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2 Modelng and Smulaton of Chemcal System Vaporzaton at Hgh Temperature: Applcaton to the Vtrfcaton of Fly Ashes and Radoactve Wastes by Thermal Plasma 8 Imed Ghlouf College of Scences, Department of Physcs, Al-Imam Muhammad Ibn Saud Unversty, Ryadh, Kngdom of Saud Araba 1. Introducton The treatment, at hgh temperatures, of such chemcal systems as the fly ashes and radoactve wastes requres the control of ts element volatlty. Precsely, t requres followng the evoluton of the system durng treatment and determnng the composton of the system n all phases. For a closed chemcal system, the calculaton of ts composton s carred out by the method of free enthalpy mnmzaton developed by Erksson [1]. However, for open systems, the problem s not defntvely solved yet. A computer code smulatng the volatlty of the elements present n an oxde system was developed by Pcheln [2] and Bade [3]. Ths computer code was modfed by Ghlouf to control the vaporzaton of the elements present n a chlorde and oxde system durng the fly ashes vtrfcaton by plasma and to study the radoelement volatlty durng the treatment of radoactve wastes by thermal plasma [4-9]. In ths chapter we present a method used n our computer code, whch s developed to smulate and to modulate a chemcal system vaporzaton at hgh temperature. Ths method s based on the calculaton of composton by free energy mnmzaton of the system, coupled wth the mass transfer equaton at the reactonal nterface. Ths couplng s ensured by fxng the equvalent partal pressure of oxygen n the mass transfer equaton and those characterzng the complex balances. Ths chapter contans fve parts: In the frst part we wll present the method used to the calculaton of composton by free energy mnmzaton of a closed system, precsely we wll develop the equatons characterzng the complex balances at the reactonal nterface. In the second part we wll gve the mass transfer equaton of oxygen. In the thrd part we wll present the method used n our study to determne the dffuson coeffcents of gas speces essentally for complex molecules lke vapor metals. In the fourth part we wll apply the computer code to smulate the radoelement volatlty durng the vtrfcaton of radoactve wastes by thermal plasma. In the last part we wll present the results obtaned by the computer code durng the study of radoaelement volatlty.

3 168 Heat and Mass Transfer Modelng and Smulaton 2. Descrpton of the model In the model, the speces dstrbuton n the lqud and gas phases s obtaned teratvely usng the calculaton of system composton coupled wth the mass transfer equaton. The quantty of matter formed n the gas phase s dstrbuted nto three parts: The frst part s n equlbrum wth the bath, the second part s dffused n the dffuson layer, and the thrd part s retaned by the bath under the electrolyss effects (Fgure 1). The gas composton at the surface s thus modfed. It s not the result of a sngle equlbrum lqud-gas, but nstead, t s the outcome of a dynamc balance comprsng: a combned acton of reactonal balances, electrolyss effects, and dffusve transport. The flux densty of a gas speces ( J L ) lost n each teraton s gven by: Where D J and L D R J J J (1) R J are, respectvely, the dffuson flux densty and the flux retaned by the bath for the gas speces. The vaporzaton model s applcable to several types of complex chemcal systems. It s ndependent of the geometrcal confguraton of the vaporzaton system, but t s developed based on the followng three hypotheses: a. The chemcal system conssts of two phases: a vapor phase, whose speces are regarded as perfect gases, and a homogeneous sothermal lqud phase. b. The model s mono-dmensonal: t does not ntroduce dscretzaton on the varable space, but enables to calculate the composton of the two phases at each tme nterval. c. The mass transfer at the nterface s controlled by the gas speces dffuson n the carrer gas because the reacton knetcs at the lqud/gas nterface are very fast. 5 cm Dffuson flux Retaned flux Gas n equlbrum wth the bath A = 28 cm 2 Homogeneous lqud phase Dffuson layer Interface (A) Fg. 1. Smplfed dagram used to establsh the assumptons of the model

4 Modelng and Smulaton of Chemcal System Vaporzaton at Hgh Temperature: Applcaton to the Vtrfcaton of Fly Ashes and Radoactve Wastes by Thermal Plasma Calculaton of the gas/ lqud system composton The free energy of a system made up of two phases; a vapor phase formed by Ml(1) speces and a condensed phase consstng of Ml (2) speces s as follows: Ml(1) Ml(1) Ml(2) (2) G n g RTLogp n g RTLog 1 Ml(1) 1 where g s the formaton free enthalpy of a speces under standard condtons, R s the perfect gas constant, T s the temperature, and n s the mole number of speces. The two terms p and X are, respectvely, the partal pressure of a gas speces, assumed a perfect gas, and the molar fracton of speces n the lqud phase assumed deal. Equaton (2) can be wrtten dfferently as: Ml(1) Ml(1) Ml(2) G g n g n F n LogP Log n Log RT 1 RT Ml(1) 1 RT n g nl where P s the total pressure, phase ( n g Ml(1) 1 n condensed phase ( n (3) ) and n l l n g Ml(1) Ml(2) n ). Ml(1) 1 represents the total mole number of the speces n the gas represents the total mole number of the speces n the Let us assume that the system under study conssts of L basc elements. Hence, the conservaton of the elements mass results n: Ml(1) Ml(1) Ml(2) an an B 1, L (4) 1 Ml(1) 1 where a s the atoms grams number of the element n the chemcal speces and B s the total number of atoms grams of the element n the system. The equvalent partal pressure of oxygen s gven by: P O2 no2 P (5) n g where n O2, representng the equvalent mole number of oxygen, s gven by: n Ml(1) a n (6) O2 L 1 where a L s the atoms grams number of oxygen n the chemcal speces. Combnng (5) and (6) leads to:

