Modeling Condensed Mode Cooling for Ethylene Polymerization: Part

Subscriber access provided by READING UNIV

Article

Modelling condensed mode cooling for ethylene polymerization. Part II. Impact of Induced Condensing Agents on Ethylene Polymerization in an FBR operating in Super-Dry Mode. Rita Alves, Muhammad Ahsan Bashir, and Timothy F.L. McKenna Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b02963 • Publication Date (Web): 25 Oct 2017 Downloaded from http://pubs.acs.org on October 30, 2017

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

Industrial & Engineering Chemistry Research is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Industrial & Engineering Chemistry Research

Modelling condensed mode cooling for ethylene polymerization. Part II. Impact of Induced Condensing Agents on Ethylene Polymerization in an FBR operating in Super-Dry Mode. Rita Alves, Muhammad Ahsan Bashir, Timothy F.L. McKenna* University de Lyon, CNRS, CPE-Lyon, UCB Lyon-1, Chimie Catalyse Polymères et Procédés (C2P2), 43 Blvd du 11 Novembre 1918, 69616 Villeurbanne Cedex, France *[email protected]

1 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 46

Graphic for TOC.

Abstract The Sanchez-Lacombe Equation of State (SL EoS) was used to estimate the concentration of ethylene and different induced condensing agents (ICA) in polyethylene, and the effects of adding an ICA on parameters such as reactor temperature, production rate and particle size were discussed. A simple CSTR-like reactor model was validated from production data, and the results reveal that serious errors will be found in the prediction of the reactor temperature and production rate if the interaction between ethylene and ICA is not accounted for. It is also shown that adding an ICA can lead to increased production rates at the cost of decreased catalyst mileage.


Page 3 of 46


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 4 of 46

1. Introduction Industrial processes for the production of polyethylene (PE) can be divided into different categories according to the phase in which the polymerization takes place: solution, slurry, gas-phase processes, with the latter two being more significant in terms of production volumes. While slurry phase processes are commercially important for a number of reasons, gas-phase processes are even more widely used due to their versatility. They can be used to produce resins with a full range of densities, from linear low density polyethylene (LLDPE) to high density polyethylene (HDPE) in the same process.1 The only type of reactors used for production of gas-phase PE are Fluidized Bed Reactors (FBR), since this is the only reactor type that can be used to evacuate enough heat from the reactor to achieve commercially pertinent rates of polymerization.1 A diagram of a typical FBR for PE production is shown in Figure 1. The reactor is essentially an empty cylinder with an expansion zone at the top (to reduce the gas velocity and help prevent any fine particles from flowing out of the reactor and into the recycle compressor), and a distributor plate at the bottom. Catalyst (or prepolymerized catalyst) is fed into the reactor at point slightly above the distributor plate, and the fluids are typically fed through the bottom of the reactor, usually (but not always) below the distributor plate. The polymer is removed through a product discharge valve, following into a series of degassing tanks to separate the unreacted monomer. The gaseous recycle stream is compressed, cooled and afterwards mixed with fresh monomer, hydrogen and eventually other compounds, then fed back into the reactor.


Page 5 of 46

Compressor

Heat Exchanger

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


C2H4

Catalyst

H2 Comonomer ICA N2

Figure 1. Unipol process for polyethylene production.

As mentioned above, one of the key points in the safe and economical operation of an FBR to produce PE is heat removal; a typical commercial scale reactor will generate several 10s of megawatts of energy during a polymer production rate that can surpass 750 kt/year.1 In fact, heat removal is the single most important factor that places an upper limit on the PE production rate. It is well-known that most of the heat generated by the polymerization is removed via the gas phase as it flows over the particles in the bed. However, this is limited by the maximum flow rate of gas through the bed, and by the temperature of the feed stream. The feed stream temperature is typically regulated with cooling water, and can be as low as is economically possible when operating in “dry mode” (i.e. when only ethylene, vaporized comonomer, hydrogen and nitrogen are present in the feed). Increasing the



