Two-phase modelling and simulation of the hydrothermal fractionation of holm oak in a packed bed reactor with hot pressurized water

1 Two-phase modelling and simula ion o he hyd o he mal ac iona ion o holm 1 oak in a packed bed eac o wi h ho p essu ized wa e 2 3 A. Cabeza, F. Sob ón, F.M. Yed o, and J. Ga cía-Se na* 4 5 High P essu e P ocesses G oup, Depa men o Chemical Enginee ing and 6 En i onmen al Tech., Uni e si y o Valladolid, 47011 Valladolid, Spain 7 8 *Co esponding au ho : Tel.: +34 983184934 9 E-mail: jgse[email p o ec ed] (J. Ga cía-Se na) 10 11 Abs ac 12 13 Hyd o he mal ac iona ion has been ho oughly s udied in o de o de elop a 14 sus ainable p ocess o eco e he suga s o he biopolyme s con ained in biomass. 15 Howe e , a physico-chemical model which conside s he main in ol ed physical 16 phenomena, like po osi y a ia ions, has no been ully de eloped. Thus, he objec i e 17 o his wo k was o app oach a mo e ealis ic model han o he ye published, 18 inco po a ing also a no el eac ion pa hway o biomass ac iona ion. I es ablishes 19 ha cellulose and hemicellulose begin hei ac iona ion in he solid, b eaking in wa e - 20 soluble oligome s and suga . Besides, deace yla ion eac ions and insoluble oligome 21 o ma ion om cellulose we e conside ed. Kine ics ollowed he A henius’ law and and 22 i has been demons a ed ha an au oca aly ic kine ic model can be success ully used 23 o simula e he biomass b eaking in soluble oligome s. The p ocess was ca ied ou in 24 a ubula eac o cha ged wi h 5 g o holm oak and con inuously ed wi h ho 25 p essu ized wa e . To assess he mass ans e be ween he solid and liquid, 4 26 olume ic lows (5mL/min, 10mL/min, 20mL/min and 40 mL/min) and wo pa icle 27 diame e s (3mm and 6mm) we e used. In he same way, empe a u e was se be ween 28 175ºC and 207ºC. The la e was he main a iable due o i s e ec in biomass 29 solubili y and kine ics. The model was sol ed by he Runge-Ku a’s me hod wi h 8 h 30 o de o con e gence and i s disc e iza ion was pe o med by a new modi ica ion o he 31 o hogonal colloca ion me hod on ini e elemen s. I was alida ed by i ing o al o ganic 32 ca bon (TOC) wi h Absolu e A e age De ia ion (A.A.D. be ween 16.3% and 55.8%), 33 ace ic acid concen a ion (A.A.D. be ween 44.4% and 84.4%) and pH p o iles (A.A.D. 34 be ween 5.6% and 9.7%). Besides, he mass ans e be ween he solid and he liquid 35 was checked and he de ia ions o he simula ion we e lowe han 8.5%. 36 Keywo ds: Au oca aly ic kine ic, wo-phase simula ion, holm oak, hyd o he mal 37 ac iona ion, packed bed eac o . 38 39 40 41 42 43 44 45 46 2 1. In oduc ion 47 Fo se e al decades pe ol has been used as he main sou ce o ene gy and aw 48 ma e ial. Ne e heless, i is no a sus ainable sou ce and o he op ion will be needed in 49 a nea u u e. One likely op ion would be biomass, and se e al in e na ional ins i u ions, 50 such as he Eu opean Union o he O ganisa ion o Economic Co-ope a ion and 51 De elopmen , ha e shown in e es abou i (King, 2009; OCDE, 2009; O ganisa ion, 52 2011). The gene al idea is o de elop a hyd olysis p ocess o ob ain he suga s p esen 53 in biomass, which will be con e ed in o liquid uels in a ollowing p ocess. In addi ion, 54 he ex ac ion o he biomass phenolic compounds would be in e es ing due o he ac 55 ha hey would be used as aw ma e ial o chemical indus y. Thus, biomass hyd olysis 56 ha e been s udied ho oughly and in di e en ways, such as, enzyma ic hyd olysis, 57 acid o alkaline hyd olysis (Al a ez-Vasco and Zhang, 2013; Cha les e al., 2004; Feng 58 e al., 2012; Gao e al., 2013; Yoon e al., 2014). One o he mos p omising op ion 59 would be he biomass ac iona ion by hyd o he mal p ocesses, as a subc i ical 60 condi ions as a supe c i ical condi ions, because hey can ex ac he main ac ion o 61 hese suga s only using wa e as eac i e (Can e o e al., 2013; Ga o e e al., 2002; M. 62 Se ik Tunc, 2008; Moniz e al., 2013; Pa ajó e al., 2004; Rissanen e al., 2014; Zaka ia 63 e al., 2015). Subc i ical condi ions e e o all empe a u e and p essu e below he 64 c i ical poin and, supe c i ical condi ions, when hey a e beyond i (Figu e 1). Focusing 65 in wa e , subc i ical wa e means a liquid a high p essu e and empe a u e wha 66 p o ide i special p ope ies, such as lowe dielec ic cons an and densi ies (Asl and 67 Khajenoo i, 2013; F anck, 1970; K use and Dinjus, 2007; Teo e al., 2010). 68 69 Figu e 1: Phase diag am o wa e P-T (Asl and Khajenoo i, 2013). p: iple poin , bp: boiling poin , Tc, Pc and ρc: 70 c i ical empe a u e, p essu e and densi y espec i ely. 71 Rega ding modelling, some s udies ha e been pe o med in o de o es ablish a 72 eac ion pa hway and kine ic equa ions o ep oduce he expe imen al beha iou o he 73 hyd olysis eac o s. All o hem conside ha biomass is o med by h ee polyme ic 74 ac ions: cellulose, hemicellulose and lignin. Cellulose and hemicellulose a e suga - 75 based biopolyme s and lignin is an a oma ic biopolyme o med by phenylp opane 76 uni s. Cellulose and hemicellulose a e di e en ia ed by hei s uc u e and composi ion. 77 The o me is a linea polyme cons i u ed by hexoses and he la e is an amo phous 78 and b anched polyme o hexoses and pen oses (Boble e , 1994; P. Ha msen, 2010). 79 The mos ex ended models a e based on i s o de kine ics o cellulose and 80 hemicellulose assuming ha hey decompose in o in e media e oligome p oduc s. 81 These oligome s would con inue a u he bond clea age gene a ing he inal 82 monome ic suga s (pen ose and hexoses). In addi ion, he deg ada ion o hese suga s 83 in o se e al acids can be conside ed (Cha les e al., 2004). 