Absorption Equilibrium and Kinetis for Ethylene-Ethane Separation with a Novel Solvent Travis A. Reine, R. Brue Eldridge 2004 The University of Texas at Austin Prepared for Presentation at 2004 Annual Meeting/November 7-12/Reative Separations II Unpublished AIChE Shall Not Be Responsible For Statements or Opinions Contained in Papers or Printed in its Publiations Introdution The separation of olefins and paraffins is of primary importane in the hemial industry. The prodution of polymers and other speialty hemials from mono-olefins suh as ethylene requires the olefin to be of extremely high purity (>99.9%). 1 In order to ahieve suh a high degree of separation from the lose boiling point mixture of ethylene/ethane, distillation towers with an enormous number of trays are operated at high pressures and ryogeni temperatures (between -40ºC and -90ºC). At these ryogeni temperatures, losed heat loops are often used with ethylene or propylene as the working fluid. Even with the high level of heat integration present in a modern ethylene unit, the energy expenditure is enormous making up 6.2% of the total yearly energy requirement of all distillation proesses. 2 Despite the high apital and energy osts assoiated with ryogeni distillation, it has remained the dominant tehnology for light olefin/paraffin separations for many years beause of its proven effetiveness and reliability. The method of olefin/paraffin separation ertainly holds an enormous potential for apital and energy ost savings if a more effiient tehnique is developed. Many alternatives have been investigated inluding extrative distillation, absorption, adsorption, and membranes. 3 Chemial absorption possesses the most attrative harateristis of the gas-liquid proesses, but an in-depth study into the equilibrium and kinetis of the absorption of ethylene is laking in the literature. By using a stirred-ell for measuring ethylene uptake, equilibrium and kineti data were aquired for a novel absorption solution omprised of traditional organi solvents and CuCl. Experimental The setup for the autolave experiments is shown in Figure 1 following absorption experimental tehniques ommon in the literature. 4,5 The basi equipment was a 1 gallon, stainless steel vessel used to transfer a known amount of gas into a 500 stainless steel autolave for gas-liquid ontating. The gases used in the autolave experiments were hemially pure grade ethylene (99.5%) and ethane (99.0%) from Air Liquide.
P Magneti Stirrer P Vent C2H4 C or 2 H 4 or C2H6 C 2 H 6 High Pressure Vessel TC TC Vauum N 2 Feed Liq. Feed Gas Cylinder Autolave and Heater Figure 1. Autolave apparatus experimental setup To begin an absorption experiment, a weighed amount of liquid was added to the autolave, and pure gas from the high pressure vessel was added while reording the initial onditions. After the gas was harged, the stirrer was turned on and measurements were taken at very short intervals (i.e. every 10 to 15 seonds). Typial stirrer speeds for the kineti experiments (between 100 and 300 r.p.m.) were muh lower than the equilibrium experiments (between 600 and 800 r.p.m.) beause higher stirrer speeds aused distortions in the flatness of the liquid interfaial area. As the hange in autolave pressure with time dereased due to the system approahing equilibrium, the pressure and temperature readings were taken less frequently. Eventually, a steady ondition was obtained where the pressure no longer hanged as seen in Figure 2 for the pressure reading with time for a partiular experiment. One the final equilibrium onditions were reorded, the stirrer was stopped and the solution was either regenerated or kept for a subsequent absorption or desorption experiment.