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 6 of 46

flow rate of gas through the reactor would help, but this limited in scope: if the flow rate is too low, the bed collapses, and if it is too high, a significant fraction of the particles will be blown out of the bed and into the recycle stream.2 The only other effective means of improving the heat removal capacity of the reactor is to alter the physical nature of the feed stream. Compounds such as ethane, propane or butane can be introduced into the reactor in what can be referred to as “super dry mode,” leading to two main consequences: i) increased ability to remove heat through a higher gas phase heat capacity; ii) increased ethylene concentration in the amorphous polymer phase (co-solubility effect). Note that heavier alkanes can be used as well, but then the feed stream can only be cooled so far in this case without condensation taking place.1,2 However, even more heat can be removed when the reactor is operated in what is called “condensed mode”. In this case the recycle stream is compressed, and then cooled by passing it through at least one external heat exchanger to a temperature below that of the dew point of the gas mixture. The resulting stream is then fed into the lower zone of the reactor in such a way that the liquid is sprayed into the reacting zone, and the droplets of liquid are vaporized by the heat of reaction. Alkanes such as isomers of butane, pentane or hexane are most commonly used to this end. In the case of super dry mode, or condensed mode, the compounds used to help heat removal can be referred to as induced condensing agents (ICA). Monomers such as 1-butene, or 1-hexene can also be liquefied and contribute to energy evacuation as well, but since they are reactive, we will differentiate between liquefied reactants and chemically inert ICA. In the current paper, we will look at the impact of vaporized ICA on the performance of a FBR operating in super dry mode. In normal condensing mode, it has been shown that the liquid droplets evaporate rapidly, and that the clear majority of the powder bed in a 6 ACS Paragon Plus Environment

Page 7 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


typical reactor contains only solid particles and a continuous gas phase.3 Thus, using a super dry mode simulation to investigate the importance of accounting for the interactions between the different components present is a reasonable first step in understanding how to represent the thermodynamics of the polymerization. In a series of recent papers from our research group, experimental work has shown that adding a chemically inert ICA (isomers of pentane or hexane) has a significant effect on the observed rate of polymerisation during gas phase polymerization on Ziegler-Natta catalysts, even in a closed, semi-batch reactor.4,5,6 For example, adding 2 bars of npentane to 7 bars of ethylene provokes an increase of 40% in the average activity as compared to 7 bars of ethylene alone. This was attributed to the fact that the presence of heavier alkanes can increase the solubility of lighter compounds such as ethylene, thus adding n-pentane to the gas phase polymerization of ethylene provokes an increase in the monomer concentration at the active sites, and thus an increase in the observed reaction rate. It was also seen that the higher the solubility of an ICA in the polymer is, the greater its enhancing effect on the solubility of ethylene in the polymer will be. Furrhermore, the swelling of the amorphous phase of the PE can also change the actual volume of the particles, and perhaps have an influence on the fluidisation behaviour of reacting powder.7 It would clearly be interesting to understand what, if any, impact this co-solubility effect would have on reactor operation. An earlier paper by Hutchinson and Ray discussed the importance of understanding the importance of solubility in multicomponent systems, and pointed out that heavier alkanes can enhance the solubility of lighter components such as ethylene.8 They also showed that by using the correct ethylene concentration (i.e. that at the active sites corrected for the cosolubility effect), one finds similar reactivity ratios in slurry and gas



