INTRODUCTION. Keywords: Adiabatic Conditions, Methyl, Nitrophenol, DSC, Φ-Factor, Kinetics, Thermal Runaway, Time to Maximum Rate (TMR)

Transcription

1 Etimation of Time to Maximum Rate unde Adiabati ondition (TMR ad ) Uing Kineti Paamete Deived fom DS - Invetigation of Themal Behavio of 3-methyl--nitophenol Betand RODUIT *, Fanz BROGLI **, Faneo MASARELLO ***, Miha SHWANINGER ***, Thoma GLARNER ****, Jaque WISS *****, Maku LUGINBÜHL ******, aig WILLIAMS ******, Piee REUSE ******* * AKTS AG Advaned Kineti and Tehnology Solution, TEHNOAk 3, 396 Side, Switzeland, boduit@aktom ** iba Shweizehalle AG, PO Box, H- Bael, Switzeland, fanzbogli@ibaom ** DSM Nutitional Podut Ltd, Safety laboatoy, 33 Sieln, Switzeland, faneomaaello@dmom *** F Hoffmann-La Rohe Ltd, Safety laboatoie, 7 Bael, Switzeland, thomaglane@oheom **** Novati Phama AG, Novati ampu, WSJ-, Bael, Switzeland, jaquewi@novatiom ***** Syngenta op Potetion Münhwilen AG, WMU 3, 333 Münhwilen, Switzeland, makuluginbuehl@yngentaom ****** Swi Safety Intitute, Shwazwaldallee, WRO-, Bael, Switzeland, pieeeue@wiih Abtat: Kineti paamete of the deompoition of hazadou hemial an be applied fo the etimation of thei themal behavio unde any tempeatue pofile Peented pape deibe the appliation of the advaned kineti appoah fo the detemination of the themal behavio alo unde adiabati ondition ouing eg in bath eato in ae of ooling failue The kineti of the deompoition of diffeent ample (diffeent manufatue and bathe) of 3-methyl--nitophenol wee invetigated by onventional DS in non-iothemal (few heating ate vaying fom to K/min) and iothemal (ange of -6 ) mode The kineti paamete obtained with AKTS-Themokineti Softwae wee applied fo alulating eation ate and poge unde diffeent heating ate and tempeatue and veified by ompaing imulated and expeimental ignal Afte appliation of the heat balane to ompae the amount of heat geneated duing eation and it emoval fom the ytem, the knowledge of eation ate at any tempeatue pofile allowed the detemination of the tempeatue ineae due to the elf-heating in adiabati and peudo-adiabati ondition Applied advaned kineti appoah allowed imulation the oue of the Heat-Wait-Seah (HWS) mode of opeation of adiabati aloimete The themal afety diagam depiting dependene of Time to Maximum Rate (TMR) on the initial tempeatue wa alulated and ompaed with the eult of HWS expeiment aied out in the ytem with Φ-fato amounting to 3 The influene of the Φ-fato and eation poge eahed at the end of the HWS monitoing on the TMR i diued Peented alulation lealy indiate that even vey mino eation poge edue the TMR ad of h haateiti fo a ample with initial eation poge amounting to zeo Deibed etimation method an be veified by jut one HWS-AR, o by one oetly hoen ISO-AR un of eaonable duation by knowing in advane the dependene of the TMR on the initial tempeatue fo any Φ-fato Popoed poedue eult in ignifiant hotening of the meauing time ompaed to a afety hazad appoah baed on eie of AR expeiment aied out at the beginning of a poe afety evaluation Keywod: Adiabati ondition, Methyl, Nitophenol, DS, Φ-Fato, Kineti, Themal Runaway, Time to Maximum Rate (TMR) INTRODUTION Diffeential Sanning aloimety (DS) (-3) and Aeleating Rate aloimety (AR) (-9) ae often ued fo the peie detemination of the heat flow geneated (o onumed) by a ample duing expeiment aied out in non-iothemal o iothemal (DS), adiabati o peudo-adiabati ondition (AR) In the DS tehnique the heating ate, being the vey impotant expeimental paamete, i abitaily hoen by the ue, in ontay, in AR, the tempeatue ineae duing exothemi eation eult fom the elf-heating of the mateial The unaway eation ae geneally invetigated by the time-onuming AR expeiment o in iothemal (ISO-AR) o heat-wait-eah (HWS) mode In the peent pape we diu the appliation of the DS tae afte advaned kineti analyi fo the detemination of the Time to Maximum Rate unde adiabati ondition (TMR ad ) and imulation of the oue of AR expeiment