Modeling of the Temperature Profile in an Ethylene Polymerization

Mar 7, 2013 - Fluidized-Bed Reactor in Condensed-Mode Operation. Ye-feng Zhou,. † ..... The estimation of the key bed properties is based on the use...
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Modeling of the Temperature Profile in an Ethylene Polymerization Fluidized-Bed Reactor in Condensed-Mode Operation Ye-feng Zhou,† Jing-dai Wang,*,† Yong-rong Yang,† and Wen-qing Wu‡ †

State Key Laboratory of Chemical Engineering and Department of Chemical and Biological Engineering, Zhejiang University, Hangzhou 310027, P. R. China ‡ SINOPEC Tianjin Company, Tianjin 300271, P. R. China S Supporting Information *

ABSTRACT: Condensed-mode operation of an ethylene polymerization fluidized-bed reactor is of great significance in academic and industrial circles. Based on the classical emulsion−bubble two-phase model, this article proposes an FBR model for condensed-mode operation by taking into consideration the addition of a condensed liquid and its evaporation. In this model, two different flow regimes, the gas−liquid−solid (G−L−S) and gas−solid (G−S) zones, are assumed to coexist in one FBR. Moreover, the emulsion phase in the FBR is regarded as being in plug flow in the G−L−S zone and in well-mixed flow in the G− S zone, whereas the bubble phase is always treated as being in plug flow throughout the whole FBR. Modeling of the temperatures of the emulsion and bubble phases allows the temperature profile of the ethylene polymerization FBR to be obtained. The simulation results show that the bed temperature rises sharply in the G−L−S zone above the gas distributor and then remains nearly constant in the G−S zone. Moreover, the G−L−S zone gradually expands upward with a corresponding increase in condensed liquid in the recycling stream. The simulated results compare fairly well with those from an industrial FBR unit. Based on the proposed model, the effects of bubble size on heat transfer and bed temperature profile were also studied. fluidization velocity. Catalysts are fed continuously to the reactor. The fluidized particles disengage from the reactant gas at the expanded section of the reactor top, and the unreacted gas later combines with fresh feed streams and recycles into the reactor bottom through the gas distributor. Because the ethylene polymerization reaction is a highly exothermic reaction, the heat produced in the reaction process must be removed before the recycling gas is returned back to the reactor. Because of low heat-transfer capacity of the reactor, the conversion per pass of ethylene through the bed is very low, approximately 2−5%. With the application of condensed-mode operation, the recycling gas at the reactor inlet is converted into gas−liquid feed when the gas temperature is lower than its dew point. The liquid part of the feed is called the condensed liquid. Much more reaction heat would be taken away from the reactor through the evaporation of the condensed liquid, thereby greatly improving the conversion per pass and polymer production. Some researchers have investigated the heat-removal capacity to push forward condensed-mode technology.2,3 Figure 2 shows the relation between the condensed-liquid content and the polymer yield of an industrial reactor. It should be noted that the condensedliquid content is controlled by changing the composition and reactor inlet temperature of the recycling gas. Besides, other related parameters, such as reactor temperature and recycling gas flow-rate, are kept almost constant for these industrial experiments so that their effects on production capacity are negligible.

1. INTRODUCTION The gas-phase olefin polymerization reactor has been recognized as a principal method for polyolefin production because of its low level of pollution effects on the environment, low investment capital costs, and flexible production, among other reasons. A schematic diagram for a typical reactor of this type is shown in Figure 1. In this figure, the gas feed to the reactor comprises ethylene, comonomers, hydrogen, and inert components. These gases provide the fluidization and heat-transfer media and supply reactants for the growing polymer particles. Generally speaking, industrial fluidized-bed reactors (FBRs) often operate at temperatures of 75−110 °C and pressures of 20−40 bar.1 The superficial gas velocity varies from 6 to 10 times the minimum

Received: Revised: Accepted: Published:

Figure 1. Industrial fluidized-bed polyethylene reactor. © 2013 American Chemical Society

