The Model for Theoretical Determination of Composition of a Heterogeneous Equilibrium Mixture in the Course of Chemical Reactions. and.

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1 Slavko Djuri} Thechical College Doboj Reublic Serska Milo{ Kuburovi} Professor University of Belgrade Faculty of Mechanical Engineering Aleksar Jovovi} Assistant University of Belgrade Faculty of Mechanical Engineering The Model for Theoretical Determination of Comosition of a Heterogeneous Equilibrium Miture in the Course of Chemical Reactions C + HO + H C + H CH The work resents a new way of calculation of the comosition of a heterogenous equilibrium miture in the course of chemical reactions imortant in engineering ractice: soot roduction coal gasification waste yrolysis refining flue gases by dry semi-dry treatments. In the avaiable literature the calculation of equilibrium comosition of only the homogeneous (gaseous) hase is alied. This work resents three ways of calculation: based uon the number of moles based uon the sum of the number of moles the calculation of the comosition of only the homogeneous miture. The reactions C + HO + H C + H CH have been considered since in the available reference literature there is the largest number of data on the comosition of the equilibrium homogeneous miture concerning these reactions. The results of the calculation of the comosition of the homogeneous (gaseous) hase as a art of a heterogeneous miture are identical with the results obtained by the ortodo calculation of only the homogeneous hase. Keywords: chemical equilibrium content of the solid hase model.. INTRODUCTION The calculation of content of the solid hase in the course of heterogeneous chemical reactions are imortant for a great number of rocesses: waste material treatment by alying the yrolysis rocedure soot roduction coal gasification flue gas treatment. In the available reference literature neither methodology nor results of calculation of the solid hase content in the equilibrium miture can be found. The derived eressions refer solely to chemical reactions in the gaseous miture [] with note that the equilibrium constant alies both to homogeneous heterogeneous equilibrium mitures. In the heterogeneous reactions the Law on the effect of masses takes simlified form mostly i.e. in the heterogeneous mitures the ressure the concentration of solid hase comonents need not to be taken into account []. However there are rocesses in which it is necessary to determine the content of the solid comonent in the equilibrium miture. In heterogeneous reactions the chemical otentials of solid comonents remain constant indenendently on the degree of the course of the reaction. The necessary condition is that these comonents should not be Received: June 00 acceted: March 00. Corresondence to: Aleksar Jovovi} Faculty of Mechanical Engineering Deartment of Process Engineering 7. marta Belgrade Yugoslavia t.ajovovic@alfa.mas.bg.ac.yu consumed until the chemical equilibrium has been established []. The model offered in these aer gives an answer to what conditions (ressure temerature initial comonents concentration) the solid hase comonents are comletely consumed. Since the content of the solid hase in the heterogeneous miture is determined only by measuring it [] the imortance of the resent aer is best suorted by this reason of devising such a model. In order to satisfy the material balance of the chemical reaction the solid hase must also be taken into account in the calculation of the reaction roducts.. THE CALCULATION METHODOLOGY By calculating we assume that reactions occur by solid fuel gasification [5]: C + () C + H O + H () C + H CH. () The calculation methodology of content of the equilibrium miture of the reaction () is shown in the available literature [6]. The following three methods of the content calculation are shown in this aer: - calculation based uon the number of moles - calculation based uon the sum of the number of moles - calculation of comositions of only homogeneous miture. The calculation of only a homogeneous miture is well known it can be found in the literature [7]. In Faculty of Mechanical Engineering Belgrade. All rights reserved. FME Transactions (00)

