Polyethylene Flash Separators

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Ind. Eng. Chem. Res. 2004, 43, 1768-1778

Nonequilibrium Behavior in Ethylene/Polyethylene Flash Separators Alberto Buchelli,* Michael L. Call, and Allen L. Brown Lyondell/Equistar Chemicals, LP, La Porte Complex, 1515 Miller Cut-Off Road, Houston, Texas 77536

Costas P. Bokis,† Sundaram Ramanathan,‡ and John Franjione§ Aspen Technology, Inc., Ten Canal Park, Cambridge, Massachusetts 02141

In this work, we investigated various approaches for the modeling of the high- and low-pressure separator units downstream from a low-density polyethylene tubular reactor using the Polymers Plus software package. First, we examined the performance of thermodynamic equilibrium by using the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state. Experimental data taken from the open literature were used to obtain the model parameters. Comparison with data from an Equistar plant showed that the PC-SAFT simulations agreed very well with the low-pressure separator residual-ethylene solubility measurements. There were, however, significant discrepancies between the model and the plant data for the highpressure separator, indicating that the high-pressure separator is not operating at equilibrium conditions. A further investigation was performed where a physical mechanism based on a bubble formation model was evaluated and a mathematical correlation using dimensionless numbers developed. The resulting model yielded high-pressure separator predictions that agreed adequately with plant data. Introduction Polyethylene is one of the most widely produced and studied commodity polymers in industry. Low-density polyethylene (LDPE) is produced in tubular or autoclave reactors at high pressures. The mixture of ethylene/ polyethylene leaving a LDPE tubular reactor is typically flashed through a series of two gas-polymer separators in order to remove the unreacted ethylene from the polymer. The two gas-liquid flash separators operate at quite different temperatures and pressures. To accurately predict the flash separators’ performance, a study of the thermodynamic phase equilibrium behavior of an ethylene/polyethylene mixture was undertaken. The vapor-liquid equilibrium (VLE) in flashing units is of major importance because it determines the residual amounts of monomer and other gases in the polymer leaving the high- and low-pressure separators (HPS and LPS). In addition, the VLE in these flash separators determines to a large extent the flows and compositions of streams in many of the LDPE plant process units. Plant data were used to validate the equilibrium stage model predictions for the LPS and HPS. On the basis of using a single flash at a specified temperature and pressure, the solubility of ethylene in the polymer was compared with plant-measured values for the LPS. This was accomplished via the use of a perturbed-chain statistical associating fluid theory (PC-SAFT) equation * To whom correspondence should be addressed. Tel.: 713336-5214. Fax: 713-336-5391. E-mail: Alberto.Buchelli@ Equistarchem.com. † Present address: ExxonMobil Research and Engineering, 3225 Gallows Road, Fairfax, VA 22037. ‡ Tel.: 617-949-1000. Fax: 617-949-1030. E-mail: Sundaram. [email protected]. § Present address: Voridian Global PET Technology, P.O. Box 2002, Kingsport, TN 37662.

of state (EOS). However, in the case of the HPS, the equilibrium-based ethylene, model-predicted solubility showed major deviations from the plant-measured values. Because of the fact that the HPS is not in equilibrium conditions, a mathematical model was developed to account for this phenomenon. The HPS model was developed via a physical mechanism based on a bubble formation process that led to the development of a mathematical correlation relating the process variables in the HPS. Mass- and heat-transfer effects in the pipeline bringing the fluid from the LDPE tubular reactor outlet into the HPS were proposed. The effect of the hydrodynamic conditions on the HPS nonequilibrium thermodynamic behavior was postulated. The prediction of the HPS performance included an understanding of the interrelationship between heat- and mass-transfer effects, polymer residence time, operating temperature and pressure, fluid viscosity, and flash separator geometry. Dimensional analysis equations were used to predict separation factors and separation efficiency as a function of the process and geometric conditions. In this fashion, an improved prediction of the separation behavior in the HPS was obtained. Process Description A typical flowsheet showing a high-pressure LDPE 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 (2.4 × 108 Pa) at the high- pressure letdown valve to nearly 260 bar (0.26 × 108 Pa) at the inlet to the mixing block. Because of the expansion process, a temperature increase on the tubular reactor outlet fluid stream (reverse Joule-Thompson effect) occurs. The ethylene