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phase propylene polymerization process by employing a comprehensive kinetic model. In addition to such bubble-related modeling studies, investigations of the particle size distribution (PSD) in polymerization FBRs have also received extensive attention from researchers. In the modeling of PSDs, most reactor models have employed residence time distribution (RTD) functions to calculate steady-state PSDs by assuming that the solids in the reactor are completely mixed. Choi et al.17 used a steady-state population balance model (PBM) with a simplified multigrain model to investigate the effects of feed catalyst size distribution and catalyst deactivation on the PSDs and average molecular properties of products. Zacca et al.18 incorporated the concept of a size selection factor into the catalyst RTD model to calculate the PSD of the product stream. Hatzantonis et al.19 developed a PBM to calculate PSDs by taking into consideration the growth, attrition, elutriation, and agglomeration of particles. Kim and Choi20 combined multicompartment PBM with a size-dependent particle-transfer model to simulate particle segregation phenomena and PSDs. In addition, they also investigated the effects of various operating conditions in an FBR on the PSD using their model. Dompazis et al.21,22 applied a random pore polymeric flow model (RPPFM) to examine the growth of single catalyst/polymer particles. They then employed a dynamic discretized PBM together with the RPPFM to calculate the dynamic evolution of the PSDs in different compartments of an FBR. 1.2. Simulations Using Computational Fluid Dynamics (CFD). In recent years, CFD simulations have attracted extensive attention for hydrodynamics modeling in olefin polymerization FBRs. Using CFD, Kaneko et al.23 conducted simulations based on the discrete element method to investigate the mechanism of hot-spot and lump formation. Their numerical code incorporated reaction-rate and energy balances for the calculations, and thus, they were able to evaluate the maximum possible temperature rise by numerical simulation. Later simulation studies24−28 have mainly focused on hydrodynamics and heat transfer in olefin polymerization FBRs, including efforts to obtain concentration, temperature, and velocity fields using different drag models. In addition, using CFD, Rokkam et al.29 performed simulations of electrostatic phenomena, which play an important role in steady production in industrial gas-phase polymerization FBRs. Condensed-mode operation plays a critical role in the stability and performance of polyolefin production in industrial FBRs. However, at present, most modeling studies assume noncondensed-mode operation. Just a few articles24,30,31 have considered condensed-mode operation, but the simulated results were not verified by industrial data, so they lack accuracy. The axial temperature profiles of industrial polyethylene FBRs can reflect the conditions of fluidization and heat transfer and help to supply useful verification means for simulation results; thus, such profiles are an important focus of research in reactor modeling. This article attempts to improve the classical emulsion− bubble two-phase model for FBRs by introducing coexisting multi-temperature zones, namely, the gas−liquid−solid (G−L− S) and gas−solid (G−S) zones, in one reactor. The modified model takes into consideration the added condensed liquid and its evaporation in the emulsion phase to construct an ethylene polymerization FBR model that is suitable for condensed-mode operation. Modeling of the temperatures of the emulsion and bubble phases allows the temperature profile of the polyethylene FBR in steady state to be obtained. The profile modeled in this

Figure 2. Relation between reactor production rate and condensedliquid content of recycling gas.

Because of the advantages of gas-phase olefin polymerization FBRs, modeling studies of such reactors have attracted extensive attention in academia over recent years. Research has mainly focused on the reactor hydrodynamic model and simulations using computational fluid dynamics (CFD), as described in the next two sections. 1.1. Reactor Hydrodynamic Model. Early modeling developments concerning FBRs concentrated on homogeneous single-phase and two-phase models.4 Based on these early fundamental models, gas-bubble models and multiphase models were later developed.5−7 It should be noted that catalytic gasphase olefin polymerization FBR models have been given much more attention by researchers and are well-developed. Choi and Ray8 first developed a gas-phase olefin polymerization FBR model based on two-phase fluidization theory. McAuley et al.9 compared the predictions of Choi and Ray’s constant-bubble-size model with those obtained from the solution of a simpler wellmixed single-phase model. McAuley et al. concluded that the differences in the predictions of temperature and monomer concentration obtained from these two models were not significant in the operating regimes of industrial FBRs. It should be pointed out that most two-phase models regard the emulsion phase as a well-mixed flow and the bubble phase as a plug flow, whereas some researchers10,11 have treated both the emulsion and bubble phases as plug flows and achieved a good understanding of the reactor dynamics. The early modeling studies on gas-phase polymerization FBRs8,9 simply employed a constant mean bubble size along the reactor bed and did not take into consideration the effects of varying bubble size in their models. The correlations proposed by Davidson and Harrison12 provided the maximum stable bubble size for the modeling of an FBR with a constant bubble size. The critical gas-bubble size affects the steady-state emulsion-phase temperature and concentration.9 Therefore, to assess the effects of bubble size on the reactor dynamic and steady-state operation, Hatzantonis et al.13 conducted a comparative study of the wellmixed, constant-bubble-size, and bubble-growth models. Later, Kiashemshaki et al.14 improved the reactor model based on the assumption that polymerization reactions occur not only in the emulsion phase but also in the bubble phase. Furthermore, Sharami et al.15,16 also considered that the reaction occurred in the bubble phase and predicted polymer properties in the gas4456

