A novel mathematical model of formulation design of emulsion explosive

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1 J. Iran. Chem. Res. 1 (008) Journal of the Iranan Chemcal Research IAU-ARAK A novel mathematcal model of formulaton desgn of emulson explosve Mng Lu *, Qfa Lu Chemcal Engneerng College, Nanjng Unversty of Scence and Technology, Nanjng 10094, PR Chna Receved 3 June 008; receved n revsed form 9 September 008; accepted 14 September 008 Abstract A novel mathematcal model has been developed to ad the formulaton of emulson explosves. Ths mathematcal model calculated heat of exploson, oxygen balance and raw materal cost as a functon of explosve ngredents, and the soluton of the mathematcal model was obtaned by a MS Excel program. The effects of the dfferent content of NH 4 NO 3, NaNO 3, H O, and span-80 and composte fuel ol on the heat of exploson and the specfc volume of emulson explosve were dscussed based on the proposed mathematcal model. The results show that (1) wth the ncreasng of the content of NH 4 NO 3, the heat of exploson and the specfc volume ncrease. () The better content of NaNO 3, H O and Span-80 n the formulaton of emulson explosve are 7%~9%, 9%~10%, 1.5%~% respectvely, and ths formulaton results n an oxygen balance of zero or close to zero. Keywords: Mathematcal model, Emulson explosve, Exploson, oxygen balance 1. Introducton The commercal emulson explosves developed n the early 1s [1, ] are very mportant blastng means because of ther hgher detonaton parameters and better water-resstant characterstcs [3, 4]. Ammonum ntrate used n the emulson explosves s the prmary oxdzer and sodum ntrate s frequently added to mprove the propertes of the oxdzer soluton. The ol phase conssts of varous mneral ols, waxes, and even polymers. Explosve propertes are usually prmary consderaton durng the formulaton of emulson explosves. A non-optmum explosve formulaton should result n a poor explosve performance and an ncrease n noxous fumes, all of whch are detrmental to the overall blastng objectves. The object of the present work s to develop a novel mathematcal model to mprove the formulaton desgn of emulson explosves. The contents of ths paper are as follows: 1) a novel computer aded method for the formulaton of emulson explosves; ) the establshment of a mathematcal model for the formulaton of emulson explosves; 3) the computer aded formulaton desgn and optmzaton of emulson explosve and, 4) numerous reasonable formulatons wth an oxygen balance of zero or close to zero.. Mathematcal model * Correspondng author. Tel.: ; fax: E-mal address: lumng30@16.com (M. Lu)

2 M. Lu and Q. Lu / J. Iran. Chem. Res. 1 (008) Explosve propertes are usually prmary consderaton durng the formulaton of ndustral explosves [5]. Because explosve propertes are a functon of the heat of exploson (Qv) of an explosve, the heat of exploson s selected as the prmary fgure of mert for our mathematcal model. Emulson explosves consst of Carbon (C), Hydrogen (H), Oxygen (O), Ntrogen (N) and sodum (Na). The general emprcal formula of emulson explosves s C a H b O c N d Na h. Assumed the specfc emprcal formula s, C a H b O c N d Na h, then the molar mass of component s gven as m and the molar number of component n 1 kg explosve s 10x /m, where x s the percent mass content of component. The equaton for the reacton of an explosve contanng C, H, O, N, Na s gven n equaton (1). C a H b O c N d Na h = n = 1 10x m ( C h b d NaO + H O + N b h + (a c + + ) CO a H b O c N d Na h b + ( c a) CO h ) (1) where a = Σ10a x /m, b = Σ10b x /m, c = Σ10c x /m,and d = Σ10d x /m, h = Σ10h x /m, The mathematcal formula (where the prmary fgure of mert s Heat of Exploson) s shown n equaton (). h b d b + h Qv = H Na ( ) O + H H O + H N + c a H n b h 10 + (a c + + ) H CO x H m = 1 CO () The mathematcal expressons for the other fgures of mert are: Oxygen Balance (OB) = Σa x = 100η Varable Sum (VS) = Σx = 100 Cost Sum (CS) = Σp x = p/10 Lower lmts and upper lmts = s < x <t, where = 1,,, n. In ths mathematcal model the followng defntons are employed: H f Heat of formaton for the ngredents, the entre explosve or explosve products (kj.mol -1 ) g the molar number of the exploson products; the content of component of the explosve; x m the molar mass of component ; a the oxygen balance of component (%); η the oxygen balance of the explosve (%); p raw materal cost of component, RMBy.t -1 ; p raw materal cost of explosve, RMBy.t -1 ; s lower lmt of component ; (%); t upper lmt of component ; (%). 3. Mathematcal expresson for formulatons of emulson explosves 3.1 Ingredents of emulson explosves and ther chemcal parameters The oxdzer of emulson explosves s usually made up of ammonum ntrate and sodum ntrate, and the fuel s a mxture of varous mneral ols and waxes. The formula, molar mass, heat of formaton, oxygen balance and raw materal cost of these components are gven n Table 1 [6-9].