200 Partial Pressure Ethylene (psi) 160 120 80 40 0 0 20 40 60 80 100 120 140 Time (min) Figure 2. Pressure profile of a typial ethylene absorption experiment In order to alulate the amount of absorbed gas at equilibrium or at any time during the experiment, the following assumptions were made: (1) The absorption liquid was nonvolatile at the absorption onditions. At ambient temperature the total vapor pressure ontribution of the liquids is less than 0.01 psi. (2) The amount of absorbed gas in the initial liquid was negligible. Comparison of equilibrium results from fresh and regenerated solutions showed this to be a good approximation. (3) There was no gas phase mass transfer resistane. The experiments were performed with pure absorption gases. With these assumptions, a mass balane was used to relate initial moles of gas in the harged autolave with moles of gas in the vapor spae at any given time during the experiment. n = n n (1) absorbed autolave, harged autolave, time V autolave P P n absorbed = (2) R ZT autolave, harged ZT autolave, time The ompressibility, Z, was alulated for eah ondition by the three-parameter Prausnitz and Pitzer orrelation as developed by Smith, Van Ness, and Abbott. 6 Results and Disussion Equilibrium Eah absorption experiment from a partiular gas harge produed an equilibrium value of gas onentration in the liquid at a given gas partial pressure. A ompilation of multiple experiments over a range of gas harges yielded the equilibrium behavior of the absorption gas. Figure 3 shows that the CuCl absorption solution has a muh higher apaity for ethylene than ethane. The trendline through the ethane equilibrium data was fitted with a y-interept of zero, and the R 2 value of the line was 0.996 with a slope of 0.00201 mol (L psia) -1. For physial solubility, the Henry s law onstant an be defined as m = (3) P
where is onentration of the gas in the liquid phase, P is the partial pressure of the gas, and the * supersript refers to the equilibrium ondition. The ethylene in CuCl solution equilibrium data was definitely not desribed by Henry s law; in fat, the solution still had an ethylene apaity over 0.45 M at atmospheri pressure. 1.2 Moles C 2 H x per liter of solution 1.0 0.8 0.6 0.4 0.2 Ethylene in CuCl soln Ethylene in Cu-free soln Ethane in Cu-free soln Ethane in CuCl soln 0.0 0 50 100 150 200 Partial Pressure C 2 H x, psia Figure 3. Ethylene and ethane equilibrium with CuCl and Cu-free solutions In order to determine how muh of the ethylene absorption was due to physial solubility in the liquid, a opper-free solution was prepared with the liquids in the same molar ratio as in the CuCl ase. Comparison of equilibrium data obtained for this solution with ethylene and ethane in Figure 3 showed that the opper-free solution had higher apaity for ethylene over ethane. The ethylene apaity of the opper-free solution was muh lower than the opper ase suggesting that hemial effets were indeed important. Like ethane in CuCl solution, both ethylene and ethane with the opper-free solution showed absorption equilibrium following Henry s law. For ethylene, the R 2 value of the line was 0.993 with a slope of 0.00322 mol (L psia) -1. For ethane, R 2 value of the line was 0.997 with a slope of 0.00245 mol (L psia) -1. With ethane, the opper-free solution demonstrated higher solubility than the CuCl solution; therefore, a salting-out effet was observed. Sine the CuCl solution exhibited a very high olefin apaity, the derease in paraffin solubility due to the presene of the CuCl resulted in a greater improvement in seletivity than if the salting-out had not ourred. Seletivity is defined here as the ratio of ethylene absorbed to ethane absorbed at equilibrium. total seletivity = (4) methane P For the opper-free solution, the ratio of the solubilities of the gases was 1.3, whih was independent of pressure. Taken to muh higher pressures, the liquid eventually beame saturated with the gas, but for gas pressures less than ~150 psia, no deviation from Henry s law was found.
In order to aount for CuCl effets and estimate the degree of physial solubility of ethylene with the opper solution, an analogy with the non-reative ases was used. This tehnique alled the N 2 O analogy in CO 2 absorption is ommonly employed to find the solubility of CO 2 in an amine solution. 7 Usually the CO 2 solubility is found by assuming that the ratio of the solubility of the reative gas (CO 2 ) to the non-reative gas (N 2 O) in a non-reative liquid (water) is the same as the ratio of the solubility of these gases in the reative liquid (amine solution). The opper-free solution referred to with non-cu subsript in the following equation was the non-reative solution in the analogy. methylene non-cu m ethane Cu methylene Cu = (5) methane non-cu ( 0.00322)( 0.00201) mol m ethylene Cu = = 0.00264 (6) 0.00245 L psia In order to suessfully desribe the absorption proess, an equilibrium model was developed based on the simple first-order reation. + + Cu + C H Cu C (7) ( ) 2 4 2H 4 where the equilibrium onstant is defined by [ + Cu ( C 2H 4 K )] eq + [ Cu ][ C H ] = (8) 2 where the ativity oeffiients are negleted here for simplifiation. In fat, for onentrated reative absorption systems, the use of ativity oeffiients is generally superfluous and an lead to substantial errors when alulating equilibrium and rate onstants for different solution ompositions. 