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(7) The evaporation of the condensed liquid occurs only in the emulsion phase, and the only liquid-phase component considered in the model is isopentane, which is the main condensing medium in the gas−liquid mixture. In this study, the condensed liquid is assumed to be distributed uniformly on the surface of the particles at the bottom of FBR (G−L−S zone), whereas there is no liquid in the bed above the critical height HL (G−S zone). Therefore, the emulsion phase is assumed to include two distinct parts: G−L−S three-phase zone containing condensed liquid and G−S two-phase zone without liquid. These assumptions enable us to put forward one viewpoint: two zones with different temperatures can coexist in one FBR. 2.2. Evaporation Model. The evaporation model used in this work was adapted from the book Transfer Phenomena,34 in which the calculation of the instantaneous rate of evaporation of a freely falling drop is introduced. This equation is x − xA ∞ E∞ = K xm(πD0 2) A0 1 − xA0 (1)

work was verified with industrial data. Moreover, according to the industrial temperature measurements and modeling results, an FBR operated in condensed mode can be divided into two distinct temperature zones, namely, the G−L−S zone and the G−S zone, a fact that provides guidance for industrial FBR operations and new method for optimizing production performance.

2. MODIFIED TWO-PHASE MODEL FOR FBR IN CONDENSED-MODE OPERATION A schematic diagram of the modified two-phase model used in this work for an FBR operated in condensed mode is shown in Figure 3. To help provide a clear understanding of the modeling

The mean mass-transfer coefficient, Kxm; the mole fractions of isopentane vapor at the droplet surface and in the gas (far from the drop), xA0 and xA∞, respectively; and other physical properties can be estimated under certain steady-state conditions. More calculation details can be found in ref 34. In a polyethylene industrial reactor, a substantial amount of condensed liquid is assumed to be distributed uniformly on the particle surface in the form of a liquid film, and thus, a solid particle coated by liquid can also be seen as a “special” liquid drop. Therefore, the diameter of the liquid drop (D0) can be determined by the particle size and the amount of liquid coated on the particle surface. The mole fraction changes with the vapor pressure of the isopentane, which is dependent on the surrounding temperature in different locations of the reactor. Under certain steady-state conditions, the evaporation rate of a single liquid drop varies with the emulsion-phase temperature as shown in Figure 4. Figure 4 shows that the evaporation rate of

Figure 3. Schematic diagram of the two-phase model for an FBR in condensed-mode operation.

approach, the assumptions included in this FBR model are summarized in the next section. These assumptions were also made by Choi and Ray8 and McAuley et al.9 2.1. Model Assumptions. (1) The fluidized bed comprises two phases, a bubble phase and an emulsion phase. Reactions occur only in the emulsion phase, which is at the minimum fluidization conditions. Thus, the voidage in the emulsion phase equals the critical fluidizing voidage. Gas in excess of the amount required for minimum fluidization passes through the bed in the form of bubbles. (2) The bubbles grow only to their maximum stable size. Because the bubbles reach their maximum size near the base of the bed, all of the bubbles in the bed are assumed to be of uniform size. The bubbles travel up through the bed in plug flow at a constant velocity. Heat- and mass-interchange coefficients are average values over the height of the bed. (3) The small region above the gas distributor exhibits an obvious temperature gradient, whereas above this region, the temperature remains almost constant. Thus, the emulsion phase in the small region is assumed to be in plug flow, whereas above this region, it exhibits complete mixing flow. (4) The radial concentration and temperature gradients in the bed are negligible because the bubbles are distributed uniformly across the bed. This assumption of a uniform radial distribution of the bubbles is supported by the work of Glicksman et al.32 (5) There is negligible resistance to heat and mass transfer between the gas and solids in the emulsion phase. This assumption is valid when catalyst particles are sufficiently small and their catalytic activity is not extremely high.33 (6) The size of the polymer particles is represented by their mean size. Neither elutriation of fines nor particle agglomeration are considered in this model.