10.1021/ie0302037 CCC: $27.50 © 2004 American Chemical Society Published on Web 03/02/2004

Ind. Eng. Chem. Res., Vol. 43, No. 7, 2004 1769

Figure 1. LDPE process flowsheet.

injected into the mixing block is used to cool the reactor outlet stream prior to entering the HPS. The polymer/ ethylene fluid entering the HPS is split into a polymerrich outlet liquid phase containing 70-80% polymer by weight and an ethylene-rich outlet gas phase. The outlet gas contains mostly ethylene and some small amounts of wax. The off-gas from the HPS is 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 high- and low-temperature coolers and then discarded into a dumpster. The offgas is then sent to the suction of a secondary compressor, where the pressure is raised to about 2750 bar (2.75 × 108 Pa). 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 HPS is sent to the LPS. In the LPS, the pressure is further reduced to about 1.4 bar (0.0014 × 108 Pa) 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 LPS 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, to the primary compressor, where it mixes with freshly made up ethylene. Parts a and b of Figure 2 show typical industrial layouts of the inlet and outlet fluid piping ports for the HPS and LPS, respectively. Equilibrium-Stage Approach Modeling. The steps used to approach the simulation of the LPS and HPS were the following. First, we selected a thermodynamic model that is suitable to the conditions and species involved in the process. Then, we obtained the purecomponent and binary interaction parameters of the selected model based exclusively on experimental data published in the open literature. Next, we compared the predictions of the model against measurements taken from the plant. This step provided insight about the proximity of the separation stages to thermodynamic equilibrium. The LDPE tubular reactor process involves such species as polyolefins, hydrocarbons, and light gases. In addition, the pressure conditions range from nearambient (in the LPS) to thousands of atmospheres (inside the reactor). These process characteristics indicate the requirement of using an EOS. There are numerous EOSs in the literature. A review of the use of some EOSs for LDPE process simulation was presented by Orbey et al.1. For the present investigation, we have selected the PC-SAFT EOS. This EOS was

Figure 2. Typical layouts of the inlet and outlet fluid piping ports: (a) HPS; (b) LPS.

proposed by Gross and Sadowski2 while performing work at the Technical University of Berlin. These investigators showed that PC-SAFT could describe the pure-component and mixture thermodynamic properties better than the original SAFT EOS.3 In addition, they showed that PC-SAFT possesses better predictive capability than SAFT. To apply the PC-SAFT EOS to our system of interest (a mixture of ethylene, LDPE, and other small alkanes and light gases), we need three pure-component parameters for each species. These parameters are the segment number m, the segment energy /k, and the segment diameter σ. One can obtain these parameters by doing a multiproperty data fit (usually vapor pressure, liquid density, and liquid heat capacity data). Ethylene experimental data for vapor pressure, supercritical density, and supercritical heat capacity were taken from work by Sychev et al.4 for the parameter estimation. LDPE has no vapor pressure; therefore, only liquid density data5 were used to estimate the PC-SAFT parameters. More details on the thermodynamic par-

1770 Ind. Eng. Chem. Res., Vol. 43, No. 7, 2004

Figure 3. Density of ethylene as calculated using PC-SAFT.

Figure 4. Density of LDPE as calculated using PC-SAFT. Table 1. PC-SAFT Pure-Component Parameters for LDPE and Ethylene parameter

LDPE

ethylene

r ()m/MW) /k (K) σ (Å)

0.041 317 46 267.179 575 3.475 071 1

0.054 372 0 181.331 214 3.488 222 3

ameter estimation are available in work by Bokis et al.6 Parameters for all other species have been taken directly from the paper of Gross and Sadowski.7 Table 1 lists the regressed parameters for LDPE and ethylene. With the parameters listed in Table 1, the purecomponent properties of LDPE and ethylene are described very accurately over very large ranges of temperatures and pressures. Figure 3 shows a comparison of the densities measured by Sychev et al.4 to PC-SAFTpredicted densities for ethylene. Figure 4 shows a comparison of the densities measured by Olabisi and