8 The onentration of dissolved ethylene in equation (8) is given by using the solubility from equation (6) with equation (3). The onentration of opper:ethylene omplex is found by subtrating the alulated physial solubility from the total ethylene onentration in the liquid for eah equilibrium point. The resulting ethylene absorption was entirely due to hemial omplexation with opper. hemial = total P methylene Cu (9) The onentration of free opper an be found by a total opper balane, and equation (8) an be rewritten as total mp K eq = (10) ( Cu total total + mp )( mp ) where Cu total is the total opper onentration, and m is the alulated Henry s law onstant for the ethylene in opper ase, 0.00264 mol (L psia) -1. Cu total was found by flame atomi absorption to be 1.13 M, but it will be treated as an unknown to allow the model freedom to fit the data. Rearrangement of equation (10) in order to find the unknowns K eq and Cu total yields the following linear equation total = K eq ( total mp ) + ( 1+ K eq Cu total ) (11) mp where the slope is K eq and the y-interept is 1+ K eq Cu total. Figure 4 shows the linear fit to this equation of the equilibrium data points below 100 psia. The R 2 value of the linear fit was 4
0.888 and the value of K eq from the slope of the line was 45.2 L/mol. The alulated value of the total opper onentration was 0.65 M, whih was 58% of the atual value of 1.13 M. 25 20 15 * total mp * 10 5 y = -45.193x + 30.352 R 2 = 0.8875 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 * total - mp * Figure 4. Linear fit for first-order equilibrium model The ethylene absorption from the first-order equilibrium model is shown to fit the data very well in Figure 5. A omparison of the physial and hemial effets is also shown in Figure 5. Examining the total ethylene absorption at pressures over ~40 psia revealed that the slope of the equilibrium data was nearly the same as the alulated physial solubility. As a result, the alulated hemial absorption plateaued around 40 psia at an ethylene onentration around 0.58 M in the liquid. With the hemial absorption reahing an asymptoti limit, the opper solution is fully loaded hemially, and higher pressures result only in inreased physial absorption. Sine the opper onentration was 1.13 M, this would lead to the assumption that about half of the opper in solution partiipates in a 1:1 omplex with ethylene. This ould be a result of oordinating ligand strength that inhibits the ethylene exhange equilibrium or a result of partial degradation of the opper(i) state due to oxidation. Another possibility is that all of the opper(i) is ative and forms a 2:1 omplex with ethylene; however, this theory was disounted from experimental data with other ligands.
1.0 Moles C 2 H 4 per liter of solution 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0 20 40 60 80 100 Partial pressure C 2 H 4, psia Total absorption - first order model Cal. hemial absorption Cal. physial solubility Figure 5. Calulated hemial and physial equilibrium For the opper solution, the seletivity defined by equation (4) was highest at the lowest gas pressures beause the physial solubility effets were dominated by the hemial omplexation effets. At atmospheri pressure, the pure gas seletivity was about 15. At partial pressures over about 40 psia, the seletivity is muh lower due to the fat that the opper sites are beoming saturated while the physially solubility remains unhanged. A tradeoff existed for ethylene absorption and operating pressure suh that higher pressures led to higher ethylene apaity but lower seletivity and lower pressures led to higher seletivity and lower apaity. The maximum ethylene/ethane seletivity was found at vauum pressures, but the low ethylene apaity at low pressures would be prohibitory to optimum proess design. Sine the extent of the hemial effets was observed to be around 40 psia in Figure 5, this ethylene pressure should be the maximum operating partial pressure. Higher seletivities an be realized at lower pressures at the expense of absorption apaity. Kinetis Stirred ells have been used frequently in the literature for gas absorption, and the experimental tehnique of operating the gas and liquid bathwise to obtain kineti information has been demonstrated by Jamal and Meisen 4 and Xu et al. 9 By harging pure absorption gas and reording the pressure derease, investigators have alulated reation oeffiients for appropriate models to fit the experimental data. In a similar manner, this present study ompared the fitting apability of five different kineti models to determine whih model best desribed the experimental data. In developing a kineti expression for ethylene absorption, the film theory is assumed to be valid for the system to simplify the alulations. Dankwerts 8 has shown that for most ases of gas absorption with hemial reation, the simple film theory provides equivalent auray to the other more ompliated models like penetration theory and surfae renewal theory. In order to solve for the onentration of eah omponent in the liquid phase, the following key assumptions about the interfaial and bulk onentrations were neessary as shown shematially in Figure 6.
