

Volume of one catalyst particle (m3)

\(v_{{\text{G}}}\) :

Total volume of gas dissolved in the n-hexane (m3)

\(v_{{\text{L}}}\) :

Total volume of liquid in the slurry (m3)

\(v_{{\text{s}}}\) :

Total volume of solid in the slurry (m3)

V R :

Volume of the reactor (m3)

\({\upalpha }\) :

Probability of propagation

\(\theta\) :

Mean residence time of the reactor (s)

\(\lambda\) :

Moment of the live polymer chains (kg/kmol)

\(\mu\) :

Moment of the dead polymer chains (kg/kmol)

\(\mu_{{\text{G}}}\) :

Viscosity of the gas (Pa s)

\(\mu_{{\text{L}}}\) :

Viscosity of the liquid (Pa s)

\(\rho_{C}\) :

Density of the catalyst (kg/m3)

\(\rho_{{\text{L}}}\) :

Density of the liquid (kg/m3)

\(\rho_{{\text{M}}}\) :

Density of the monomer (kg/m3)

\(\rho_{{\text{P}}}\) :

Density of the polymer (kg/m3)

\(\rho_{{\text{S}}}\) :

Density of the solvent (kg/m3)

\(\rho_{{\text{S,avg}}}\) :

Average density of the macroparticle [kg (catalyst + polymer)/m3 macroparticle]

\(\sigma_{{\text{L}}}\) :

Surface tension of liquid (N/m)

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Authors and Affiliations

  1. Department of Chemical Engineering, University of Petroleum and Energy Studies, Dehradun, Uttarakhand, 248007, India

    Amit K. Thakur, Santosh K. Gupta & Pranava Chaudhari

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  1. Amit K. Thakur
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  2. Santosh K. Gupta
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  3. Pranava Chaudhari
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Correspondence to Pranava Chaudhari.

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Thakur, A.K., Gupta, S.K. & Chaudhari, P. Modeling and simulation of an industrial slurry phase ethylene polymerization reactor: effect of reactor operating variables. Iran Polym J 29, 811–825 (2020). https://doi.org/10.1007/s13726-020-00840-6

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