Modeling Fouling Effects in LDPE Tubular Polymerization Reactors

Thanks are due to Mike Brown, Tom Srnka, and Mike Hurst, members of the Lyondell-Equistar Process Engineering Management Team, for allowing the ...
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Ind. Eng. Chem. Res. 2005, 44, 1474-1479

Modeling Fouling Effects in LDPE Tubular Polymerization Reactors. 1. Fouling Thickness Determination Alberto Buchelli,* Michael L. Call, and Allen L. Brown Lyondell Chemical Company, Equistar Chemicals, LP, La Porte Complex, 1515 Miller Cut-Off Road, Houston, Texas 77536

Andrew Bird,† Steve Hearn, and Joe Hannon Performance Fluid Dynamics (PFD) Limited, 40 Lower Leeson Street, Dublin 2, Ireland

Fouling in a low-density polyethylene (LDPE) tubular polymerization reactor is caused by the polyethylene/ethylene mixture forming two phases inside the reactor. Some of the polymer-rich phase is deposited on the reactor’s inside wall, which considerably reduces heat-transfer rates. At a given reactor pressure, the reactor inside wall temperature is the critical parameter in determining when fouling occurs and this is controlled by the coolant stream temperatures. In this work, plant data and a heat-transfer model were used to determine the fouling thickness in a LDPE industrial reactor and the speed at which the foulant material is deposited. Introduction Fouling in LDPE tubular polymerization reactors is caused by thermodynamically driven phase separation of polymer and ethylene. This phase separation occurs in the “cold-near” wall region of the tubular reactor. The polymer-rich phase then sticks to the reactor’s inside wall and causes a reduction of heat transfer through the wall, due to the low thermal conductivity of the deposited material. This can result in an increase in temperatures due to reduction of the rate of heat transfer and could potentially lead to dangerous ethylene decompositions in the reactor. Since plant data clearly shows fouling behavior in the reactor, the objective of this work was to determine the fouling thickness in an industrial polymerization reactor by means of plant data and a heat-transfer model. Process Description A typical flowsheet showing a high-pressure lowdensity polyethylene tubular reactor process is shown in Figure 1. Some of the ethylene gas leaving the discharge of a primary compressor is directed to a mixing block to be mixed with the LDPE tubular reactor outlet stream. The reactor stream outlet pressure drops from about 2400 bar at the high-pressure let-down valve to nearly 260 bar at the inlet to the mixing block. Due to the expansion process and the onset of the reverse Joule-Thompson effect, a temperature increase on the tubular reactor outlet fluid stream occurs. The ethylene injected into the mixing block is used to cool the reactor outlet stream prior to entering the high-pressure separator. The polymer/ethylene fluid entering the highpressure separator is split into a polymer-rich outlet liquid phase containing 70-80% polymer by weight and an outlet ethylene-rich gas phase. The outlet gas contains mostly ethylene and some small amounts of wax. The off-gas from the high-pressure separator is * To whom correspondence should be addressed. E-mail: [email protected]. Tel.: 713-336-5214. Fax: 713-336-5391. † Tel.: +353 1 6612131. Fax: 353 1 6612132. E-mail: [email protected].

further contacted with fresh ethylene prior to being cooled off in a system of high-/low-temperature coolers. The wax is removed downstream from both the highand low-temperature coolers and then sent to a waste stream. The off-gas is then sent to the suction of a secondary compressor where the pressure is raised to about 2750 bar. The gas is then split and one part is sent to the tubular reactor preheat section and the other part to the cold shot coolers prior to entering the tubular reactor at different axial locations. The polymer-rich outlet liquid phase from the bottom of the high-pressure separator is sent to the lowpressure separator. In the low-pressure separator, the pressure is further reduced to about 1.4 bar and a bottom polymer stream containing parts per million (ppm) of ethylene is sent to the extruder where the polymer is pelletized. The off-gas from the low-pressure separator passes through a wax removal section where it is cooled further. This gas is first sent to the purge compressor system, then to the ethylene purification system and, finally, on to the primary compressor where it mixes with fresh makeup ethylene. Industrial LDPE tubular polymerization reactor units typically consist of high-pressure tubes connected in series and varying in size and having lengths as long as several thousand feet. Typical reactor diameters are in the range from 1 to 2.5 in. The reactor can be constructed in a rectangular coil configuration with both straight and curved tubes. On the outside of the reactor tubes there are heating/cooling jackets. Typical reactors have a preheat section where ethylene is heated with steam on the jackets and a reaction section where the heat of polymerization may be removed by either cooling water or hot water in a countercurrent flow fashion. The reactor may be divided in many zones and the coolant temperature and flow rate controlled in each zone. A picture of a typical tubular LDPE polymerization reactor is shown in Figure 2. Initiator is injected in the front end and at several axial locations in the reactor. Also, cold ethylene is introduced upstream of the initiator injection point. A typical three-step process axial temperature profile taken from Bokis et al.1 in a tubular LDPE polymeri-

