Ind. Eng. Chem. Res. 1994,33, 306-310
306
SEPARATIONS Supercritical Antisolvent Fractionation of Polyethylene Simulated with Multistage Algorithm and SAFT Equation of State: Staging Leads to High Selectivity Enhancements for Light Fractions Chang-keng Chen, Marco A. Duran, and Maciej Radosz' Exxon Research and Engineering Company, Annandale, New Jersey 08801
A multistage algorithm coupled with the SAFT equation of state is demonstrated on supercritical antisolvent (SAS) fractionation of a model polyethylene with ethylene and 1-hexene. Staging is found to improve the overall solvent selectivities, especially for lights removal. The degree of improvement increases with decreasing size of lights: the smaller the lights the greater the sensitivity to staging. As for the single-stage fractionation, conditions that favor high solvent densities, e.g., high pressure and low ethylene concentration, usually favor high capacities but low selectivities. The temperature effect, however, is not monotonic.
Introduction Supercritical antisolvent (SAS) fractionation is an extractive process that allows for separating polydisperse mixtures of macromolecules having uniform chemical microstructure into fractions of varying average molecular weight. Typically, the solvent-rich extract contains a low molecular weight fraction (lights) and the polymer-rich raffinate contains a high molecular weight fraction (heavies). In the SAS process, one controls the solvent selectivity and capacity not only with temperature and pressure, but also with solvent composition, by adjusting the antisolvent concentration, as proposed by Radosz (1992). The solvent capacity is defined as the polymer solubility in weight percent, while the solvent selectivity is defined as the ratio of partition coefficients for the separated components, both in the state of phase equilibrium. Chen et al. (1993) developed a block-algebra simultaneous flash algorithm that allows for thermodynamic optimization of single-stage SAS processes. Such an algorithm is crucial because conventional flash algorithms do not converge well for polymer solutions in supercritical fluids. Chen et al. (1993) also quantified the effects of antisolvent concentration, pressure, and temperature on the solvent capacity and selectivity for a polyethylene + ethylene + 1-hexenesystem. They found that high solvent densities favor high capacities but low selectivities. However, they also found that, regardless of the process conditions, the capacity-selectivity relationship can be represented as a single monotonic curve. This means that, for the system studied by Chen et al. (1993), one cannot improve selectivity beyond that read from the capacityselectivity curve, as long as one operates a single-state process. One general way to achieve improvement is to apply the concept of multiple equilibrium stages. The goal of this work, therefore, is to quantify staging effects on fractionation of polyethylene (PE)with supercritical ethylene and 1-hexene. For this, we need a multistage algorithm and a thermodynamic model in the form of an equation of state (EOS). 0888-5885/94/2633-0306$04.50/0
Multistage Algorithm and EOS The multistage fractionation problem, assuming isothermal stages, is to solve a system of material balance, equilibrium, and consistency equations. For example, for two-phase equilibria, we have the following system of equations: material balance:
+
L j - l ~ i j - l Vj+Iyij+l
+ Fjzij - (Lj + U j b i j ( vj + Wj)Yij= 0
(1)
for i = 1, ...,N for j = 1, ...,M
for i = 1, ..., N for j = 1, ..., M consistency:
N
c y i j- 1 = 0
(3)
i=l
5xij-
1= 0
(4)
i=l
for j = 1,...,M where N is the number of species in the mixture and M is the number of theoretical stages in the column. The mass or molar flow rates at stage j are designated as Lj for the lower phase, Vj for the upper phase (vapor,supercritical fluid, or liquid), Fj for the feed stream, and Uj and Wj for the side streams. The weight (or mole) fraction of component i (i = 1, ...,N) at stage j (I' = 1,..., M) is X i j in the polymer-rich phase, y i j in the solvent-rich phase, and z i j in the feed stream. Kij, the separation factor of component i at stage j , K-factor for short, is defined as 0 1994 American Chemical Society