Simha5 to PC-SAFT-predicted densities for LDPE. Besides pure-component properties and parameters, it is very important to obtain the appropriate binary interaction parameter kij, which will allow correct representation of the VLE behavior of the system. To achieve this, we need to use experimental VLE data between LDPE and ethylene, preferably in the range of conditions of the HPS and LPS. In this work, we have used the data of Rousseaux et al.8 These investigators reported ethylene solubility data in linear polyethylene at temperatures between 130 °C (403.15 K) and 220 °C (493.15 K) and pressures up to about 260 bar (0.26 × 108 Pa). While the solubility data are for a low molecular weight linear polyethylene, which is different in chemical structure from branched LDPE, they are consistent with (limited) proprietary data for the solubility of ethylene in LDPE at similar conditions. We decided to use the data of Rousseaux et al.8 because it was the


Figure 5. VLE of a LDPE/ethylene binary mixture using PCSAFT. kij ) -0.056 870 8.

Figure 6. Polyethylene/ethylene phase diagram calculated using PC-SAFT [monodispersed PE (MW ) 15 000)].

largest available data set covering the typical pressure range of the HPS. Four isothermal data sets are available from Rousseaux et al.,8 at 130 °C (403.15 K), 160 °C (433.15 K), 190 °C (463.15 K), and 220 °C (493.15 K). In fitting these data sets, we regressed the binary interaction parameter kij of the PC-SAFT EOS. The experimental and predicted solubilities are plotted in Figure 5. Very good agreement between the model and the data is observed. The resulting kij parameter between LDPE and ethylene was found to be -0.0569. Using this parameter value with the PC-SAFT EOS and assuming a monodispersed polymer for the phase-equilibrium calculations, the phase diagram shown in Figure 6 was constructed. At this stage, we can compare the simulations from the thermodynamic framework described above with the plant measurements for the LPS and HPS. The typical operating temperature in the LPS is about 195 °C (468.15 K), and the typical operating pressure is 1.6 bar (0.0016 × 108 Pa). Figure 7 shows this comparison for the LPS. It is apparent that the model predictions are in very good agreement with the plant measurements. Note that there is no parameter fitting to the plant data. This good agreement between the model and LPS plant data indicates that the LPS is quite close to thermodynamic equilibrium, certainly close enough as an assumption for doing an overall mass balance in a LDPE plant environment. The picture is very different for the HPS. Figure 8 shows the comparison of the model predictions with the plant measurements. It is clear that the model severely underpredicts the fraction of ethylene in the polymer stream that leaves at the bottom of the HPS. This

Figure 7. Model predictions for the LPS.

Figure 8. Equilibrium-stage model predictions for the HPS.

disagreement between model predictions and plant data exists despite the fact that the EOS binary parameter was obtained from literature data in the same temperature and pressure ranges as those in the HPS. The typical operating temperature in the HPS is about 240 °C (468.15 K), and the typical operating pressure is 265 bar (0.275 × 108 Pa). This suggests that there are other nonequilibrium factors that affect the fluid behavior in the HPS. The next section of this investigation deals with the HPS using a nonequilibrium-stage approach. HPS Nonequilibrium-Stage Modeling. As was shown in the previous section, the HPS plant performance indicates that its behavior is not accurately predicted assuming an equilibrium-stage approach. Therefore, a nonequilibrium-stage model of the HPS is herein proposed. The purpose of this section is threefold. First, we will explain the proposed physical mechanism of ethylene bubble formation and disengagement downstream of the high-pressure letdown valve into the HPS. Second, we will propose a simplified description of this mechanism and show how it was implemented in Aspen Plus. Finally, we will present some of the results obtained from the use of the mathematical equations and correlations developed. Proposed Physical Mechanism Consider what happens to the reactor effluent as its pressure decreases from the reactor exit pressure to the HPS pressure. At some intermediate pressure [around 1000 bar (1.0 × 108 Pa) and temperature around 300 °C (573.15 K) in Figure 6], the two-phase region is entered, and droplets of liquid polymer are formed in the ethylene/LDPE mixture as shown in Figure 9a. When the two-phase region is entered, the process fluid