Figure 4. Relation between evaporation rate and emulsion-phase temperature.

one drop increases with the surrounding temperature, and thus, the evaporation rate increases with bed height in the fluidizedbed reactor. The main specific operating conditions for the calculations can be found in the Supporting Information. 4457

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Table 1. Modified Model Equations of an FBR in Condensed Mode G−L−S zone

G−S zone

bubble phase mass balance equations

plug flow dC b K = m (C b − Ce) ub dh

plug flow dC b K = m (C b − Ce) ub dh

heat balance equations

dTb Hm = (Te − Tb) ubρg c pg dh

dTb Hm = (Te − Tb) ubρg c pg dh

plug flow

emulsion phase mass balance equations

[A t umf dCe + A t dh K m(C̅ b − Ce)]M w − XHR pΔH dh/H = 0

complete mixing flow Ce = constant

heat balance equations

H0 = H1 + H2 + H3 + H4 + H5

Te = constant

H0 = R p(ΔHr dh/HL)

H1 = A t umf ρp c pg dTe + J c pp

⎛ W ⎞ H2 = qlc pl dTe + ΔH vE∞⎜ dh⎟ ⎝ Hms ⎠

H3 = A t dh Hm(Tb̅ − Te)δ

H4 = A t dh δK m(C̅ b − Ce)M w c pg(Tb̅ − Te)

H5 = πD dh Uh(Te − T∞)

2.3. Model Equations. According to the model assumptions listed in section 2.1, the model equations of the FBR operated in condensed mode are reported in Table 1. In this table, H0 is the reaction heat, H1 is the gas and solid heat exchange arising from the temperature rise of the emulsion phase, H2 is the sum of the sensible heat and the evaporation latent heat of the liquid phase, H3 is the interphase heat exchange between the bubble and emulsion phases, H4 is the heat transfer driven by mass exchange between the bubble and emulsion phases, and H5 is the heat loss to the surroundings through the reactor wall. In the gas-phase polymerization process, the recycling gas comprises a large amount of inert gas, and the single-pass conversion of ethylene in the recycling gas is as low as 2−5%; therefore, the mass transfer between the gas phase and the emulsion phase can be ignored in this work. In the simulations, Cb and Tb are used to substitute the mean values of the bubblephase concentration of ethylene and temperature, C̅ b and T̅ b, respectively. In summary, the heat transfer, instead of mass transfer, is the main focus of this work. 2.4. Model Parameters and Operating Conditions of the Reactor. The accurate prediction of all FBR model parameters (e.g., umf, db,max, ub, Hbe) is crucial to the mathematical modeling of the reactor. The estimation of the key bed properties is based on the use of semiempirical and empirical correlations available in the published literature. These correlations provide estimates of the critical bed properties, including the minimum fluidization velocity, bubble volume fraction, bubble size, bubblephase gas velocity, solid circulation rate, and heat-transfer coefficient, in terms of the process operating conditions and variables. It should be pointed out that some correlations are strongly dependent on the type of solids in the bed. According to Geldart’s classification of solids,35 gas-phase catalytic olefin FBRs contain largely solids of type B. In Table 2, the various correlations employed in this work for the estimation of the bed properties are summarized. A more detailed review of this subject can be found elsewhere.13 In addition, the numerical values of selected operating conditions and the physical and transport properties of the reaction system are reported in Table S1 of the Supporting Information. 2.5. Computational Procedure. The computational procedure employed in this work mainly consists of three essential parts: evaporation rate model, modified two-phase model equations, and heat equilibrium model verification. The

dh dTe H

Table 2. Correlations Used in the Modified Two-Phase Model physical parameter minimum fluidization velocity bubble velocity bubble volume fraction solids circulation rate mass-transfer coefficients

formula 2

ref 0.5

Remf = (29.5 + 0.0357Ar )

− 29.5

ub = (u − umf ) + 0.711 gdb δ=

u0 − umf ub

J ≈ aρp (1 − εmf )(u0 − umf )A t

Kbc = 4.5

⎛ g 0.5D0.5 ⎞ umf ⎟ + 5.85⎜ 2.5 db ⎝ db ⎠

Lucas et al.36 Davidson and Harrison12 Kunii and Levenspiel6 Kunii and Levenspiel6 Kunii and Levenspiel6

