Optimal Operation of the Cyclic Claus Process

Transcription

1 17 h European Symposum on Compuer Aded Process Engneerng ESCAPE17 V. Plesu and P.S. Agach (Edors) 7 Elsever B.V. All rghs reserved. 1 Opmal Operaon of he Cyclc Claus Process Assanous Abufares a and Sebasan Engell a a Process Conrol Lab (BCI-AST), Deparmen of Bochemcal and Chemcal Engneerng, Unversä Dormund, 441 Dormund, Germany, E-mal: a.abufares@bc.un-dormund.de; s.engell@bc.un-dormund.de Absrac The dynamc analyss and opmzaon of he novel cyclc Claus process, a four-sep, one-bed, vacuum swng adsorpve reacor (VSAR) s suded. The paral dfferenal and algebrac equaons descrbng he physcal behavor of he sysem are saed n a dmensonless form. The model equaons are solved usng gproms, and a NLP problem s formulaed o maxmze a performance objecve funcon. A rsqp based opmzaon s used o search for he opmum operang parameers. Snce he reacan feed me s an mporan facor for he effcency of a cyclc process, our work n hs sudy focuses on aanng maxmum reacans feedng me a hgh converson, explorng he opmal desgn and operang parameers for he reacor. Keywords Adsorpve reacor, cyclc Claus process, vacuum swng adsorpve reacor, process opmzaon, adsorben/caalys dsrbuon sraegy. 1. Inroducon and background The cyclc Claus process s a novel process ha combnes he reacon of hydrogen sulfde wh sulfur doxde and he adsorpon of waer vapor n an adsorpve reacor o maxmze converson and o reduce down sream gas mpures. A γ-alumna oxde caalys and a 3A zeole adsorben for he selecve removal of waer from he reacon zone are used n he novel negraed process for he equlbrum lmed Claus reacon [1,,3,4]: H S g SO g = 3 S g + H O g Δ H = 18 kj mol ( ) ( ) ( ) ( ). + n n r m

2 A. Abufares e al The major advanages of hs novel process are reduced capal and operang coss and ncreased energy effcency due o he elmnaon of ner-sage coolers and separaors. In addon, he converson of he exohermc equlbrum lmed Claus reacon s enhanced by affecng he knecs and hermodynamcs of he reacon sysem va he manpulaon of he concenraon profle of he by-produc waer. The mulfunconal reacor concep for he Claus process was proposed by Agar [1]. Hs research group [,3,4,5] conduced expermenal work o assess he feasbly of he developed process and proposed general gudelnes for he dsrbuon of he caalys o adsorben rao on he reacor level. Desorpon was no consdered n hese sudes. Xu, L, and Rodrgues [6] developed a new generalzed sraegy for adsorpve reacor performance enhancemen by conrollng he subsecon wall emperaures. In hs paper, a four-sep one-bed dmensonless model of a vacuum swng adsorpve reacor (VSAR) s presened for he novel cyclc Claus process. A sysemac sraegy s used for he opmzaon of hs novel Claus process akng no consderaon he man varables ha affec he desgn and he operaon of he vacuum swng adsorpve reacor. An overall NLP formulaon of he opmzaon problem of he operang and desgn parameers o maxmze he column producon rae s formulaed and solved. As he soluon of nonlnear, non-convex problems, may depende on he sarng pon, and convergence may be dffcul o esablsh, a wo level approach was chosen. Frs converson and feedng me were maxmzed for subses of he overall degrees of freedom. The soluon obaned was used o nalse he soluon of he full problem.. Mahemacal developmen A sandard Skarsrom 4-sep, one-bed, VSAR cycle consss of: pressurzaon, feed, evacuaon and purge-evacuaon are proposed for he novel cyclc Claus process. The parabolc sysem of equaons descrbng he physcal behavor are normalzed and he followng model resuls. Componens mass balance: ( y P) Dax = L Toal mass balance: P + Q u Fϕ = Reacon rae [3]: s ) ( y P) u s x L ( y PU ) ρc + F(1 ϕ x c s ( UP) r ρc s + ν F(1 ϕ) L x c R xn s r ν R xn + Fϕν ad Q R xn = k1 p y H S yso P k p y H O P