84 3 Sand a Ri as e al. (Ri as e al., 2014) s udied he acidic p ocessing o hemicellulosic 85 saccha ides om pine wood and hey de eloped a monophasic globalised kine ic 86 model wi h i s o de kine ics espec o he biomass. Tha model was sui able o i 87 hei expe imen al da a, R2 be ween 0.975 and 0.998. Sasaki e al. (Sasaki e al., 2002) 88 assessed he kine ic and mechanism o cellobiose (disaccha ide composed by wo 89 glucoses) hyd olysis. This monophasic model again used i s o de kine ics and i 90 could ep oduce he expe imen al beha iou . P onyk and Mazza (P onyk and Mazza, 91 2010) de eloped a kine ic model wi h i s o de kine ics o he hemicellulose hyd olysis 92 om T i icale S awa in a packed bed eac o , aking in o accoun he mass ans e 93 be ween solid and liquid. They assumed ha wo ypes o hemicellulose can be 94 p esen , one easily deg adable and o he ha dly deg adable. They conside ed ha he 95 po osi y o he bed emains cons an du ing he p ocess oo. Jussi V. Rissanen e al. 96 (Rissanen e al., 2014) s udied he ex ac ion o sp uce hemicellulose and hey 97 de eloped a kine ic model which could ep oduce he expe imen al beha iou in a 98 cascade luidised ba ch eac o , using kine ics o n h o de o solid biomass. Mo eo e , 99 hey also conside ed he p o on concen a ion in kine ics (wi h n h eac ion o de oo) 100 because ace ic acid and o he o ganics a e p oduced and sol ed du ing he ex ac ion. 101 The e o e, he e a e se e al models which deal wi h biomass hyd o he mal 102 ac iona ion and hey ha e ob ained good esul s. Howe e , hey a e ocused in 103 hemicellulose o cellulose ac iona ion and no in bo h o hem a he same ime. In 104 addi ion, hey do no conside some obse ed physical phenomena, such as, po osi y 105 changes in a bed eac o o p o ons e ec in all kine ics in liquid phase. 106 Thus, he aim o his a icle was o de elop a new kine ic model o biomass 107 hyd o he mal ac iona ion which could ep oduce he global expe imen al beha iou in 108 he mos ealis ic way as i was possible. T ying o unde s and how his hyd o he mal 109 eac ion akes place and analysing he e ec o he pa icle diame e , ope a ing 110 empe a u e and liquid low a e. So, i was aken in o accoun he e ec o pH, po osi y 111 a ia ions and solubili y o he di e en biomass ac ions in ho wa e (K use and 112 Dinjus, 2007; Mille -Chou and Koenig, 2003; Teo e al., 2010) in a no el eac ion 113 pa hway. The selec ed eac o was a ubula eac o , in o de o s udy he p ocess in a 114 semi-con inuous p ocess, ed wi h ho p essu ized wa e . The s udied biomass was 115 holm oak because i is one o he mos common ees in he sou h o Spain and 116 was es, which could be used as aw ma e ial, a e p oduced each yea du ing i s 117 p uning. Rega ding kine ics, a new o mula ion was inco po a ed oo. An au oca aly ic 118 model is conside ed because i was assessed, in a p e ious s udy abou biomass 119 he mal deg ada ion du ing a he mog a ime ic analysis (Cabeza e al., 2015), ha i 120 can ep oduce he s ong mass changes in biomass a ce ain imes o empe a u es. 121 2. Expe imen al 122 2.1. Ma e ial and me hods 123 2.1.1. Raw ma e ials 124 Holm Oak b anches we e selec ed as s udied biomass because i is one o he main 125 sou ce o woody was es in he sou he n Spain. I was cha ac e ized by he Na ional 126 Renewable Ene gy Labo a o y (NREL) – De e mina ion o S uc u al Ca bohyd a es 127 and Lignin in Biomass- s anda ds. In o de o check he ep oducibili y, he me hod was 128 applied h ee imes. The biomass was d ied and milled in he selec ed diame e s, 3 129 and 6 mm. Ex ac i es we e calcula ed g a ime ically by Soxhle me hod acco ding o 130 he De e mina ion o Ex ac i es in Biomass. The ini ial composi ion o he biomass 131 4 sample is collec ed in Table 1. The alue o he lignin includes he ex ac i e lignin 132 (2.36%) and he acid soluble lignin (1.05%). 133 Table 1: Ini ial composi ion o he holm oak sample 134 Cellulose Hemicellulose Lignin g/g g/g g/g 0.4806 0.2060 0.3134 135 136 All chemicals we e p o ided by Sigma. The eac i e compounds o he HPLC analysis 137 we e: cellobiose (+98%), glucose (+99%), uc ose (+99%), glyce aldehyde (95%), 138 py u aldehyde (40%), a abinose (+99%), 5-hyd oxyme hyl u u al (99%), lac ic acid 139 (85%), o mic acid (98%), ac ylic acid (99%), mannose (+99%), xylose (+99%), 140 le ulinic acid (+99%) and galac ose (+99%). Fo analysis o ca bohyd a es and lignin, 141 sul u ic acid (98%) and calcium ca bona e (≥ 99.0%) we e used. Fo he de e mina ion 142 o ex ac i es n-hexane (95%) was selec ed as sol en . Dis illed wa e was used in all 143 assays. 144 2.1.2. Expe imen al de ice 145 The hyd o he mal ac iona ion p ocess was ca ied ou in a semiba ch eac o cha ged 146 wi h app ox. 5 g o d y holm oak. To a oid pa icle losses wo me allic il e s we e used, 147 which we e loca ed a he op and bo om o he eac o . The eac o (R-01) was a 148 mic o ube model SS316 piping wi h a leng h o 38 cm and an ex e nal diame e o ½ 149 inch. This eac o and a p ehea e (E-02, AISI 316, leng h=200 cm, O.D.=1/8 inch) 150 we e in oduced inside a ch oma og aphic o en HP568 (F-01). The sys em was ed by 151 a Jasco model PU-2080 pump (P-01) and he p essu e was se using a go- 152 backp essu e al e (V-01) o main ain he liquid phase. Aimed a sa ing ene gy, a 153 concen ic ube hea exchange (E-01, 1/4”-3/8”) o 70 cm was ins alled be o e he 154 inpu o en (hea in eg a ion). Finally, a second concen ic ube hea exchange (E-03, 155 1/4”-3/8”) o 15 cm was used o cool he p oduc low down o oom empe a u e (25- 156 30ºC). A p ocess low diag am o he pilo plan is shown in Figu e 2. 