⎛ ε u D ⎞0.5 Kce = 6.78⎜ mf 3b ⎟ ⎝ db ⎠

1 1 1 = + Km Kbc Kce heat-transfer coefficients

Hbc =

4.5umf ρg c pg db

⎛ g 0.5k ρ c ⎞0.5 g g pg ⎟ + 5.85⎜⎜ 2.5 ⎟ ⎠ ⎝ db

Kunii and Levenspiel6

⎛ ε u ⎞0.5 Hce = 6.77(kgρg c pg)0.5 ⎜ mf 3 b ⎟ ⎝ db ⎠

1 1 1 = + Hm Hbc Hce

modified two-phase model equations are the core part of the procedure. In this modified model, the emulsion phase is assumed to include the G−S and G−L−S zones. The height of the interface between the G−S and G−L−S zones, HL, is closely dependent on the feeding rate and evaporation rate of the condensed liquid. To be specific, the evaporation end point is determined by the following differential equation

∫0

HL

ϕE∞

W dh ≥ 0.9999ql Hmp

(2)

where HL is the height of G−L−S zone, W is the total bed weight, ql is the flow rate of the condensed liquid, and mp is the mass of one particle. W/(Hmp) dh represents the number of particles in 4458

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Figure 5. Calculation procedure of the modified two-phase model for an FBR in condensed-mode operation.

industrial FBR. Wliq represents the mass fraction of condensed liquid in the feeding recycling gas. It can be obtained from the figure based on the fact that the temperature profile curves can be divided into two segments: the relatively low-temperature region with a high temperature gradient and the high-temperature region with a low temperature gradient. The figure demonstrates that the temperature profiles for different condensed-liquid contents are different. To be specific, as the feeding rate of condensed liquid increases, the low-temperature zone (G−L−S) just above the gas distributor expands upward to a greater height, which enhances the heat-transfer capability as well as the polymer yield of the FBR. 3.2. Modeling Temperature Profile Curves. Figure 7 shows the simulation results for the emulsion-phase temperature Te, the bubble-phase temperature Tb, and the superficial bed temperature T at different condensed-liquid contents. The superficial bed temperature was determined from the temperatures of the two phases according to the relation

the differential unit of height dh. To correct errors caused by differences between practical and theoretical evaporation rate, the correction factor ϕ is introduced into this criterion. The evaporation rate of one drop, E∞, should be calculated by eq 1 in advance. Equation 2 gives the total evaporation rate of liquid in the G−L−S zone of height HL. Once the criterion has been reached, HL can be obtained, and then the calculation for the G− S zone begins. To ensure a rational and accurate heat allocation for different zones in the bed, the heat equilibrium program is used to verify the modeling results. If the modeling results are confirmed to be correct by the program, the obtained temperature profiles of the bubble phase, the emulsion phase, and the bed are valid. Otherwise, the reaction heat is redistributed to the two reaction zones for another round of two-phase model calculations. Figure 5 shows the calculation flowchart for the modified two-phase model of an FBR operated in condensed mode.

3. MODELING RESULTS AND VERIFICATION 3.1. Temperature Profiles of an Industrial FBR. Figure 6 shows actual temperature profile curves for an industrial FBR with different condensed-liquid contents. The actual bed temperatures were obtained by thermocouples installed in the

T = δTb(h) + (1 − δ)Te(h)

(3)

in which the effect of the gas-bubble volume fraction δ on the weighting fraction is taken into consideration. In Figure 7, HL is the height of the G−L−S zone, and XH is the proportion of the reaction heat allocated to the G−L−S zone. It can be obtained from the simulation results in that the bed temperature undergoes a dramatic change in the G−L−S zone whereas only a slight change occurs in the G−S zone. In addition, the proportion XH and the height HL both increase with added liquid content, making the large temperature gradient in the G−L−S zone gentler. It should be noted that the superficial bed temperature calculated by the model was found to be nearly the same as that measured in the industrial bed reactor (about 360 K). From Figure 7a, we found that, if the coexistence of the two temperature zones had not been considered, it would have been impossible to simulate the low-temperature region with a large gradient. Instead, a high temperature can be obtained at a very low height of the reactor even with a large amount of condensed liquid. Table S2 (Supporting Information) lists the main parameters in the industrial operation and the simulation results of the modified model. 3.3. Comparison between Modeled Temperature Profile and Industrial Measurements. To validate the

Figure 6. Bed-temperature axial profile curves of an industrial FBR for different condensed-liquid contents. 4459

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Figure 7. Modeling temperatures Te, Tb, and T along the bed height of the FBR at different condensed-liquid contents.