Figure 9. Physical mechanism of ethylene entrainment: (a) formation of droplets of the liquid polymer phase in the reactor effluent; (b) appearance of ethylene bubbles within polymer phase droplets; (c) expansion of ethylene bubbles in polymer droplets; (d) coalescence of the polymer phase.

composed mostly of LDPE/ethylene is still well above the critical point of the mixture. These droplets are in equilibrium with the ethylene/LDPE mixture. Thus, the liquid droplets contain dissolved ethylene, up to 60-70 wt % according to the LDPE/ethylene phase diagram shown in Figure 6. As shown in Figure 9b, two things happen as the pressure is further reduced. First, more droplets of the liquid polymer saturated with ethylene appear. Because these droplets first appear at a lower pressure, they have less dissolved ethylene than those droplets formed at higher pressure. Second, the liquid droplets formed at higher pressure now have more ethylene than their solubility limit at the new lower pressure. The extra ethylene that can no longer be dissolved forms small bubbles of ethylene within the droplet. As the pressure is reduced more (Figure 9c), new droplets appear until essentially all of the polymer is removed from the ethylene-rich phase. Then, new ethylene bubbles appear in the existing polymer droplets and existing ethylene bubbles grow larger. The mass of ethylene in an individual bubble does not increase, but at a decreased pressure, the ethylene density is less, so the volume of the bubble increases. At this point, the liquid polymer droplets will coalesce to form a distinct liquid phase, as shown in Figure 9d. This should happen efficiently and rapidly because the droplets are so sticky and because they constitute a substantial fraction of the stream volume. On the other hand, the ethylene bubbles will not be so fast to disengage from the liquid polymer. To break free, they have to thin out the layer of polymer surrounding them and overcome surface tension forces. In theory, ethylene could diffuse from the liquid polymer directly into the ethylene-rich phase or even into the ethylene bubbles. However, diffusion through a polymer is a far slower process than either the coalescence or the disengagement process.

Because the amount of ethylene in the polymer phase exiting the HPS (around 25-30%) is less than 60-70%, it is clear that some (but not all) of the ethylene bubbles do separate from the polymer in the HPS. It is equally clear that there is almost no entrained ethylene in the LPS bottoms. Why is there such a significant difference in the separation efficiency when the two separator sizes are similar? We believe the answer has to do with ethylene bubble growth inside each polymer droplet. Inside the HPS, each bubble will grow in volume by the ratio of the ethylene density at the bubble’s formation pressure to the ethylene density at the HPS pressure. In going from pressures of around 1000 bar (1.0 × 108 Pa) (cloud point) to those of around 265 bar (0.2 × 108Pa) (HPS operating pressure), the density may decrease by a factor of 2 or so. Thus, the bubble volume only doubles. In going from the HPS to the LPS, however, the ethylene density may decrease by a factor of 200 or more. Thus, the bubbles grow much larger. As the surface area of each bubble grows, the thickness of the polymer layer between bubbles decreases, allowing bubbles to coalesce and eventually separate from the polymer phase. The ethylene cooling stream is a stream of cooler ethylene gas that combines with the reactor effluent after the letdown valve but before entering the HPS vessel. At the point where the cooling stream joins the reactor effluent, the reactor effluent pressure has been reduced to approximately the HPS pressure. Thus, the reactor effluent has already separated into an ethylene phase and a polymer phase with entrained ethylene bubbles. When the cooling ethylene mixes with the reactor effluent, it would be expected that the cooling flow would rapidly reach thermal equilibrium with the ethylene phase of the reactor effluent. The cooling ethylene would also cool the polymer phase, although not necessarily to thermal equilibrium. Because of the limited mobility of both dissolved and entrained gases in the polymer droplets, there should be little if any mass transfer between the cooling ethylene and the polymer phase. Perhaps, some of the cooling ethylene might be entrained as bubbles in the polymer phase as a result of turbulence. However, these would tend to be much larger bubbles than the microscopic ethylene bubbles formed during the depressurization of the polymer phase. Thus, any cooling ethylene entrained in the polymer phase would be easily disengaged in the HPS. Nonequilibrium-Stage Model To determine the amount of ethylene entrained in the HPS bottoms, we need to answer two questions: (1) How much ethylene is rejected from the polymer phase to form ethylene bubbles? (2) What fraction of the ethylene bubbles initially generated remains entrained with the polymer? The amount of initial bubbles can be calculated as the amount of ethylene that is dissolved in the polymer at the pressure where the droplets are formed but that cannot be dissolved at the HPS pressure. This can be calculated explicitly using Aspen FLASH unit operations. The Aspen Plus flowsheet for the simplified HPS model is shown in Figure 10. In this flowsheet, unit F1 is an adiabatic flash at the pressure where polymer droplets are formed [∼975 bar (0.975 × 108 Pa) according to Figure 6], F2 is an adiabatic flash at the HPS pressure, and S is a split block. Stream 1 is the tubular reactor effluent, stream 2 is the ethylene-rich phase at