157 F-01 T-01 P-01 E-01 V-01 E-03 T-02 P oduc s Cooling wa e Cooling wa e Dis illed wa e R-01 E-02 158 Figu e 2: P ocess low diag am o he pilo plan . T-01: eed 159 wa e ank, P-01: eed pump, E-01: hea eco e , F-01: o en. 160 E-02: eed p ehea e , R-01: packed bed eac o . E-03: coole , 161 V-01: backp essu e al e and T-02: sample ank. 162 5 Samples o he ou pu liquid we e aken om he ank T-02 measu ing pH, o al o ganic 163 con en (TOC) and ace ic acid concen a ion. The solid inside o he eac o was 164 collec ed and quan i ied oo. The analy ical me hods a e desc ibed nex . 165 2.1.3. Solid phase cha ac e iza ion. Lignin and suga con en 166 The solid phase cha ac e iza ion was done ollowing he me hod p o ided by he 167 Na ional Renewable Ene gy Labo a o y (NREL) – De e mina ion o S uc u al 168 Ca bohyd a es and Lignin in Biomass. The e o e, a sample o 300 mg (mi) was ea ed 169 wi h 3 mL o sulphu ic acid (72%) ollowed by an incuba ion o 30 min a 30ºC. Then, 170 84 mL o dis illed wa e we e in oduced and i was incuba ed o one hou a 121ºC. 171 The esul an suspension was il e ed unde acuum, washing wi h dis illed wa e , and 172 d ied a 105ºC o 24 h. Then, he solid was weigh ed (m1) and calcined a 550ºC o 24 173 h and weigh ed (m2) again. So, he acid insoluble lignin would ob ained 174 by (𝑚1−𝑚2)𝑚𝑖 ⁄. The eco e ed liquid was used o ob ain he con en o acid soluble 175 lignin by spec opho ome y, measu ing he abso bance a 320 nm and using he 176 ecommended abso p i i y a a wa eleng h o 30 l· g-1·cm-1. In addi ion, 30 mL we e 177 neu alized wi h calcium ca bona e up o pH=6-7 ollowed by a il e ing using 0.2 µm 178 il e s and inally analysed by high p essu e liquid ch oma og aphy (HPLC). The used 179 HPLC column was SUGAR SH-1011 (Shodex). The mobile phase was a solu ion o 180 0.01N o sul u ic acid and Milli-Q wa e . In o de o ob ain he hemicelluloses, 181 celluloses and deg ada ion p oduc om suga s con en wo de ec o we e used: a 182 Wa e s IR de ec o 2414 (210 nm) and Wa e s dual λ abso bance de ec o 2487 (254 183 nm). 184 2.1.4. Liquid phase cha ac e iza ion 185 The hyd o he mal ac iona ion o biomass gene a es a complex mix u e o suga s and 186 oligome s, which is di icul o analyse. So, an acid hyd olysis was pe o med o 187 con e hese oligome s in o hei monome ic suga s. Samples o 10 mL we e 188 hyd olyzed adding 4 mL o sulphu ic acid and hey we e incuba ed o 30 min a 30ºC. 189 A e , 86 mL o dis illed wa e we e added and he sample was incuba ed o one hou 190 mo e a 121ºC. Then, i was neu alized wi h calcium ca bona e un il pH=6-7 and 191 il e ed using 0.2 µm il e s. Finally, i was analysed by HPLC as explained in he be o e 192 sec ion. 193 In addi ion, he pH and o al o ganic ca bon (TOC) we e measu ed. The pH was 194 de e mined by Nahi a model 903 and he TOC was measu ed by Shimadzu equipmen 195 model TOC-VCSH. The ca bon concen a ion o he s anda d solu ions co esponds o 196 500 mg C/L. 197 2.2. P ocedu e 198 2.2.1. E ec o he olume ic low 199 The e ec o he liquid low was assessed by pe o ming 4 expe imen s a di e en 200 olume ic lows (5 mL/min, 10 mL/min, 20 mL/min and 40 mL/min) o wo in e als o 201 empe a u e, one a ound 180 ºC and ano he a ound 190 ºC. P essu e was main ained 202 a 100 ba g o ensu e he liquid phase o he wa e . The aim was o analyse how he 203 mass ans e is modi ied wi h he in low. 204 2.2.2. E ec o he pa icle diame e 205 6 In o de o s udy how he pa icle diame e a ec s o he p ocess wo diame e s we e 206 used, 3 mm and 6 mm. This pa ame e has impo ance because i a ec s di ec ly he 207 mass ans e and he o e all p ocess due o he changes in he solid po osi y. 208 2.2.3. E ec o he ope a ing empe a u e 209 Expe imen s om 175ºC and 207ºC we e pe o med di ided in h ee se s. One se o 210 h ee cases a ound 180ºC, o he h ee a ound 190ºC and wo a 207ºC. The idea was 211 o analyse how small changes in empe a u e a ec he biomass deg ada ion in e ms 212 o solubili y, as kine ics has been conside ed in o he s udies (Can e o e al., 2013; 213 Rissanen e al., 2014; Sasaki e al., 2002). 214 All he expe imen s and hei ope a ional condi ions a e shown in Table 2. 215 Table 2: Ope a ional condi ions o he pe o med expe imen s 216 Expe imen Ope a ing Tempe a u e Pa icle diame e Real low Ini ial mass Ope a ing ime ºC mm mL/min g min 1 175 3 3.8 5.3124 94 2 207 3 9.6 5.3207 94 3 185 3 17.8 5.3308 94 4 180 3 32.7 5.2603 94 5 190 6 2.4 5.2637 94 6 207 6 9.5 5.4993 94 7 195 6 19.3 5.2520 94 8 180 6 34.9 5.2207 94 217 2.2.4. Model alida ion 218 The aim o he model is o ep oduce he gene al beha iou o he sys em, conside ing 219 empe a u e, low, pa icle diame e , pH and he main biopolyme s and oligome s 220 du ing he eac ion. Fo his eason, he TOC and he pH o each expe imen we e 221 measu ed and i ed. In addi ion, ace ic acid concen a ion in liquid phase was 222 conside ed in he expe imen s wi h a pa icle diame e o 3 mm. The la e was aking 223 in o accoun because his compound would be he main sou ce o p o ons and, o his 224 eason, he basis o he au ohyd olysis. Suga concen a ion in liquid phase was only 225 simula ed in o de o check i he simula ion ag ees wi h he beha iou epo ed by 226 o he au ho s. 227 3. Modelling 228 3.1. Hyd o he mal deg ada ion a subc i ical condi ions 229 Biomass ac iona ion s a s in solid phase wi h hemicellulose and cellulose clea age 230 in o oligome s o dec easing molecula weigh . In bo h cases, a a ce ain polyme 231 leng h hey became wa e -soluble, being