2 this aer the reaction C + HO + H C + H CH is considered... The calculation based uon the number of kilomoles In the course of reactions C + H O + H C + H CH the number of kilomoles of the comonents in the miture after the chemical equilibrium has been established amounts to: - for the reaction () () Carbon: nc a () () Water vaor: n b H O (5) () Carbon-monokside: n (6) () Hydrogen: n H (7) - for the reaction () () Carbon: nc a (8) () Hydrogen: n c H (9) () Methane: n CH (0) where: a a - number of carbon kilomoles taking art in the reactions () () resectively b - number of water vaor kilomoles taking art in the reaction () c - number of hydrogen kilomoles taking art in the reaction () -number of carbon-monoiode (hydrogen) kilomoles in the miture after the chemical equilibrium has been established the reaction () - number of methane kilomoles in the miture after the chemical equilibrium has been established the reaction (). The total number of kilomoles in the miture after the chemical equilibrium has been established are following: heterogeneuos miture (solid gaseous hases): - for the reaction () () () () () () n ( s) nc O + n ) n ( s) ( ( a ) + ( b ) + + a + b - for the reaction () () () () () () n ( s) () nc + n CH ( a ) + ( c ) + a + c () homogeneous miture (gaseous hase only): - for the reaction () () () () n ( g) () nh O + n n ( g) ( ) ( b ) + + b +. () - for the reaction () () () () n ( g) nh + n CH () ( c ) + c. () The mole contents of the comonents in the miture after the chemical equilibrium of reactions () () has been established amounts to: heterogeneuos miture: - for the reaction () n () C a C (5) ( )() a + b n s n () H O b H O (6) () a + b n () (7) () a + b n () H H (8) () a + b Nomenclature a [kmol] - number of C kilomoles entering the reaction () a [kmol] - number of C kilomoles entering the reaction () b [kmol] - number of H O kilomoles entering the reaction () c [kmol] - number of H kilomoles entering the reaction () n [kmol] - number of kilomoles in the equilibrium miture K [Pa] - chemical equilibrium constant of the reaction C + HO + H K [Pa ] - chemical equilibrium constant of the reaction C + H CH K ' [-] - chemical equilibrium constant of th reactions () () reduced to ressure of 000 Pa [Pa] - ressure [ kmol ] kmol - mole content of the comonent in the heterogeneous equilibrium miture (solid gaseous hase) y kmol mole content of the comonent in the homogeneous equilibrium miture (gaseous hase) [ ] kmol [kmol] - number of kilomoles in the equilibrium miture number of H kilomoles in the equilibrium miture after the chemical equilibrium has been established the reaction () [kmol] - number of kilomoles in the equilibrium miture number of CH kilomoles in the equilibrium miture after the chemical equilibrium has been established the reaction (). Subscrits C - carbon CH - methane - carbon-monoide H - hydrogen g - gaseous s - solid I J M - sulementary value. 8 Vol. 0 No 00 FME Transactions

3 - for the reaction () n () C a C () a + c (9) n () H c H () a + c (0) n () CH CH () a + c () homogeneous miture: - for the reaction () n () H O b y H O () b + () n () y () () b + () nh y H () n () ( g) b + - for the reaction () n () H c yh (5) () c n () CH ych. () c (6) The artial ressures of the comonents in the homogeneous miture (gaseous hase) after the chemical equilibrium has been established are: - for the reaction () b H O y H O b + (7) y b + (8) H y H b + (9) - for the reaction () c H yh c (0) CH y CH c () where is the total ressure in the reactor sace after the chemical equilibrium of the reactions () () has been established. The chemical equilibrium constant of the reactions () () is defined by eression: H K H O b (a) CH ( c ) K. ( ) H c (b) By solving equation (a) (b) at given a a b c K K is obtain the unknown values: ± b K ( + K ) () c ( ± / + K ). ().. The calculation based uon the sum of the number of kilomoles For heterogeneous miture after the chemical equilibrium has been established in the course of the reactions C + H O + H C + H CH the following deendencies hold: - for the reaction (): the above stated eresions (7) (8) (9) - for the reaction (): the above stated eresions (0) () - for the reaction () C + H O + + H (5a) C C + I H H O + (5b) H C C + J (5c) O H O + H H K H O H ( C ) O (5d) - for the reaction () + + (6a) C H CH Σ C C + CH M (6b) Σ H H + CH CH CH ( C ) K (6c) H H where: Σ C Σ H Σ O - the total number of kilomoles of carbon hydrogen oygen resectively in the miture before the chemical equilibrium has been set u IJM - sulementary values. The last equation of eression (5a-d) is obtained on the following way: C H O H H O + + H C H O + + H H O H H O ; H ; C C C H O H yh O ; yh C ; y. C C The last equation of eression (6a-c) is obtained in the similar way. The solutions of the system of four equations (eressions (5a-d)) with four unknown values C H O H the system of three equations (eression (6a-c) with three unknown values C H C are: H - for the reaction () A C + B C + C 0 (7) FME Transactions Vol. 0 No 00 9