pefomed in both mode We popoe an advaned kineti elaboation of the DS data whih allow ontuting link between the eult olleted in diffeent expeimental ondition: (i) DS ignal eoded in non-iothemal ondition (ontant tempeatue ie) uing heating ate in the ange geneally between - K/min (ii) Iothemal DS data obtained at diffeent tempeatue (heating ate amount to K/min) (iii) AR data obtained fom adiabati (Φ) o peudo-adiabati ondition (Φ>) in whih the tempeatue ie hange pogeively fom zeo to eveal K/min due to the ample elfheating Thi poe depend mainly on the kineti of the deompoition, adiabati tempeatue ie, p of the ample and Φ-fato

2 The key fato allowing the imulation of the eation oue unde any tempeatue mode i the knowledge of the kineti paamete depiting the dependene of the ate of heat evolution on diffeent heating ate Thee kineti paamete ae alulated fom the non-io o iothemal ignal uing advaned kineti analyi baed on the diffeential ioonveional appoah (-3) Ioonveional method of the kineti detemination ae baed on the aumption that the eation ate dα/ fo a given eation poge α i only a funtion of the tempeatue Thi aumption i valid fo mot of the deompoition eation but a it i not an axiom it need to be veified in eah analyi If the ioonveional aumption i valid, the alulated kineti paamete an be applied fo imulating the eation ate at any tempeatue hange mode uh a: (i) non-iothemal (ontant heating ate) (ii) iothemal (ontant tempeatue) (iii) adiabati (pogeive tempeatue ie due to elf-heating of the ample) Depending on the type of tehnique and expeimental et-up eg non-iothemal o iothemal DS, HWS o ISO-AR, the poe of data olletion an be moe o le time onuming Below we popoe the optimization of the expeimental poedue whih will be illutated by the pedition of the TMR value fo the 3-methyl-- nitophenol (MN), AS N o : -3-, uing the eult olleted in a ound obin tet in whih few patiipant have invetigated the diffeent bathe of MN in diffeent aloimete uing ompany peifi expeimental et-up In the poedue popoed by u all non-io and iothemal data deliveed by the patiipant of the tet wee ued fo the detemination of the kineti paamete of the eation of the MN deompoition and the heat of the eation H The oetne of the poedue of the detemination of kineti paamete wa veified by the ompaion of the expeimental and imulated ignal The DS deived kineti paamete wee applied fo the imulation of the adiabati expeiment EXPERIMENTAL Fo the detemination of the kineti paamete of the deompoition of MN oiginating fom diffeent upplie and diffeent bathe, the DS tehnique wa applied Diffeent DS appaatu fom vaiou manufatue wee ued The meaued data wee ubequently expoted in ASII fomat and elaboated with AKTS-Themokineti Softwae The deompoition of the MN wa invetigated in non-io expeiment in the ange of to 3 at diffeent heating ate of,,,, and K/min and, iothemally, at tempeatue,,, 3,, and 6 All expeiment wee pefomed in gold plated high peue ealed uible () with a ample ma vaying between and mg RESULTS AND DISUSSION DS DATA- ELABORATION AND SIMULATION The typial DS ignal of MN eoded in noniothemal ondition i peented in Figue (top) Afte endothemi melting (maximum of endo-peak ented at, the ample tat to deompoe Fo the depited ample, analyed with the heating ate of K/min, the maximum of the exo-peak i ented at 93 With the applied igmoid-type baeline the detemined eation heat and tempeatue of the beginning and the end of the deompoition amount to about -9 J/g; 99 and 3, epetively In ode to peent the eult fo all ample in one diagam (Figue, bottom) they ae nomalized and the eation oue i diplayed a the dependene of the eation ate (ate of the hange of the eation poge α vaying between and at the beginning and the eation end, epetively) on the tempeatue HeatFlow (W/g) Reation ate (-/) E-3 E-3 E-3 E- Exo 6 ( ) Heat : -,96 (J/g) T : 99 and 33 ( ) Top of Peak : 93 ( ) Peak Height : (W/g) Baeline Type : Tangential Sigmoid 7 Tempeatue ( ) 6 Tempeatue ( ) Figue (Top) Typial DS tae of 3-methyl-- nitophenol eoded at K/min and igmoid baeline ontution (Bottom) The eation ate fo all ample at K/min Depite of the diffeent expeimental etup and ample oigin the epoduibility of the DS tae i aeptable The ompaion of the DS tae eoded fo diffeent ample on diffeent aloimete at the ame heating ate of K/min (Figue, bottom) how quite high epoduibility of the eult Expeimental diepany between the uve onen mainly the ouene of a mall themal event in the egion of the deteted deompoition onet a well a the tempeatue of the exothemal event All data olleted in non-iothemal and iothemal expeiment ae diplayed in Figue

3 Reation ate (-/) Reation ate (-/) Reation poge (-) Reation poge (-) 3 6 6E- E- E- 3E- E- E Tempeatue ( ) 6 9 Figue Reation ate dα/ and pogee α oeponding to the nomalized DS-ignal fo the deompoition of all 3-methyl--nitophenol ample unde non-iothemal (top) and iothemal (bottom) ondition The value of the heating ate and tempeatue ae maked on the uve The ompaion of the expeimental and imulated ignal at hoen expeimental ondition i hown in the epetive inet The imulation of the expeimental data (ee inet in Figue ) equie the detemination of the kineti paamete of the deompoition eation It wa done applying a diffeential ioonveional method baed on Fiedman appoah () 3 The eation ate an be expeed a 3 ( α ) dα E ( A( α ) f ( α )) exp( ) () R T(t) whee t, T(t), E(α) and A(α) ae the time, tempeatue, appaent ativation enegy and peexponential fato at onveion α, epetively In logaithmi fom one an wite: dα ln ln ( A( α ) f ( α )) 9 ( α ) E R 3 ) T(t 6 () whee E(α)/R and ln(a(α) f(α)) ae the lope and the inteept with the vetial axi of the plot of ln(dα/ ) v /T(t) (Figue 3, top), f(α) depit the diffeential fom of the funtion of the eation poge α depending on the eation mehanim ln(reation ate(-/)) (-) E (kj/mol) Ln(A(alpha) f(alpha)(/)) E(kJ/mol) oelation oeffiient /T (/K) alpha E kj/mol 6 Reation poge alpha (-) 3 alpha 9 E 3 kj/mol Figue 3 (Top) Diffeential ioonveional analyi of the deompoition of 3-methyl--nitophenol baed on the noniothemal and iothemal data The value of the heating ate and tempeatue ae maked on the uve (Bottom) Appaent ativation enegy, pe-exponential fato and a oelation oeffiient a a funtion of the eation poge α The logaithm of the eation ate i peented a a funtion of the eipoal tempeatue fo the diffeent tempeatue and heating ate (Figue 3, top) The diffeential ioonveional analyi allow finding the Aheniu dependene fo any, abitaily hoen deompoition poge α The lope of thi dependene give the appaent ativation enegy and peexponential fato at eah tage of the deompoition poge α (Figue 3, bottom) Fo example we ee that fo a eation poge α of the appaent ativation enegy amount to about kj/mol and fo α 9 the appaent ativation enegy i only lightly lage (diffeent lope) and amount to a 3 kj/mol The ontution of the baeline of the DS ignal (Figue, top) play an impotant ole in the oet detemination of the eation poge whih i baed on the integation of the DS ignal aea Inoet baeline ontution influene the integal intenity of the ignal what lead to the inoet detemination of the eation poge what, in tun, influene the value of the kineti paamete In ode to optimize the detemination of the kineti paamete fom DS tae in AKTS-Themokineti Softwae Veion 3 the eation ange i divided into inteval and the evaluation of the appaent ativation enegy E(α) and peexponential fato A(α) f(α) i aied out fo Ln(A(alpha) f(alpha)(/)) (-) oel oeff (-) 3