solubilised. These solubilised oligome s su e 232 a u he hyd olysis p ocess and hey con inue deg ading in smalle oligome s down o 233 hei espec i e monome s. Finally, hese monome s (mainly educed suga s) can 234 b eak in o se e al deg ada ion p oduc s, such as hyd oxyme hyl u u al, u u al, o mic 235 acid, lac ic acid and o he s (Al a ez-Vasco and Zhang, 2013; Feng e al., 2012). An 236 7 illus a ion o his hyd o he mal deg ada ion wi h he e olu ion o he solid and liquid 237 phase wi h ime and along he eac o is schema ised in Figu e 3. Once he eac o was 238 ed, wa e would s a o deg ade and o sol e biomass. Thus, i is expec ed ha , 239 because o his ex ac ion, he size o he pa icle s a s o dec ease, s a ing in he eed 240 o he eac o . The eac o beha ed like a ixed bed ex ac ion column, hus, solid is 241 deple ed om bo om o op and liquid is mo e concen a ed a he ou le ( op exi in his 242 case). 243 z 244 Figu e 3: Expec ed beha iou in liquid and solid phase 245 inside he hyd o he mal eac o . 246 3.2. Biomass solubili y 247 The solubili y o polyme s in wa e mainly depends on h ee ac o s: molecula weigh , 248 c ys allini y and amoun o ac i e g oups. The highe he c ys allini y and he molecula 249 weigh a e, he lowe he solubili y is. Howe e , concen a ion o ac i e g oups 250 enhances wa e solubili y (Mille -Chou and Koenig, 2003). Cellulose is insoluble in 251 wa e due o i s c ys allini y and i s low ace yla ion deg ee, so only oligome s wi h a 252 e y low molecula weigh would be wa e soluble. Ne e heless, a high empe a u es 253 wa e dielec ic p ope ies ha e a emendous change which could enhance cellulose 254 solubili y (F anck, 1970; K use and Dinjus, 2007; Teo e al., 2010). Fo example, i s 255 ela i e alue changes, a 25 MPa, om 83 a 25 ºC o 43 a 207 ºC, and om 81 o 33 256 a he same empe a u es and 100 ba . In con as , hemicellulose has a lo o ace yl 257 g oups in i s s uc u e and i is amo phous. So, i is expec ed ha hemicellulose 258 oligome s wi h high molecula weigh could be solubilised. On he o he hand, lignin is 259 a complex s uc u e and some pa s could be soluble. 260 3.3. Au ohyd olysis 261 Ano he p ocess ha akes place in he eac o is he deace yla ion o hemicellulose 262 (Ga o e e al., 2002; Pa ajó e al., 2004) and cellulose (Gao e al., 2013), which 263 elease ace ic acid om de solid o he liquid phase. This emission o ace ic acid 264 implies a highe amoun o p o ons in he liquid phase, enhancing he hyd olysis 265 eac ions in his phase. 266 3.4. Reac ion pa hway 267 The eac ion mechanism is shown in Figu e 3.The idea was o de elop a pa hway 268 which would be able o ep esen he main phenomenological s eps o he p ocess, i.e. 269 he biomass solubilisa ion and he suga s o ma ion. To his end, o each cellulosic 270 ac ion wo oligome s we e used, one o ep esen he i s soluble oligome and o he 271 8 o symbolize he las oligome be o e suga p oduc ion, which would co espond o he 272 dime . In addi ion, he deace yla ion o hemicellulose and cellulose we e added. The 273 o ma ion o an insoluble oligome om cellulose was in oduced aimed a aking in o 274 accoun hose cellulose ac ions ha could no decompose in o suga s a he ope a ing 275 condi ions and he cha o ma ion om cellulose polyme . Besides, a p o on 276 consump ion eac ion was in oduced because a he s a o he ope a ion pH 277 inc emen s we e obse ed. So, i is assumed ha ce ain amoun o ino ganic 278 compounds wi h basic beha iou was p esen in biomass. This alue was ini ially ixed 279 a 1% in o de o p o ide enough subs ance o he neu aliza ion bu wi hou dis u bing 280 he ini ial composi ion a lo . The solubilisa ion o cellulose and hemicellulose a high 281 empe a u es was added oo. The o ma ion o deg ada ion p oduc s was no aking 282 in o accoun because i s alue a he ope a ional condi ions was e y low and hey 283 could no be quan i ied easibly. Finally, hexoses (C6) o ma ion om cellulose and 284 hemicellulose was also conside ed. 285 CELLULOSE CELLULOSE OLIGOMER 1 CELLULOSE OLIGOMER 2 CELLULOSE OLIGOMER 3 ACETIC ACID WATER CELLULOSE OLIGOMER 1 CELLULOSE OLIGOMER 2 H+ CELLULOSE OLIGOMER 3 WATER ACETIC ACID SUGARS C6 H+ INSOLUBLE CELLULOSE OLIGOMER CELLULOSE T>195ºC HEMICELLULOSE HEMICELLULOSE OLIGOMER 1 HEMICELLULOSE OLIGOMER 1 H+ WATER HEMICELLULOSE T>195ºC HEMICELLULOSE OLIGOMER 2 HEMICELLULOSE OLIGOMER 2 HEMICELLULOSE OLIGOMER 3 HEMICELLULOSE OLIGOMER 3 H+ ACETIC ACID WATER SUGARS C5 1 39 15 5 2 4 11 10 76 12 814 16 HEAT HEAT HEAT HEAT WATER WATER WATER HEAT HEAT HEAT WATER WATER H+ H+ H+ WATER BASE WATER BASE BASE H+ 13 286 Figu e 4: Reac ion pa hway o he cellulosic ac ion o 287 biomass. 288 3.5. Kine ic model 289 3.5.1. Assump ions 290 In o de o simpli y he modelling he ollowing assump ions we e done: 291  The solid phase is homogeneous and uni o m and i beha es as a whole. Thus, 292 he e a e nei he empe a u e no concen a ion p o iles wi hin he solid along 293 he eac o . 294  The solid po osi y only depends on he o al concen a ion o he solid phase. 295  The e a e no signi ican di usional e ec s in he solid o liquid phase. 296 9  Lignin beha es as an ine , aking as negligible he 2.36% o soluble lignin 297 measu ed. 298  The eac ion o de o all he kine ics is 1 o he biomass compound. In liquid 299 phase, i is also conside ed ha he kine ics depend on p o ons concen a ion 300 wi h o de 1. 