4 I ( J ) H O + J ( + I) C ; I + I C (8)(9) J + I J I H J ( + I) C (0) where: A J ( + I) ( + K ) B ( + K ) [ I ( J ) J ( + I) ] I C I J K I ( J ) + I. Values I J have been based uon the conditions: C a I Σ Σ H b (a) a J Σ C Σ O b I. (b) - For the reaction () C M + M 8 K M M + M ( K ) (a) ( M M ) + K ( K ) M M ] [ + M + K H (b) M ( + K ) [ CH M K M [ M ( + K ) ] ( M + M ) ( + + K )] The value M has been based uon the condition: (c) M ΣC / ΣH a / c ().. The calculation of the comosition of a homogeneous miture only For homogeneous miture after the chemical equilibrium has been established in the course of the reactions C + HO + H C + H CH the following deendencies hold: - for the reaction () H O yh O ; y ()(5) H y (6) H H y y H K (7) H O y H O y H O + y + yh ; y y H. (8)(9) Keeing in mind that initial concentrations are not considered but only stechiometry of the rocess - that constitutes a fault of this model (calculation) - it can be writen: from eression (8) (9) follows: yh O y (50) from eression (7) follows: y K y (5) there from: y H O [ + K K ( + K ) ] (5a) [ K + K ( K ] [ K + K K ] y + ) (5b) y H ( + ) (5c) - for the reaction () H y H CH CH (5) (5) CH K ; y y H + y CH H CH. (55)(56) The solutions of the system of two equations (55) (56) with two unknown values y H y CH are: + + K yh K (57a) + K - + K ych K. (57b) The value of the chemical equilibrium constant K is reduced to the ressure o Pa is thus determined by the eression: K ' K / o n (58) whereby the numerical value of the change of the number of kilomoles in the gaseous hase in the course of the reactions is () (): n b + bh b H O + kmol n bch b H kmol K n K o K ' o (59) K n K' o K ' o. (60) It is an interesting question at which value of dimension I ΣC/ΣH M ΣC/ΣH at given temerature in the equilibrium miture the reactions () () does not eist solid hase i.e. C 0. The answer can be obtained by using eression (7) () the first equation of eressions () (). - for the reaction () [ C I ( + K + + ) I ( I)( K ) + K 6I ( + K ) 6 ( I I K + K I ) 0. (6) The eression (6) is transformed to an equivalent eression: I ( + K) ( + K) K C ( + I) ( + K) 0. (6) Since + I > 0 + K > 0 unequation (6) is transformed to unequation: I ( + K) ( + K) K 0 (6) whose set of solutions is: ( + K ) K I. (6) + K The set of solutions of unequation (6) is equivalent to the set of solutions of the starting unequation (6). - for the reaction () (eression (.a)) C 0. (65) 50 Vol. 0 No 00 FME Transactions

5 The eression (65) is transformed to an equivalent eression: M ( M + + K ) 0. ( + K) ( M + K + ) (66) Since M > 0 K > 0 unequation (66) is transformed to inequation: M + + K 0 (67) whose set of solutions is: M ( / + K ). (68) The set of solutions of unequation (68) is equivalent to the set of solutions of the starting inequation (65).. THE CALCULATION RESULTS The model of theoretical determination of comosition of a heterogeneous equilibrium miture resented in this aer has been used several times has been confirmed in solving ractical engineering roblems such as: waste material treatment by alying yrolysis rocedure coal gasification treatment of flue gas. The numerical eamle has been devised with the adoted values of the ressure of 0 5 Pa the temerature of 77 K (500 C) so selected for the sake of comarison of the results obtained with the data quoted in the available literature. At the temerature of 77 K the value of the chemical equilibrium constants of the reactions () () are K ' K '. 09 [7]. By using eression (59) (60) are obtain the values K Pa K Pa where is: 0.-coefficient of constant chemical equilibrium of the reaction C + H CH [5]. By substituting K for the numerical values in the eressions (6) (68) are obtain conditions: I M (69) At the values I M 0. 5 the temerature of 500 C the solid hase does not eist in the equilibrium miture of the reactions () () ( C 0). Table. The contents of a heterogeneous a homogeneous miture of the reaction C + H O + H at temerature of 500 C Heterogeneous miture Homogeneous miture C H O H y H O y y H Calculation based uon the number of moles eressions (5) to () I0.50 b kmol a kmol J b. kmol I0.75 a kmol J I.00 a kmol J.00 b kmol Calculation based uon the sum of the number of moles - eressions (7) to (0) I0.50 J I0.75 J I.00 J Calculation of the comosition of the homogeneous miture only eression (5) Table. The contents of a heterogeneous a homogeneous miture of thereaction C + H CH at temerature of 500 C Heterogeneous miture Homogeneous miture C H CH y H y CH Calculation based uon the number of moles eressions () to (6) M 0.50 a kmol c kmol M.00 a kmol c kmol M.50 a kmol c 0.66 kmol Calculation based uon the sum of the number of moles eression () M M M Calculation of the comosition of the homogeneous miture only eression (57) FME Transactions Vol. 0 No 00 5