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 46

phase polymerizations. These same authors compared gas and slurry polymerizations, but did not investigate reactor behaviour under a range of operating conditions. Since fluidized beds are widely used in many forms, one can find numerous models for predicting their behaviour in the open literature.9,10,11 Such studies describe fluidized beds in great detail and provide an extensive list of empirical correlations which may be used to estimate properties of importance when designing FBR. Studies on the modelling of FBRs in the specific case of PE production are numerous as well, and exhibit many levels of complexity. For example, Choi and Ray,12 and Grosso and Chiovetta13 proposed a 2 phase model of a bubbling FBR which included an emulsion phase (mixture of particles and vapour) and a bubble phase (vapour only), and were able to track temperature and concentration gradients in the reactor assuming a constant bubble size. Other groups extended this analysis to include variable bubble sizes with a uniform emulsion phase,14 with regard to the temperature and concentration gradients in the gas phase. And, even more complex models have been developed that divide the different phases into separate zones in order to obtain a more accurate picture of the gradients as well as of the particle size distribution in the reactor.15 However, in terms of the impact of adding ICA to the reactor, very few studies have been published in the open literature. A series of studies looked at the impact of the addition of ICA on the heat balance around FBRs for PE production, but did not look at the impact of the ICA on the product itself, nor its impact on the reaction rate.15,16 Other authors have studied the impact of adding an ICA to the feed stream, and demonstrated that cooling the feed stream, and including an evaporation term in the heat balance allows one to increase the reaction rate, and thus obtain higher levels of production. 16,17,18

However, none of the papers published in the field of reactor modelling considers


Page 9 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


the impact that ICA might have on the swelling of the polymer particles, nor on the observed rate of reaction. In the current paper, we propose to investigate the impact of adding an ICA on the overall reactor behaviour. To do so, we will use a simplified approach to model the reactor model and assume that the residence time distribution of the reactive powder bed in the FBR is that of a continuous stirred tank reactor. It has been shown elsewhere that this simplification has a limited impact on the calculation of the final PSD and conversion in the reactor.19

On the other hand, we will include a more complex

description of the solubilities of different species in the reactor to allow for interactions between the different species in the polymer phase, as these interactions turn out to be significant. In the event that co-solubility effects have an impact on reactor operation, more complex models (that include single particle models) can be developed in the future.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 46

2. Modelling Development Model Description The development of the mathematical model used here will be divided into different sections: mass and heat balances, calculation of the particle size distribution, FBR design equations and thermodynamic model. The present model is based on the following simplifying assumptions:

•

Reactor is operating at steady-state;

•

The residence time distribution of the FBR is that of an ideal CSTR;

•

We will consider super-dry mode only – i.e. no liquid droplets in the feed, only vapour phase ICA;

•

Catalyst activation is instantaneous;

•

The rate of polymerization will be modelled using a global propagation constant (not attempt is made to differentiate between families of active sites);

•

Catalyst particles are considered spherical;

•

The elutriation of solids is neglected;

•

Gas entrainment by production discharge is neglected;

•

The solid feed to the reactor consists only of fresh catalyst (no prepolymerization);

•

No breakage or aggregation is considered;


Page 11 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


•

The gaseous outlet of the reactor consists of unreacted ethylene, ICA and nitrogen;

•

The solid outlet of the reactor consists of a polymer phase, containing the polymer and catalyst particles, as well as dissolved ethylene and ICA;

•

Heat transfer between the growing particles and the gas phase is by convection only.

All correlations for bed density, heat transfer coefficients and other reactor properties are calculated using an average size for catalyst and for polymer particle. It is, of course, possible to adopt a more detailed modelling approach, such as full scale population balances. However, since the objective of this work is to explore how important it is to use accurate thermodynamic models, the additional complication created by using complex models is not useful at this point.

2.1.

