A Simple Approach for Prediction of the Volume of Explosion Gases of Energetic Compounds

Indian Journal of Engineering & Materials Sciences Vol. 22, December 2015, pp. 701-706

A simple approach for prediction of the volume of explosion gases of energetic compounds

b M Jafaria,b, M Kamalvanda, M H Keshavarzb*, A Zamanib & H Fazeli aDepartment of Chemistry, Faculty of Science, Yazd University, Yazd P.O. Box 89195/741, Islamic Republic of Iran bDepartment of Chemistry, Malek-ashtar University of Technology, Shahin-shahr P.O. Box 83145/115, Islamic Republic of Iran Received 30 June 2014; accepted 8 May 2015

A reliable novel method is introduced for prediction of the volume of explosion gases (VExp Gas) of energetic compounds containing nitroaromatic, acyclic and cyclic nitramine, nitrate ester and nitroaliphatic compounds. It is based on the ratios of carbon and hydrogen atoms to oxygen atoms as well as the correcting function for decreasing overestimated value of VExp Gas. The reliability of the new method is tested and compared with outputs of complex detonation performance and thermochemical computer codes, which require the experimental values of the condensed phase heats of formation of energetic compounds. For 69 different types of energetic compounds, where the measured data are available, statistical parameters of the new model are good as compared to the predicted results of computer codes.

Keywords: Volume of explosion gases, Energetic compound, Molecular structure, Correlation

The expenditure related to synthesis of a new high of moles of gaseous products per unit weight and/or a performance energetic compound requires the greater release heat of detonation. development of theoretical methods. Prediction of its Volume of explosion gases and the heat of detonation or combustion performance is not only detonation are two variables that have been employed cost-effective but also environmentally desirable and in prediction of power of explosives16,17. Since the time saving at early stages of the development power of an energetic compound as its capacity for process. Predictive methods for estimation of doing useful work, it depends on the expansion of performance, sensitivity and physical properties allow gaseous products for doing works such as blasting to identify promising candidates for additional study down rock or propelling a chunk of metal18. Although and elimination of poor candidates from further ballistic mortar, Trauzl lead block, underwater consideration. The search in safe deriving of a new explosion, cylinder, Hess, Kast and plate dent tests are explosive with high performance, but is insensitive common methods for measuring the power of enough to permit safe handling, is one of the explosives19,20, they do not always give the same order important issues to scientist and engineering who of ranking when applied to different classes of handle energetic molecules. Detonation parameters energetic compounds21. Several new correlations have such as pressure, velocity and heat have been been developed to predict the power of high regarded as the principal measures of performance of explosives through ballistic mortar and Trauzl lead detonating explosives for many years1-3. block tests12-16. Also, it was indicated that the heat of Detonation reactions of explosives are usually detonation and the number of moles of gaseous complicated and violent because they show high products per gram of explosive are two important reaction rates, high temperatures, complicated product factors for prediction of the Chapman-Jouguet compositions and so on. For an explosive containing detonation pressures and velocities of CHNOFCl high detonation velocity1,4-11 or power12-16, the explosives7,22. formation of light gaseous products and a high In contrast to the heat of detonation where different positive heat of formation are two fundamental approaches have been developed, there is no suitable parameters. Such explosive provides a greater number method for prediction of volume of explosion gases of energetic materials. Volume of explosion gases, in ______*Corresponding author litres per kg of explosive material, is the volume of (E-mail: [email protected]; [email protected]) the gases (fumes) that is formed by the explosive 702 INDIAN J. ENG. MATER. SCI., DECEMBER 2015