10.1021/ie040157q CCC: $30.25 © 2005 American Chemical Society Published on Web 02/05/2005

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Figure 1. Low-density polyethylene process flowsheet.

reactor. In Figure 4, typical clean (lower) and fouled (high) temperature profiles in a LDPE reactor are shown. The temperature difference between the maximum and minimum temperatures along the reactor’s axis shows the effect that fouling has on the temperature profile after a certain amount of time. Typical LDPE tubular polymerization reactors may have high ethylene conversion giving up to 25% polyethylene leaving with the outlet stream going to the highpressure separator. Fouling Thickness Inference via a Heat-Transfer Model

Figure 2. Typical tubular LDPE polymerization reactor.

zation reactor is shown in Figure 3. The graph indicates the effect of the initiator promoting the reaction causing a temperature increase. Also shown is the process stream cooling due to the coolant flow in the reactor’s jackets. Finally, the process stream temperature drops due to the injection of the ethylene cooling stream into the bulk of the reaction fluid stream ahead of the initiator injection point. Also, temperature profiles for the coolant in the reactor’s jackets are shown for different zones in the

The thickness of fouling in the reactor’s wall can be calculated from the change in overall heat-transfer coefficient under clean and fouled conditions in the reactor. To calculate the overall heat-transfer coefficient, the process side, coolant side, foulant, and wall heattransfer resistances are needed. These can be estimated either from the physical properties (e.g., wall thermal conductivity from Perry and Green2) or from correlations of dimensionless numbers (Pr, Re, Nu). To accomplish that, the physical properties of the reactor stream must be determined. Physical Properties. Physical property data was calculated from correlations in the open literature such as that in Bokis et al.,1 Luft and Steiner,3 and Stanislawski and Luft.4 The physical property data are used in determining the heat-transfer coefficients from dimensionless numbers, namely, the Reynolds number, Prandtl number, and Nusselt number. In general, the mixture properties are functions of the pure component properties estimated at the required temperature and pressure. The thermal properties for the polymerization and cooling region in the reactor are given in the sections below. The equations below are accurate in the temperature range 423-573 K and in the pressure range 150-250 MPa.

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Figure 3. Typical axial temperature profile in a tubular LDPE polymerization reactor (taken from Bokis et al.1).

Figure 4. Maximum and minimum temperature measurements and temperature difference (Tmax - Tmin) along a reactor axial distance over a time period.

Density. The mixture density is given by the following expression:

Fm )

1 (Xe/Fe) + {(1 - Xe)/Fpe}

(1)

The pure component densities Fpe and Fe are functions of pressure P (in MPa) and temperature T (in K) according to the following equations:

Fe ) 3203.35 - 601.2 log P - 1267.75 log T + 335.8(log P)(log T) (2) Fpe )

-4

9.61 × 10

1 (3) + 7 ×10-7T - 5.2 × 10-7P

The ethylene density correlation is accurate to 2.3% or better for temperatures between 423 and 573 K and pressures between 150 and 250 MPa. The polymer density correlation is accurate to 2.4% for temperatures between 423 and 573 K and pressures between 150 and 250 MPa. The mixture density would be expected to show similar accuracy (2.4%) over the same temperature and pressure range.

Specific Heat Capacity of Mixture. The specific heat capacity of the mixture at constant pressure is

Cpm ) XeCpe + (1 - Xe )Cppe

(4)

Cpe ) 1695.7 + 2.22T - 0.189P

(5)

Cppe ) 1172 + 3.35T

(6)

The ethylene heat capacity correlation is accurate to 3.7% or better for temperatures between 423 and 573 K and pressures between 150 and 250 MPa. The polymer heat capacity correlation is accurate to 1.8% for temperatures between 423 and 573 K and pressures between 150 and 250 MPa. The mixture heat capacity would be expected to show similar accuracy (3.7%) over the same temperature and pressure range. Thermal Conductivity. Equation 7 gives the thermal conductivity of the mixture:

Km ) XeKe + (1 - Xe)Kpe - 0.72(Kpe - Ke)Xe(1 - Xe) (7) Ke ) 6.28 × 10-2 + 16.28/T + (4.19 × 10-4)P Kpe ) 0.274 + 10.47/T + (2.91 × 10-4)P

(8) (9)

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The thermal conductivity of the tube wall (AISI 4333 material) used was 21.7 Btu/[(h ft2)(°F/ft)] taken from Perry and Green.2 The ethylene thermal conductivity correlation is accurate to 3.0% for temperatures between 423 and 573 K and pressures between 150 and 250 MPa. The polymer thermal conductivity correlation is believed to be accurate to 5% for temperatures between 423 and 573 K and pressures between 150 and 250 MPa. The mixture thermal conductivity is believed to be accurate to 6.7%, based on comparisons with more recently available correlations. Viscosity of the Mixture. The viscosity of the mixture is

µm ) (µeXe)(µpe(1-Xe))

(10)

µe ) 10.25 × 10-5 - 10.39 × 10-6(T - 347)0.3 +

(

Ui ) 1/

)

Ai ro A i 1 1 + + Rf + RfoAi/Ao (16) ln + hi 2πkwL ri Ao ho

In eq 16, Rf is the process side fouling resistance which is unknown. Equation 16 (with Rf ) 0) allows calculation of U under clean conditions. Calculation of Rf is not possible using this method, but it serves as a check on the accuracy of the physical property calculations, when compared to the overall heat-transfer coefficient estimated from the plant data (method 2). Method 2: From Plant Data. As an alternative to calculating the overall heat-transfer coefficients from individual coefficients via eq 16, one can calculate the heat-transfer coefficient directly from the temperature differences and heat transferred in the reactor using eq 17.

q ) UiA∆Tlm

4.68 × 10-7P0.8 (11) log(µpe) ) 0.227 + 2015/T + 3.33 × 10-13P (12) The ethylene viscosity correlation is accurate to 10.0% for temperatures between 423 and 573 K and pressures between 150 and 250 MPa. The solution (mixture) viscosity correlation, while simple, is not as accurate. Compared to the best available solution viscosity prediction methods, the equations here provide estimates which are 35% high for a 10% polymer solution. Reynolds Number. The dimensionless Reynolds number is calculated from the formula

Fmud Re ) µm

(13)

The Reynolds number in the reactor pipe was found to be always greater than 3.3 × 104. Overall Heat-Transfer Coefficients in Each Reactor Zone. There are two main methods of calculating the overall heat-transfer coefficients in each reactor zone. The first is to use correlations of dimensionless numbers calculated from the physical properties and operating conditions. This method allows calculation of an overall heat-transfer coefficient under clean conditions only, as the fouling resistance is unknown. The second method uses the heat transferred and the log mean temperature difference to directly calculate an overall heat-transfer coefficient. This approach can be used under both clean and fouled conditions, and, therefore, can be used to estimate the process side fouling resistance from a heat balance. Method 1: From Correlations. The heat-transfer coefficients for the process and coolant side are calculated using eq 14 from Coulson and Richardson.5

Nu ) 0.027Re0.8Pr0.33

(14)

where

Nu )

Cpµ hd ; Pr ) K K

(15)

Calculations of Nusselt number (Nu) for the process side and coolant side led to predictions of the inside and outside heat-transfer coefficients, respectively. These are then used in eq 16 to calculate the overall heattransfer coefficient.

(17)

The value of q can be calculated from the heat rise of the water coolant stream as

q)m ˘ cp(tco - tci)

(18)

and the ∆Tlm from eq 19.

∆Tlm )

((Tpi - tco) - (Tpo - tci)) ln

[

]

(Tpi - tco)

(Tpo - tci)

(19)

The overall heat-transfer coefficient under clean and fouled conditions can be calculated from eq 17. Values of the overall heat-transfer coefficients estimated at two different times using both methods are shown in Table 1 for the different zones (1 to 9) in the reactor. Time 1 represents clean conditions in Zone 2, and Time 2 represents fouled conditions in Zone 2. The heat balances show some discrepancies (particularly when the coolant fluid temperature to the jackets is increased during the fouling removal process called defouling). This causes very little heat to be transferred from the reactor to the jacket fluid, so the relative error of the heat balance can be large. In general, Zone 2 has a good heat balance (1.00 ( 0.05). Comparison of the values of U at Time 1 from Table 1 shows a higher U calculated from correlations (method 1) than estimated from plant data (method 2). Method 1 is more prone to error due to the unknown accuracy of the correlations of physical properties used in calculating the process side heat-transfer coefficients. Method 1 cannot predict the decrease in heat-transfer coefficient due to fouling, but only calculates the process, coolant, and wall heat-transfer resistances based on the flow rates and physical properties. At Time 2 in Zone 2, the value of U has dropped from 668 W/(m2 K) to 455 W/(m2 K) as estimated from the plant data. This indicates a buildup of fouling in this zone over time. Calculation of the fractional resistance to heat transfer is also possible. The outside film heat-transfer coefficient is obtained from a correlation (eqs 14 and 15). The wall heat-transfer resistance is calculated from term 2 on the right-hand side of eq 16 and the fouling resistance is calculated from the increase in overall heat-transfer coefficient between clean and fouled conditions. The rest of the heat-transfer resistance is assumed to be in the process side boundary layer. The results for Zone 2 are given in Table 2. One can see that