3 Opmal operaon of he cyclc Claus process 3 Adsorpon knecs (LDF model) [3]: Q ))/(y P ))) ((a/c ) y P. 75 H O H O = 6D s /d p( 1/( 1 + (. 75a/(ε pc Momenum equaon: P 18 μ u (1- ε ) = 3 x ε dp p Performance ndces: Converson = L U ( Feed of H S Effluen of H S ) Feed of H (mol/s) (mol/s) S Q) Flux = τ cyc τ1 nc ( y PU ) dτ ; Pr = c u A x= 1 = 1 Flux ( Effluen of H S + Effluen of SO ) x= 1(mol/s) Y mpury = ( Effluen of S + Effluen of H S + Effluen of SO ) x= 1(mol/s) Table 1 shows he sysem boundary condons. Smulaon daa s gven n [,3] Table 1. Boundary condons for dfferen seps x = x = 1 Pressurzaon y = yf, f Feed y = yf, U fsar P f Evacuaon y / x =, Pv Purge y / x =, Pv P = P y / x =, U = UP = y / x =, P = Pf P = y / x =, U = P = = UP = U psar P y, v where: y : molefracon of componen ; u : reference velocy (.1 m/s); p : reference pressure (1135 Pa); T f : bed feed emperaure (53 K); s : cycle sep me (s); Q: normal. sold concenraon; P: normal. pressure; U: normal. velocy; τ: normal. me; x: normal. Lengh, F: phase rao ((1-ε)/ε, wh ε beng column porosy); U fsar, U psar : normal. nersal veloces of feed and purge seps; P v : normal. vacuum pressure; P f : normal. feed pressure; A: area (m ). The model equaons were dscrezed usng orhogonal collocaon on fne elemens (OCFEM, 3, ) and a BDF mehod wh varable sep sze for spaal and emporal dscresaon. A he cyclc seady sae (CSS), he process saes a he sar and a he end of he cycle are dencal. The mass balance a he CSS was consdered as an ndcaon of he numercal accuracy and as a consran for verfcaon of he cyclc seady sae n opmzaon.

4 4 A. Abufares e al 3. Formulaon of he opmzaon problem The effecve cleanng of he adsorben plays a major role n enhancng converson and producng hgh pury produc. If he adsorben regeneraon s no complee, affecs he producon durng he nex sep. The bed s perodcally desorbed usng ner gas N a low pressure. The cycle me, he veloces of he feed and purge seps, he purge pressure, he operang emperaure and he dsrbuon of he adsorben and caalys are he operang and desgn parameers ha affec he performance of he adsorpve reacor. These degrees of freedom were ncluded n an NLP opmzaon problem o maxmze he converson and o deermne he opmal operaon of he VSAR for he cases of unform and non-unform adsorben dsrbuon. The resuls are shown n able. Max(Converson) Κ s.. Ympury Y mpury ; mbcss ε css ; css horzon fnal ; max Κ mn Κ Κ where; Κ non unform { l 1, l, l3, ϕ1, ϕ, ϕ3, T f, Pv, 1,, 3, 4, u fsar, u psar } Κ { ϕ T, P,,,,, u, u } unform, f v where: css : cyclc seady sae smulaon me (s); mb css : relave mass balance error; Pr: producon rae [mol/s]; φ 1, φ, φ 3 : adsorben volume fracon n each zone; l 1, l, l 3 : bed reacon and equlbrum zones lenghs; ε css :.7; Flux : normalzed oupu fluxes a he feed sep; Y mpury : average mpury dry bass; nc: number of componens excludng ner; Κ: vecor of decson varables. Table. Opmzaon resuls for dfferen sold dsrbuons Decson vars T f P v U fsar U psar Nonunform Unform Bounds Mn Max Decson vars φ φ 1 φ φ 3 l 1 l l 3 Nonunform Unform Bounds Mn Max Max converson Nonunforrm = Unform = The opmum parameers resul n a hgh converson and a cleaned bed. I s clear ha boh dsrbuons can provde hgh converson. In addon, he hree fsar psar max