reaction20. It can be calculated from the chemical this temperature under adiabatic conditions, which composition of the explosive by computer codes can be used for calculating the maximum ability of an through the calculation of the moles of gaseous explosive to do work18. Decomposition products can products. It can also be determined experimentally by be estimated by some computer codes such as the Bichel Bomb20. In practice, the composition of the BKW27, CHEETAH28, and REAL29 with an products as well as the volume of gases are appropriate empirical equation of state such as determined at the moment of freezing chemical Becker-Kistiakosky-Wilson (BKW-EOS)30 and the equilibrium, i.e., after fast cooling explosion products Jacobs-Cowperthwaite-Zwisler (JCZ-EOS)31,32, which preferably to the standard temperature and pressure depend on temperature and pressure. The BKW-EOS, (STP) conditions2,18. which is used extensively for calculating the The purpose of this work is to introduce a simple detonation properties of high explosives, has the correlation for prediction of volume of explosion following form27,30: gases of important classes of energetic compounds   including nitroaromatic, acyclic and cyclic nitramine, PV κ∑ kn ii βκ ∑ kn ii 1+= exp  … (1) nitrate ester and nitroaliphatic compounds. For these RT α α compounds where the measured values were ()TV +θ  ()TV +θ  available, the reliability of the new method will be tested and compared with outputs of detonation where P, V, R, T and ni represent pressure, molar gas volume, gas constant, absolute temperature and mole performance code using two equations of state and the th ProPEP (Propellant Performance Evaluation Program) fraction of the i gaseous component, respectively. code23 as thermochemical computer code. The summation extends over all components of the gaseous mixture and the covolume factors, ki, Complex Mixture of Detonation or Combustion represent excluded volume. The parameters α, β, κ, Products and θ are empirical constants, which are adjusted to Detonation24 or combustion25 products are complex fit measured detonation properties. mixtures of the large numbers of molecular species In contrast to the BKW-EOS, which has weak because their concentrations change with temperature theoretical basis, the JCZ-EOS has a strong and pressure as well as they may consist of more than theoretical basis. For the JCZ-EOS, the total pressure one mixture in more than one phase. Depending on can be described by the sum of volume dependent the contribution of various elements and molecular term and a term which is function of both the volume structures, for an explosive with general formula of and the temperature31. The Jacobs-Cowperthwaite- CaHbNcOd, the major detonation or combustion Zwisler-3 EOS (JCZ3-EOS) uses exponential 6 (EXP 6) products are CO, CO2, H2O, N2 and solid carbon as intermolecular potentials on the basis of P-V-T 31,32 well as minor amounts of H2, NH3, O2, NO and other relationships similar to the Mie-Grüneisen EOS . chemical species may be produced. The amount of each product depends on the stoichiometry of the Development of the New Correlation reaction and the effects of other equilibriums within Upon decomposition of CaHbNcOd explosives, all gaseous products such as the water gas equilibrium nitrogen atoms transform to N2 molecules, thus the and Boudouard equilibrium26 : ratios of the number of carbon atoms to oxygen atoms (rC/O) and hydrogen atoms to oxygen atoms (rH/O) may H O + CO→ H + CO consider as the concentration contributions of 2 ← 2 2 different products that contain C, H, and O. In other

words, (rC/O) and (rH/O) can be used to estimate the →CCO+ 2CO← 2 distribution of oxygen atoms between carbon and hydrogen atoms in products. However, (rC/O) and By detonation, energy of an explosive can be (rH/O) have been used for prediction of Qdet of released in the form of heat. Under adiabatic non-aromatic33 and aromatic34 energetic materials. conditions, the evolved heat determines the work The study of the volume of explosion gases (VExp Gas) capacity of the explosive2,18. Under this situation, the for various energetic compounds has shown that it is temperature of detonation/explosion is the maximum possible to use (rC/O) and (rH/O) for prediction of the temperature. Thus, the detonation products can attain VExp Gas. JAFARI et al.: PREDICTION OF THE VOLUME OF EXPLOSION GASES OF ENERGETIC COMPOUNDS 703

Results and Discussion V= y + y r + y r + y V … (2) Exp Gas 0 1C / O 2 H / O 3 Corr

The contributions of rC/O, rH/O, and VExp Gas The reported values of volume of explosion gases Where y0 to y3 are the adjustable coefficients to for different energetic compounds are given in Table 1 provide the contributions of various variables; (rC/O) which are used to derive a suitable correlation of the and (rH/O) represent the ratio of carbon and hydrogen following form for the prediction of volume of atoms to oxygen atom, respectively, and show the explosion gases: contribution of oxygen atoms between carbon and Table 1 – Comparison of the predicted volume of explosion gases (l/kg) of the present method, BKW-EOS30, JCZ3-EOS31,32 and the ProPEP code the with experimental data20