Figure 10. Flowsheet for a simplified HPS nonequilibrium-stage model.

the polymer droplet formation pressure, stream 3 is the polymer droplets with dissolved ethylene, stream 4 is the ethylene, which generates bubbles in the polymer, and stream 5 is the polymer with some dissolved ethylene. In the splitter S, stream 4 is divided into ethylene bubbles that disengage from the polymer phase (stream 6) and ethylene bubbles that remain entrained in the polymer (stream 7). Thus, stream 9 is the total HPS overhead, and stream 8 is the HPS bottom’s polymer with dissolved and entrained ethylene. The cooling flow (stream 10) mixes with the nonentrained ethylene (stream 2). The mixed ethylene (stream 2a) exchanges heat (only) with stream 3 in a fictitious direct-contact heat exchanger X1. Because this exchanger represents the partial thermal equilibration in the HPS and piping downstream of the letdown valve, the stream pressures out of exchanger X1 should be equal to the HPS pressure. The exchanger X1 outlet polymer plus entrained ethylene (stream 3a) goes to flash F2, and the exchanger X1 outlet ethylene phase (stream 2b) mixes with the disengaged ethylene (stream 6). The ad hoc parts of this model are how to set the pressure in flash F1, how to set the split fraction in S, and how to set the heat transferred in X1. The pressure in F1 should be set at a pressure that is below the mixture cloud point by a small amount so that the ethylene-rich stream 2 contains negligibly high polymer. On the basis of the phase diagram for the ethylene/ LDPE system shown in Figure 6, the proper pressure depends only slightly on the reactor effluent polymer fraction, the temperature, and the polymer molecular weight. Using a fixed value of pressure [e.g., 975 bar (0.975 × 108 Pa)] should introduce only a small error, which will be absorbed in the split fraction correlation. Nonequilibrium-Stage Mathematical Model Equations and Correlations The separation efficiency factor Se is defined as the percentage of stream 4 that becomes stream 6. The higher the separation efficiency, the less ethylene that

is entrained as bubbles in the polymer stream leaving the bottom of the HPS. The plant separation efficiency Se for the HPS is typically in the range from 80 to 95%, while the separation efficiency in the LPS is essentially 100%. For the backcalculation of the separation efficiency from plant data (split fraction to stream 6 in splitter S) and the HPS cooling flow, three ASPEN Plus design specifications were needed. The manipulated variables were (1) the HPS cooling flow rate, (2) the heat exchanged in the fictitious exchanger X1, and (3) the split fraction to stream 6. The output parameters to be matched to plant data were (1) the ethylene in stream 8, (2) the temperature of stream 8, and (3) the temperature of stream 9. Buchelli et al.9 defined the separation factor Sf as a dimensionless group that will reflect the values of variables in the HPS influencing the separation efficiency. The separation efficiency Se would be zero at a separation factor Sf of zero and would approach 100% efficiency as the separation factor Sf becomes very large. Therefore, the separation factor Sf is defined from its relation to separation efficiency Se as

Se ) 100(1 - e-Sf)

(1)

Applying fundamental principles of dimensional analysis and taking into account the physics of the problem at hand, Buchelli et al.9 expressed the separation factor as a function of the product of the density ratio and a dimensionless time. This dimensionless time is the ratio of the liquid residence time in the HPS or LPS and the diffusion time required for the ethylene bubbles to travel from the bulk of the fluid to the surface of the liquid pool inside the separator and become disengaged. The separation factor intuitively must increase with increasing residence time in the HPS. We also might expect that the separation factor decreases as the polymer phase viscosity increases because viscous polymer impedes ethylene bubble movement. We also expect that the separation efficiency Se and thus the separation factor Sf increase as the bubble expansion increases.