Mass Balances

The general form of the ethylene mass balance is written as follows:

Q, − Q, − R T, P ∙ V ∙ MW − Q, = 0

(1)

Where Q, is the ethylene mass flow rate entering the reactor, Q, is the ethylene

mass flow rate exiting the reactor, R is the reaction rate at a given temperature and

pressure , V is the catalyst volume in the bed and Q, is the flow rate of ethylene dissolved in the outlet polymer stream. This last variable can be defined as:

Q, =

C ∙ MW ∙ Q ∙ w ρ

(2)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 46

is the concentration of ethylene in the amorphous polymer phase, Q is the Where C

PE production rate (as defined in equation (15)) and w is the weight fraction of amorphous phase in the polymer, which varies with the temperature.20 The general form of the alkane mass balance is given as:

Q !", − Q !", − Q !", = 0

(3)

Where Q !", is the ICA mass flow rate entering the reactor, Q !", is the ICA mass

flow rate exiting the reactor and Q !", is the flow rate of ICA dissolved in the polymer

phase. The Q !", equation is similar to the ethylene:

Q !", =

C!" ∙ MW !" ∙ Q ∙ w ρ

(4)

Where C !" is the concentration of ICA in the amorphous polymer phase. Since the ICA is a chemically inert compound, and we are not interested in modelling the molecular weight distribution in this work, the kinetic scheme considered here will be the homopolymerization of ethylene. Even though the polymerization includes several well-known steps, a simple expression for the overall reaction is enough to reflect the impact of the cosolubility effect:21 R = k ∙ C∗ ∙ C

(5)

Where k represents the kinetic rate constant. C ∗ is the active sites concentration on the catalyst is given by equation (7), presented below: 22

Q ⁄ρ ∙ C'∗ − k ∙ V! ∙ C ∗ − C∗ = ,

() *

∙ C∗ = 0

!∗+

(6)

(7)

- ∙*./


Page 13 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Q is the catalyst mass inlet flow rate, ρ is the catalyst density, τ is the average

residence time and C'∗ is the initial concentration of active sites. It is important to

mention the use of Arrhenius Law to predict the kinetic rate (k and catalyst

deactivation (k constants at the reaction temperature, as described in equations (8) and (9).

E 1 1 1 k = k 234 ∙ exp 8 ∙ : − ?@ R T E 1 1 1 k = k 234 ∙ exp 8 ∙ : − ?@ R T

(8)

(9)

In Equation (5) C is the ethylene concentration in the amorphous polymer phase. This

last parameter is of the utmost importance and an accurate estimation is likely needed in order to predict the polymerisation rate. C changes with the presence of different

ICAs, comonomers, and with the operating conditions (reactor temperature and pressure). It is important to point out that at present, no EoS can accurately predict this parameter à priori in multicomponent systems (when one of the components is a polymer), which leaves fitting of these models to the experimental data as the only option.23 A thermodynamic model was implemented to estimate the polymer density, and ethylene and ICA concentration in the polymer phase. The chosen model was the Sanchez-Lacombe Equation of State (SL EoS),24,25 a widely applied model in the polymer industry due to its simplicity and good accuracy. This model is described in section 2.5.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

2.2.

Page 14 of 46

Energy Balances

Inside the reactor two temperatures can be observed: The bulk temperature (TA ) and the

solid particles temperature (T> ).

The rate of heat transfer between the growing particles and the continuous phase can be written as follows:26

h ∙ A ∙ T>−TA = V, ∙ Rp ∙ D−∆H G

(10)

Rearranging (10),

T> −TA =

d I ∙ R ∙ D−∆H G

(11)

6 ∙ KKK d ∙ h L

Where ∆H is the heat of reaction and h represents the convective heat transfer coefficient.26 The reactor heat balance is written as follows:

∆H − ∆H + ∆HN – Gas superficial velocity (m.s-1) V – Catalyst volume in fluidized bed (m3) V, – Catalyst Particle volume (m3) w – Amorphous phase mass fraction (-) W – Weight solids in fluidized bed (kg) z – Compressibility factor (-) Greek letters ∆H – Heat of reaction (J/mol) δ – Average gas fraction (-) ε – bed porosity (-) μ – Gas phase Viscosity (Pa.s) ρ – Density (kg/m3) τ – Average residence time (s) Subscripts b – Bulk (gas) phase C – Catalyst



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 42 of 46

d – dissolved in amorphous PE Et – Ethylene ICA – Induced Condensing Agent in – Entering reactor mf – Minimum fluidization out – Exiting reactor p – Particle PE - Polyethylene pol – Polymer s – Solid phase

5. Associated Content Supporting information The gas-phase physical and thermal properties estimation has been elaborated.