Ts2 for five different contents of condensed liquid. Ts1 was obtained from the equation

model for the temperature profile, industrial measurements were employed to verify the modeling results. Figure 8 compares the

T = δTb(h) + (1 − δ)Te(h)

industrial measurements Ti with the simulation results Ts1 and 4460

(4)

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Figure 8. Comparison between the modeled temperature profile and industrial measurements.

in which only the gas-bubble volume fraction is considered in the

in which the gas volume fraction and specific heat capacities of the gas and solid phases were both considered in the weighting calculation. From Figure 8, it can be seen that Ts2 fits the industrial bed measurements more satisfactorily than Ts1, which indicates that eq 5 is more reasonable than eq 4 for the weighting calculation. In other words, the specific heat capacities of the gas and solid phases play essential roles in the weighting calculation for the bed temperature. However, regardless of the equation

weighting calculation, whereas Ts2 was obtained from the equation ⎡ ⎛ c pg ⎞ ⎛ c pg ⎞⎤ ⎟⎟Tb(h) + ⎢1 − δ ⎜⎜ ⎟⎟⎥Te(h) T = δ ⎜⎜ ⎢⎣ ⎝ c pg + c pp ⎠ ⎝ c pg + c pp ⎠⎥⎦

(5) 4461

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Figure 9. Effects of gas-bubble diameter on the temperature profile and heat transfer.

applied for the weighting calculation, the bed temperature above the gas distributor in the G−L−S zone was found to increase sharply at first and then remain almost constant along the bed height in the G−S zone. In this regard, one can concluded that the simulation results fit the industrial data satisfactorily. 3.4. Effect of Gas-Bubble Size on FBR Temperature Profile. As an important component in a gas−solid FBR, gas bubbles play a critical role in heat transfer in the fluidization process. The effects of the gas-bubble size on the temperature profile and heat transfer were thus studied in this work. Figure 9 shows three temperature profiles of FBRs for different bubble diameters (db = 0.1, 0.15, and 0.2 m). By comparing the three profiles, the changes in the heat transfer of the FBR can be clearly seen. Table S3 (Supporting Information) shows the ultimate temperatures of the emulsion and bubble phases, as well as the temperature difference between the two phases, at different bubble sizes. From these simulation results, it can be deduced that the larger the bubble size, the smaller the heat-transfer coefficient between

the bubble and emulsion phases. At the same time, as the gasbubble size increases, the rise velocity of the gas bubbles also increases, which results in a decrease of the heat-transfer rate between the two phases. To achieve heat equilibrium (Te = Tb) between the two phases, much more time or reactor space is required, making the temperature difference between the two phases at the bed level (represented by ΔT in Figure 9) relatively large. Furthermore, the decline of the interphase heat-transfer efficiency leads to a decrease of the height of the G−L−S zone. This is because the polymerization reaction heat transferred from the emulsion phase to the bubble phase decreases and more reaction heat is removed by liquid evaporation occurring in the emulsion phase, which results in an obvious reduction in the height required for liquid evaporation, HL. In research concerning gas bubbles in FBRs, there has been an ongoing debate about whether a gas bubble grows infinitely along the bed. There are two opposite statements concerning this question in academia and industry. However, it can be concluded from the simulation results reported here that there must be a 4462

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polymerization FBR operated in condensed mode. The axial temperature profile is obtained from this modified two-phase model. The obtained profile actually consists of two distinct segments: a small G−L−S zone with large temperature gradients and a G−S zone with small temperature changes. As the condensed-liquid content increases, the G−L−S zone expands upward to a greater height in the bed, and the heat-transfer capacity in this zone becomes enhanced. At different liquid contents, the simulation temperature profile derived from the improved model fits the industrial temperature measurements satisfactorily, which ensures the reliability of the improved model in our work. The effects of the gas-bubble size on the bed temperature profile and heat transfer were also studied in this work. We found that the larger the bubble size, the lower the heat-transfer rate between the bubble phase and the emulsion phase, leading to a decrease of the heat-transfer efficiency in the FBR. Moreover, some inferences concerning the improvement of polymer MWD and polymer product performance based on the coexisting G− L−S and G−S zones are made. However, these hypotheses still need to be further verified.

maximum stable gas-bubble size in an FBR. To be specific, the heat-transfer capacity between gas bubbles and particles would deteriorate if the gas bubbles grew infinitely along the bed height, leading to overheating of the local particles or other heat-transfer problems. Therefore, we take the opinion that gas bubbles have a maximum stable size. If the size exceeded its maximum value, the bubbles would break apart during the rising process.