4 eah diffeential eation poge α In an ideal ituation, ie without expeimental noie and with the ioonveional aumption holding in %, the um of all oelation oeffiient of all 9999 taight line obtained in the oodinate expeed in the eq and depited in Figue 3 (top) hould eah the maximum value of 9999 AKTS-Themokineti Softwae applie non-linea numeial analyi fo baeline optimization to ineae that um towad that maximum numbe by adjuting the tangent ued fo the ontution of all igmoid baeline The um of all egeion oeffiient i a meaue of the quality of the expeimental data (level of expeimental noie, oetne of baeline ontution, oet hoie of the tempeatue in the iothemal expeiment, et) and the oetne of the aumption onening the ioonveional piniple tating that the eation ate depend only on the tempeatue The optimized adjutment of the baeline hange additionally the tandad deviation of the value of the eation heat H The mean value of the H wa meaued fom the DS tae by alulating the aveage of the value meaued at diffeent heating ate (noniothemally) and tempeatue (iothemally) The tandad deviation i alulated uing the following fomula: n ( H H ), i i σ (3) n whee H i the mean value of the heat of eation obtained fom the vaiou DS tae, i the H, i heat of eation detemined fom eah DS tae and n i the numbe of applied heating ate and tempeatue The um of all oelation oeffiient amount to 99 and the mean eation heat H to -7±6 J/g Quite lage deviation of the um of the egeion oeffiient fom it maximal value and elatively lage tandad deviation of the H value eult mainly fom the expeimental eo ie the not optimal hoie of tempeatue in iothemal mode of the invetigation At too high iothemal tempeatue (a and 6 ) the ignifiant pat of the data olleted at the beginning of the deompoition i not fully appliable in kineti analyi Due to the time equied fo the tempeatue ettling in the ample, ome pat of the deompoition (a lage a tempeatue i highe) ou at tempeatue lowe than et Alo, if the eation ate ae high, the poblem of the time ontant of the meauing eno - ee eg in (6,7) - tat to play an impotant ole in the oet evaluation of the themogam Thee emak ae illutated by the eult of the iothemal themal deompoition of the MN at 6 depited in Figue Due to the vey fat eation at the beginning, the ignifiant pat of the deompoition ou in not well defined expeimental ondition what lead to the deeaing of the auay of the kineti analyi Thi iue will be diued in detail in a fothoming pape The optimal poedue of the eoding of DS data whih ae late ued fo kineti alulation onit in aying out - non-iothemal expeiment in the ange of heating ate of - K/min and one o two iothemal expeiment athe in lowe limit of the appliable tempeatue ange The veifiation of the oetne of the kineti paamete an be ahieved by ompaing the oue of the expeimental and imulated ignal HeatFlow (W/g) 6 - Exo Heat : -,66 (J/g) T : 6 and 99 ( ) t : and (h) Top of Peak : 639 ( ) / 339 (h) Peak Height : 9 (W/g) Baeline Type : Hoizontal Lat Point Time (min) Figue Expeimental (ymbol) and imulated (olid line) DS ignal of MN deompoed iothemally at 6 Note that the ignifiant pat of the eation ou in vey naow time ange and in not well defined tempeatue ADIABATI AND PSEUDO-ADIABATI ONDITIONS Kineti paamete alulated fom DS meauement an be ued fo deibing themal behavio at any heating ate theefoe alo fo pogeive heating ate (elf-heating ate) whih oepond to themal unaway eation in adiabati o peudo-adiabati ondition a in AR expeiment o in a bath eato ontaining a lage amount of ubtane (in ae of ooling failue) Howeve, when onideing the poblem of modelling of the adiabati eation two impotant fato have to be taken into aount: (i) the appliation of advaned kineti, whih popely deibe the ompliated, multitage oue of the deompoition poe, (ii) the effet of heat balane in the adiabati ytem when all (fully adiabati) o majoity (peudoadiabati) of the geneated eation heat tay in the ytem in ontay to the DS expeiment whee it i aumed that all geneated heat i fully tanfeed to the envionment 6