Figure 11. Plot of the separation factor term Y versus the density ratio term X.

Additionally, the ethylene bubbles will have to be disengaged from the liquid polymer pool in the HPS while traveling upward to the gas-liquid surface inside the HPS or LPS. The required travel time is a function of the liquid level in the separator. Without going into the mathematical derivation and based on dimensional analysis, a correlation equation for the separation factor was proposed by Buchelli et al.9 having the following form:

Sf ) k1(F1/F2 - 1)a(τ/τd)

(2)

After some algebraic manipulations, eq 2 is expressed as a function of the process variables that can be measured in the plant’s separators as follows:

( )( )

F1 -1 Sf ) K F2

a

τT H2η

(3)

where F1 and F2 are the densities of streams 2 and 4, τ is the polymer phase residence time in the separator liquid pool, τd is the ethylene diffusion time in the liquid pool in the HPS or LPS, T is the absolute temperature in the separator, H is the average height of the polymer phase in the liquid pool in the separator, η is the polymer phase viscosity, and K and a are constants to be determined. Given plant measurements, the unknown coefficients in eq 3 can be found from a linear regression of the logarithm of the separation factor term, Y ) SfH2η/Tτ, against the logarithm of the density ratio term, X ) F1/F2 - 1. Determining stream 3a and 2b outlet conditions leaving the direct-contact heat exchanger X1 can be done using a value of UA (heat-transfer coefficient times the heat-transfer area). The heat exchanged in X1 can be determined either by an approach temperature or a UA factor times the logarithmic mean temperature difference. The equation that was proposed by Buchelli et al.9 in this study for UA has the following form:

[

UA ) a(Re × Pr)b ) a

]

4(w2a + w3)Cp πDk

b

(4)

where w is a stream mass flow, the subscripts refer to stream numbers as above, Cp is the heat capacity, D is the pipe diameter, k is the thermal conductivity, and a and b are parameters to be determined. Because the physical properties are not expected to change significantly over typical HPS conditions, eq 4 can be further

simplified to give

UA ) a(w2a + w3)b

(5)

where a and b are parameters to be determined (different from those in equations 3 and 4). The outlet hot stream temperature condition in a cocurrent heat exchanger where UA and the mass flow rates of the streams entering the exchanger are known can be predicted from a differential energy balance according to Bell.10 Using the results for a cocurrent heat exchanger, the outlet stream temperature in the directcontact heat exchanger is given by the following equation:

T3a ) fT3 + T2a + (T3 - T2a) exp[-(1 + f)(UA/w3Cp3)] (6) 1+f where f is given by

f ) w3Cp3/w2aCp2a

(7)

The temperature T2b can be calculated by an overall energy balance in a heat exchanger according to Bell10 as

T2b ) T2a + f(T3 - T3a)

(8)

or based on the plant data obtained from the HPS, on the basis of a temperature approach in a heat exchanger according to Bell,10 T2b becomes

T2b ) T3a - Tapproach

(9)

Results Figures 11-18 show the actual results that were obtained in the modeling of the HPS as a nonequilibrium-stage operation. Figures 11 and 12 show the data reduction of plant measurements used for fitting the parameters (K and a) for the correlation shown in eq 3. The data in Figure 12 show values for the HPS (lower middle part of the graph) and the values for the LPS (upper right-hand side of the graph). The data analysis included both the LPS and HPS systems. This approach was necessary in order to find parameters K and a in eq 3 that would give a correlation that was statistically significant. The correlation coefficient determined in Figure 12 was equal to 0.9788, which is considered adequate.


Figure 12. Logarithmic plot of the separation factor term Y versus the density ratio term X.

Figure 13. Measured versus model-predicted separation efficiencies in HPS using eq 3.

Figure 14. Measured versus model-predicted separation factors in HPS using eq 3.