No. Name Formula Density Exp. BKW-EOS JCZ3-EOS ProPEP New (g/cc) Code method

1 Ammonium nitrate (AN), complete H N O 1.5 980 1071 (-91) 830 (150) 1027 (-47) 4 2 3 979 (1) reaction 2 Ammonium dinitramide (ADN) H4N4O4 1.8 1084 987 (97) 888 (196) 903 (181) 990 (94) 3 Hydrazine nitrate H5N3O3 1.6 1001 1095 (-94) 819 (182) 1001 (0) 1064 (-63) 4 Tetranitromethane (TNM) CN4O8 1.6 685 750 (-65) 655 (30) 704 (-19) 686 (-1) 5 Nitromethane (NM) CH3NO2 1.1 1059 1057 (2) 903 (156) 1100 (-41) 983 (76) 6 Methyl nitrate CH3NO3 1.2 873 954 (-81) 954 (-81) 872 (1) 948 (-75) 7 Nitrourea CH3N3O3 1.7 853 889 (-36) 783 (70) 871 (-18) 948 (-95) 8 Nitroguanidine (NQ) CH4N4O2 1.7 1042 944 (98) 847 (195) 1028 (14) 1039 (3) 9 Urea nitrate CH5N3O4 1.7 910 950 (-40) 705 (205) 909 (1) 986 (-76) 10 Methylamine nitrate (MAN) CH6N2O3 1.4 1191 1055 (136) 1108 (83) 1138 (53) 1060 (131) 11 Triaminoguanidine nitrate (TAGN) CH9N7O3 1.5 1163 1066 (97) 983 (180) 1178 (-15) 1171 (-8) 12 3-Nitro-1,2,4-triazole-5-one (NTO) C2H2N4O3 1.9 855 773 (82) 747 (108) 861 (-6) 869 (-14) 13 Polyvinyl nitrate (PVN) (C2H3NO3)n 1.6 958 896 (62) 757 (201) 1006 (-48) 906 (52) 14 Hexanitroethane (HNE) C2N6O12 1.9 734 735 (-1) 700 (34) 672 (62) 681 (53) 15 Ethyleneglycol dinitrate (EGDN) C2H4N2O6 1.5 737 806 (-69) 806 (-69) 810 (-73) 734 (3) 16 1,1-Diamino-2,2-dinitroethene (FOX-7) C2H4N4O4 1.9 779 859 (-80) 900 (-121) 908 (-129) 927 (-148) 17 Ethyl nitrate C2H5NO3 1.1 1101 1031 (70) 1050 (51) 1230 (-129) 980 (121) 18 ethylene dinitramine (EDNA) C2H6N4O4 1.7 1017 943 (74) 1000 (17) 1045 (-28) 983 (34) 19 Ethanolamine dinitrate C2H7N3O6 1.5 927 992 (-65) 1009 (-82) 945 (-18) 967 (-40) 20 Guarnylureadinitramide (FOX-12) C2H7N7O5 1.8 910 917 (-7) 834 (76) 964 (-54) 984 (-74) 21 Ethylenediamine dinitrate (EDD) C2H10N4O6 1.6 1071 1004 (67) 908 (163) 1091 (-20) 1022 (49) 22 Glycidyl Azide Polymer (GAP) C3H5N3O 1.3 946 825 (121) 787 (159) 1006 (-60) 1059(-113) 23 glycerol trinitrate (NG or nitroglycerine) C3H5N3O9 1.6 716 782 (-66) 783 (-67) 722 (-6) 722 (-6) 24 1,3,5-Trinitroso-1,3,5-triazinane C3H6N6O3 1.5 996 919 (77) 1001 (-5) 1100 (-104) 976 (20) 25 1,3,5-Trinitro-1,3,5-triazinane (RDX) C3H6N6O6 1.8 903 902 (1) 983 (-80) 908 (-5) 927 (-24) 26 N,N-bis(2,2,2-trinitroethyl)nitramide C4H4N8O14 2.0 693 758 (-65) 758 (-65) 694 (-1) 697 (-4) (BTNENA) 27 [2-Nitro-3-(nitrooxy)-2-[(nitrooxy) C4H6N4O11 1.7 705 772 (-67) 771 (-66) 760 (-55) 717 (-12) methyl]propyl]-nitrate (NIBTN) 28 butane-1,2,3,4-tetrayl tetranitrate (ETN) C4H6N4O12 1.7 704 771 (-67) 771 (-67) 759 (-55) 715 (-11) 29 Nitromethyl propanediol dinitrate C4H7N3O8 1.5 890 935 (-45) 973 (-83) 896 (-6) 913 (-23) 30 Butane-1,2,4-triyl trinitrate C4H7N3O9 1.5 836 910 (-74) 788 (48) 856 (-20) 909 (-73) 31 diethyleneglycol dinitrate (DEGN) C4H8N2O7 1.4 991 955 (36) 1009 (-18) 1028 (-37) 934 (57) 32 dioxyethylnitramine dinitrate (DINA) C4H8N4O8 1.5 924 959 (-35) 817 (107) 933 (-9) 927 (-3) 33 cyclotetramethylene tetranitramine (HMX) C4H8N8O8 2.0 902 879 (23) 978 (-76) 908 (-6) 927 (-25) 34 Trinitropyridine (TNPy) C5H2N4O6 1.8 818 768 (50) 803 (15) 837 (-19) 810 (8) 35 Trinitropyridine-N-oxide (TNPyOX) C5H2N4O7 1.9 777 783 (-6) 822 (-45) 779 (-2) 820 (-43) 36 1,3-Bis(2,2,2-trinitroethyl)urea (BTNEU) C5H6N8O13 1.9 697 762 (-65) 762 (-65) 733 (-36) 705 (-8) 37 Pentaerythritol Tetranitrate (PETN) C5H8N4O12 1.8 780 852 (-72) 776 (4) 780 (0) 900 (-120) 38 1-(Nitrooxy)-2,2-bis[(nitrooxy)methyl] C5H9N3O9 1.5 966 946 (20) 793 (173) 967 (-1) 920 (46) propane (TMETN) 39 Pentaerythritol trinitrate (PETRIN) C5H9N3O10 1.5 902 928 (-26) 791 (111) 918 (-16) 916 (-14) 40 1,3,5-Triazido-2,4,6-trinitrobenzene C6N12O6 1.7 755 799 (-44) 786 (-31) 800 (-45) 752 (3) (TATNB) (Contd) 704 INDIAN J. ENG. MATER. SCI., DECEMBER 2015