5 HEAT BALANE In heat tanfe poblem it i onvenient to wite a heat balane and to teat the onveion of hemial enegy into themal enegy a heat geneation The enegy balane in that ae an be expeed a Q Q in out 3 Net heat tanfe + Q { Heat geneation Q t { Enegy toage () The enegy balane of an exothemi eation taking plae in emi-adiabati ondition (AR aloimete o bath eato) an ead a follow Fo the adiabati poe a eg in bath eato with lage ize (> m 3 ), it an be aumed that M >>M (jaket) o that we obtain dt dα Tad, tue (with Φ ) () and finally T f ( t, kineti, H, p, ) () The gaphial peentation of the main paamete of the poe unning in the adiabati ondition i peented in Figue dα dt dt UA ( Tenv T ) + M ( H ) M + M Net heat tanfe Heat geneation Enegy toage () with M: ma, p : peifi heat, T: tempeatue, U: oveall heat tanfe oeffiient, A: ontat ufae between the ample and the aloimeti ell o ontaine, H : heat of eation, indie, and env: aloimeti ell o ontaine, ample and envionment, epetively In a fully adiabati envionment (U) all the heat eleaed i ued to heat the ample and the aloimeti ell o ontaine If thee i themal equilibium within the ample and the ell then dt T ( t) T ( t) > dt dt (6) and the whole ytem will have the ame tempeatue ie ate, theefoe we an implify the above equation to: dt M ( H ) dα (7) M + M that an be ewitten a dt dα Tad, tue () Φ with: - the adiabati tempeatue ie: ( H ) Tad, tue (9) - the phi fato: Φ M + M M dα - the eation ate alulated fom the kineti paamete (eq and ) deived fom the DS tae uing ioonveional analyi () Figue Gaphial peentation of key paamete of the poe in the adiabati ondition Self-heating ate and T ad ae expeed by the eq and 9, epetively It ome fom the above equation that uing the kineti baed appoah fo pediting the eation poge α(t) and ate dα/ one an, in tun, pedit the development of the tempeatue T(t) and dt/ and Time to Maximum Rate (dt/) max fo eveal initial tempeatue afte integation of dt/ Thi allow ontuting a themal tability diagam The imulation of an AR uve and it TMR an be obtained imilaly fo any initial tempeatue Howeve, one ha to additionally onide the effet of the veel inetia and take into aount the value of the Φ-fato whih influene: - the T ad, meaued beaue it ome fom above that T T ad, meaued ad, tue Φ - and the TMR ad in diffeent way, depending on the deompoition kineti Detemination of TMR may be alo influened by ome unetaintie in the value of vaiou paamete uh a the adiabati tempeatue ie T ± σ eulting fom deviation in heat H ± : σ ad dt T ± σ d ± σ α ad (3) Φ Afte all, the numeial integation of dt/ enable to pedit TMR in ISO-AR tet fo eveal initial tempeatue T o and Φ-fato within ome onfidene inteval

6 SIMULATION OF ISO- AND HWS ADIABATI EXPERIMENTS In time-onuming adiabati expeiment it eem to be advantageou to ue the kineti paamete fo the pedition of the adiabati tempeatue at whih the poe an be invetigated in a eaonable time ale Suh pedition lead to the optimization of the expeimental wok beaue if an ISO-AR tet i pefomed at an initial tempeatue that i too low, then the duation of the expeiment an lat ove hou o even day In the uent tudy fo a MN ma of 97g and the AR bomb with Φ 3, taking p J/(g K) and an aveage heat eleae H - 7±6 J/g we obtained dt 3 ( H ) dα Φ p 7 ± 6 J / g dα dα 3 ± 33 K J /( g K) () The initial tempeatue may ontain ome unetaintie Fo an initial tempeatue T o auming a deviation T o ±, afte integation one obtain - a onevative TMR of h fo T o + and T ad a bet TMR pedition of a 6 hou fo T o and T ad 3 - a non-onevative TMR of 63 h fo T o 3 and T ad The afety diagam baed on thee alulation i peented in Figue 6 Reult hown in Figue 6 illutate how the kineti paamete obtained fom DS data enable to etimate peiely the initial tempeatue of an ISO-AR whih eult in eaonable duation of the data olletion without neeity of aying out ome peliminay HWS teting Howeve, the AR tet aied out in a HWS mode an be imulated a well A peented in Figue 7 (ymbol) the tempeatue at the detetion limit whih oepond uually to a elf-heating ate of K/min amount to a 3 with Φ-fato 3 and wa eahed afte 9h The time emaining fom thi point to the meaued TMR (ee Figue 7) amount to 67 9h 3 h The meaued TMR value i onitent with the alulated eult peented in Figue 6 onfiming that an initial ISO-AR tempeatue of lead to a TMR of about 