Page 43 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


6. References (1)

Soares, J. B. P.; McKenna, T. F. L. Polyolefin Reaction Engineering; WileyVCH, 2012.

(2)

Bragança, A.; Morschbacker, A.; Rubbo, E.; Miro, C.; Barlem, T.; Mukherjee, A. Process for the Gas Phase Polymerization and Copolymerization of Olefin Monomers. US 6864332 B2, 2005.

(3)

Alizadeh, A.; McKenna, T. F. L. Condensed Mode Cooling in Ethylene Polymerisation: Droplet Evaporation. Macromol. Symp. 2013, 333, 242–247.

(4)

Namkajorn, M.; Alizadeh, A.; Somsook, E.; McKenna, T. F. L. Condensed Mode Cooling for Ethylene Polymerisation : The Influence of Inert Condensing Agent on the Polymerisation Rate. Macromol. Chem. Phys. 2014, 215, 873–878.

(5)

Alizadeh, A.; Namkajorn, M.; Somsook, E.; McKenna, T. F. L. Condensed Mode Cooling for Ethylene Polymerization: Part I. The Effect of Different Induced Condensing Agents on Polymerization Rate. Macromol. Chem. Phys. 2015, 216, 903–913.

(6)

Alizadeh, A.; Namkajorn, M.; Somsook, E.; McKenna, T. F. L. Condensed Mode Cooling for Ethylene Polymerization: Part II. From Cosolubility to Comonomer and Hydrogen Effects. Macromol. Chem. Phys. 2015, 216, 985–995.

(7)

Kanellopoulos, V.; Mouratides, D.; Tsiliopoulou, E.; Kiparissides, C. An Experimental and Theoretical Investigation into the Diffusion of Olefins in SemiCrystalline Polymers: The Influence of Swelling in Polymer-Penetrant Systems. Macromol. React. Eng. 2007, 1, 106–118.

(8)

Hutchinson, R. A.; Ray, W. H. Polymerization of Olefins through Heterogeneous Catalysis. VIII. Monomer Sorption Effects. J. Appl. Polym. Sci. 1990, 41, 51–81.

(9)

Davidson, J.; Harrison, D. Fluidized Particles; Cambridge University Press, 1963.

(10)

Kunii, D.; Levenspiel, O. Fluidization Engineering, 2nd editio.; Reed Publishing Inc., 1991.

(11)

Wen-Ching, Y. Handbook of Fluidization and Fluid-Particle Systems; CRC Press, 2003.

(12)

Choi, K. Y.; Ray, W. H. The Dynamic Behavior of Fluidized Bed Reactors for Solid Catalysed Gas Phase Olefin Polymerization. Chem. Eng. Sci. 1985, 40, 2261–2279.

(13)

Grosso, W. E.; Chiovetta, M. G. Modeling a Fluidized-Bed Reactor for the Catalytic Polimerization of Ethylene: Particle Size Distribution Effects. Lat. Am. Appl. Res. 2005, 35, 67–76.

(14)

Hatzantonis, H.; Yiannoulakis, H.; Yiagopoulos, A.; Kiparissides, C. Recent Developments in Modeling Gas-Phase Catalyzed Olefin Polymerization Fluidized-Bed Reactors: The Effect of Bubble Size Variation on the Reactor’s Performance. Chem. Eng. Sci. 2000, 55, 3237–3259.

(15)

Ashrafi, O.; Mostoufi, N.; Sotudeh-Gharebagh, R. Two Phase Steady-State 43 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 44 of 46

Particle Size Distribution in a Gas-Phase Fluidized Bed Ethylene Polymerization Reactor. Chem. Eng. Sci. 2012, 73, 1–7. (16)

Jiang, Y.; McAuley, K. B.; Hsu, J. C. C. Nonequilibrium Modeling of Condensed Mode Cooling of Polyethylene Reactors. AIChE J. 2004, 43, 13–24.