5 17 Heat and Mass Transfer Modelng and Smulaton n Ml(1) PO 2 g aln P 1 (7) The calculaton of the system composton to the balance coupled wth the mass transfer equaton, at constant temperature T and constant pressure P, conssts of mnmzng the functon F under the constrants of (4) and (7). The Lagrange functon becomes: L Ml(1) Ml(2) Ml(1) P O2 L1 L g P (8) L n n a n B a n n where represents the Lagrange multplers and the functon ξ (n ) s the Taylor seres expanson of F (wth orders hgher than two beng neglected). To mnmze F (n) subect to (4) and (7), t s requred to have: L n =1,,Ml(1)+Ml(2) (9) L =1,,L, L+1 (1) From (9), the expresson of the mole number of a speces n the vapor phase or n the lqud phase can be deduced. That s to say: For gases: For lqud: L g n n g PO2 ( ( ) L1 L ) RT 1 P ng ng n LogP Ln a a n (11) L g n nl ( ( ) ) RT 1 nl nl n Ln a n (12) wth n Ml(1) g 1 Ml(1) Ml(2) n and nl Ml(1) 1 n Substtutng (11) and (12) n (1) results n a system of L+3 equatons, whose unknown factors are the Lagrange multplers (Π 1, Π 2,, ΠL, Π L+1 ), u 1, and u 2. ng nl wth u1 1 and u 2 1. n n g l Solvng ths set of equatons then usng (11) or (12), as needed, gves the values of n. These values n represent the mproved values over the frst teratons n (1). A loop of teratons s thus defned by usng n (k) n the place of the n k-1 for the k th teraton.

6 Modelng and Smulaton of Chemcal System Vaporzaton at Hgh Temperature: Applcaton to the Vtrfcaton of Fly Ashes and Radoactve Wastes by Thermal Plasma Transfer equaton 4.1 Determnaton of the stochometrc coeffcent To smplfy the wrtng and calculaton of the mass transfer equaton at the nterface, a dmensonless quantty X, called stochometrc coeffcent of a metal J, has been ntroduced and correspondng to : no (13) n where n O- s the mole number of oxygen n the lqud phase related to metal J, whereas the term nm represents the total mole number of metal J n the lqud phase, whch contans m speces. For example f N s the total mole number of metals n the mxng melted materal, for an unspecfed metal J, the expressons of X s as follows : M m 1 a n k N m 1 1 an a a (14) a and a k are respectvely the stochometrc coeffcents of the element J, and oxygen n speces. n represents the number of moles of speces. s the valence of metal J n oxde. 4.2 Example In an ntal mxture of Al-S-Fe-O-Cl, for example, the speces whch can exst n the lqud phase at 17 K are as follows: SO 2, Fe 2 SO 4, Fe 3 O 4, FeO, Al 2 O 3, AlCl 3, FeCl 2. The ron stochometrc coeffcents X Fe n the system s gven by the followng expresson: X Fe 4 (4 n ) 4n n n 3 n n Fe SO Fe O FeO Fe SO Fe O FeO (15) 4.3 Transfer equaton From equaton (13), the oxygen mole number n the lqud phase related to metal J, can be deduced,.e. n. n (16) O M If equaton (16) s dfferentated relatvely to tme and each term s dvded by the surface of the nterface value A, t comes : 1 dn 1 dn O M 1 d nm (17) A dt A dt A dt