The plant-measured and model-predicted separation efficiencies and separation factors in the HPS are shown in Figures 13 and 14, respectively. There is some scatter in the data in both instances. The plant-measured separation efficiencies lie in the 80-95% range, while the model-predicted separation efficiencies vary from 60% to over 99%. The discrepancies between plantmeasured and model-predicted values are much smaller in the case of the nonequilibrium model than they are

in the case of the equilibrium base model shown in Figure 8. However, this is not surprising because the nonequilibrium-stage model takes into account process phenomena that are not considered with the equilibrium-stage approach. The plant data for the HPS and LPS that were analyzed and used for developing the separation factor Sf correlation had a lot of noise in them. This may be due, in part, to the error in the measurement of some


Figure 15. Measured versus model-predicted separation factors in HPS using eq 10.

Figure 16. Measured versus model-predicted separation efficiencies in HPS using eq 10.

of the variables that we were trying to correlate. In particular, in the LPS data collection process, the temperature of the LPS had to be assumed constant because there was no temperature indication. The assumed temperature was based on a single manual reading using a temperature gun on a pipe downstream of the LPS. In addition, the flow going into the LPSs is not measured in the data acquisition system. Further, the residual ethylene left in the polymer pellets was assumed to be constant for all of the data points used in the LPS calculations, again because of the absence of routinely measured values. Overall, there were some restrictions and assumptions regarding correct measurement of the process variables in the LPS and HPS.

To obtain a better agreement between the plantmeasured and model-predicted separation efficiencies and separation factors in the HPS, a slightly different form of eq 3 was also fitted to the plant data. A constant term was added to the initial form of eq 3 as follows:

Sf ) B + K

( )( ) F1 -1 F2

a

τT H2η

(10)

Once the correlation parameters (B, K, and a) were determined for the new form of eq 10, the newly calculated and measured separation efficiencies and separation factors were compared. A great improvement between the model-predicted and plant-measured sepa-


Figure 17. Model predictions versus the experimental ethylene fraction for the HPS using separation factors developed via eq 10.

Figure 18. UA versus flow rate in exchanger X1 of the HPS model using equation 5.

ration efficiencies and separation factors is shown in Figures 15 and 16 opposite to those shown in Figures 14 and 13. In Figure 17, the model-predicted ethylene fraction in the HPS bottoms stream compared to the plant measurements shows excellent agreement. This shows that the nonequilibrium-stage approach to the HPS modeling via eqs 1 and 10 results in much better model predictions than the equilibrium-stage approach modeling results shown in Figure 8. Although the data in Figure 11 have some noise, they show the general behavior of the functional groups involved in the definition of eq 3. On the basis of these observations, we feel that for engineering design and simulation purposes, eqs 1 and 10 should do a fair to good job helping to predict the performance of the HPS. Despite these limitations, the information developed herein appears to be the best publicly available knowledge pertaining to the modeling of an ethylene/polyethylene HPS system.

Finally, the data shown in Figure 18 show that in order to adequately model exchanger X1, a fairly constant value of UA should be taken, regardless of the flow conditions going through the fictitious directcontact heat exchanger X1. Further, the data analyzed in the study suggested that, for modeling purposes, the approach temperature (temperature difference between streams 3a and 2b) should be about 1 °C (1 K). Conclusion On the basis of using a single flash at a specified temperature and pressure, the solubility of ethylene in the polymer shows excellent agreement with plantmeasured values for the LPS. This indicates that the parameters chosen in the PC-SAFT EOS were adequate and that the LPS operates at near-equilibrium conditions. However, in the case of the HPS, the ethylene model-predicted solubility showed major deviations from