(17)

Jiang, Y.; McAuley, K. B.; Hsu, J. C. C. Heat Removal from Gas-Phase Polyethylene Reactors in the Supercondensed Mode. Ind. Eng. Chem. Res. 1997, 36, 1176–1180.

(18)

Mirazei, A.; Kiashemshaki, A.; Emanmi, M. Fluidized Bed Polyethylene Reactor Modeling in Condensed Mode Operation. Macromol. Symp. 2007, 259, 135–144.

(19)

McAuley, K.; Talbot, J. P.; Harris, T. A Comparison of Two-Phase and Well Mixed Models for Fluidized Bed Polyethylene Reactors. Chem. Eng. Sci. 1994, 49, 2261–2279.

(20)

Chmelař, J.; Smolná, K.; Haškovcová, K.; Podivinská, M.; Maršálek, J.; Kosek, J. Equilibrium Sorption of Ethylene in Polyethylene: Experimental Study and PC-SAFT Simulations. Polym. (United Kingdom) 2015, 59, 270–277.

(21)

Floyd, S.; Choi, K. Y.; Taylor, T. W.; Ray, W. H. Polymerization of Olefins through Heterogeneous Catalysis III. Polymer Particle Modelling with an Analysis of Intraparticle Heat and Mass Transfer Effects. J. Appl. Polym. Sci 1986, 32, 2935–2960.

(22)

McAuley, K. B.; Macdonald, D. A.; McLellan, P. J. Effects of Operating Conditions on Stability of Gas-Phase Polyethylene Reactors. AIChE J. 1995, 41, 868–879.

(23)

Bashir, M. A.; Monteil, V.; Kanellopoulos, V.; Al-haj Ali, M.; McKenna, T. F. L. An Equation of State-Based Modeling Approach for Estimating the Partial Molar Volume of Penetrants an Polymers in Binary Mixtures. Ind. Eng. Chem. Res 2013, 52, 16491–16505.

(24)

Sanchez, I. C.; Lacombe, R. H. Satistical Thermodynamics of Polymer Solutions. Macromolecules 1978, 11, 1145–1156.

(25)

Sanchez, I. C.; Lacombe, R. H. Statistical Thermodynamics of Fluid Mixtures. J. Phys. Chem 1976, 80, 2568–2580.

(26)

Floyd, S.; Choi, K. Y.; Taylor, T. W.; Ray, W. H. Polymerization of Olefins Through Heteregeneous Catalysis IV. Modeling of Heat and Mass Transfer Resistance in the Polymer Particle Boundary Layer. J. Appl. Polym. Sci 1986, 31, 2231–2265.

(27)

Cui, H.; Mostoufi, N.; Chaouki, J. Characterization of Dynamic Gas–solid Distribution in Fluidized Beds. Chem. Eng. J. 2000, 79, 133–143.

(28)

McAuley, K. B.; Talbot, J. P.; Harris, T. J. A Comparison of Two-Phase and Well-Mixed Models for Fluidized-Bed Polyethylene Reactors. Chem. Eng. Sci. 1994, 49, 2035–2045.

(29)

Wen, C.; Fan, L. Models for Flow System and Chemical Reactors; Marcel Dekker: New York, 1979.

(30)

Soares, J. B.; Hamielec, A. E. Effect of Reactor Residence Time Distribution on 44 ACS Paragon Plus Environment

Page 45 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


the Size Distribution of Polymer Particles Made with Heterogeneous ZieglerNatta and Supported Metallocene Catalysts. a Generic Mathematical Model. Macromol. Theory Simulations 1995, 4, 1085–1104. (31)

Coulson, J. M.; Richardson, J. F. Chemical Engineering; Bath Press, 2002.