Table 1 – Comparison of the predicted volume of explosion gases (l/kg) of the present method, BKW-EOS30, JCZ3-EOS31,32 and the ProPEP code the with experimental data20 —(Contd)

No. Name Formula Density Exp. BKW-EOS JCZ3-EOS ProPEP New (g/cc) Code method

41 1,3,5-Trinitrobenzene (TNB) C6H3N3O6 1.8 805 729 (76) 805 (0) 893 (-88) 808 (-3)

42 2,4,6-Trinitrophenol (picric acid) C6H3N3O7 1.8 826 722 (104) 616 (210) 866 (-40) 818 (8)

43 2,4,6-Trinitrobenzene-1,3-diol (TNR) C6H3N3O8 1.8 814 695 (119) 700 (114) 820 (-6) 826 (-12)

44 2,3,4,6-Tetranitroaniline (TeNA) C6H3N5O8 1.9 813 757 (56) 793 (20) 820 (-7) 826 (-13)

45 1,3-Dinitrobenzene C6H4N2O4 1.5 907 709 (198) 743 (164) 855 (52) 801 (106)

46 2,4,6-Trinitroaniline (TNA) C6H4N4O6 1.8 838 735 (103) 799 (39) 903 (-65) 827 (11) 47 2-Amino-4,6-dinitrophenol (picramic C6H5N3O5 1.7 847 696 (151) 671 (176) 850 (-3) 839 (8) acid) 48 Ammonium 2,4,6-trinitrobenzen-1-olate C6H6N4O7 1.7 909 757 (152) 697 (212) 913 (-4) 866 (43) (ammonium picrate) 49 1,3,4,5,6-Pentakis(nitrooxy) C6H8N6O18 1.6 694 759 (-65) 759 (-65) 698 (-4) 709 (-15) hexan-2-yl nitrate (MHN)

50 2,2-Bis(nitrooxymethyl)butyl nitrate(ETTN) C6H11N3O9 1.5 1009 915 (94) 797 (212) 1071 (-62) 931 (78)