Ind. Eng. Chem. Res., Vol. 33, No. 2, 1994 307 Table 1. Polymer ComDosition on a Solvent-Free Basis. component PE 600 PE l k PE 2k
component PE 3k PE 8k PE 20k
wt%
0.0178 0.118 0.127
Extract
wt%
0.0848 0.0796 0.5724
Polymer Feed High Temperature
The total feed contains 15 wt % polymer and 85 wt % solvent. The solvent is a mixture of ethylene (antisolvent) and 1-hexene (solvent). (I
and hence is a function of temperature, pressure, and composition. The K-factors in eq 2 are calculated from the SAFT equation of state. The SAFT expression of the residual Helmholtz energy, ares, is given by
YiJXii,
=p
f + adisp
(5) where adiaPis the dispersion energy and the reference energy (arel is the sum of the hard-sphere, chain, and association contributions: aref
=
+ achain
+ aaaaoc
(6) A more detailed description of the theory is provided by Huang and Radosz (1990, 1991). In this work, the PE model systems do not exhibit specific interactions that lead to association, thus is set equal to zero. The SAFT pure-component and binary parameters used in this work are the same as those reported by Chen et al. (1993). The system of M X N material balance equations (l), M X N equilibrium equations (2), and 2M consistency equations (3, 4) is treated as a mathematical system of M(2N + 2) nonlinear algebraic equations in the X i j , yij, and Lj unknowns. To solve these equations simultaneously, we use the SAFT equation of state coupled with a multistage algorithm based on an iterative method proposed by Naphtali and Sandholm (1971). Example of Feed Composition and Column Configuration This approach is used to simulate multistage fractionation of P E with a mixture of 1-hexene and supercritical ethylene. Here 1-hexene is the main solvent component whereas supercritical ethylene is an antisolvent. This is an example of a supercritical antisolvent (SAS)separation process proposed by Radosz (1992)for polymeric mixtures. PE, in this case, is a collection of model SAFT molecules and does not mimic any real specific polyethylene. This PE is composed of six pseudocomponents having molecular weights of 500,1000, 2000, 3000,8000, and 20 000; their weight percent is given in Table 1 (k represents 1000). The solvent components and PE are fed countercurrently into a multistage column, as illustrated in Figure 1. As usual, the mixture is allowed to separate into polymer-rich and solvent-rich phases that reach the state of phase equilibrium at each stage. The temperature gradient along the column depends on how the solubility of the polymer pseudocomponents (solvent capacity) varies with temperature. In general, the top of the column should be the low-capacity zone, whereas the bottom of the column should be the highcapacity zone; this will allow for reflux formation. Therefore, in cases where the solvent capacity decreases with increasing temperature, the top of the column should be at lower temperatures. Conversely, in cases where the solvent capacity increases with increasing temperature, the top of the column should be at higher temperatures. In both cases, the extract stream (the solvent-rich phase)
-4
Ethylene t 1 - Hexene
Low Temperature
Rafflnate
Figure 1. Simplified flow diagram of a multistage column for supercritical antisolvent (SAS) fractionation of polymer. The polymer feed enters the column at the top stage while the solvent feed (mixture of ethylene and 1-hexene) enters the column at the bottom stage. The column temperature increases linearly from bottom to top. 20 7.m
0"' 5&104
"
1.0~10~
1.5~10~
CAPACITY, WEIGHT FRACTION
Figure 2. When solvent has high concentration of ethylene, in this case 30 w t % ,increasing temperature increases selectivity (alongthe 2k/3k lines) but decreases capacity (polymer solubility), for a singlestage case. Example at 200 bar, 30 wt % ethylene.
