Simulation and optimization of the separation of Rare Earth Elements

Transcription

1 Abstract Smulaton and optmzaton of the separaton of Rare Earth Elements Carlos Fernández Antón Department of Chemcal Engneerng, Lund Unversty, Sweden December 2012 The subject of ths work was to study the feasblty of the purfcaton of REE va on-exchange chromatography from an ndustral pont of vew. The decson varables were the loadng volume, eluton volume and gradent. The study s based on a feed stock wth manly heavy REE, domnated by Erbum and Ytterbum. The fnal product conssted n separated fractons of REE wth a purty requrement of 99% for the element to retreve. It was concluded that the process s economcally feasble. The producton cost optmzaton showed eght dfferent operaton ponts whch confrmed that the costs ncreased rapdly when the demand on yeld ncreased. Retreve Ytterbum and Thulum mnmzed producton costs, but retrevng Holmum and Erbum was stll possble f the ncrease n producton costs s affordable. Keywords: Rare earth elements, chromatography, smulaton, optmzaton, benefts, producton costs Introducton Rare Earth Elements (REE) are a group of 17 elements, 15 that belong to the chemcal group lanthandes and yttrum and scandum. REE are used nowadays n new technologes such as electroncs devces and mltary applcatons. Even though consumers do not have drect need of REE they are necessary for the producton of end use products, what makes them as demanded as the fnal products for whch they are necessary. The world demand of these elements s ncreasng as well as the purty requrements. Because they have very smlar chemcal structures and propertes REE are dffcult to separate. The most common commercal separaton technque s lqud-lqud extracton but for hgh valued products preparatve onexchange chromatography s also used [1]. The subject of ths work was to study the feasblty of the purfcaton of REE va onexchange chromatography from an ndustral pont of vew. The man objectve was to optmze the separaton process to provde dfferent operaton ponts dependng on the need that the ndustry may have. The decson varables were the loadng and eluton volumes as well as the gradent step of the eluent. The value for these varables was optmzed for each objectve and the other desgn varables had beforehand fxed values. The fnal product conssted n separated fractons of REE wth a purty requrement of 99% for the element to retreve. Each dfferent element had a dfferent sellng prce and was present n a dfferent amount n the feed. Theory The model used throughout the smulatons n ths work was a reacton dspersve model whch descrbes the dsperson and convecton n the moble phase as well as the adsorpton nto the statonary phase [1].

2 Column model The concentraton of each component n the moble phase follow the equaton: 2 C C C Dax vln r (1) 2 ads, t z z where s the concentraton of component n the moble phase, s the dsperson coeffcent and s the lnear velocty of the moble phase and the reacton rate of component defned as: 1 C q rads, (2) t E where s the column porosty (column vod), the concentraton of component adsorbed onto the statonary phase and the total porosty. For the ntrc acd, whch s consdered to be nert, there s no reacton rate on Eq. (1). Adsorpton model The adsorpton model s based n a compettve Langmur sotherm [2] wth moble phase modfer, whch s ntrc acd and affects Henry s constant thus affects the retenton of the REE: REE q q j kkn ( H C (1 ) q ) (5) t q j max, j where s the knetc constant wth an arbtrary value, the maxmum capacty n the statonary phase for component j and s the Henry s constant of component modfed by the acd as follows: H 0, H (6) C acd where s calbrated parameter of component, the calbrated constant of component and the concentraton of ntrc acd. A Drchlet boundary condton descrbes the concentraton at the nlet: ( t,0) (3) C C nlet, where s the concentraton of component at the nlet and s a gven value durng the loadng tme and zero after t. At the outlet of the column,.e. at z=l, where only convectve transport s consdered a von Neumann boundary condton s defned: C ( t, L) 0 (4) z Ths model can descrbe adsorpton and desorpton at dfferent modfer concentratons and dsplacements between the dfferent components. It can also descrbe overloadng and produce stff peaks as results of hgh loadng [3]. Methods Smulaton The smulatons were performed n MATLAB usng the method of lnes where space s dvded nto a set of grd ponts. The number of grd ponts was modfed through ths work between but n most of the cases was set to 50 or 100. The dscretzed model was solved wth the ode15s solver n MATLAB, whch s a BDF mult-step mplct method wth varable order solver for stff ordnary dfferental equatons wth a medum accuracy. In order to speed up the code the lghtest elements, present n extremely low concentratons were merged together n a pool wth ts characterstcs equal to the heavest of the merged elements. The code was wrtten followng the scheme n Fgure 1. Calbraton The calbraton of the model was beyond the scope of the present work even though s a necessary step for the smulaton, so the dfferent parameters such as knetc parameters and column parameters were obtaned from the prevous work of [4] and [5] where lnear experments were conducted to fnd parameters β and H 0 and overload experments to fnd the capacty of the column.