6h Howeve, ome mino eation poge α ou duing the initial peiod of a HWS-AR tet when the ample i till in the heat-wait-eah mode When the detetion limit of the AR appaatu i eahed, the eation poge α i no longe, but α > Having the kineti deiption of the eation ate deived fom the DS data, one an etimate that the eation poge α afte the 9 h of HWS teting (Figue 7) amount to about 9 (a %) The imulation of the adiabati tempeatue ie fom that tempeatue of 3 an be futhe alulated and i peented in Figue 7 a a olid line The numeial eult ae in aodane with the expeimental data and indiate that the alulated emaining TMR i a h Peented eult how that the good fit of imulated and expeimental eult in HWS-AR tet an be additionally applied fo the veifiation of the alulated kineti paamete t: 67 (h) T: 6 ( ( 3 Tempeatue ( ) X : 6 Y : Tempeatue ( ) 3 6 t: 9 (h) T: 3 ( ) Reation Poge: 9 (-) 6 Reation Poge (-) Figue 6 Themal afety diagam fo 3-methyl-- nitophenol imulated fo the following paamete: H -7±6 J/g, T ad (- H )/( P Φ) 3±33, Φ 3 and P J/g/ Fo an initial ISO-AR tempeatue of, TMR amount to a 6h with the onfidene inteval (ange -63h) alulated fo the adiabati tempeatue lowe by K (top uve) and highe by K (bottom uve) Figue 7 Typial AR tet fo 3-methyl--nitophenol aied out in HWS mode Having the kineti deiption of the eation ate fom the DS data, one an etimate that the eation poge α afte a 3 h of HWS teting amount to about 9 (a %) Fom the time at whih the tempeatue of the detetion limit (3 ) wa eahed the value of TMR amount to a h (67-9h) Solid line depit the imulation being in a good ageement with the expeimental HWS-AR data peented a ymbol 6

7 The next impotant advantage of the ue of the kineti paamete deived fom DS data onit in the poibility of the imulation of the eation oue in fully adiabati ondition (Φ ) fo the totally not deompoed ample (α) what i vey diffiult to ahieve fom the expeimental point of view Suh a imulation i peented in Figue depiting the afety diagam fo 3-methyl--nitophenol alulated fo few initial tempeatue by the poedue applied fo the imulation of TMR in ISO-AR hown in Figue 6 Depending on the deompoition kineti and T ad, the initial tempeatue diffeently influene the TMR ad value and the ate of the tempeatue evolution unde adiabati ondition Fo Φ the detemined TMR ad i about hou at an initial tempeatue of about 69 (fo that tempeatue a moe onevative value fo TMR ad i 676 h) The itial value TMR ad hou, ommonly aepted a the afety limit in the indutial ale, i obtained at about (fo that tempeatue a moe onevative value fo TMR ad i h) The onfidene inteval i detemined imilaly a explained in Figue 6 Tempeatue ( ) X : Y : 66 X : Y : 6 Figue Themal afety diagam fo 3-methyl-- nitophenol in fully adiabati ondition with Φ The hoie of the initial tempeatue tongly influene the adiabati indution time With H -7±6 J/g, T ad (- H )/( P Φ) 9±3 and P J/g/, TMR ad ae and h fo initial tempeatue of 66 and 6, epetively Dahed line depit the onfidene inteval 3 3 Table Summay of the eult of detemination of the initial tempeatue leading to TMR ad h with AKTS- Themokineti Softwae by uing all DS data olleted in ound obin tet (*) Two HWS-AR with Φ-fato 3 and DS with K/min wee applied Detemination of the initial tempeatue leading to TMR ad h wa done by ombining the non-iothemal DS data of K/min with the AR data uing AKTS-Themokineti Softwae Patiipant of ound obin tet Heating ate applied (non-iothemal) Tempeatue applied (iothemal) H ± σ Initial tempeatue fo TMR ad h Sum of all oel oeff A,,,,,,, 96± B,,,, 7 ± ,,, 6 3 ± D,,,,, 3, 33 ± E(*), F 9,,, ± G, 3,,, 6 6 ± The Table ontain the eult of the alulation of the TMR ad fo all expeimental data deliveed by the patiipant of the ound obin tet Depite the vaiety of the expeimental et-up and diffeent oigin of the ample the mean value of the initial tempeatue at whih TMR ad h amount to 7 ±3 whih i in aodane with the tempeatue diplayed in the Fig The TMR ad value alulated