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Table 1. Overall Heat-Transfer Coefficients Calculated at Two Different Times time 1

time 2

zone

heat balance qcool/qprocess

method 1 U W/(m2 K)

method 2 U W/(m2 K)

heat balance qcool/qprocess

method 1 U W/(m2 K)

method 2 U W/(m2 K)

1 2 3 4 5 6 7 8 9

0.59 1.05 1.06 1.63 3.36 1.68 0.22 1.43 0.86

1592 1488 1455 1448 1433 1031 1241 1221 1199

395 668 696 335 408 535 204 265 474

1.55 1.02 2.36 1.09 2.13 0.45 0.04 0.95 1.07

1580 1458 1457 1441 1428 1261 1225 1222 1197

252 455 452 517 471 429 200 314 578

Table 2. Fractional Resistance to Heat Transfer in Zone 2 fractional resistance to heat transfer (%) inside film

outside film

wall

coolant fouling

polymer fouling

33.6

3.1

18.5

4.0

40.8

Table 3. Cooling Section Simulations Cooling Section (Zone 2) process simulation 1 2

condition clean fouled

coolant

Tin, °F

Tin, °F

Tout, °F

553 553

112 112

168 168

the two largest resistances to heat transfer are from the process side fouling and the inside film resistance. The tube wall is also a significant heat-transfer resistance. The cooling section simulations for Zone 2 are shown in Table 3 for the process and coolant fluids under clean and fouled conditions. Fouling Thickness Calculations. The fouling thickness is then calculated based upon the change in overall heat-transfer coefficient from clean to fouled conditions. Under fouled conditions, the overall heat-transfer coefficient is lower. The value of the fouling resistance is calculated from eq 20.

Rfmax )

(U1 )

fouled

(U1 )

clean

(20)

If Ufouled is calculated just before defouling, eq 20 gives

the maximum foulant heat-transfer resistance in the reactor. Assuming the foulant is polymer attached to the wall, the foulant resistance is related to a foulant thickness by eq 21,

Rf ) (1/kpolymer)(ri - tf)ln(ri/(ri - tf))

(21)

where kpolymer is the polymer thermal conductivity and tf is the foulant thickness. A large thermal conductivity or small foulant thickness leads to less heat-transfer resistance. Evaluation of the fouling thickness in Zone 2 is shown in Figure 5. It is clear from Figure 5 that the foulant layer thickness is predicted to increase to about 0.35 mm over 10 h. After this amount of time, defouling occurs and the fouling layer thickness drops. The rise in foulant layer thickness appears to be linear over time. The calculated deposition rate is only 0.00004 kg/s (0.314 lb/h) corresponding to an estimated mass-transfer coefficient of 4.63 × 10-7 m/s. A common approach in chemical engineering is to calculate mass-transfer rates based upon analogy with heat-transfer rates. The masstransfer coefficient hD can be related to the heat-transfer coefficient by eq 22:

hD )

h CpF

(22)

For example, for Zone 2, the heat-transfer coefficient under clean conditions is 1160 W/(m2 K), the specific heat capacity is 2900 J/(kg K), and the density is 530 kg/m3. This gives a mass-transfer coefficient of 7.55 ×

Figure 5. Calculated foulant thickness in Zone 2 of the reactor over time, showing fouling buildup over 10 h, followed by a decrease in foulant thickness after defouling.