6 Basing uon condition (69) the following values have been adoted for the analysis I0.5; 0.75;.0; a kmol (Table ) M0.5;.0;.5; a kmol (Table). The value I.0 corresonds to stechiometric relationshi of C H O for the reaction () value M0.5 corresonds to stechiometric relationshi of C H for the reaction (). By increasing the number of carbon kilomoles in the initial comonents of the reaction () (the increase in value of I) the mole content of carbon ( C ) increases in the heterogeneous miture whereas the mole content of the comonents in the homogeneous miture ( y H O y y H ) does not change (Table ). By increasing the number of carbon kilomoles in the initial comonents of the reaction () (the increase in value of M) the mole content of carbon ( C ) increases in the heterogeneous miture whereas the mole content of the comonents in the homogeneous miture ( y H y CH ) does not change (Table ). The results determined by using eressions (5) to () () to (6) (the calculation based uon the number of moles) are identical to the ones determined by using eressions (7) to (0) () (the calculation based uon the relation of the sum of the number of moles). The comosition of the homogeneous miture determined by using eressions (9) to (6) (5) (56) resectively conforms to the results of the calculation of the homogeneous miture resented in the available literature [7].. NCLUSION The resented model emerged from solutions to ractical engineering roblems (waste material treatment by alying the yrolysis rocedure soot roduction coal gasification flue gas treatment). For the sake of satisfying the material thermal balance in heterogeneous systems the solid hase content in the equilibrium miture must be taken into account. At given relationshi of the masses of the initial comonents there eists a definite temerature at which the solid hase ceases to eist in the equilibrium miture. For the considered reactions the following conditions can be established by utilising the model resented here. In course of articular chemical reactions the calculation is simlier if eressions (5) to (6) are used. With simultaneous reactions taking art in the reaction sace the comleity of solving of the model according to eressions (5) to (6) is the same as according to eressions (7) to (). The results of the calculation of the homogeneous (gaseous) hase as a art of the heterogeneous miture (eressions (5) to (6) (7) to ()) are identical with results of the calculation of the homogeneous hase only (eressions (5) (57)). LITERATURE [] Bošnjaković F. Thermal science vol. III (serbian: Nauka o tolini III dio) Tehnička knjiga Zagreb986. [] Wiberg E. Inorganic chemistry (serbian: Anorganska kemija revod sa nemačkog) Školska knjiga Zagreb 967. [] Daniels F. Alberty A.R. Physical chemistry (in Russian) John Wiley Sons Inc. New York Mir Moskva 978. [] Bilodeau J.F. Therien N. Proul P. Cernik S. Chornet E. A Mathematical Model of Fluidised Bed Biomass Gasification Canadian Journal of Chemical Engineering (99) [5] GumW. Kures Hbuch der Brennstoff und Feuerungstechnik Sringer-Verlag Berlin 96. [6] Kuburović M. A new way calculation of a heterogeneous equilibrium miture in the course of a chemical reaction Transactions Vol.7 No.-5 Faculty of Mechanical Engineering of the University in Belgrade 998. [7] Voronjec D. Kuburović M. Thermodynamics of multicomonent systems chemical thermodynamics - roblems solutions (in serbian: Problemi i termodinamike višekomonentnih sistema i hemijske termodinamike) Mašinski fakultet Belgrade 99. ODRE\IVAWE RAVNOTE@NOG STAWA SASTAVA HETEROGENE ME[AVINE PRI ODVIJAWU REAKCIJE C + HO + H I C + H CH S. \uri} M. Kuburovi} A. Jovovi} Rad redstavqa nov na~in ira~unavawa sastava heterogene ravnote`ne me{avine hemijskih reakcija va`nih u in`ewerskoj raksi: roivodwi ~a i gasifikaciji ugqeva irolii otada re~i{}avawu dimnih gasova suvim i olusuvim ostucima. Rad oisuje tri na~ina ira~unavawa i to: asnovana na broju kilomolova sumi broja kilomolova i ira~unavawu sastava samo homogene me{avine. 5 Vol. 0 No 00 FME Transactions