The interfaial onentration of ethylene in the liquid is given by the physial solubility in equilibrium with the gas phase ethylene pressure. From the alulated Henry s law onstant in equation (6), the unomplexed ethylene onentration at the interfae is given by A, i = m ethylene Cu P (12) where P is the measured pressure, whih is a funtion of time. For simpliity, the omplexation reation (7) is rewritten as k A + B k1, 2 C (13) where k 1 and k 2 are forward and reverse reation rate oeffiients, respetively, A is unomplexed ethylene, B is opper not omplexed to ethylene, and C is the opper-ethylene omplex. The reation is assumed to our exlusively in the film of thikness x L, so that in the bulk of the liquid there is no more reation proeeding. This assumption leads to the requirement that the bulk liquid is in equilibrium. For the kineti experiment, the total onentration of ethylene in the liquid total is the measured value as a funtion time. Sine a model desribing the equilibrium for reation (13) has already been established, equation (10) an be rearranged for the bulk pseudo-equilibrium pressure, P b. This pressure is alled the bulk pseudo-equilibrium pressure beause the vapor-liquid system is not atually at equilibrium, but the bulk liquid is at an equilibrium state due to the assumption that the entire reation ours in the film. After solving the quadrati equation for P b from equation (10), the bulk onentration of A, B, C are given by A, b = methylene Cu Pb (14) B, b Cu total C, b = (15) C, b = total A, b (16) where Cu total is the alulated opper onentration to fit the equilibrium data and not the atual opper onentration. P A P A P A P A P A Gas Phase N A = mp A, i k 1 k 2 N A N B N C A A + B C 0 G/L Interfae Film x L B b C b A b B b A b C b B b Liquid Bulk Figure 6. Shemati of gas-liquid onentrations In order to determine the kineti effets due to hemial reation, the enhanement fator is defined as the ratio of the atual rate of ethylene absorption to the rate for stritly physial absorption.
Robserved Robserved Φ = = (17) R k a physial L ( ) A, i The observed rate of absorption was alulated at all points throughout the experiment based on hange in moles in the gas phase, and the interfaial and bulk ethylene onentrations were found as desribed previously. To ompare the different models used to desribe the kineti behavior, the reation rate oeffiients and any other adjustable parameters were varied until the model fit the observed rate of absorption at the start of the kineti experiment. For the reversible, finite rate reation (13), Onda et al. 10 have developed a method of solution for Φ that an be used to model the absorption rate. The unknown parameters that were adjusted were the forward reation rate oeffiient and the ratio of diffusivities D B /D A and D C /D A. Sine no information was known about the relative diffusivities of the opper-ethylene omplex and the unomplexed opper, the ratios were adjusted simultaneously suh that they maintained equal values to one another. The reation rate oeffiient was found to ounterat the diffusivity ratio suh that a derease in the diffusivity ratio required an inrease in the reation rate oeffiient and vie versa. This relationship is intuitive beause the diffusion of material into and out of the reation film must be balaned by the rate whih material reats in the film. Figure 7 shows the effets of diffusivity ratios of 0.25 and 1 on the fitted reation rate oeffiient (with units of L/mol s) for the finite, reversible model, where the reation rate oeffiients were adjusted until the alulated rate was equal to the observed rate at time = 0 for eah fit. 30 A, b D/D = 0.19, Instan. 10 6 Absorption Rate (mol/s) 25 20 15 10 5 D/D = 0.25, k1 = 5400 D/D = 1, k1 = 550 Observed 0 0 10 20 30 40 50 Time (min) Figure 7. Finite, reversible model fitting parameters The ase where D B /D A = 1 showed the losest fit to the observed experimental data; however, it is more reasonable to assume that the opper speies will have a lower diffusivity than dissolved, unreated ethylene. The instantaneous, reversible model in Figure 7 showed an aeptably good fit to the data while allowing only one value for the diffusivity ratio of 0.19. Using the Wilke-Chang equation to estimate the diffusivities gives a ratio of about 0.25, whih is lose to the value alulated from the instantaneous, reversible model.