3 Fgure 1. Structure of the code. REEobjectve calculates the value of the objectve functon whle REEsolve and smplefracfast calculate the amount of product wth the 99% purty requrement. REEmodel contans system of dfferental equatons. Auxlary functons perform the Fnte Volume Method 2-pont backward dscretzaton of the frst dervatve and 3-pont central of the second dervatve. Optmzaton The optmzaton method used n the present work s the Pattern Search algorthm due to the non-smooth characterstcs of the problem. Ths method manly conssts on the mnmzaton of an objectve functon through the modfcaton of the value of a set of varables called decson varables. Pattern search s a drect search method for solvng optmzaton problems. Pattern Search method does not requre any nformaton about the gradent of the objectve functon and so they works well on non-dfferentable, stochastc, and even dscontnuous objectve functons. Addtonally Pattern search s also effectve at fndng a global mnmum because of the nature of ts search. The varables are bounded for both prevent unphyscal values such as negatve volumes and unrealstc values. In the present work the decson varables were loadng volume, eluton volume and gradent step. All the other varables were convenently calbrated and ts values known. To study the feasblty of an ndustral process several costs and revenues can be consdered for the calculaton of the benefts. The frst objectve functon was defned as the annual benefts (Eq. 7). B S FC VC RMC (7) Where S s the annual revenue of sellng the product (Eq. 8), FC are the Fxed Costs representng the nvestments to set up the process, such as new equpment, VC are Varable Costs meanng the costs of runnng the process, such as electrcty, solvents and labor (Eq. 9) and RMC are the Raw Materals Costs. S n c REE 1 sellng prce prod (8) where prod s the amount produced of each REE and n c the number of cycles per year. VC (SC V ρ DC V C ) n (9) e e where SC s the steam cost to regenerate the eluent, s the volume of eluent, s ts densty, s the amount of feed charged n the column and s the total amount of REE n the feed. A dfferent approach s to evaluate the producton costs for dfferent product dstrbuton whch led to the second objectve functon (Eq. 10), the producton costs. From ths pont of vew the am s to make the producton as cheap as possble, decdng afterwards a proper sellng prce. The advantage of ths analyss s that the product dstrbuton s much wder, allowng the successful producton of more elements, whch s appealng from a commercal pont of vew. FC 1 DC PC (( SC Vc ) ) (10) REE nc YG prod 1 where FC, SC and DC are as n Eqs 7-9; c V s the total volume used n one cycle and Y G s the global yeld. The parameter ω s ntroduced to force the yeld to be wthn certan values: f f c

4 f yeld threshold (11) 1 f yeld threshold In Eq. (10) fxed costs are dvded per the number of cycles as t was necessary to have ndrectly the tme of operaton taken nto account on the objectve functon. Otherwse the optmzaton would lead to an analytcal chromatograph, whch s unfeasble for the ndustral scale. Results and dscusson Annual benefts optmzaton The benefts functon was optmzed frst for 50 grd ponts and then the soluton refned for 100 grd ponts. The optmum values for the decson varables were obtaned, see Table 1. The chromatogram wth the retreved fractons can be seen n Fgure 2. Table 1 Optmzed values for the decson varables Decson varable Value V load (CV) V eluton (CV) step The results showed that the process can be mplemented wth postve annual benefts wth the gven costs and sellng prces. Due to the composton of the feed, whch has a percentage of Ytterbum hgher than 70%, the optmal operaton ponts conssts n overloadng as much as possble the column n order to retreve as much Ytterbum as possble wthout collectng any other fractons except for Thulum, see Table 2. Table 2 Numercal results for the benefts optmzaton Parameter Value Y G (kg/kg) Y TM (kg/kg) Y Yb (kg/kg) PC/PC mn Ths s caused by several factors, Ytterbum s one of the easest ones to collect as t s the last peak and the separaton wth Thulum s reasonably good, see Fgure 2. The separaton of Thulum on tself s also good, even though no baselne separaton s acheved. Furthermore the sellng prce for Ytterbum s approxmately on the average, whch can lead to hgh benefts, and the sellng prce for Thulum s the hghest one of all the REE. It s mportant to notce that the optmzed process does not wat for the eluton of all the Ytterbum despte the last fractons of Ytterbum would consst on pure Ytterbum. Ths s because t s not worth to wat for the eluton of low amounts, nstead s more benefcal to start the followng batch and perform more cycles per year. Fnally, even though the yearly benefts are maxmzed n ths operaton pont t may be not wse to produce only two elements. Instead t may be more nterestng for a company to have a wder product range whch can modfy dependng on the need of the market. Ths dea justfes the followng studes to analyze the cost of wdenng the product dstrbuton. Producton costs optmzaton The producton costs analyss was based on the dea that the sellng prce was no longer beforehand known but a value that could be negotated wth the potental buyers at the tme of the producton. Ths means that the process was optmzed for dfferent yeld requrements n order to retreve more elements than just Ytterbum and Thulum, see Table 3. Even though after the prevous results t was known that the productvty would decrease followng ths approach, the possblty to wden the range of products was assumed to compensate the lower productvty. The productons costs versus global yeld are represented n Fgure 3. Dfferent composton of the product dstrbuton retreved can be seen n Fgure 4. The producton costs ncrease almost exponentally when a hgher yeld was requred. As expected from the results n prevous sectons unless REE dfferent from