301 302 3.5.2. Solid phase balances 303 The model o he ac iona ion used a non-s a iona y mass balance o each compound 304 p esen in biomass assuming ha he concen a ion in he solid could be calcula ed as 305 he p oduc o he liquid equilib ium concen a ion and an equilib ium cons an (𝑪𝑺𝒋=𝑯𝒋· 306 𝑪𝑳𝒋 ∗), see equa ion ( 1 ): 307 𝑑(1−ℰ)·𝐶𝑆𝑗 𝑑𝑡 =𝑟𝑗−𝑘𝑗·𝑎·(𝐶𝐿𝑗 ∗−𝐶𝐿𝑗) ( 1 ) Taking in o accoun ha he po osi y was de ined by equa ion ( 2 ), equa ion ( 1 ) could 308 be ew i en in equa ion ( 3 ). 309 ℰ=1−𝜑·𝐶𝑡 ( 2 ) 310 𝑑𝐶𝑆𝑗 𝑑𝑡 =1 1−ℰ·[𝑟𝑗−𝜑·𝐶𝑆𝑗·𝑑𝐶𝑡 𝑑𝑡 −𝑘𝑗·𝑎·(𝐶𝐿𝑗 ∗−𝐶𝐿𝑗)] ( 3 ) 311 Fo he ine compound he mass balance is shown in equa ion ( 4 ). 312 𝑑(1−ℰ)·(𝐶𝑡−∑𝐶𝑆𝑗 𝑗=𝑁 𝑗=1 ) 𝑑𝑡 =0 ( 4 ) 313 3.5.3. Liquid phase balances 314 In he same way ha in he solid phase, he model was ob ained by he non-s a iona y 315 mass balance o each compound p esen in his phase, see equa ion ( 5 ). 316 𝛿ℰ·𝐶𝐿𝑗 𝛿𝑡 +𝑢 𝐿·𝛿𝐶𝐿𝑗 𝛿𝑧 =𝑟𝑗+𝑘𝑗·𝑎·(𝐶𝐿𝑗 ∗−𝐶𝐿𝑗) ( 5 ) And equa ion ( 5 ) could be ans o med in equa ion ( 6 ) by in oducing he de ini ion o 317 he po osi y, gi en in equa ion ( 2 ). 318 𝛿𝐶𝐿𝑗 𝛿𝑡 =1 ℰ·[𝑟𝑗−𝑢 𝐿·𝛿𝐶𝐿𝑗 𝛿𝑧 −𝜑·𝐶𝐿𝑗·𝑑𝐶𝑡 𝑑𝑡 +𝑘𝑗·𝑎·(𝐶𝐿𝑗 ∗−𝐶𝐿𝑗)] ( 6 ) 319 3.5.4. Kine ics 320 The kine ics o each compound in bo h phases a e gi en by he gene ic exp ession ( 7 321 ). 322 16 12 1.7045 571 0.9821 13 3.3634 1170 0.9843 14 7.0680 1053 0.9803 15 10.1160 3392 0.9129 16 2.3708 1516 0.9800 476 Table 5 and Figu e 12 show he alues o he accele a ion ac o s which we e di e en 477 o m ce o. β1,Co1 and β2,Co2 inc eased hei alues wi h empe a u e and low. Which was 478 expec ed because hey we e used o simula e he biomass b eaking in o oligome s o 479 dec easing molecula weigh . And, i empe a u e o low a e inc eased, his b eaking 480 would be mo e ab up . So, highe accele a ion ac o would be needed. On he o he 481 hand, β11,Co1, β11,Co2, β15,Co1 and β15,Co2 showed he opposi e beha iou . This could be caused by 482 he ac ha hey we e used o simula e he e ec o he biomass deg ada ion in ace ic 483 acid p oduc ion. So, wi h highe empe a u es and lows, he eleasing would be as e . 484 I is ema kable ha β11,Co1, β11,Co2, β15,Co1 and β15,Co2 ha e he same alues. This was caused 485 by he ac ha all o hem ep esen he ace ic acid o ma ion. 486 Table 5: Accele a ion ac o s. 487 Expe imen β1,Co1 β2,Co2 β11,Co1 β11,Co2 β15,Co1 β15,Co2 1 2.2 9.0 11.0 11.0 11.0 11.0 2 3.0 10.5 7.0 7.0 7.0 7.0 3 4.0 12.0 4.5 4.5 4.5 4.5 4 3.5 11.0 4.0 4.0 4.0 4.0 5 2.5 10.0 10.0 10.0 10.0 10.0 6 3.0 10.5 7.0 7.0 7.0 7.0 7 4.1 12.5 4.0 4.0 4.0 4.0 8 3.5 11.0 3.8 3.8 3.8 3.8 Co1: cellulose; Co2: hemicellulose. 488 489 490 Figu e 12: Accele a ion ac o s e olu ion. β11,Co1 was only 491 ep esen ed because i had he same alues ha β11,Co2, 492 β15,Co1 and β15,Co2. 493 494 17 4.2.2. Mass ans e pa ame e s 495 Table 6 collec s he calcula ed alues o he equilib ium cons an s o he soluble 496 componen s a he s udied empe a u es. The ela ion wi h empe a u e was con i med 497 as linea by a eg ession analysis whose coe icien R2 was e e g ea e han 0.9507 498 (Figu e 13). I is ema kable ha compound 1 and 2 (cellulose and hemicellulose 499 espec i ely) would s a o sol e a empe a u es g ea e han 195ºC. This could be 500 explained by changes in he pola i y o he wa e wi h empe a u e. 501 Table 6: Equilib ium cons an s (dimensionless) be ween solid and liquid phases. 502 T Co1 Co2 Co3 Co4 Co5 Co6 Co10 Co12 1 Co13 ºC 190 0.00 0.00 0.34 0.40 0.34 0.52 3.50 0.15 0.08 175 0.00 0.00 0.10 0.15 0.10 0.30 2.00 0.03 0.05 195 0.15 0.10 0.40 0.48 0.40 0.58 4.00 0.20 0.09 185 0.00 0.00 0.24 0.27 0.24 0.36 3.00 0.09 0.07 180 0.00 0.00 0.13 0.16 0.13 0.30 2.50 0.06 0.06 207 0.50 0.45 0.52 0.63 0.52 0.72 4.80 0.28 0.12 R2 - - 0.9724 0.9715 0.9724 0.9507 0.9902 0.9886 0.9963 Co1: cellulose; Co2: hemicellulose; Co3: cellulose oligome 1 ( i s oligome soluble om 503 cellulose); Co4: hemicellulose oligome 1 ( i s oligome soluble om hemicellulose); Co5: 504 cellulose oligome 2 (las oligome om cellulose be o e suga p oduc ion); Co6: 505 hemicellulose oligome 2 (las oligome om hemicellulose be o e suga p oduc ion); Co10: 506 ace ic acid; Co12: hemicellulose oligome 3 (deace yla ed oligome om hemicellulose); 507 Co15: cellulose oligome 3 (deace yla ed oligome om cellulose); Co13: base (ino ganic 508 compound). 1Compound 12 and 15 had he same equilib ium cons an . 509 510 511 Figu e 13: Equilib ium cons an e olu ion wi h empe a u e. 512 Compound 5 and 15 we e no showed because hey had he 513 same equilib ium cons an ha compound 3 and 12 514 espec i ely. 515 516 Table 7 and Table 8 shows he calcula ed mass ans e coe icien s (mul iplied by he 517 speci ic exchange a ea) ob ained om he adjus men s. Table 7 ha e he pa ame e s 518 wi h a pa icle diame e o 3 mm and Table 8 wi h a pa icle diame e o 6 mm. The 519 necessi y o use wo se s o pa ame e s would be explained by he ac ha he 520 18 exchange a ea depends on he pa icle diame e . In addi ion, i was checked he 521 ela ion be ween hem and he liquid low. And i esul ed as linea wi h R2 highe han 522 0.9434. The changes o hese mas ans e coe icien s a e ep esen ed in Figu e 14 523 and Figu e 15 o 3 mm and 6 mm espec i ely. 524 Table 7: Mass ans e coe icien s (min-1 ·102) wi h a pa icle diame e o 3mm. 525 Q Co1 Co2 Co3 Co4 Co5 Co6 Co10 Co121 Co13 mL/min 3.8 0.0 0.0 2.6 15 2.6 22 200 1.5 0.9 9.6 1.1 1.1 3.0 18 3.0 25 220 1.6 1.2 17.8 0.0 0.0 4.0 20 4.0 27 340 1.8 1.5 32.7 0.0 0.0 8.0 26 8.0 37 500 2.1 2.0 R2 - - 0.9434 0.9905 0.9434 0.9795 0.9825 0.9980 0.9923 Co1: cellulose; Co2: hemicellulose; Co3: cellulose oligome 1 ( i s oligome soluble om 526 cellulose); Co4: hemicellulose oligome 1 ( i s oligome soluble om hemicellulose); Co5: 527 cellulose oligome 2 (las oligome om cellulose be o e suga p oduc ion); Co6: hemicellulose 528 oligome 2 (las oligome om hemicellulose be o e suga p oduc ion); Co10: ace ic acid; Co12: 529 hemicellulose oligome 3 (deace yla ed oligome om hemicellulose); Co15: cellulose oligome 530 3 (deace yla ed oligome om cellulose); Co13: base (ino ganic compound). 