7 172 Heat and Mass Transfer Modelng and Smulaton The nterfacal densty of molar flux of a speces s: J 1 dn (mole.s A dt -1.m -2 ) (18) Introducng equaton (18), n equaton (17), leads to: L nm d L L J ( JO) M.( ) JM (19) A dt ( J O) M represent the surfacc molar flux denstes of oxygen related to metal J from the L lqud phase, whereas ( J M ) s the equvalent densty of molar flux of a metal J from the lqud phase. The total surfacc denstes of molar flux of oxygen from the lqud phase s expressed by: L L O N ( J ) ( J ) (2) 1 L O M If n the equaton (2) ( J O) M s replaced by ts expresson gven by the equaton (19) t follows: d ( J ) ( J ) n. dt N N L L 1 O M M (21) 1 A 1 Indcatng by Ng, the number of speces whch can exst n the vapor phase, the expressons of the total denstes of molar flux of oxygen and an unspecfed metal J n gas phase are: Ng G G O akj 1 ( J ) (22) G M ( J ) a J (23) Ng 1 where J G s the molar flux densty of a gas speces. The mass balance at the nterfacal lqud to gas s expressed by the equalty between the equvalent denstes of molar flux of an element n the two phases,.e. : L G G ( J ) ( J ) (24) The use of matter conservaton equatons at the nterface, for oxygen and metals, and the combnaton of equatons (16), (17), (18), (19) and (2), lead to the followng equaton. ( ) dx. dt N Ng N G G 1 X JM a kj nm 1 1 A 1 (25)

8 Modelng and Smulaton of Chemcal System Vaporzaton at Hgh Temperature: Applcaton to the Vtrfcaton of Fly Ashes and Radoactve Wastes by Thermal Plasma 173 The equaton (25) s the oxygen matter conservaton equaton or the transfer equaton at the nterface. Argon s used as a carrer gas. In the plasma condtons, t s supposed that argon s an nert gas, so ts molar flux densty s zero: G Ar The densty flux for a gas speces s gven by: J (26) x w G D p p w J ( ) JT. p (27) RT w x where p and p represent the nterfacal partal pressure and the partal pressure n the carrer gas of speces respectvely; J T s the total mass flux densty wth n 1 G G n w T 1 Ar 1 J J, J and p 1 atm, s boundary layer thckness, and D s dffuson coeffcent. 5. Flux retaned by the bath The Faraday's frst law of electrolyss states that the mass of a substance produced at an electrode durng electrolyss s proportonal to the mole number of electrons (the quantty of electrcty) transferred at that electrode [1]: Q M m (28) q N where m s the mass of the substance produced at the electrode (n grams), Q s the total electrc charge passng through the plasma (n coulombs), q s the electron charge, v s the valence number of the substance as an on (electrons per on), M s the molar mass of the substance (n grams per mole), and N A s Avogadro's number. If the mole number of a substance s ntally n, ts mole number produced at the electrode s: A n Q n (29) qvn A The nterfacal densty of molar flux of a speces s: J 1 dn (mole.s -1.m -2 ) (3) A dt R The densty ( J ), of molar flux of a speces retaned by the bath under the electrolyses effects, can be obtaned by substtutng (29) n (3) to yeld: J d n R 1 1 qvna Q dn n dq (31) A dt A dt A. qn. v dt A

9 174 Heat and Mass Transfer Modelng and Smulaton dq I dt represents the current n the plasma and constant. Equaton (31) becomes: 1 F qn Cmol. s Faraday's A J R I n (32) AFv.. 6. Numercal soluton Newton s numercal method solves the mass balance equatons (26), (27) and (28) wth respect to the nterfacal thermodynamc equlbrum, the unknown parameters beng the nterfacal partal pressure P w, the stochometrc coeffcent X J and the molar flux denstes G J. The convergence scheme s as follows: - We calculate the lqud-gas nterfacal chemcal composton of the closed system by usng Ercksson s program. The oxygen partal pressure s then defned by the convergence algorthm. - The recently known values of p w and X J are ntroduced nto the mass equlbrum equatons whch can be solved after a seres of teratve operatons up to the algorthm convergence. - At the begnnng of the next vaporzaton stage, the system s restarted wth the new data of chemcal composton. The tme ncrement s not constant and should be adusted to the stage n order to prevent convergence nstabltes when a sudden local varaton of the mass flux densty occurs. 7. Estmaton of the dffuson coeffcents Up to temperatures of about 1 K, the bnary dffuson coeffcents are known for current gases, oxygen, argon, ntrogen etc. For temperatures hgher than 1 K, the dffuson coeffcents of the gas speces n the carrer gas are calculated accordng to level 1 of the CHAPMAN-ENSKOG approxmaton [11]: D T ( M M )/2M M P 2 (1.1)* * T ( ) (33) In ths equaton D s the bnary dffuson coeffcent (n cm 2.s -1 ), M and M are the molar masses of speces and. P s the total pressure (n atm), T s the temperature (n K), * k T T s the reduced temperature, K s the Boltzmann constant, s the collson dameter (n Å), s the bnary collson energy and (1.1)* * ( T ) s the reduced collson ntegral. For an nteracton between two non-polar partcles and : (34)