is obtained at the top stage and raffinate stream (the polymer-rich phase) is obtained at the bottom stage. In the example shown in Figure 1, the top of the column is a high-temperature zone. As demonstrated by Chen et al. (1993), this will be applicable to solvents having high ethylene concentration. For example, when our reference solvent has 30 wt 5% ethylene, the capacity decreases with increasing temperature. This is shown in Figure 2 where the selectivity along the 2k/3k lines is plotted versus the solvent capacity at different temperatures. For 30 wt 5% ethylene, the capacity decreases with increasing temperature. The purpose for the multistage column shown in Figure 1is to separate PE lights from P E heavies. The overhead (solvent-rich extract stream) contains the polymer lights, whereas the bottoms (polymer-rich raffinate stream) contains the polymer heavies. In this work, the lights are arbitrarily defined as the polyethylene pseudocomponents with molecular weights equal to or less than 2000. The heavies are defined as the polyethylene pseudocomponents with molecular weights greater than 2000. We will focus on how such a separation of lights from heavies is affected by staging, ethylene concentration, pressure, and temperature.
Staging Effect While partitioning of the heavies is found to be relatively insensitive to staging, partitioning of the lights is found
308 Ind. Eng, Chem. Res., Vol. 33, No. 2, 1994 3.5
I
10 I-
x X
0 X
X A A
-10
%
-20
v
z
-30 -40
-50 u
-60'
"'
0
"
'
4000
1
" " " " " " " '
8OOO
"
12000
""
"
,
"
16000
Figure 3. K-factors increase with increasing number of stages for the light pseudocomponents, but do not increase much for the heavy pseudocomponents. Example at 200 bar, 15 w t % polymer, 30 w t % ethylene, 25C-200 'C.
1.5
1
2
2.5
,9 b 3
2
Figure 6. Increasing extract yield decreases the weight percent of the 2k- fraction (lights with molecular weight (MW) less than 2000) in raffinate. Data obtained from single-stageSAFT simulation. Feed composition is 15w t % polymer. Symbolsof the same type represent the same temperature and pressure, unless otherwise specified, but different weight percent ethylene: 5, 15, 30, 45. The higher the ethylene concentration the lower the extract yield. 3.5
E
0.5
LIGHTS (2k-) IN SOLVENT FREE RAFFINATE, WEIGHT PERCENT
PE MOLECULAR WEIGHT
loooo
0
20000
1
0
[+--8 - - - ......
......p"......"."................
0.1
2
3
4
5
6
7
8
NUMBER OF STAGES
Figure 4. Increasingnumber of stages increasesthe 500/lkselectivity to a much greater extent than the lk/2k and 2k/3k selectivities. Example at 200 bar, 15 wt % polymer, 30 w t % ethylene, 250-200 OC.
to be very sensitive to staging. This is shown in Figure 3 in terms of K-factors (weight basis), plotted as ln(K) versus molecular weight. Here the K-factor is defined as the ratio of the weight fraction of component i (i = 1, ...,N) in the extract stream to that in the raffinate stream, and designated as Ki,e/r. This Ki,e/r is different from Kij which is defined as the ratio of the weight fractions of component i (i = 1, ..., N) in the solvent-rich phase to that in the polymer-rich phase at the same stagej . As shown in Figure 3, the K-factors for the heavies do not vary much as the number of stages increases from two to eight. However, as shown in the inset in Figure 3, the K-factors for the lights can be greatly increased by staging. For example, the K-factor for PE500increases by 2 orders of magnitude when the number of stages increases from one to eight. This will affect selectivity. The selectivity, characterized as the Ki,e/JKjpe/rratio, can be improved by increasing the numbers of stages. However, the extent of improvement will depend on how one defines the lights. This is illustrated in Figure 4. The improvement is most significant for the K(500)lK(1000) selectivity which increases linearly from about 10 for two theoretical stages to more than 1000 for eight stages. As one makes the lights heavier and heavier, e.g., by shifting the focus to the separation along the lkl2k and 2k13k lines, the selectivity improvement due to staging becomes smaller and smaller; the K(lk)/K(2k) and K(2k)lK(3k)
0 0.5 1 1.5 2 2.5 3 LIGHTS (2k-) IN SOLVENT FREE RAFFINATE, WEIGHT PERCENT
Figure 6. Increasing the number of stages from one to four decreases the weight percent of lights (PE 2k-) in raffinate for a given extract yield. The single-stage conditions are the same as those in Figure 5.