3 35 M. Lu and Q. Lu / J. Iran. Chem. Res. 1 (008) Mathematcal expresson for formulaton of emulson explosves Provded that the amount of AN, SN, Water, Span-80, wax and mneral ol are respectvely desgnated as x 1, x, x 3, x 4, x 5 and x 6, then: a=0.561x x x 6 b=0.500x x x x x 6 c=0.375x x x x 4 d=0.50x x h=0.118x and, Formula (3) gves the general formula for Heat of Formaton of emulson explosves. 10x H m f ( ) = x x x x 4 (3) and then the prmary fgure of mert (Maxmum Heat of Exploson) s gven by formula (4). MaxQ v =51.08x x -3.07x x x x 6 (4) Formula (4) s assumed as followng condtons: 0x x 39x4 346x5 346x6 = 100K x 1 + x + x3 + x4 + x5 + x6 = x x + 15x4 + 4x5 + 3x6 P /10 70 x1 8 5 x 15 8 x x4 3 x5 4 1 x6 3 For formula (4), the values η and P may be assumed, n general η 0. Table 1 Physcal chemstry parameters of the raw materals of emulson explosves No. Emprcal MW Hf OB Cost Ingredent formula (g/mole) (kj/mole) (%) (RMBy/t) 1 N O 3 H 4 AN O 3 NNa NA H O water 18 4 C 4 H 44 O 6 Span C 18 H 36 Wax C 1 H 6 mneral ol Computer solutons To arrve at a soluton, a computer was employed. The mathematcal formulas constructed prevously were nputted nto a MS Excel program. The mathematcal soluton vared wth dfferent oxygen balance values (η) and raw materal costs P.

4 4. Results and dscusson M. Lu and Q. Lu / J. Iran. Chem. Res. 1 (008) Effect of formulaton desgn on the heat of exploson and the specfc volume Te heat of exploson s the energetc sources to release the explosve power and the specfc volume s the medum to transfer the power. The heat of exploson calculated based on the aforementoned mathematcal model and here the specfc volume was equal to the total volume produced by all gaseous materals after exploson n standard state. The effects of the dfferent contents of NH 4 NO 3, NaNO 3, H O, and Span-80 and composte fuel ol on the heat of exploson and specfc volume were dscussed by the mathematcal model as follows. 4.. Effect of oxdant Comparson ammonum ntrate wth sodum ntrate Ammonum ntrate (AN) s used as the basc oxdant n the emulson explosves and sodum or calcum ntrate s often added to mprove the propertes of the oxdzer soluton. Oxdant s an mportant ngredent n the emulson explosves that supples oxygen n the exploson reacton and ts oxygen balance values s hgher than zero. For an oxdant, the oxygen balance value only ndcates that how much oxygen t can supply n the exploson reacton, but does not demonstrate how much energy t can offer. Furthermore, the hgher oxygen balance value can not explan the hgher energy was released n the exploson reacton. For example, 1 mol ammonum ntrate can supply 0.5 mol oxygen n the exploson reacton, at the same tme, can offer 17.4 kj energy. However, 1mol sodum ntrate can supply 1.5 mol oxygen but absorb kj energy n the exploson reacton. Therefore the release or absorpton of energy for an oxdant s an mportant characterstc parameter whch s related wth the energetc contrbuton of an oxdant and ammonum ntrate s a good oxdant for the energetc contrbuton of ndustral explosves Effect of ammonum ntrate The effects of the dfferent contents of AN on the heat of exploson and the specfc volume are shown n Fg. 1. As seen from Fg. 1, the heat of exploson and the specfc volume would be mproved when the content of AN was ncreased. Ths was attrbuted to hydrogen, oxygen and ntrogen n AN molecule. After exploson hydrogen and oxygen were transformed nto water havng hgh heat of formaton whch was useful to mprove the heat of exploson, and ntrogen became N whch was, however, help to mprove the specfc volume. Therefore, the AN content may be ncreased reasonably n the formulaton desgn of emulson explosves Heat of explosve X AN / % Fg. 1 The effect of AN content on the heat of exploson and specfc volume