10 Modelng and Smulaton of Chemcal System Vaporzaton at Hgh Temperature: Applcaton to the Vtrfcaton of Fly Ashes and Radoactve Wastes by Thermal Plasma (35) 2 The values relatng to current gases needed for our calculatons are those of Hrschfelder [11]. For the other gas speces, such as the metal vapor, the parameters of the ntermolecular potental reman unknown whatever the nteracton potental used. Ths makes mpossble the determnaton of the reduced collson ntegral. For ths reason the partcles are regarded as rgd spheres and the collson ntegrals are assmlated to those obtaned wth the rgd spheres model [12]. That s equvalent to the assumpton: (1.1)* * T ( ) = 1 (36) r r (37) The terms r and r are the rad of the colldng partcles. For the monoatomc partcles, the atomc rad are already found. For the polyatomc partcles, the rad of the complex molecules A n B m are unknown. Thus t has been supposed that they had a sphercal form and ther rad were estmated accordng to [12]: AB A B r nr mr (38) n m In the above expresson, r A and r B are ether of the onc radus, or of the covalence radus accordng to the exstng bndng types. The rad of all the ons whch form metal oxdes and chlordes are extracted from the Shannon tables [13]. At hgh temperature (T > 1 K), the D varaton law wth the temperature s close to the power 3/2 [14]. For ths reason the dffuson coeffcents of the gas speces are calculated wth only one value of temperature (17 K). For the other temperatures the followng equaton s appled: T2 D ( T2) D ( T1). T1 3 2 (39) 8. Applcaton of the model To smulate the same emsson spectroscopy condtons n whch the expermental measurement are obtaned, the contanment matrx used for ths study s formed by basalt, and ts composton s gven n table 1. At hgh temperatures (T > 17K), n the presence of oxygen and argon, the followng speces are preserved n the model: - In the vapor phase: O 2, O, Mg, MgO, K, KO, Na, Na 2, NaO, Ca, CaO, S, SO, SO 2, Al, AlO, AlO 2, Fe, FeO, T, TO, TO 2, and Ar. - In the condensed phase : CaSO 3,Ca 2 SO 4, CaMgS 2 O 6, K 2 S 2 O 5, SO 2, Fe 2 SO 4, Fe 3 O 4, FeO, FeNaO 2, Al 2 O 3, CaO, Na 2 O, Na 2 SO 3, Na 2 S 2 O 5, K 2 O, K 2 SO 3, MgO, MgAl 2 O 4, MgSO 3, Mg 2 SO 4, CaTSO 5, MgT 2 O 5, Mg 2 TO 4, Na 2 T 2 O 5, Na 2 T 3 O 7, TO, TO 2, T 2 O 3, T 3 O 5, and T 4 O 7.

11 176 Heat and Mass Transfer Modelng and Smulaton Elements Mg K Na Ca S Al Fe T Chemcal form MgO K 2 O Na 2 O CaO SO 2 Al 2 O 3 FeO TO 2 % n mass Caton mole number Table 1. Composton of basalt Ths study focuses on the three radoelements 137 Cs, 6 Co, and 16 Ru. Ruthenum s a hgh actvty radoelement, and t s an emtter of, and radatons, wth long a radoactve perod. However, Cesum and Cobalt are two low actvty radoelements and they are emtters of and radatons wth short-perods on the average (less than or equal to 3 years) [15]. To smplfy the system, the radoelements are ntroduced separately n the contanment matrx, n ther most probable chemcal form. Table 2 recaptulates the chemcal forms and the mass percentages of the radoelements used n the system. The mass percentages chosen n ths study are the same as that used n expermental measurements made by [9, 16]. radoelement 137Cs 6Co 16Ru Most probable chemcal form Cs 2 O CoO Ru % n mass Table 2. Chemcal Forms and Mass Percentages of radoelement The addton of these elements to the contanment matrx, n the presence of oxygen, leads to the formaton of the followng speces: - In the vapor phase: Cs, Cs 2, CsK, CsNa, CsO, Cs 2 O, Cs 2 O 2, Ru, RuO, RuO 2, RuO 3, RuO 4, Co, Co 2, and CoO. - In the condensed phase: Cs, Cs 2 O, Cs 2 O 2, Cs 2 SO 3, Cs 2 S 2 O 5, Cs 2 S 4 O 9, Ru, CoAl, CoO, Co 2 SO 4, CoS, CoS 2, Co 2 S, and Co. These speces are selected wth the assstance of the HSC computer code [17]. In the smulaton, the selected formaton free enthalpes of speces are extracted from the tables of [18-2]. 9. Smulaton results In ths part we wll present only the results of radoelement volatlty obtaned by our computer code durng the treatment of radoactve wastes by plasma. However the results of heavy metal volatlty durng fly ashes treatment by thermal plasma can be fnd n [4,5]. 9.1 Temperature nfluence To have the same emsson spectroscopy condtons n whch the expermental measurement are obtaned [9, 16], n ths study the partal pressure of oxygen n the carrer gas P O 2 s fxed at.1 atm, the total pressure P at 1 atm, and the plasma current I at 25 A. Fgures 2 and 3 depct respectvely, the nfluence of bath surface temperatures on the Cobalt and Ruthenum volatlty. Up to temperatures of about 2 K, Cobalt s not volatle. Beyond ths