curves in Figure 4 are much flatter, but the selectivity improvement due to staging is still significant. A better way to illustrate such an improvement is to consider the total extract yield that is required to reduce the concentration of lights in the raffinate. In general, the goal is to minimize the extract yield for a given concentration of lights in the raffinate. An example of the extract yield dependence on the concentration of 2klights (2k and smaller) in the raffinate that was obtained by Chen et al. (1993) for single-stage extraction of PE with ethylene and 1-hexene is shown in Figure 5. Regardless of the extraction conditions, all the points fall near a single smooth curve illustrating that the extract yield has to increase in order to decrease the 2kconcentration in the raffinate. One expects that improved selectivity will shift the curve down and to the left, toward the lower left corner of Figure 5. This will mean higher raffinate purity (lower 2kpercent) for a given extract yield or lower extract yield for a given raffinate quality. This type of improvement can indeed be accomplished by staging. This is illustrated in Figure 6 on a four-stage case for a separation along the 2k/3k lines. The improvement in this case is especially significant if the goal is to
Ind. Eng. Chem. Res., Vol. 33, No. 2, 1994 309 I
3.5 I
I
4 STAGES
0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 LIGHTS (3k-)IN SOLVENT FREE RAFFINATE, WEIGHT PERCENT
100 100
Figure 7. Increasing the number of stages from one to four has little effect on the weight percent of lights (PE 3k-) in raffinate for agiven extract yield.
150
200
250
300
PRESSURE, BAR
Figure 10. Increasing pressure decreases selectivity (in this case along the 2k/3k lines) for a four-stage column. Example for 15 wt % polymer, 30 wt % ethylene, 250-200 O C , four-stage column.
8 5
-100
E
-200 15
20
25
30
35
40 ETHYLENE WEIGHT PERCENT
45
Figure 8. Increasing antisolvent (ethylene) concentration increases selectivity (in this w e along the 2k/3k lines) for a four-stage column. Example for 200 bar, 15 wt % polymer, 250-200 O C , four-stagecolumn.
"~
-20
-250 0
4000
8000
12000
16000
2oooO
PE MOLECULAR WEIGHT
Figure 11. Increasing pressure increases K-factor for a given molecular weight and decreases the ln(K)versus MW slope, hence decreasesselectivity. Example for 15wt 5% polymer, 30wt % ethylene, 250-200 "C, four-stage column.
'&.
t
-: I,,F!,,, ,
, , , , , , , , , , , ,
,
, , ,
1
2 Id
M l*I
,,,,, ,,,,
oRW%= M = 45
m
-120 0
4000
8000
12000
16000
20000
PE MOLECULAR WEIGHT
Figure 9. Decreasing antisolvent (ethylene) concentration increases K-factors for a given molecular weight and increases the ln(m versus MW slope, hence increases selectivity. Example for 200 bar, 15 wt % polymer, 250-200 "C, four-stage column.
achievehighraffinate purity (low 2k-percent). The degree of improvement is even greater for smaller lights. Conversely, the improvement due to staging becomes negligible if we consider separation along 3k/5k lines. As shown in Figure 7,there is practically no difference between singlestage and four-stage column performance. Therefore, we will use theK(2k)/K(3k)selectivity in a four-stage column to probe the effects of other process conditions.
t 100"'" 460 465
"
"
" " I
470
'
475
.
'
'
480
'
'
'
,
485
' " ' .
490
'
495
TEMPERATURE, kelvin
Figure 12. Increasing temperature at the top of the column, at constant temperature at the bottom of the column, slightly increases selectivity (in this case along the 2k/3k lines). Example for 200 bar, 15 wt % ' polymer, 30 wt % ethylene, four-stage column.