5 Effect of sodum ntrate M. Lu and Q. Lu / J. Iran. Chem. Res. 1 (008) Generally, n order to lower the crystallod pont of oxdant, NaNO 3 was used as another oxdant n emulson explosves. The effects of the dfferent contents of NaNO 3 on the heat of exploson and specfc volume are shown n Fg Heat of explosve X NaNO3 / % Fg. The effect of NaNO 3 content on heat of exploson and specfc volume The heat of exploson and the specfc volume were optmal when the NaNO 3 content was 7% as shown n Fg.. Consderng that ncreasng the content of NaNO 3 would lower the crystallod pont of the mxture of ammonum ntrate and sodum ntrate, whch s benefcal to the safety of the producton process of emulson matrx, the best theoretcal formulaton of emulson explosve conssts of 7% ~ 9% NaNO Effect of water Water was used as a solvent of oxdant n emulson explosve, whch made fuel ol mx wth oxdant fully, and the exploson effcency reach to maxmum. Water was changed nto vapor after the exploson, evaporatve heat was needed n ths process and so the heat of exploson of emulson explosve was lower than that of powder AN explosve. The effects of the dfferent contents of H O on the heat of exploson and specfc volume were dscussed by the mathematcal model. As seen from Fg. 3, the best theoretcal formulaton of emulson explosve conssts of 9% ~ 10% H O Effect of Span-80 The effects of the dfferent emulsfer (Span-80) contents on the heat of exploson and specfc volume were dscussed by the mathematcal model. The results are shown n Fg.4. The best theoretcal formulaton of emulson explosve conssts of 1.5% ~.0% Span Effect of oxygen balance The oxygen balance was nfluenced by the contents of composte fuel ol n emulson explosve. The more the composte fuel ol used was, the more negatve the oxygen balance was. Wth the ncreasng of the weght percent of the composte fuel ol, the heat of exploson decreased and the volume of toxc gases (.e., CO) produced after the exploson ncreased.

6 M. Lu and Q. Lu / J. Iran. Chem. Res. 1 (008) Heat of explosve Fg. 3 The effect of water content on heat of exploson and specfc volume X HO / % Heat of explosve X Span-80 / % Fg. 4 The effect of Span-80 content on heat of exploson and specfc volume However, when oxygen balance value was hgher than zero (η>0)) the volume of toxc gases.e. NO produced after the exploson ncreased. Therefore, t was very mportant that oxygen balance value be zero (or close to zero) n order that formulatons should have hgher heat of exploson and lower toxc gas volumes. The effects of the dfferent oxygen balance values on the heat of exploson and the specfc volume are shown n Fg.5. The best theoretcal formulaton of emulson explosve conssts of 7%~9%NaNO 3, 9%~10%H O, 1.5%~%Span-80 respectvely for hgher heat of exploson, specfc volume and lower toxc gas volume Valdatng the model Some performance of a number of emulson explosves contanng glass mcro-balloons were studed expermentally and theoretcally. For each of the explosves, detonaton velocty and power of explosve were measured, and oxygen balance and heat of exploson were calculated. The nfluence of the content of NH 4 NO 3 NaNO 3, H O, and Span-80 n the emulson matrx respectvely on detonaton velocty and power of explosve was examned.