by the peented method ae le onevative a thoe deived by uing the etimation of Kelle et al () He peented the etimation method fo TMR ad fom non-iothemal DS meauement baed on the model of zeoth ode eation Simila appoah wa peented in the pape of Pate at al (9) whih veified hi model by Dewa veel expeiment They popoed the linea egeion poedue to find out a onevative value of the initial tempeatue that lead to TMR ad h a a funtion of T Onet : If one etimate oughly fom Figue that the poible deteted onet lay between and, then aoding the Kelle appoximation TMR ad h will be eahed fo initial tempeatue between 97 and 7 Thee value ae 3- moe onevative ompaed to peented by u value of Nevethele, thi of Kelle ule of thumb an be onideed a an inteeting peliminay tep in a themal hazad aement fo detemining TMR ad h INFLUENE OF Φ-FATOR ON THE REATION OURSE The inteeting featue of the imulation method peented in thi pape i the poibility of the ompaion of the pedited ignal in iothemal, peudo-adiabati and fully adiabati ondition TMR ad, h [K] 6 T Onet [K]+ K () 7

8 Tempeatue ( ) 6 6 HWS-AR Φ 3 7 Φ Φ 7 Time (day) Φ 3 Φ3 Φ E Φ E Figue 9 ompaion between the T-t elationhip (top) and eation poge (bottom) in iothemal (T6 ) and adiabati ondition TMR ad wee alulated fo a tating tempeatue of 6 with Φ 3 and, epetively uing the value of H -7±6 J/g and p J/g/ Unde iothemal ondition the eation poge α afte a day amount to only a 3 (3%) The deeae of the Φ fato eult in ignifiant hotening of the time equied fo the total deompoition whih ou afte and day fo Φ fato 3 and, epetively Reation Poge (-) the heat evolution ate K/min i eahed afte 3 h ie h befoe TMR ad value of h Duing thi initial peiod of the adiabati eation the ample tat to deompoe, the eation poge at the point of the detetion limit amount to 9 (a %) Even uh a mall eation poge an influene the value of the time emaining to h, thi iue i diued in the following paagaph Self-heating ate ( /min) Self-heating ate ( /min) E+7 E+6 E+ E+ E+3 E+ E+ E+ E- E- E-3 E+ E+7 E+6 E+ E+ E+3 E+ E+ E+ E- E- E Tempeatue ( ) 6 Time: 3 (h) Tempeatue: 66 ( ) Self-heating ate: ( /min) Reation poge: At a ontant tempeatue of one an ee (Fig9) that the eation poge α afte 3 day amount to about 3 (a 3%) only The deeae of the Φ value ignifiantly hange the time equied fo the total deompoition A peented in thi figue the total deompoition unde fully adiabati ondition ou afte day ( h) howeve, with Φ3 (value applied with AR aloimete Fig 6) the eation end afte a day Note that iothemal ondition an be numeially etieved by etting an exeptionally lage value of the themal inetia fato uh a Φ E to ahieve an inignifiant adiabati tempeatue ie T ad If the Φ i vey high all heat eleaed by the eation i diipated to the uounding A a onequene, the ample tempeatue emain ontant beaue with dt fo vey lage value of Φ we have dα Tad, tue (6) Φ dt and T ( α ) T ( α ) T iothemal (7) Simulated an be not only the tempeatue but the ate of the heat evolution duing elf-heating poe a well The imulated eation ate in fully adiabati ondition (Φ) a a funtion of tempeatue (top) and time (bottom) i peented in Figue The imulation indiate that the typial detetion limit of Figue Simulated elf-heating ate uve fo 3-methyl- -nitophenol unde adiabati ondition (Φ) a a funtion of tempeatue (top) and time (bottom) alulated fo an initial tempeatue of Typial detetion limit of adiabati aloimete ( K/min) i eahed afte 36 hou ie hou befoe TMR ad h Reation poge at 36 h amount to about 9 (a %) INFLUENE OF REATION PROGRESS OURRING DURING INITIAL PERIOD OF HWS ADIABATI EXPERIMENT ON DETERMINATION OF TMR ad The oet intepetation and imulation of the adiabati expeiment equie intoduing into onideation the poblem of the etain, unknown degee of the deompoition of the invetigated mateial whih tat to deompoe befoe the tempeatue of the detetion limit i eahed Thi, even being elatively mall, eation poge lead to the hotening TMR ad value ompaing to the value haateiti fo the abolutely not deompoed mateial having the eation poge α The imulation of the TMR ad fo the ample with diffeent initial deompoition degee α (in the ange -%) i depited in Figue The value of TMR ad h fo the initial tempeatue of about and the ample with α deeae to 33; 9; 79 and 97h fo the ample with the eation poge of, ;, and, epetively Peented eult of the imulation lealy how that a peial ae ha to be taken when intepeting eult of TMR ad obtained expeimentally fo the ample with unknown deompoition degee (like in HWS-AR) Thi unontolled eation poge depend not only