12 Modelng and Smulaton of Chemcal System Vaporzaton at Hgh Temperature: Applcaton to the Vtrfcaton of Fly Ashes and Radoactve Wastes by Thermal Plasma 177 value, any ncrease of temperature causes a consderable ncrease n both the vaporzaton speed and the vaporzed quantty of 6 Co. Ths behavor was also observed for 137 Cs [8]. Contrarly to Cobalt, Ruthenum has a dfferent behavor wth temperature. For temperatures less than 17 K and beyond 2 K, Ruthenum volatlty ncreases whth temperature ncreases. Whereas n the temperature nterval between 17 K and 2 K, any ncrease of temperature decreases the 16 Ru volatlty. To better understand ths Ru behavor, t s necessary to know ts composton at dfferent temperatures. Table 3 presents the mole numbers of Ru components n the gas phase at dfferent temperatures obtaned from the smulaton results. speces Ru RuO RuO 2 RuO 3 RuO 4 Mole numbers 17K K K Table 3. Mole numbers of Ru components n the gas phase at dfferent temperatures.42 T=17 K Mole Number of Co remander n the lqud phase T=25 K T=22 K T=24 K P O2 =.1atm I=25 A Tme (s) Fg. 2. Influence of temperature on Co volatlty The frst observaton that can be made s that the mole numbers of Ru, RuO, and RuO 2 ncrease wth temperature, contrary to RuO 3 and RuO 4 whose mole numbers decrease wth ncreasng temperatures. These results are logcal because the formaton free enthalpes of Ru, RuO, and RuO 2 decrease wth temperature. Therefore, these speces become more stable when the temperature ncreases, whle s not the case for RuO 3 and RuO 4. A more nterestng observaton s that at temperatures between 17 and 2 K the mole numbers of Ru, RuO, and RuO 2 ncrease by an amount smaller that the amount of decrease of the

13 178 Heat and Mass Transfer Modelng and Smulaton mole numbers of RuO 3 and RuO 4 resultng n an overall reducton of the total mole numbers formed n the gas phase. At temperature between 2 and 25 K the opposte phenomenon occurs. Mole number of Ru remander n the lqud phase T = 25 K P O2 =.1 atm I = 25 A T = 2 K T = 17 K Tme (s) Fg. 3. Influence of temperature on Ru volatlty 9.2 Effect of the atmosphere The furnace atmosphere s supposed to be constantly renewed wth a composton smlar to that of the carrer gas made up of the mxture argon/oxygen. For ths study, the temperature s fxed at 25 K, the total pressure P at 1 atm and the plasma current I at 25 A. Fgures 4 and 5 present the results obtaned for 6 Co and 16 Ru as a functon of P. O 2 For 6 Co, a decrease n the vaporzaton speed and n the volatlzed quantty can be notced when the quantty of oxygen ncreases,.e., when the atmosphere becomes more oxdzng. The presence of oxygen n the carrer gas supports the ncorporaton of Cobalt n the contanment matrx. The same behavor s observed n the case of 137 Cs n accordance wth P [8]. O 2 When studyng the Ruthenum volatlty presented n the curves of fgure 5 t s found that, contrary to 6 Co, ths volatlty ncreases wth the ncrease of the oxygen quantty. Ths dfference n the Ruthenum behavor compared to Cobalt can be attrbuted to the redox character of the maorty speces n the condensed phase and gas n equlbrum. For 6 Co, the oxdaton degree of the gas speces s smaller than or equal to that of the condensed phase speces, hence the presence of oxygen n the carrer gas supports the volatlty of 6 Co. Whereas 16 Ru, n the lqud phase, has only one form (Ru). Hence, the oxdaton degree of the gas speces s greater than or equal to that of lqud phase speces and any addton of oxygen n the gas phase ncreases ts volatlty.

14 Modelng and Smulaton of Chemcal System Vaporzaton at Hgh Temperature: Applcaton to the Vtrfcaton of Fly Ashes and Radoactve Wastes by Thermal Plasma Mole Number of Co remander n the lqud phase P O2 =.1 atm P O2 =.5 atm P O2 =.3 atm P O2 =.1 atm Tme(s) Fg. 4. Influence of the atmosphere nature on the Co volatlty Mole number of Ru remander n the lqud phase P O2 =.1 atm T=25 K I=25 A P O2 =.1 atm P O2 =.3 atm P O2 =.5 atm Tme (s) Fg. 5. Influence of the atmosphere nature on the Ru volatlty

15 18 Heat and Mass Transfer Modelng and Smulaton 9.3 Influence of current To study the nfluence of the current on the radoelement volatlty, the temperature and the partal pressure of oxygen are fxed, respectvely, at 22 K and at.2 atm, whereas the plasma current s vared from A to 6 A. Fgures 6 and 7 depct the nfluence of plasma.4 Mole Number of Co remander n the lqud phase I = 6 A I = 3 A I = A Tme (s) Fg. 6. Influence of plasma current on Co volatlty.64 Mole number of Cs remander n the lqud phase tme (s) Fg. 7. Influence of current on Cs volatlty