51 hexamethylene triperoxide diamine (HMTD) C6H12N2O6 1.6 1075 874 (201) 834 (241) 1112 (-37) 976 (99)

52 Triethyleneglycol dinitrate (TEGN) C6H12N2O8 1.3 1065 917 (148) 883 (182) 1079 (-14) 951 (114)

53 2,4,6-Trinitrobenzoic acid C7H3N3O8 1.7 809 697 (112) 718 (91) 830 (-21) 810 (-1)

54 2-Methyl-1,3,5-trinitrobenzene (TNT) C7H5N3O6 1.7 825 739 (86) 786 (39) 908 (-83) 824 (1)

55 3-methyl-2,4,6-trinitrophenol C7H5N3O7 1.6 844 765 (79) 833 (11) 925 (-81) 832 (12) 56 2-methoxy-1,3,5-trinitrobenzene C7H5N3O7 1.6 844 765 (79) 833 (11) 925 (-81) 832 (12) (methyl picrate)

57 N-methyl-N,2,4,6-tetranitroaniline (Tetryl) C7H5N5O8 1.7 861 788 (73) 884 (-23) 935 (-74) 838 (23)

58 1-Methyl-2,4-dinitro benzene C7H6N2O4 1.5 807 687 (120) 675 (132) 860 (-53) 825 (-18)

59 2-Methyl-1,3-dinitrobenzene C7H6N2O4 1.5 807 691 (116) 692 (115) 870 (-63) 825 (-18)

60 2-Methyl-4,6-dinitrophenol C7H6N2O5 1.6 832 703 (129) 689 (143) 867 (-35) 836 (-4)

61 2-(2,4,6-trinitrophenoxy) ethyl nitrate C8H6N4O10 1.7 878 789 (89) 655 (223) 915 (-37) 844 (34)

62 2,4-dimethyl-1,3,5-trinitrobenzene (TNX) C8H7N3O6 1.6 843 738 (105) 769 (74) 913 (-70) 841 (2)

63 2-ethoxy-1,3,5-trinitrobenzene (Ethyl picrate) C8H7N3O7 1.6 859 760 (99) 796 (63) 926 (-67) 846 (13) 64 N-Ethyl-N,2,4,6-tetranitroaniline C8H7N5O8 1.6 874 795 (79) 874 (0) 967 (-93) 850 (24) (Ethyltetryl) 65 N-(2,4,6 Trinitrophenyl-N-nitramino)- C10H8N8O17 1.9 787 839 (-52) 694 (93) 788 (-1) 857 (-70) trimethylolmethane Trinitrate(Heptryl)

66 Dipentaerythritol hexanitrate (DPEHN) C10H16N6O19 1.6 878 897 (-19) 772 (106) 897 (-19) 906 (-28)

67 bis(2,4,6-trinitrophenyl)amine (Hexyl) C12H5N7O12 1.6 791 752 (39) 805 (-14) 881 (-90) 799 (-8)

68 Nitrocellulose (NC) (C12H14N6O22)n 1.7 871 833 (38) 891 (-20) 829 (42) 881 (-10)

69 2,2',4,4',6,6'-Hexanitrostilbene (HNS) C14H6N6O12 1.7 766 710 (56) 754 (12) 863 (-97) 787 (-21) hydrogen atoms to form various gaseous products; the conditions: (i) contain carbon atom; and parameter VCorr is the correcting function which is (ii) − − bad ≥ 02/2 . For other explosives, there is no needed for explosives with positive oxygen balance. need to introduce a correcting function and VCorr is zero. If a large amount of oxygen atoms exist, all carbon and hydrogen atoms convert to carbon dioxide and Multiple linear regression method35 was used to water molecules, respectively. The overall effect of find the optimized correlation as: joining more atoms and producing large molecules is reducing the total volume of gas mixture. Thus, in V Exp Gas =878.2 − 126.0rCO// + 111.7 rHO − 176.7 V Corr these cases a correcting parameter should be used, in … (3) order to decrease the overestimated value of VExp Gas. Therefore, the value of VCorr is equal to 1.0 for The predicted values of volume of explosion gases CaHbNcOd explosives which have both of these for 69 energetic materials are given in Table 1. JAFARI et al.: PREDICTION OF THE VOLUME OF EXPLOSION GASES OF ENERGETIC COMPOUNDS 705