Ethylene Concentration, Pressure, and Temperature Effects In general, the selectivity increases with increasing ethylene concentration. For example, the K(2k)/K(3k) selectivity increases by an order of magnitude in a fourstage column when the ethylene concentration is increased
310 Ind. Eng. Chem. Res., Vol. 33, No. 2, 1994 5 -5 -15 h
i5
5
-25
-35 -45
-55
0
4000
8000
12000
16000
20000
PE MOLECULAR WEIGHT
Figure 13. Increasingtemperature at the top of the column decreases K-factors for a given molecular weight and increases the ln(K) versus MW slope. Example for 200 bar, 15 w t % polymer, 30wt % ethylene, four-stage column.
from 15 to 45 w t 7%,as shown in Figure 8. This is because increasing the ethylene concentration not only decreases K-factors for a given molecular weight but also increases the slope of the ln(K) against PE molecular weight curves, as shown in Figure 9. The selectivity in a four-stage column increases with decreasing column pressure, This is shown in Figure 10, where the K(2k)/K(3k) selectivity decreases from over 20 000 to less than 10 as the pressure increases from 100 to 300 bar. This is because increasing pressure drastically reduces the ln(K) versus molecular weight slope, as shown in Figure 11. By contrast, the temperature dependence, in this case, is very weak. As shown in Figure 12, the K(2k)/K(3k) selectivity only slightly increases with increasing temperature at the top of the column. This is consistent with a weak dependence of the ln(K) versus molecular weight slope shown in Figure 13. These antisolvent, pressure, and temperature effects on polymer fractionation can be qualitatively explained in terms of the solvent density: the fractionation conditions that favor high solvent densities are found to favor high capacities but low selectivities.
fractionation of a model polyethylene with ethylene and 1-hexene. SAFTrelates macroscopic partitioning between the equilibrium phases to microscopic properties, such as molecular size and dispersion energy. The multistage model predicts the effects of multiple theoretical stages. Staging is found to improve the overall solvent selectivities, especially for lights removal. The degree of improvement increases with decreasing size of lights: the smaller the lights the greater the sensitivity to staging. As for the single-stage fractionation, conditions that favor high solvent densities, e.g., high pressure and low ethylene concentration, usually favor high capacities but low selectivities. The temperature effect, however, is not monotonic.
Literature Cited Chen, S.;Economou, I. G.; Radosz,M. Density-tuned Polyolefin Phase Equilibria: 11. Multicomponent Solutions of Alternating Poly(ethylene-propylene) in Supercritical and Subcritical Olefins. Experimental and SAFT Model. Macromolecules 1992,25,3089. Chen, C.; Duran, M. A.; Radosz, M. Phase Equilibria in Polymer Solutions. Block-Algebra,Simultaneous Flash Algorithm Coupled with SAFTEquation of State, Applied to Single-StageSupercritical Antisolvent Fractionation of Polyethylene. Ind. Eng. Chem. Res. 1993,32,3123. Huang, S. H.; Radosz, M. Equation of State for Small, Large, Polydisperse, and Associating Molecules. Znd. Eng. Chem. Res. 1990,29,2284. Huang, S. H.; Radosz, M. Equation of State for Small, Large, Polydisperse, and Associating Molecules: Extension to Fluid Mixtures. Ind. Eng. Chem. Res. 1991,30, 1994. Naphtali, L. M.; Sandholm, D. Multicomponent Separation Calculations by Linearization. AIChE J. 1971, 17, 148. Radosz, M. Supercritical Mixed-Solvent Separation of Polydisperse Polymers. Eur. Pat. Appl. EP489574 A2 10,June 1992;U.S.Serial No. 892,462,now allowed, 1993.
Received for review June 21, 1993 Revised manuscript received October 7, 1993 Accepted October 19, 1993'
Conclusions ~
A multistage model coupled with the SAFT equation of state is demonstrated on supercritical antisolvent (SAS)
~
~~~~
* Abstract published in Advance ACS Abstracts, December 15, 1993.