Simplifiations to the reversible, finite rate model inluded instantaneous and/or irreversible reation. The form of eah of these simplified models is given in Table 1, and the values of the fitting parameters were found by solutions for the reation rate developed by Dankwerts. 8 These alulated rates from the various models are shown in Figure 8. From Figure 8, all three irreversible models deviated from the experimental data to a greater extent at longer reation times. The reversible models followed the appropriate shape of the experimental data throughout the entire range. The finite, reversible ase at a reasonable diffusivity ratio required a very high reation rate oeffiient (5400 L/mol s); therefore, a good approximation was found with the instantaneous, reversible ase that also showed an exellent fit to the data. Table 1. Reation model form and parameters Type Form D B /D A k Inst., irrev. Pseudo-1st Finite, irrev. Inst., rev. Finite, rev. A + B C 0.17 NA k B A 1 C NA 159 s -1 k1 A + B C 0.25 222 L/mol s A + B C 0.19 NA A + 2 k B k 1, C 0.25 5400 L/mol s 10 6 Absorption Rate (mol/s) 30 25 20 15 10 5 0 0 10 20 30 40 50 Time (min) Figure 8. Comparison of reation kineti models a b d e Inst, irrev Pseudo-1st Finite, irrev Inst, rev Finite, rev Observed Physial a b d e In omparison to the observed data and the reation models, the alulated rate of physial absorption from equation (17) is also shown in Figure 8. At the beginning of the experiment the observed absorption rate was muh higher than the alulated physial absorption rate with an enhanement fator of 3.66. Near the end of the experiment, the observed absorption rate approahed the physial absorption rate leading to enhanement
fators near unity for times over about 40 minutes. At the low stirrer rate used for the kineti experiments, equilibrium was found to require very long times evident by the very slow approah of the experimental absorption rate to zero. After the rate slowed onsiderably (at times over about 40 minutes in Figure 8), the stirrer rate was inreased to aelerate vaporliquid equilibrium. Conlusion The equilibrium and kinetis of ethylene absorption were investigated with the autolave apparatus, and the data was found to show good agreement with a simple reation model that was first-order in ethylene. The equilibrium showed that most of the hemial omplexation took plae at ethylene partial pressures below about 50 psia. Beyond this point, the equilibrium urve showed the same slope as predited by physial solubility alone. The apaity of the opper solution for hemial omplexation was found to be signifiantly lower than the atual onentration of opper(i) ions able to form a 1:1 ethylene-opper omplex. The seletivity of ethylene to ethane absorption was found to be greatest at lower pressures reating a tradeoff with apaity for the optimum absorption pressure. Both high ethylene apaity and high ethylene to ethane seletivity are preferred, but these two effets at in opposite diretions with ethylene pressure. The modeling of the reation kinetis showed the reversible models to exhibit the best fit with the experimental data. Due to the lose fit of the instantaneous, reversible model, the reation was assumed to be very fast, and the diffusivity ratio D B /D A was estimated to be 0.19. Further work that would lend validity to this model would be to experimentally find the diffusivity of the ethylene-free opper(i) speies in solution. Another reommendation for future work is to perform the autolave equilibrium experiment on a sample of a mixed ethylene-ethane stream from an atual industrial proess stream. Repeated experiments should onfirm that the absorption solution is robust enough to handle the impurities present before attempting implementation on a larger sale.
Nomenlature a hemial total Cu total D i k K eq * k L m n N i P R R j T V x L Z Φ interfaial mass transfer area solute onentration in liquid onentration of ethylene in solution solely due to hemial absorption total onentration of ethylene in solution due to both physial and hemial absorption total opper onentration diffusivity of solute i in liquid solution reation rate oeffiient equilibrium onstant physial mass transfer oeffiient Henry s law onstant for physial solubility number of moles molar flux of omponent i pressure gas onstant rate of reation or mass transfer temperature volume length of liquid film where reation and diffusion our ompressibility fator enhanement fator Supersripts and subsripts * denotes equilibrium ondition 1 denotes forward reation rate 2 denotes reverse reation rate A,B,C denotes omponent b denotes bulk ondition denotes interfaial ondition i
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