16 Modelng and Smulaton of Chemcal System Vaporzaton at Hgh Temperature: Applcaton to the Vtrfcaton of Fly Ashes and Radoactve Wastes by Thermal Plasma 181 current on the Cobalt and Cesum volatlty. The curves of these fgures ndcate that the ncrease of the plasma current consderably ncreases both the vaporzaton speed and the vaporzed quantty of 6 Co and 137 Cs. In the model, the electrolyses effects are represented by the ons flux retaned by the bath, gven by equaton (32), whch depends essentally on the plasma current. As the evaporaton knetcs decrease wth ntensty current, the bath s n cathode polarzaton whch prevents 6Co and 137 Cs from leavng the lqud phase. Theses results assert the valdty of equaton (32) used by ths computer code and conforms to the expermental results obtaned by spectroscopy emsson [9, 16]. The same behavor s observed n the case of 16 Ru as a functon of plasma current. 9.4 Influence of matrx composton Three matrces are used n ths study and ther compostons are gven n table 4. Matrx 1 s obtaned by the elmnaton of 29 g of Slcon for each 1 g of basalt, whereas matrx 2 s obtaned by the addton of 65 g of Slcon for each 1 g of basalt, and matrx 3 s basalt. Fgures 8 and 9 depct the nfluence of contanment matrx composton, respectvely, on the Cobalt and Cesum volatlty. The ncrease of slcon percentage n the contanment matrx supports the ncorporaton of 6 Co and 137 Cs n the matrx. For 137 Cs, the ncrease of slcon percentage n the contanment matrx s accompaned by an ncrease n mole numbers of Cs 2 S 2 O 5 and Cs 2 S 4 O 9 n the condensed phase. The presence of these two speces n addton to Cs 2 SO 3 n sgnfcant amounts (between 1-3 and 1-2 mole) prevents Cs from leavng the lqud phase and reduces ts volatlty. For Cobalt, the ncrease of slcon percentage n the system supports the confnement of 6 Co n the condensed phase n the Co 2 SO 4 form. Ruthenum s not consdered n ths study because, n the lqud phase, t has only the Ru form and any modfcaton n the contanment matrx has no effect on ts volatlty..4 Mole Number of Co remander n the lqud phase Matrx 1 Basalt Matrx Tme (s) Fg. 8. Influence of matrx composton on Co volatlty

17 182 Heat and Mass Transfer Modelng and Smulaton Mole numbers of Cs remander I the lqud phase Matrx 1 Basalt Matrx Tme(s) Fg. 9. Influence of matrx composton on Cs volatlty 9.5 Dstrbuton of Co and Ru on ts elements durng the treatment Fgures 1 and 11 depct the dstrbuton of Cobalt components on the lqud and gas phases. In the gas phase, Cobalt exsts essentally n the form of Co and, to a smaller degree, n the CoO form. In the lqud phase, Cobalt s found n quas totalty n CoO, Co and Co 2 SO 4 forms. Fgure 12 presents the dstrbuton of Ruthenum components on the lqud and gas phases. In the gas phase, Ruthenum exsts essentally n the form of RuO 2 and, to a smaller degree, n the form of RuO 3 and RuO, whereas Ru and RuO 4 exst n much smaller quanttes compared to the other forms. In the lqud phase, Ruthenum has only the Ru form. CoO Mole number (n log) CoS CoAl Co Co 2 SO4 Co 2 S Tme (s) Fg. 1. Varaton of the mole numbers of Co composton n the gas phase

18 Modelng and Smulaton of Chemcal System Vaporzaton at Hgh Temperature: Applcaton to the Vtrfcaton of Fly Ashes and Radoactve Wastes by Thermal Plasma 183 CoO -3.5 Co Co 2 SO4 Mole number (n log) CoS CoAl Co 2 S tme (s) Fg. 11. Varaton of the mole numbers of Co composton n the lqud phase -1 Ru Mole number (n Log) RuO(g) RuO 4 (g) RuO 2 (g) Ru(g) RuO 3 (g) Tme (s) Fg. 12. Varaton of the mole numbers of Ru composton n the gas and lqud phases