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10-4 m/s from the Reynolds analogy, which is several orders of magnitude higher than that calculated from the deposition rate. This shows that the mass-transfer rate (and hence foulant deposition rate) is much less than that predicted by a Reynolds analogy, suggesting an additional mass-transfer resistance. Two possible sources of extra mass-transfer resistance are as follows: (1) the foulant is particulate and does not transfer to the wall at the same rate as dissolved polymer due to drag on the particles, and (2) not all of the polymer reaching the wall sticks to the wall becoming foulant. This factor may be affected by the wall roughness inside the reactor. Rougher walls will probably have a tendency to foul, so methods of smoothing the reactor’s wall via electropolishing may help reduce fouling in the reactor. Conclusions Fouling in a continuous LDPE polymerization reactor reduces the plant operating capacity and can complicate the reactor operation. The foulant thickness appears to grow linearly with time. Based on a mass-heat-transfer analogy, analysis of the plant data suggests that only a small fraction of the polymer that is precipitated near the reactor’s wall gets attached to the wall to produce fouling. Acknowledgment Thanks are due to Mike Brown, Tom Srnka, and Mike Hurst, members of the Lyondell-Equistar Process Engineering Management Team, for allowing the publication of this work. Also, Robert Bridges is acknowledged for having provided the financial support for conducting this research project. Dr. Raghu Narayan is thanked for reviewing the paper. Nomenclature A ) area for heat transfer, m2 Ao ) outside tube area for heat transfer, m2 Ai ) inside tube area for heat transfer, m2 Cp ) specific heat capacity at constant pressure, kJ/(kg K) Cpm ) specific heat capacity mixture, kJ/(kg K) Cpe ) specific heat capacity ethylene, kJ/(kg K) Cppe ) specific heat capacity polyethylene, kJ/(kg K) cp ) coolant fluid specific heat capacity, kJ/(kg K) d ) inside reactor diameter, m h ) film heat-transfer coefficient, kW/(m2 K) hD film heat-transfer coefficient, kW/(m2 K) ho ) outside heat-transfer coefficient, kW/(m2 K) hi ) inside heat-transfer coefficient, kW/(m2 K) kw ) wall thermal conductivity, kW/(m K) K ) thermal conductivity, kW/(m K)

Kpolymer ) solid polymer thermal conductivity, kW/(m K) Km ) mixture thermal conductivity, kW/(m K) Ke ) ethylene thermal conductivity, kW/(m K) Kpe ) polyethylene thermal conductivity, kW/(m K) L ) reactor length, m m ˘ ) mass flow rate, kg/s Nu ) Nusselt Number P ) pressure, N/m2 Pr ) Prandtl Number Re ) Reynolds Number Rfo ) coolant side fouling resistance, (m2 K)/kW Rf ) process side fouling resistance, (m2 K)/kW Rfmax ) maximum process side fouling resistance, (m2 K)/ kW ri ) inside reactor radius, m ro ) outside reactor radius, m tf ) fouling thickness, m T ) temperature, K Tpi ) process side inlet temperature, K Tpo ) process side outlet temperature, K tci ) coolant side inlet temperature, K tco ) coolant side outlet temperature, K ∆Tlm ) logarithmic mean temperature difference, K q ) heat flow, kW Ui ) total heat-transfer coefficient, kW/(m2 K) u ) inside reactor fluid velocity, m/s Xe ) mass fraction of ethylene µ ) viscosity, kg/(m s) µm ) mixture viscosity, kg/(m s) µe ) ethylene viscosity, kg/(m s) µpe ) polyethylene viscosity, kg/(m s) F ) density, kg/m3 Fm ) mixture density, kg/m3 Fe ) ethylene density, kg/m3 Fpe ) polyethylene density, kg/m3

Literature Cited (1) Bokis, C. P.; Ramanathan, S.; Franjione, J.; Buchelli, A.; Call, M. L.; Brown, A. L. Physical Properties, Reactor Modeling, and Polymerization Kinetics in the Low-Density Polyethylene Tubular Reactor Process. Ind. Eng. Chem. Res. 2002, 41, 10171030. (2) Perry, R. H.; Green, D. Perry’s Chemical Engineering Handbook Sixth Ed.; McGraw-Hill: New York, 1984. (3) Luft, G.; Steiner, R. Calculation of Molecular Weight Distributions in the High-Pressure Polyethylene Process. Chem.Ztg., Chem. App. 1971, 95, 11-15. (4) Stanislawski, U.; Luft, G. Dynamic Viscosity of Supercritical Ethene. Ber. Bunsen-Ges. Phys. Chem. 1987, 91, 756-759. (5) Coulson, J. M.; Richardson, J. F. Chemical Engineering Volume 1 Fourth Edition; Pergamon Press: New York, 1990; p 319.

Received for review May 14, 2004 Revised manuscript received November 30, 2004 Accepted November 30, 2004 IE040157Q