1Compound 12 and 531 15 had he same mass ans e coe icien . 532 533 Table 8: Mass ans e coe icien s (min-1 ·102) wi h a pa icle diame e o 6 mm. 534 Q Co1 Co2 Co3 Co4 Co5 Co6 Co10 Co121 Co13 mL/min 2.4 0.0 0.0 2.4 14 2.4 20 180 1.4 0.8 9.5 1.0 1.0 2.5 15 2.5 24 215 1.5 1.1 19.3 1.5 1.5 4.5 16 4.5 30 350 2.0 1.5 34.9 0.0 0.0 8.2 18 8.2 38 520 2.3 2.0 R2 - - 0.9522 0.9978 0.9522 0.9984 0.9868 0.9583 0.9956 Co1: cellulose; Co2: hemicellulose; Co3: cellulose oligome 1 ( i s oligome soluble om 535 cellulose); Co4: hemicellulose oligome 1 ( i s oligome soluble om hemicellulose); Co5: 536 cellulose oligome 2 (las oligome om cellulose be o e suga p oduc ion); Co6: hemicellulose 537 oligome 2 (las oligome om hemicellulose be o e suga p oduc ion); Co10: ace ic acid; Co12: 538 hemicellulose oligome 3 (deace yla ed oligome om hemicellulose); Co15: cellulose oligome 539 3 (deace yla ed oligome om cellulose); Co13: base (ino ganic compound). 1Compound 12 and 540 15 had he same mass ans e coe icien . 541 542 Figu e 14: Mass ans e coe icien s e olu ion wi h liquid 543 low o a pa icle diame e o 3 mm. Compound 5 and 15 544 19 we e no showed because hey had he same mass ans e 545 coe icien ha compound 3 and 12 espec i ely. 546 547 Figu e 15: Mass ans e coe icien s e olu ion wi h liquid 548 low o a pa icle diame e o 6 mm. Compound 5 and 15 549 we e no showed because hey had he same mass ans e 550 coe icien ha compound 3 and 12 espec i ely. 551 4.3. Simula ed beha iou 552 As i was men ioned in pa 3.7, a simula ion o he solid and liquid phase was 553 pe o med in o de o compa e i wi h he expe imen al beha iou showed by o he s 554 au ho s. In Figu e 16 i is shown he b eaking o cellulose in solid phase o he i s 555 expe imen . I can be obse ed ha he cellulose would decompose i s in o he i s 556 soluble oligome which would b eak in o he las oligome be o e he suga o ma ion. 557 In addi ion, his las oligome would b eak in o ace ic acid and a deace yla ed oligome . 558 In pa allel, he o ma ion o insoluble oligome would ake place oo. A he end o he 559 ope a ion, cellulose would be p esen only as oligome s and he a ia ion o he 560 cellulose mas would be o 29%. Hemicellulose b eaking was simula ed oo. The 561 beha iou was simila o he cellulose bu he a ia ion o he concen a ion was highe 562 (86%). The 14% o hemicellulose ha emained in solid would be as deace yla ed 563 oligome due o hei lowe solubili y. 564 565 Figu e 16: Cellulose b eaking in solid phase. Co1: cellulose; 566 Co3: cellulose oligome 1 ( i s oligome soluble om 567 cellulose); Co5: cellulose oligome 2 (las oligome om 568 cellulose be o e suga p oduc ion); Co15: cellulose oligome 569 3 (deace yla ed oligome om cellulose); Co17: insoluble 570 cellulose oligome . 571 20 572 Figu e 17 shows he simula ion o he hemicellulose oligome s decomposi ion in liquid 573 phase o he expe imen 1. I is ema kable ha he main pa o biomass is ex ac ed 574 as oligome and ha a he end o he p ocess, only suga s would be ob ained. 575 576 Figu e 17: Hemicellulose oligome s b eaking in liquid phase. 577 Co4: hemicellulose oligome 1 ( i s oligome soluble om 578 hemicellulose); Co6: hemicellulose oligome 2 (las oligome 579 om hemicellulose be o e suga p oduc ion); Co7: Suga s 580 C6; Co8: Suga s C5; Co12: hemicellulose oligome 3 581 (deace yla ed oligome om hemicellulose). 582 The simula ions o he es o he expe imen s we e pe o med oo. The maximum 583 con e sion o hemicellulose and cellulose was achie ed in he expe imen 2, 94% and 584 61% espec i ely. These esul s would be expec ed because i was done a he highes 585 empe a u e (207ºC) and wi h he lowes pa icle diame e (3mm). In addi ion, i 586 con i ms he idea o empe a u e is he main p ocess a iable, which was also exposed 587 in he sec ion 4.1. 588 Hemicellulose esul s ag ee wi h he beha iou epo ed by o he au ho s. M. Se ik 589 Tunc e al. (M. Se ik Tunc, 2008) s udied he hyd o he mal ac iona ion o ha dwood 590 biomass a 150ºC o 500 min. They ound ha cellulose was no ex ac ed a any ime 591 and ha a ound 67 % hemicellulose was eco e ed a 500 min (23% a 100 min). In 592 addi ion, hey epo ed ha he main o he ex ac ed biomass was as oligome and ha 593 a he end o he p ocess only monome s we e ob ained. Ca l P onyk e al. (P onyk and 594 Mazza, 2010) assessed he hyd o he mal ac iona ion o i icale s aw also a 150ºC 595 and hey ob ained simila esul s o M. Se ik Tunc e al. Jussi V. Rissanen e 596 al.(Rissanen e al., 2014) analysed he hemicellulose ex ac ion om sp uce om 597 120ºC o 170ºC, eco e ing 80% o hemicellulose a 170ºC wi h an ope a ing ime o 50 598 min. Rega ding cellulose, he calcula ed yields we e highe han he epo ed by o he 599 au ho s. Mohd Ra ein Zaka ia e al.(Zaka ia e al., 2015) ob ained yield a ound 15% a 600 180ºC and 23% a 210ºC (bo h a e 10 min o ope a ion in ba ch eac o ). Pa ícia 601 Moniz e al.(Moniz e al., 2013) pe o med expe imen s also in a ba ch eac o and he 602 ex ac ion o cellulose a 170ºC was 6.2% and a 200ºC 9.8%. These disc epancies 603 could be explained by he ac ha ou sys em was a semi-con inuous p ocess, which 604 could enhance mass ans e and cellulose b eaking, wi h ope a ing ime longe han 605 10 min (94 min). Besides, he pH su e ed a ia ions du ing he p ocess in ou eac o 606 which could enhance he cellulose ac iona ion. The pH dec eased down o 3.65 in he 607 expe imen 1 and un il 3.78 in he expe imen 2. In addi ion, i was less han 4 om 34 608 min o 94 min o he o me and lowe han 4.5 om 24 min o 94 min o he la e . 