5 Fgure 2 Retreved fractons of the annual benefts optmum operaton pont. Eluent s scaled down 1000 tmes. Ytterbum and Thulum are successfully retreved at a 99% purty. Table 3 Dfferent yeld requrements for the operaton ponts of the producton costs optmzaton pont Ho Er Tm Yb Fgure 3 Normalzed producton costs vs global yeld for the dfferent operaton ponts. Legend n Table 3. Fgure 4 Normalzed amount of product for each operaton pont. Legend n Table 3, global yeld shown n brackets. The amount of Ytterbum s scaled down 50 tmes.

6 Ytterbum were explctly requred they were never retreved n order to mantan productons costs as low as necessary. When Thulum was requred to be produced wth a yeld hgher than 0.85, producton costs ncreased by 81% compared to retrevng only Ytterbum. When a dfferent elements from Ytterbum or Thulum was requred the productons costs ncreased by as much as 482% - 807%, dependng on the requrement. In spte of these ncreases on producton costs most of the dfferent operaton ponts can be operated wth benefts f proper prces are selected for the product. Conclusons Throughout the present work t was confrmed the feasblty of the purfcaton of Rare Earth Elements va on exchange chromatography from an ndustral pont of vew. Through dfferent optmzatons benefts and producton costs have been optmzed, presentng dfferent operaton ponts to proceed wth the process. The frst concluson was that the process s economcally feasble. But the operaton pont for the hghest annual benefts only retreves Ytterbum and Thulum, whch may not be a wde range of products enough, consderng that the feed s a batch wth 15 dfferent REE. Secondly, the producton costs optmzaton showed eght dfferent operaton ponts whch confrmed that the costs ncreased rapdly when the demand on yeld ncreased. The opton to retreve only Ytterbum or Ytterbum and Thulum were stll the most economcal one, but retrevng Holmum and Erbum was stll possble f the ncrease n producton costs s affordable. Durng all the optmzatons t was confrmed that s extremely dffcult to separate the lghter elements from Lanthanum to Dysprosum, as ts separaton would lead to an analytcal chromatography nstead of a preparatve chromatography. In concluson ths study showed that the on exchange chromatography s a feasble separaton operaton on the ndustral scale for the purfcaton of REE whch can be operated to retreve a varable range of products dependng on the expected revenue. References [1] Sato T. Lqud-lqud extracton of rare-earth elements from aqueous acd solutons by acd organophosphorus compounds. Hydrometallurgy. 1989; 22: p [2] Karlsson D, Jakobsson N, Peter Axelsson J, Zacch G, Nlsson B. Usng computer smulaton to assst n the robustness analyss of an onexchange chromatography step. 2005; 1063: p [3] Karlsson D, Jakobsson N, Axelsson A, Nlsson B. Model-based optmzaton of a preparatve on-exchange step for antbody purfcaton. J. Chromatogr. A. 2004; 1055: p [4] Degerman M, Jakobsson N, Nlsson B. Modelng and optmzaton of preparatve reversed-phase lqud chromatography for nsuln purfcaton. J. Chromatogr. A. 2007; 1162: p [5] Max-Hansen M, Ojala F, Kfle D, Borg N, Nlsson B. Optmzaton of preparatve chromatographc separaton of multple rare earth elements. J. Chromatogr. A. 2011; 1218: p