4. REFLECTIONS ON THE COEXISTENCE OF G−L−S AND G−S ZONES From the industrial measurements and the modeling results presented in this work, it is clear that the G−L−S and G−S zones coexist in a polyethylene FBR. The G−L−S zone is a lowtemperature zone with condensed liquid, whereas the G−S zone is a high-temperature zone without condensed liquid. As a result, the polymerization method is similar to that used in a G−L−S three-phase slurry polymerization rather than a pure gas-phase polymerization. In addition, the temperature difference between the two zones will cause an obvious distinction in the hydrogen/ ethylene and comonomer/ethylene ratios between them, further affect the polymerization reaction kinetics, and finally change both the molecular weight distribution (MWD) and the structure of the products in their respective zones.37 Thus, the two coexisting zones in one FBR can help to provide a new means for producing polyethylene with broad/bimodal MWDs. Based on the analysis presented in the preceding sections, the MWDs (in the form of degrees of polymerization) of the polymers produced in the two different reaction zones were qualitatively studied in this work using ASPEN software, and the results are shown in Figure 10. In this figure, the MWD of the

■

ASSOCIATED CONTENT

S Supporting Information *

Numerical values of selected operating conditions, physical and transport properties of the reaction system, main parameters in industrial operation, detailed simulation results of the modified model, and detailed information on Figure 9. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*Tel.: +86-571-87951227. Fax: +86-571-87951227. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The work was supported by the National Natural Science Foundation of China (Grant 21176207), National Basic Research Program of China (2012CB720500), and Specialized Research Fund for the Doctoral Program of Higher Education (20110101120020).

■ Figure 10. Degrees of polymerization (DPN) of products in different reaction zones and the final products.

final product depends on the MWDs of the G−L−S and G−S products. As the condensed liquid increases in condensed-mode operation, the MWD of the final product is widened to some extent. Therefore, the G−L−S three-phase fluidization zone not only helps to promote the heat-transfer capacity and the product yield of the FBR, but also enhances the product performance.

5. CONCLUSIONS This article proposes a polyethylene two-phase FBR model in condensed-mode operation by taking into consideration the addition of condensed liquid and its evaporation in the emulsion phase. In the present work, a model including coexisting G−L−S and G−S zones is introduced to describe an industrial ethylene 4463

NOMENCLATURE a = bubble-wake cross-sectional area, cm2 At = cross-sectional area of the bed, cm2 C = concentration of ethylene, mol cm−3 cp = heat capacity, J g−1 K−1 D = reactor bed diameter, cm D0 = diameter of liquid drop, cm E∞ = evaporation rate, g s−1 H = total bed height, cm Hm = heat-transfer coefficient, J cm−3 s−1 K−1 J = solids circulation rate, kg s−1 k = thermal conductivity, J cm−1 s−1 K−1 Km = mass-transfer coefficient, s−1 Mw = molecular weight, g mol−1 Rp = reaction heat, g s−1 u = velocity, m s−1 Uh = wall heat-transfer coefficient, J cm−2 K−1 s−1 W = bed weight of the polymer particles, g dx.doi.org/10.1021/ie302730a | Ind. Eng. Chem. Res. 2013, 52, 4455−4464

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Wliq = mass fraction of liquid in the recycling gas xA0 = mole fraction of isopentane vapor at the droplet surface xA∞ = mole fraction of isopentane vapor in the gas XH = proportion of the reaction heat allocated to the G−L−S zone Greek Letters

δ = bubble volume fraction in the bed ΔH = heat of polymerization reaction, J g−1 ΔHv = potential heat of liquid evaporation, J g−1 ε = voidage of emulsion phase ρ = density, g cm−2 Subscripts

b = bubble property e = emulsion property g = gas property l, L = liquid property mf = minimum fluidization conditions p = polymer property

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REFERENCES

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dx.doi.org/10.1021/ie302730a | Ind. Eng. Chem. Res. 2013, 52, 4455−4464