609 21 Mo eo e , he o al amoun o hemicellulose in he sample was a ound 1g and he 610 measu ed ex ac ed mass was be ween 1.6 g and 2.8 g (Figu e 5). So, a conside able 611 amoun o cellulose should be ex ac ed. 612 Finally, he mass balance be ween he solid and liquid phase was checked. Table 9 613 a ays he alues o he inal mass in he solid a e he ex ac ion calcula ed by 614 simula ion and he expe imen al da a. The disc epancies a e lowe han 8.5%. Besides, 615 he a e age di e ence be ween he simula ed and expe imen al inal mass was 0.1189 616 g and he a e age soluble lignin was 0.1253 g. The e o e, he main pa o hese 617 di e ences (and o he TOC de ia ions) would be caused by his soluble lignin 618 conside ed as ine . 619 Table 9: Compa ison be ween he simula ed and expe imen al inal mass in he solid. 620 Expe imen m eal msim Disc epancy g g % 1 3.5656 3.6333 1.90 2 2.5278 2.7324 8.09 3 2.9585 3.0238 2.21 4 2.8148 2.8345 0.70 5 2.8736 3.1070 8.12 6 2.6857 2.8498 6.11 7 2.6739 2.7401 2.48 8 2.7061 2.8366 4.82 621 5. Conclusions 622 A kine ic model o he wo-phase simula ion o he hyd o he mal ac iona ion o holm 623 oak has been de eloped. The kine ic cons an s ollow he A henius’ law and he mas 624 ans e coe icien s and equilib ium cons an ha e a linea dependency wi h low and 625 empe a u e espec i ely. This model can ep oduce he TOC, pH and ace ic acid 626 concen a ion wi h ela i e low di e ences. The de ia ions a e be ween 16.3% and 627 55.8% o he TOC, be ween 5.6% and 9.7% o he pH and be ween 44.4% and 84.4% 628 o he ace ic acid. Besides i is able o simula e he beha iou in solid and liquid phase 629 in ag eemen wi h he expe imen al da a epo ed by o he au ho s. The mass balance 630 be ween he solid and he liquid was calcula ed wi h de ia ions lowe han 8.5%, which 631 a e mainly caused by he ac ha soluble lignin is no conside ed. I is ema kable ha 632 cellulose ex ac ion is much highe han expec ed. Howe e , his esul can be 633 explained by he ac ha he sys em is a semi-con inuous p ocess wi h high ope a ing 634 imes and a s ong d op o he pH. Mo eo e , he main pa ame e s ha could a ec 635 mass ans e , e. g. pa icle diame e , olume ic low and empe a u e, a e s udied. 636 Being empe a u e he mos impo an o hem. I would be in e es ing in a u u e wo k 637 o in oduce he deg ada ion p oduc o ma ion in he model and he eleased suga s. 638 Un o una ely, ha would equi e o inc ease he numbe o i ings pa ame e e en 639 mo e. The e o e, ano he app oach should be conside ed o pe o m a mo e de ailed 640 s udy. The bes op ion would be a pobla ional model in which ac i a ion ene gies and 641 solubili y o he oligome s we e unc ion o hei molecula weigh . 642 Acknowledgemen s 643 644 22 The au ho s acknowledge he Spanish Economy and Compe i i eness Minis y, 645 P ojec Re e ence: ENE2012-33613 and he egional go e nmen (Jun a de 646 Cas illa y León), P ojec Re e ence: VA330U13 o unding. Ál a o Cabeza 647 would like o hank o he Spanish Minis y o Educa ion Cul u e and Spo s, 648 aining p og am o uni e si y p o esso s ( e e ence FPU2013/01516) o he 649 esea ch aining con ac . 650 Nomencla u e 651 652 Ac onyms 653 654 Co1: Cellulose. 655 Co2: Hemicellulose. 656 Co3: Cellulose oligome 1 ( i s oligome soluble om cellulose). 657 Co4: Hemicellulose oligome 1 ( i s oligome soluble om hemicellulose). 658 Co5: Cellulose oligome 2 (las oligome om cellulose be o e suga p oduc ion). 659 Co6: Hemicellulose oligome 2 (las oligome om hemicellulose be o e suga 660 p oduc ion). 661 Co7: Suga s C6. 662 Co8: Suga s C5. 663 Co10: Ace ic acid. 664 Co12: Hemicellulose oligome 3 (deace yla ed oligome om hemicellulose). 665 Co13: Base (ino ganic compound). 666 Co15: Cellulose oligome 3 (deace yla ed oligome om cellulose). 667 Co17: Insoluble cellulose oligome . 668 TOC: To al O ganic Con en . 669 A.A.D.: A e age absolu e De ia ion. 670 671 Subindex and supe index 672 673 pH-SIM: Simula ed pH. 674 pH: Expe imen al pH. 675 TOC-SIM: Simula ed TOC. 676 TOC: Expe imen al TOC. 677 [Ace ic acid]-SIM: Simula ed ace ic acid concen a ion. 678 [Ace ic acid]: Expe imen al ace ic acid concen a ion. 679 G eek le e s and symbols 680 23 681 ℰ: Po osi y o he bed, dimensioless. 682 𝐶𝑆𝑗: Cocne a ion o he compound “j” in he solid phase, mg/L. 683 𝑟𝑗: Reac ion a e o he compound “j”, mg/min·L. 684 𝑘𝑗·𝑎: Mass ans e coe icien mul iplied by he speci ic exchange a ea, min-1. 685 𝐶𝐿𝑗 ∗: Equilib ium concen a ion o he compound “j” in liquid phase, mg/L. 686 𝐶𝐿𝑗: A e age concen a ion o he compound “j” along he eac o in liquid phase, mg/L. 687 𝐻𝑗: Equilib ium cons an be ween he solid and he liquid, dimensionless. 688 𝐶𝑡: To al concen a ion in he solid, mg/L. 689 𝜑: Rela ion ac o be ween po osi y and he o al concen a ion in solid phase, 690 dimensionless. 691 𝐶𝐿𝑗: Concen a ion o he compound “j” in he liquid phase, mg/L. 692 Ф𝑖,𝑗: S oichiome ic coe icien o he compound “j” o he eac ion “i”, mg. 693 𝑟𝑖: Reac ion eloci y “i”, mg/min·L. 694 𝛼𝑖,𝑗: Ini ial eloci y ac o o he compound “j” in he eac ion “i”, dimensionless. 695 𝛼𝑖,𝐶𝑒𝑙: Ini ial eloci y ac o o cellulose in he eac ion “i”, dimensionless. 696 𝛼𝑖,𝐻𝑐𝑒𝑙: Ini ial eloci y ac o o hemicellulose in he eac ion “i”, dimensionless. 697 𝛽𝑖,𝑗: Accele a ion ac o o he compound “j” in he eac ion “i”, dimensionless. 698 𝛽𝑖,𝐶𝑒𝑙: Accele a ion ac o o cellulose in he eac ion “i”, dimensionless. 