19 184 Heat and Mass Transfer Modelng and Smulaton 1. Comparson wth the expermental results The expermental setup s consttuted of a cylndrcal furnace, whch supports a plasma devce wth twn-torch transferred arc system. The two plasma torches have opposte polarty. The reactor and the torches are cooled wth water under pressure by two completely ndependent crcuts. Argon s ntroduced at the tungsten cathode and the copper anode whle oxygen, helum and hydrogen are nected through a water-cooled ppe [21]. To perform spectroscopc dagnostc above the molten surface, a water cooled stanless-steel crucble s placed under the couplng zone of the twn plasma torches. Ths crucble s flled wth basalt and 1 % n oxde mass of Cs. On the cooled walls, the materal does not melt and, hence, runs as a self-crucble. The ntenstes of the Ar lne (λ = nm) and the Cs lne (λ = nm) are measured by usng an optcal emsson spectroscopy method (fgure 13). The molar rato Cs/Ar s deduced from the ntensty rato of the two lnes [9, 16]. example of spectrum: Cs lne (λ = nm) Ar O 2, H 2,... Ar λ OES Arrangement Fg. 13. Schematc of the expermental setup: (1) reactor vessel; (2) cathode torch; (3) anode torch; (4) sphercal-bearng arrangement; (5) necton lance; (6) crucble; (7) porthole; (8) optcal system; (9) monochromator; (1) OMA detector; (11) computer. Fgure 14 shows the code results n comparson wth the expermental measurements. Ths fgure reveals that the expermental and smulaton results are relatvely close. The

20 Modelng and Smulaton of Chemcal System Vaporzaton at Hgh Temperature: Applcaton to the Vtrfcaton of Fly Ashes and Radoactve Wastes by Thermal Plasma 185 small dfference between the smulaton results and the expermental measurements can be attrbuted to the measurements errors. In fact, the estmated error commtted on the measurement of the rato Cs/Ar s around 1% [9, 16]. The model calculatons assumed a bath fully melted and homogeneous from the begnnng (t = s), whle n practce the nsde of the crucble s not fully melted and there s a progress of fuson front that allows a permanent almentaton of the lqud phase n elements from the sold. These causes explan the perturbaton of the expermental measurements and the large gap between these measurements and the results obtaned by the model n the frst few mnutes. 2.E-4 Cs/Ar (molar rato) 1.5E-4 1.E-4 5.E-5.E+ 3 Tme (s) 6 9 Fg. 14. Comparson between the smulaton and expermental results n the case of Cs 11. Concluson The obectve of ths method s to mprove the evaporaton phenomena related to the radoelement volatlty and to examne ther behavor when they are subected to a heat treatment such as vtrfcaton by arc plasma. The man results show that up to temperatures of about 2 K, Cobalt s not volatle. For temperatures hgher than 2 K, any ncrease n molten bath temperature causes an ncrease n the Cobalt volatlty. Ruthenum, however, has a dfferent behavor wth temperature compared to Cobalt. For temperatures less than 17 K and beyond 2 K, Ruthenum volatlty ncreases when temperature ncreases. Whereas n the temperature nterval from 17 K to 2 K, any ncrease of temperature decreases the Ru volatlty. Oxygen flux n the carrer gas supports the radoelement ncorporatons n the contanment matrx, except n the case of the Ruthenum whch s more volatle under an oxdzng atmosphere. For electrolyses

21 186 Heat and Mass Transfer Modelng and Smulaton effects, an ncrease n the plasma current consderably ncreases both the vaporzaton speed and the vaporzed quanttes of Cs and Co. The ncrease of slcon percentage n the contanment matrx supports the ncorporaton of Co and Cs n the matrx. The comparson between the smulaton results and the expermental measurements reveals the adequacy of the computer code. 12. Acknowledgements Ths work was supported by the Natonal Plan, for Scences, Technology and nnovaton, at Al Imam Muhammed Ibn Saud Unversty, college of Scences, Kngdom of Saud Araba. 13. Nomenclature D J : dffuson flux densty for the gas speces. R J : flux retaned by the bath for the gas speces. G: free energy of a system g : formaton free enthalpy of a speces under standard condtons, R : perfect gas constant, T : temperature, n : mole number of speces. p : partal pressure of a gas speces X : molar fracton of speces n the lqud phase. P : total pressure, n g : total mole number of the speces n the gas phase, n l : total mole number of the speces n the condensed phase a : atoms grams number of the element n the chemcal speces B : total number of atoms grams of the element n the system. n O2 : equvalent mole number of oxygen L: Lagrange functon : Lagrange multplers ξ (n ) : Taylor seres expanson of F (F=G/RT) n O- : mole number of oxygen n the lqud phase related to metal J n : total mole number of metal J n the lqud phase M : valence of metal J n oxde A: value of nterface surface J : nterfacal densty of molar flux of a speces : D : m : Q : q : v : boundary layer thckness dffuson coeffcent mass of the substance produced at the electrode total electrc charge passng through the plasma electron charge valence number of the substance as an on (electrons per on)