(32)

Bashir, M. A.; Al-haj Ali, M.; Kanellopoulos, V.; Seppälä, J.; Kokko, E.; Vijay, S. The Effect of Pure Component Characteristic Parameters on Sanchez-Lacombe Equation-of-State Predictive Capabilities. Macromol. React. Eng. 2013, 7, 193– 204.

(33)

Kanellopoulos, V.; Mouratides, D.; Pladis, P.; Kiparissides, C. Prediction of Solubility of α-Olefins in Polyolefins Using a Combined Equation of State Molecular Dynamics Approach. Ind. Eng. Chem. Res 2006, 45, 5870–5878.

(34)

Bonavoglia, B.; Storti, G.; Morbidelli, M.; . 2006 , 1183. Modeling of the Sorption and Swelling Behavior of Semicrystalline Polymers in Supercritical CO2. Ind. Eng. Chem. Res 2006, 45, 1183–1200.

(35)

Bashir, M. A.; Al-haj Ali, M.; Kanellopoulos, V.; Seppälä, J. Modelling of Multicomponent Olefins Solubility in Polyolefins Using Sanchez-Lacombe Equation of State. Fluid Phase Equilib. 2013, 358, 83–90.

(36)

Novak, A.; Bobak, M.; Kosek, J.; Banaszak, B. J.; Lo, D.; Widya, T.; Harmon Ray, W.; de Pablo, J. J. Ethylene and 1-Hexene Sorption in LLDPE under Typical Gas-Phase Reactor Conditions: Experiments. J. Appl. Polym. Sci. 2006, 100, 1124–1136.

(37)

Chmelar, J.; Matuska, P.; Gregor, T.; Bobak, M.; Fantinel, F.; Kosek, J. Softening of Polyethylene Powders at Reactor Conditions. Chem. Eng. J. 2013, 228, 907–916.

(38)

Parrish, W. M. R. Solubility of Isobutane in Two High-Density Polyethylene Polymer Fluffs. J. Appl. Polym. Sci. 1981, 26, 2279–2291.

(39)

Yao, W.; Hu, X.; Yang, Y. Modeling Solubility of Gases in Semicrystalline Polyethylene. J. Appl. Polym. Sci. 2007, 103, 1737–1744.

(40)

Bashir, M. A.; Monteil, V.; Kanellopoulos, V.; Ali, M. A.-H.; McKenna, T. Partial Molar Volumes and Thermal Expansion Coefficients as an Explanation for Co-Solvent Effect of Penetrants in Multicomponent Polymer Mixtures. Macromol. Chem. Phys. 2015, 216, 2129–2140.

(41)

Alizadeh, A. Study of Sorption, Heat and Mass Transfer During Condensed Mode Operation of Gas Phase Ethylene Polymerization on Supported Catalyst, Queen’s University, 2014.

(42)

Bashir, M. A.; Monteil, V.; Boisson, C.; McKenna, T. F. L. Experimental Proof of the Existence of Mass-Transfer Resistance during Early Stages of Ethylene Polymerization with Silica Supported metallocene/MAO Catalysts. AIChE J. 2017.

(43)

Paricaud, P.; Galindo, A.; Jackson, G. Modeling the Cloud Curves and the Solubility of Gases in Amorphous and Semicrystalline Polyethylene with the SAFT-VR Approach and Flory Theory of Crystallization. Ind. Eng. Chem. Res 2004, 43, 6871–6889. 45 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 46 of 46

(44)

Condensing Mode Operation of Gas-Phase Polymerization Reactor, 2005.

(45)

Xie, T.; McAuley, K. B.; Hsu, J. C. C.; Bacon., D. W. Gas Phase Ethylene Polymerization: Production Processes, Polymer Properties, and Reactor Modeling. Ind. Eng. Chem. Res. 1994, 33, 449–479.


Modeling Condensed Mode Cooling for Ethylene Polymerization: Part

Recommend Documents