5 Opmal operaon of he cyclc Claus process 5 bed zones had shown ha he wo frs zones have smlar solds dsrbuons whle he rear zone has a hgher value of caalys volume fracon wha can be explaned by a furher mprovemen of he removal of races n hs zone. Snce he reacan feed me s an mporan facor for he effcency of a cyclc process, a long reacan feedng me s he major goal of process opmzaon. In addon, converson of a leas 99.5% s val n hs process. The effec of he feedng me on he producon rae was suded. The opmum feedng me was compued assumng ha all oher varables are kep a her prevously compued opmal values for each case. Μαx (Pr) s.. converson conversonmn ; mbcss ε css ; css horzon fnal Table 3. Aanng maxmum feedng me n each dsrbuon sraegy Sold dsrbuon Dec. var. Opmum Objecve funcon Base case Bounds Non unform [mole/s] Unform [mole/s] [mole/s] 995 As can be seen from able 3, due o he dfferen mechansms of reacon and adsorpon, he caalys and he adsorben should no be equally dsrbued n he bed n order o provde operang condons ha lead o an effcen ulzaon of boh funconales. An opmal operaon of a cyclc adsorpve reacor ha combnes hgh producvy, hgh converson and maxmum feedng me should ake no consderaon all he operang and desgn parameers. The opmzaon degrees of freedom nclude he lenghs of he bed zones, he sold raos n each bed zone, he duraons of each sep, feed and purge veloces, purge pressure, and feed emperaure. These parameers were consdered for opmzaon wh he objecve of maxmzng he bed producon rae whle mananng he hgh converson. Mahemacally: Μαx (Pr) Κ s.. converson converson mn ; mbcss ε css ; css horzon fnal ; L = Lbed mn max Κ Κ Κ ; Κ { l 1, l, l3, ϕ1, ϕ, ϕ3, T f, Pv, 1,, 3, 4, u fsar, u psar } The equaons were formulaed n he gproms (v-3.1) language and he reduced successve quadrac programmng algorhm (rsqp) mplemened n gopt was used [7]. The opmum values were obaned afer 11 NLP eraons and 13 NLP lne search seps, and ook a oal CPU me of seconds. I s obvous from he resuls (Table 4) ha he use of dfferen adsorben

6 6 A. Abufares e al volume fracons and he unng of he bed lenghs resuls n mproved adsorpve reacor performance wh respec o he feedng me. The cycle mes,, 4 resul n a desgn ha enables he connuous operaon of a reacor wh wo beds. Table 4. Opmzaon of producon rae maxmzaon Decson var T f P v U fsar U psar Opmum value Bounds Mn Max Decson var. φ 1 φ φ 3 l 1 l l 3 Opmum value Objecve Funcon Bounds Mn Pr =.19 [mole/s] Max Conclusons and fuure work The opmum desgn of a novel cyclc Claus process vacuum swng adsorpve reacor has been presened. I was found ha he adsorpve reacor can provde enhanced converson by opmzng he adsorben volume fracon n he bed. In addon, opmzaon of he operang and desgn parameers n cyclc adsorpve reacor process resuls n a hgh performance VSAR n erms of feedng me and producon rae. The producon rae can be ncreased by more han wo mes compared o he base case producon rae. In comparson o prevous work, n hs work he bed reacon and equlbrum zones lenghs, sold raos and he operang parameers were ncluded as decson varables n he opmzaon. The relave mass balance error and he cyclc seady sae smulaon me where mplemened as consrans n he Pcard eraons opmzaon. The column performance mprovemen s arbued o he choce of an operang wndow n whch all parameers nerac opmally. Fuure work wll be o develop an effcen conrol sraegy whle mananng maxmum process effcency. References 1. D.W. Agar, Chem. Eng. Sc., 54 (1999) 199. M.P. Elsner, C. Drch, and D.W. Agar, Chem. Eng. Sc., 57 () M.P. Elsner, M. Menge, C. Müller, and D.W. Agar, Caal. Today, 79-8 (3) M.P. Elsner, Ph.D. Dsseraon, Unversy of Dormund, (4) 5. P.S. Lawrence, M. Gruenewald, W. Derch and D.W. Agar, Ind. Eng. Chem. Res., 44 (5). 6. G.h. Xu, P. L and A.E. Rodrgues, Chem. Eng. Sc., 58 (3) M. Oh, and C.C. Paneldes, Compu. Chem. Engng., (1996) 611