9 Tempeatue ( ) 6 on the expeimental etting (the hoie of the initial tempeatue in adiabati expeiment) but alo on the kineti of the deompoition Depending on the kind of the ate-ontolling tep in the deompoition poe thi influene of the peliminay α value on the TMR ad an be diffeent and thi iue will be diued in ou next pape 6 7 % % 7 TMRad h % % % Figue Influene of peliminay eation poge α on TMR ad value Note that the eation poge α i diplayed in peent ONLUSION The deompoition of 3-methyl--nitophenol ample of diffeent oigin wa tudied uing DS and AR The DS eult deliveed by the patiipant of a ound obin tet and obtained with diffeent heating ate (non-iothemal mode) and at diffeent tempeatue (iothemal mode) wee elaboated by AKTS-Themokineti oftwae and applied fo the detemination of the kineti paamete of the deompoition eation Due to thei peie detemination, the vaiation of the unaway time unde tue adiabati mode (with a themal inetia fato Φ ) wa alulated fo any initial poe tempeatue Reult wee epoted in a themal afety diagam depiting the dependene of Time to Maximum Rate (TMR) on the initial tempeatue The itial value TMR ad hou wa obtained fo the initial adiabati tempeatue of about Both iothemal DS and adiabati expeiment with Φ- fato > wee ued fo the final validation of the kineti paamete The peie kineti deiption of the poe allowed imulation of the influene of the Φ-fato value on the eation oue Due to the poibility of the imulation of ISO- and HWS mode of the AR expeiment the applied method an help in the optimal hoie of the initial adiabati tempeatue what eult in hotening of the time equied fo the adiabati invetigation The knowledge of the kineti paamete of the eation allowed detemining eation poge ouing in the initial peiod of the adiabati expeiment befoe eahing by the ytem the detetion limit of the heat evolution Peented imulation howed that the influene of thi initial 9 eation poge on the TMR ad value ha to be aefully onideed beaue even not ignifiant eation poge a eg an deeae by a 6h the value of TMR ad (h fo α and a 76 fo α) REFERENES [] AZogg, F Stoeel, U Fihe and K Hungebühle, Themohim Ata,, 9, [] DJ am Ende, DBH Ripin and NP Weton, Themohim Ata,, 9, 3 [3] S-Y Liu, J-M Teng, M-K Lee and T- Wu, J Them Anal al, 9, 9, 9 [] A Bhattahaya, hem Eng J,,, 67 [] DI Towend and JTou, Themohim Ata, 9, 37, [6] YIizuka and M Suianaayanan, Ind Eng hem Re,3,, 97 [7] GT Bodman and S hevin, JHazad Mateial, 99,, [] PF Bunyan, TT Giffith and VJ Noi, Themohim Ata, 3,, 7 [9] RJA Keten, MN Boe, MM Stok and Vie, J LoPev Poe Ind,,, [] B Roduit, W Demaut, A Lunghi, P Folly, B Bege and A Sabah, J Them Anal al,, 93, 63 [] B Roduit, P Folly, B Bege, J Mathieu, A Sabah, H Ande, M Ramin and B Vogelange, J Them Anal al,, 93, 3 [] B Roduit, L Xia, P Folly, B Bege, J Mathieu, A Sabah, H Ande, M Ramin, B Vogelange, D Spitze, H Moulad and D Dilhan, J Them Anal al,, 93, 3 [3] AKTS-Themokineti Veion 3 Augut 9, Advaned Kineti and Tehnology Solution, (AKTS-Themokineti oftwae and AKTS-Themal Safety oftwae) [] Swi Intitute of Safety and Seuity, [] H L Fiedman, J Polym Si, Pat, Polyme Sympoium (6P), 96, 3 [6] KH Shoenbon, Themohim Ata, 993, 69, 3 [7] ME Patt, BE White, B Stein and EJ ott, Themohim Ata, 99, 97, 3 [] AKelle, D Stak, H Fiez, E Heinzle and K Hungebühle, JLoPevInd, 997,, 3 [9] J Pate, UWödöfe, A Kelle and K Hungebühle, JLoPevInd,, 3, 7