the plant-measured values. It is apparent that the HPS is not at equilibrium conditions. Mass- and heat-transfer effects in the pipeline bringing the fluid from the reactor outlet into the HPS and HPS hydrodynamic conditions are responsible for its nonequilibrium thermodynamic behavior. An adequate prediction of the HPS performance must include an understanding of the interrelationship between heat- and mass-transfer effects, polymer residence time, operating temperature and pressure, fluid viscosity, and flash separator geometry. Dimensional analysis equations were used to predict separation factors and separation efficiency as a function of the above process and geometric conditions. In this fashion, an improved prediction of the separation behavior in the HPS was obtained. It is important to point out that the equation for the separation factor Sf shown above could be used to predict the performance of the HPS or LPS. The operating performance of the LPS could be predicted using the simpler equilibrium-stage approach because that is sufficiently accurate at the LPS conditions. Nomenclature a ) regressed correlation parameter in eqs 2-5 b ) regressed correlation parameter in eqs 4 and 5 B ) regressed correlation parameter in eq 10 Cp ) heat capacity, J/kg‚K D ) pipe diameter, m f ) ratio of flow capacity terms, given by eq 7 H ) average height of the liquid level in the HPS or LPS, m K ) regressed correlation parameter in eqs 3 and 10 K1 ) constant in eq 2 k ) thermal conductivity, W/m‚K kij ) binary interaction parameter in the PC-SAFT EOS m ) segment number parameter in the PC-SAFT EOS Pr ) Prandtl number Re ) Reynolds number Se ) separation efficiency, defined as the ratio of stream 6 to stream 4 in the HPS model Sf ) separation factor, defined implicitly by eq 1 T ) temperature of a stream, °C (subscripted), or of an HPS vessel, K (unsubscripted) UA ) product of the heat-transfer coefficient and the heattransfer area, W/K w ) mass flow rate, kg/s X ) density ratio term, (F1/F2) - 1 Y ) separation factor regression term, SfH2η/Tτ

/k ) segment energy parameter in the PC-SAFT EOS, K η ) polymer phase viscosity in the HPS or LPS, kg/m‚s F1 ) density of stream 2, kg/m3 F2 ) density of stream 4, kg/m3 σ ) segment diameter parameter in the PC-SAFT EOS, Å τ ) polymer phase residence time in the HPS or LPS, s τd ) ethylene diffusion time in the liquid pool in the HPS or LPS, s

Literature Cited (1) Orbey, H.; Bokis, C. P.; Chen, C.-C. Equation of State Modeling of Phase Equilibrium in the Low-Density Polyethylene Process: The Sanchez-Lacombe, Statistical Associating Fluid Theory, and Polymer Soave-Redlich-Kwong Equations of State. Ind. Eng. Chem. Res. 1998, 37 (11), 4481-4491. (2) Gross, J.; Sadowski, G. Application of Perturbation Theory to a Hard-chain Reference Fluid: An Equation of State for Squarewell Chains. Fluid Phase Equilib. 2000, 168, 183-199. (3) Huang, S. H.; Radosz, M. Equation of State for Small, Large, Polydisperse, and Associating Molecules. Ind. Eng. Chem. Res. 1990, 29, 2284. (4) Sychev, V. V.; Vasserman, A. A.; Golovsky, E. A.; Kozlov, A. D.; Spiridonov, G. A.; Tsymarny, V. A. Thermodynamic Properties of Ethylene; Selover, T. B., Jr., English-Language Edition Ed.; Hemisphere Publishing Corp.: Bristol, PA, 1987. (5) Olabisi, O.; Simha, R. Pressure-Volume-Temperature Studies of Amorphous and Crystallizable Polymers. I. Experimental. Macromolecules 1975, 8 (2), 206-210. (6) 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. (7) Gross, J.; Sadowski, G. Perturbed-Chain SAFT: An Equation of State Based on a Perturbation Theory for Chain Molecules. Ind. Eng. Chem. Res. 2001, 40, 1244. (8) Rousseaux, P.; Richon, D.; Renon, H. Ethylene-Polyethylene Mixture: Saturated Liquid Densities and Bubble Pressures up to 26.1 MPa and 493.1 K. J. Polym. Sci., Polym. Chem. Ed. 1985, 23, 1771-1785. (9) Buchelli, A.; Call, M. L.; Brown, A. L.; Bokis, C. P.; Ramanathan, S.; Franjione, J. Low-Density-Polyethylene Model. Final Report of Equistar Chemicals LP; Chapter 13, Section 5, p 15, Oct 2001. Unpublished results. (10) Bell, K. J. Notes on Process Heat Transfer, Section II, Basic relations for Co-current flow in heat exchangers. School of Chemical Engineering, Oklahoma State University, Stillwater, OK, June 1989.

Received for review March 3, 2003 Revised manuscript received December 12, 2003 Accepted December 17, 2003 IE0302037

Polyethylene Flash Separators

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