699 𝛽𝑖,𝐻𝑐𝑒𝑙: Accele a ion ac o o hemicellulose in he eac ion “i”, dimensionless. 700 𝑘𝑖: Kine ic cons an , mg-1·min-1. 701 𝐶𝑓𝑗: Concen a ion o he compound “j” in he phase “ ”, mg/L. 702 𝐶𝐶𝑒𝑙: Concen a ion o cellulose in he solid phase, mg/L. 703 𝐶𝐻𝑐𝑒𝑙: Concen a ion o hemicellulose in he solid phase, mg/L. 704 𝐶𝑆𝐿𝑂: Concen a ion o he las oligome be o e suga p oduc ion ( om hemicellulose o 705 cellulose) in he solid phase, mg/L. 706 𝑢: Liquid eloci y in he eac o , m/min. 707 𝑁: Numbe o compounds, dimensionless. 708 𝑛𝑟𝑒𝑐: Numbe o eac ions, dimensionless. 709 𝐿: Leng h o he eac o , m. 710 𝑧: Coo dina e along he leng h o he eac o , dimensionless. 711 𝑡: Ope a ing ime, min. 712 24 𝑥𝑖𝐸𝑋𝑃: Expe imen al alue o he i ed a iable. 713 𝑥𝑖𝑆𝐼𝑀: Simula ed alue o he i ed a iable. 714 𝑜: To al numbe o expe imen s, dimensionless. 715 𝑘: P e-exponen ial ac o o he kine ic cons an , mg-1·min-1. 716 𝐸𝑎/𝑅: Ac i a ion ene gy, K. 717 𝑅2: Coe icien R2, dimensionless. 718 𝑇: Ope a ing empe a u e, ºC. 719 𝑚𝑟𝑒𝑎𝑙: Final solid mass, g. 720 𝑚𝑠𝑖𝑚: Simula ed inal solid mass, g. 721 722 Lis o igu es 723 Figu e 1: Phase diag am o wa e P-T (Asl and Khajenoo i, 2013). p: iple poin , bp: 724 boiling poin , Tc, Pc and ρc: c i ical empe a u e, p essu e and densi y espec i ely. 725 Figu e 2: P ocess low diag am o he pilo plan . T-01: eed wa e ank, P-01: eed 726 pump, E-01: hea eco e , F-01: o en. E-02: eed p ehea e , R-01: packed bed eac o . 727 E-03: coole , V-01: backp essu e al e and T-02: sample ank. 728 Figu e 3: Expec ed beha iou in liquid and solid phase inside he hyd o he mal eac o . 729 Figu e 4: Reac ion pa hway o he cellulosic ac ion o biomass. 730 Figu e 5: Ex ac ed biomass depending on he liquid low and pa icle diame e . 731 Figu e 6: Maximum Toc in liquid phase depending on he liquid low and pa icle 732 diame e . 733 Figu e 7: Fi ing o he TOC o he i s expe ience. TOC: expe imen al TOC;. TOC- 734 SIM: simula ed TOC. 735 Figu e 8: Fi ing o he ace ic acid concen a ion in liquid phase o he i s expe ience. 736 [Ace ic-Acid]: expe imen al ace ic acid concen a ion; [Ace ic-Acid]-SIM: simula ed 737 ace ic acid concen a ion. 738 Figu e 9: Fi ing o he pH o he i s expe ience. pH: expe imen al pH; pH-SIM: 739 simula ed pH. 740 Figu e 10: Linea eg ession o he kine ics om eac ion 1 o 8. 741 Figu e 11: Linea eg ession o he kine ics om eac ion 9 o 16. 742 Figu e 12: Accele a ion ac o s e olu ion. β11,Co1 was only ep esen ed because i had 743 he same alues ha β11,Co2, β15,Co1 and β15,Co2. 744 Figu e 13: Equilib ium cons an e olu ion wi h empe a u e. Compound 5 and 15 we e 745 no showed because hey had he same equilib ium cons an ha compound 3 and 12 746 espec i ely. 747 Figu e 14: Mass ans e coe icien s e olu ion wi h liquid low o a pa icle diame e o 748 3 mm. Compound 5 and 15 we e no showed because hey had he same mass 749 ans e coe icien ha compound 3 and 12 espec i ely. 750 Figu e 15: Mass ans e coe icien s e olu ion wi h liquid low o a pa icle diame e o 751 6 mm. Compound 5 and 15 we e no showed because hey had he same mass 752 ans e coe icien ha compound 3 and 12 espec i ely. 753 Figu e 16: Cellulose b eaking in solid phase. Co1: cellulose; Co3: cellulose oligome 1 754 ( i s oligome soluble om cellulose); Co5: cellulose oligome 2 (las oligome om 755 25 cellulose be o e suga p oduc ion); Co15: cellulose oligome 3 (deace yla ed oligome 756 om cellulose); Co17: insoluble cellulose oligome . 757 Figu e 17: Hemicellulose oligome s b eaking in liquid phase. Co4: hemicellulose 758 oligome 1 ( i s oligome soluble om hemicellulose); Co6: hemicellulose oligome 2 759 (las oligome om hemicellulose be o e suga p oduc ion); Co7: Suga s C6; Co8: 760 Suga s C5; Co12: hemicellulose oligome 3 (deace yla ed oligome om 761 hemicellulose). 762 763 Lis o ables 764 Table 1: Ini ial composi ion o he holm oak sample 765 Table 2: Ope a ional condi ions o he pe o med expe imen s 766 Table 3: Fi ings A.A.D. 767 Table 4: Kine ic cons an pa ame e s. 768 Table 5: Accele a ion ac o s. 769 Table 6: Equilib ium cons an s (dimensionless) be ween solid and liquid phases. 770 Table 7: Mass ans e coe icien s (min-1 ·102) wi h a pa icle diame e o 3mm. 771 Table 8: Mass ans e coe icien s (min-1 ·102) wi h a pa icle diame e o 6 mm. 772 Table 9: Compa ison be ween he simula ed and expe imen al inal mass in he solid. 773 774 Re e ences 775 Al a ez-Vasco, C., Zhang, X., 2013. Alkaline hyd ogen pe oxide p e ea men o 776 so wood: Hemicellulose deg ada ion pa hways. Bio esou ce Technology 150, 321-327. 777 Asl, A.H., Khajenoo i, M., 2013. Subc i ical Wa e Ex ac ion, Mass T ans e - 778 Ad ances in Sus ainable Ene gy and En i onmen O ien ed Nume ical Modeling. 779 InTech. 780 Boble e , O., 1994. Hyd o he mal deg ada ion o polyme s de i ed om plan s. 781 P og ess in Polyme Science (Ox o d) 19, 797-841. 782 Cabeza, A., Sob ón, F., Yed o, F.M., Ga cía-Se na, J., 2015. Au oca aly ic kine ic 783 model o he mog a ime ic analysis and composi ion es ima ion o biomass and 784 polyme ic ac ions. Fuel 148, 212-225. 785 Can e o, D.A., Be mejo, M.D., Coce o, M.J., 2013. Kine ic analysis o cellulose 786 depolyme iza ion eac ions in nea c i ical wa e . The Jou nal o Supe c i ical Fluids 75, 787 48-57. 788 Capa , R., Khezami, L., Bu nham, A.K., 2004. Assessmen o a ious kine ic models 789 o he py olysis o a mic og anula cellulose. The mochimica Ac a 417, 79-89. 790 Ca ey, G.F., Finlayson, B.A., 1975. O hogonal colloca ion on ini e elemen s. 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