Table 2 – Regression coefficients, standard errors, p-values, and confidence intervals for the best linear regression model (R2 = 0.92, SE = 56.36, F = 77.77, and significance F = 1.80E-21)

Coefficients Standard error P-value Lower bound (95%) Upper bound (95%)

Intercept 878.25 15.61 7.45E-57 847.07 909.43 rC/O -126.0 15.96 4.54E-11 -157.87 -94.11 rH/O 111.7 10.39 4.75E-16 90.92 132.44 VCorr -176.7 21.95 2.35E-11 -220.56 -132.90 30 Table 3 – Statistical parameters of the present method, deviations of VExp Gas using BKW-EOS and JCZ3- 30 31,32 BKW-EOS , JCZ3-EOS and the ProPEP code predictions EOS31,32 for some compounds containing –OH and –

Parameter Eq. (3) BKW-EOS JCZ3-EOS ProPEP COOH, which show intra- and inter-molecular code hydrogen bonding can affect the equilibrium concentrations of some detonation products. In Mean error (ME) 0.0 35.1 61.6 -28.5 contrast to complex computer codes, there is no need Root mean square 54.7 86.3 116.4 55.0 to use the relative concentrations of various error (RMSE) Mean absolute 38.8 75.5 94.9 40.3 decomposition products. error (MAE) Some statistical parameters of the new method, Mean absolute 4.2 8.6 10.5 4.6 detonation performance code using BKW-EOS30 and percent error JCZ3-EOS31,32 as well as the ProPEP code predictions (MAPE) Maximum of errors 147.9 201.2 240.9 181.2 were given in Table 3. Definition and importance of these parameters are given elsewhere16. The reliability of the new method compare to outputs of Detonation performance code, CHEETAH28, computer code calculates the detonation product composition in the The correlation coefficient (R2) value mainly Chapman-Jouguet point at high pressures followed by reflects the goodness of fit of the model, which is reducing it to normal conditions to obtain V . equal to 0.92 for Eq. (3). Table 2 gives statistical Exp Gas However, when V is measured experimentally in parameters of Eq. (3) corresponding to three variables Exp Gas the Bichel Bomb, decomposition products cool down r , r , and V , which allow comparing the C/O H/O Corr for some time, during which the chemical equilibrium relative weight of the variables in the model. Since shifts. Therefore, the calculated values of V standard error shows a measure of the precision of Exp Gas through detonation performance codes and evaluation of a coefficient, thus, precision of experimental data are essentially different. coefficients in Eq. (3) are measured by their standard Meanwhile, if one uses a thermodynamic code such as deviations over repeated measurements. The p-value the ProPEP code, which takes into account cooling is another useful statistical parameter for indication of down effect, it is possible to good predictions as the probability that a parameter estimated from compared to those measured in the Bichel Bomb. All experimental data. For p-value < 0.05, the effect of of the calculated statistical parameters, as shown in p-value is significant and the observed effect is not Table 3, confirm that the reliability of new model is due to random variations. As indicated in Table 2, slightly higher than the ProPEP code and much better each of variables in Eq. (3) has a highly significant than BKW-EOS30 and JCZ3-EOS31,32. These impact as evidenced by their extremely small p values assessments indicate that new model is reliable, and standard errors as well as further complementary precise and accurate. statistical parameters. Table 1 compares the predicted results of Eq. (3) Conclusions with volume of explosion gases by detonation A novel correlation has been introduced to predict the performance code using two different equations of values of V for different pure energetic 30 31,32 Exp Gas state, i.e., BKW-EOS and JCZ3-EOS , as well as compounds containing nitroaromatic, acyclic and the ProPEP code. Maximum deviations of VExp Gas for cyclic nitramine, nitrate ester and nitroaliphatic 30 31,32 both BKW-EOS and JCZ3-EOS belong to compounds. The new method is based on three hexamethylene triperoxide diamine (HMTD), which variables of rC/O, rH/O, and VCorr, which can be easily may be due to exotic peroxide bonds in this found from molecular structure of desired CaHbNcOd compound. As seen in Table 1, there are large energetic compound. As seen in Table 1, the results of 706 INDIAN J. ENG. MATER. SCI., DECEMBER 2015

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