7 39 M. Lu and Q. Lu / J. Iran. Chem. Res. 1 (008) η / % Heat of explosve 940 Fg. 5 The effect of oxygen balance on theoretc exploson heat and specfc volume The emulson matrx was prepared usng aqueous solutons of the mxture of ammonum ntrate wth sodum ntrate. The contents of other ngredents were unchanged nearly n order to mantan the oxygen balance wthn the range of ±0.5%. The compostons of the emulson matrces are gven n Table. The emulsons were prepared usng a smple faclty consstng of a thermostat and a contaner equpped wth a strrer. The soluton of oxdant was heated to 10 and then slowly added nto the contaner, n whch a preheated (100 ) mxture of fuels (ol and span-80) wth the emulsfer was agtated wth the strrer at a speed of 1440 rpm. After addng the entre amount of the oxdzer, the agtaton was contnued for about two mnutes to obtan fne emulson partcles. The fnal explosve mxtures were prepared by mxng the emulson matrces wth glass mcro-spheres (produced by 3M; mean sze about 80 µm). Mxng was performed carefully (usng the same strrer but at lower speed) untl the dstrbuton of the mcrospheres n the emulson matrx became unform. The mass fracton of mcro-spheres was %~ 3% (above 100%) n all experments. For each explosve, the detonaton velocty and power of explosve were measured. The results obtaned enabled a comparson of the effcency for testng explosve performance. They were also used to analyze the effect of formulaton on the performance of the explosves and to choose the formulatons characterzed by the best detonaton and performance characterstcs. A more quantty of ammonum ntrate, a certan extent of water and an oxygen balance of zero or close to zero are favorable for hgher heat of exploson and exploson strength. Table Formulatons and performance of emulson explosves Mass fracton of components, % AN Fuel SN H O Span ol Oxygen balance / % Calculated heat of exploson / kj kg -1 Power of explosve / ml Detonaton velocty / m s

8 M. Lu and Q. Lu / J. Iran. Chem. Res. 1 (008) Concluson Accordng to thermochemstry of exploson reacton, the mathematcal model for formulaton desgn of emulson explosve was establshed. The computer was used to ad the formulaton desgn and optmzaton of emulson explosve by a MS Excel program. The effects of the dfferent content of NH 4 NO 3, NaNO 3, H O and Span-80 and composte fuel ol on the heat of exploson and the specfc volume were dscussed based on the mathematcal model. The results show that wth the ncreasng of the content of NH 4 NO 3, the heat of exploson and the specfc volume were ncreased. The best theoretcal formulaton of emulson explosve conssts of 7%~9%NaNO 3, 9%~10%H O, 1.5%~%Span-80 respectvely, and an oxygen balance of zero or close to zero for hgher heat of exploson, specfc volume and lower toxc gas volume. References [1] R.S. Egly, A.E. Neckar, US (1964//1/15). [] N.E. Gehrg, US (1965/01/05). [3] J. Lee, P.A. Persson, Propell. Explos. Pyrot. 15 (1990) 08. [4] K. Takahash, K. Murata, Y. Kato, M. Fujta, S. Itoh, J. Mater. Proces. Technol. 85 (1999). [5] M. Lu, C. Lu, Sc. Tech. Energetc Materals 68 (007) 117. [6] M. Lu, C. Lu, J. Chn. Explosve Mat. 8 (1999) 1. [7] Z. Yuan, J. Chn. Explosve Mat. 9 (1) 1. [8] C. Lu, Z. Lu, O. L, Commercal Explosves, Ordnance Industry Press, Bejng, [9] M. Lu, Formulaton desgn of commercal explosves, Ordnance Industry Press, Bejng, 00.

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