22 Modelng and Smulaton of Chemcal System Vaporzaton at Hgh Temperature: Applcaton to the Vtrfcaton of Fly Ashes and Radoactve Wastes by Thermal Plasma 187 M : molar mass of the substance N A : Avogadro's number I: current n the plasma F: Faraday's constant * k T T : reduced temperature K : : : (1.1)* * T Boltzmann constant collson dameter bnary collson energy ( ) : reduced collson ntegral r : 14. References radus of a partcle [1] Erksson G., Rosen E., J. Chemca Scrpta, 4:193, (1973) [2] Pcheln G., Rouanet A., J. Chemcal Engneerng Scence, 46:1635, (1991) [3] Bade J. M., Chen X., Flamant G., J. Chemcal Engneerng Scence, 52:4381, (1997) [4] Ghlouf I., Baronnet J. M., J. Hgh Temperature Materals Process, volume 1, Issue 1, p , (26) [5] Ghlouf I., J. Hgh Temperature Materals Process, volume12, Issue1, p.1-1, (28) [6] Ghlouf, I., J. Hazard. Mater. 163, , (29) [7] Ghlouf, I., J. Plasma Chemstry and Plasma Processng, Volume 29, Number , (29) [8] Ghlouf I., Amouroux J., J. Hgh Temperature Materals Process, volume 14, Issue 1, p , (21) [9] Ghlouf I., Grold C., J. Plasma Chemstry and Plasma Processng, 31:19 125, (211) [1] Serway, Moses, and Moyer, Modern Physcs, thrd edton (25) [11] Hrschfelder, J. O., Curts, C. F., and Brd, R. B., (1954), Molecular Theory of Gases and Lquds, John Wlley & Sons, New-York. [12] Razafnmanana, M., (1982), "Etude des coeffcents de transport dans les mélanges hexafluorure de soufre azote applcaton à l arc électrque", Thèse, Unversté de Toulouse. [13] Shannon R. D., Prewtt C. T., (1969), "Effectve Ionc Rad Oxdes and Fluordes", Acta Cryst., Vol. B25, pp [14] Brd R. B., Stewart W. E., Lghtfood E. N., (196): "Transport phenomena" Ed. Wlly. [15] M. Jorda, E. Revertegat, Les clefs du CEA, n 3, 1995, pp [16] C. Grold, Incnératon/vtrfcaton de déchets radoactfs et combuston de gaz de pyrolyse en plasma d arc, Ph.D. Thess, Unversté de Lmoges, France, [17] Outokumpu HSC Chemstry, Chemcal Reacton and Equlbrum Modules wth Extensve Thermochemcal Database, Verson 6, (26) [18] Barn I., Thermochemcal Data of Pure Substances, Wenhem; Basel, Swtzerland; Cambrdge; New York: VCH, (1989)

23 188 Heat and Mass Transfer Modelng and Smulaton [19] Chase Malcolm, NIST-JANAF, Thermochemcal Tables, Fourth Edton, J. of Phys. and Chem. Ref. Data, Monograph No. 9, (1998) [2] Landolt-Bornsten, Thermodynamc Propertes of Inorganc Materal, Scentfc Group Thermodata Europe (SGTE), Sprnger-Verlag, Berln-Hedelberg, (1999) [21] S. Megy, S. Bousrh, J.M.,Baronnet, E.A. Ershov-Pavlov, J.K. Wllams, D.M. Iddles, J. Plasma Chemstry and Plasma Processng, 15, n 2, (1995),

24 Heat and Mass Transfer - Modelng and Smulaton Edted by Prof. Md Monwar Hossan ISBN Hard cover, 216 pages Publsher InTech Publshed onlne 22, September, 211 Publshed n prnt edton September, 211 Ths book covers a number of topcs n heat and mass transfer processes for a varety of ndustral applcatons. The research papers provde advances n knowledge and desgn gudelnes n terms of theory, mathematcal modelng and expermental fndngs n multple research areas relevant to many ndustral processes and related equpment desgn. The desgn of equpment ncludes ar heaters, coolng towers, chemcal system vaporzaton, hgh temperature polymerzaton and hydrogen producton by steam reformng. Nne chapters of the book wll serve as an mportant reference for scentsts and academcs workng n the research areas mentoned above, especally n the aspects of heat and mass transfer, analytcal/numercal solutons and optmzaton of the processes. How to reference In order to correctly reference ths scholarly work, feel free to copy and paste the followng: Imed Ghlouf (211). Modelng and Smulaton of Chemcal System Vaporzaton at Hgh Temperature: Applcaton to the Vtrfcaton of Fly Ashes and Radoactve Wastes by Thermal Plasma, Heat and Mass Transfer - Modelng and Smulaton, Prof. Md Monwar Hossan (Ed.), ISBN: , InTech, Avalable from: InTech Europe Unversty Campus STeP R Slavka Krautzeka 83/A 51 Reka, Croata Phone: +385 (51) Fax: +385 (51) InTech Chna Unt 45, Offce Block, Hotel Equatoral Shangha No.65, Yan An Road (West), Shangha, 24, Chna Phone: Fax:

25 211 The Author(s). Lcensee IntechOpen. Ths chapter s dstrbuted under the terms of the Creatve Commons Attrbuton-NonCommercal- ShareAlke-3. Lcense, whch permts use, dstrbuton and reproducton for non-commercal purposes, provded the orgnal s properly cted and dervatve works buldng on ths content are dstrbuted under the same lcense.