HUNGARIAN JOURNAL OF INDUSTRIAL CHEMISTRY VESZPREM Vol. 29. pp. 143-147 (2001) EXPLOSION AREAS OF FLAMMABLE SUBSTANCES AND THEIR NUMERICAL APPROXIMATION G. VICZIAN, M. MOLNARNE-JOBBAGY1, J. HESZBERGER and K. KOLLAR-HUNEK (Dept. of Chemical Information Technology, Bp. Univ. of Technology and Economics. Hl521 Budapest, Pf.91. HUNGARY, 1 Federal Institute of Materials Research and Testing, BAM, 12200 Berlin, GERMANY) Received: October 10,2001 This paper was presented at the 7th International Workshop on Chemical Engineering Mathematics, Bad Honnef, Germany, August 12-17 2001 CHEMSAFE® database [1], developed as a joint project between BAM, PTB and DECHEMA, contains safety characteristics of flammable liquids, gases, dusts and their mixtures. The BAM is responsible for evaluated data on gases and dusts. TRIANGLE software, originally developed by the BAM for the processing, quality assurance and visualisation of measured data describing the explosion area of ternary systems consisting of flammable, inert and oxidising gases. 2D figures in the program represent isothermal or isobaric level curves of the explosion areas. In order to better describe the limiting curve of the explosion range, by the BUTE (Budapest University of Technolcgy and Economics) the Akima- spline interpolation has been replaced by special comonoton Splines in TRIANGLE. For the 3D visualisation of the whole temperature- or pressure-dependent ternary explosion surfaces the TRIGON program of BUTE was extended. Keywords: ternary flammable systems, inerting, explosion areas, spline curves and surfaces, 2D and 3D visualisation Introduction In order to avoid explosion with flammable substances, generally applied solution in industrial processes is purging with inert gases. Reliable measured data are required concerning the explosion range of ternary systems. The CHEMSAFE® database, which is available world wide through STN International and Internet, contains rated safety characteristics of flammable liquids, gases, dusts and their mixtures, such as explosion limits, flash points, ignition temperatures, etc. The in-house version of CHEMSAFE allows a graphical representation of the measured explosion range in triangular diagrams as a function of the concentration of flammable, oxidising or inert gases. In the data processing phase a flexible software procedure is needed to solve 2D and in certain cases also 3D visualisation for the explosion area of ternary gas mixtures. The TRIANGLE program, created by BMf and extended by the common research group of BUTE and BAM, provides the 2D triangular diagrams. When the influence of additional parameters is to be shown, for 3D explosion surfaces the extended TRIGON software offers a good solution. Characteristics of the explosion range Explosion areas need to be explicitly defined by unambiguous characteristic parameters. Table I and Fig. I show the acronyms applied in CHEMSAFE. As an example, let us consider the IAR hne in Fig. I. This line represents a limit in the ternary flammable system: all mixture compositions existing on the right hand side of this line will not cause an explosion regardless of the added amount of flammable gas. The interception of the IAR line and the oxidising gas axis determines the MAI point. the minimum required inert gas content of the binary inert·oxidlsing gas system which is necessary to avoid an expJostt.m, Similarly, the ICR line gives a limiting ratio between 144 Table I Characteristic values for explosion area of ternary systems containing flammable gas I inert gas I oxidising gas Acronym in CHEMSAFE .Qescripdon Lower Explosion Limit LEL UEL ICR JAR Upper Explosion Limit Minimum Inert gas I Combustible Ratio Minimum Inert gas I AIR (Oxidising gas) Ratio' MXC MaXimum permissible Amount of Combustible MAI Minimum required Amount of Inert gas MOC or LOC Maximum Oxygen (Oxidising gas) Content or Limiting Oxygen Concentration Explosion .range :Meth.ne!Nitroal:llfAir • !l Mt-alateQI'lillc roPIN 511$49 25 'C, t.llo.ospi>o:rit: p..- Nitrogen Fig.! Representation of the explosion area inert and flammable gas at which by adding any amount of flammable gas to the system no explosion will occur. The TRIANGLE program is used for processing measured values of such systems. The boundary curve around the explosion area is generated by applying numerical interpolation on the measured data. After the .. evaluation of the characteristic values of the system the program returns the results in tables and in ternary diagrams both in Cartesian and in triangle co~ordinates. 2D approximation problems solved by comonoton parametric vector splines- Additions and extensions in TRIANGLE For the characterisation of the explosion range well determined tangent lines of the explosion areas are neededt such as the IAR or ICR lines. For these to be accurate we have to apply the best possible numerical approximation of the 2D explosion limit curves. Comonoton parametric vector splines possess the best numerical properties for this task. [2~ 5]. The conditions of comonotonity for the set of measured points {:r,; y, }:,, are given as following [4, 6]: (1) Table 2 Comparison of different interpolation methods Butene/Nitrogen/Air-System (T=297 K; P=O,l MPa) MAI MOC MXC IAR ICR Traditional Spline 51,83 9,94 2,68 1,08 36,35 Comonoton Spline 51,78 9,96 2,71 1,07 35,93 Linear Interpolation 51,78 9,98 2,72 1,07 35,71 12~----------------------------~ 10 8 6 4 -evaluated ~ measured 0+----------r----------r---------~ 0 20 40 60 Fig.2 Butene/Nitrogen/Air-System (T=297 K; P=O,l MPa) Traditional Spline interpolation 12~------------------------------~ 10 8 6 4 2 -evaluated ~ measured 0+------.-------r-------t I o 20 40 60 Fig.3 Butene/Nitrogen/Air~System (T=297 K; P=O,l MPa) Comonoton Spline interpolation where s denotes the usual arc length parameter. Then it holds for the slope coordinates x'(s) and y'(s): V s E (s; t ;s;): x:(s )· (m;}x > 0 if (mJx * 0 (2.a) - y (s )· (m; ) 1 > 0 if (mJ 1 :t: 0 [ ] x'(s) = 0 if (mi) = 0 \J SE S1_1;si : '() . ( )x (2.b) Y s =0 If m. =0 l y Using the conditions above, we created subroutines for the comonoton parametric vector splines and built them in the TRIANGLE program. Similarly, we also created subroutines for the traditional parametric vector splines l9~ 10] and compared the differently evaluated characteristics. 18 16 14 -evaluated 12 fl. measured 10 8 6 4 2 0 0 10 20 30 40 Fig.4 Methane/COiAir-System (T=297 K; P=O,l MPa) Traditional Spline interpolation 18~------------------------------, 16 14 12 10 8 -evaluated fl. measured 61-~~~~~~~ 4 2 0+-------r-------r-----~-------4 0 10 20 30 40 Fig.S Methane/C02/Air-System (T=297 K; P=O,l MPa) Comonoton Spline interpolation Some representative results are shown in Figs.2 and 3 and in Table 2. for the Butene/Nitrogen/Air ternary system, and in Figs.4, 5, and in Table 3 for the Methane/COz/ Air ternary system. In the case of the Butene/Nitrogen/ Air-system the traditional Spline interpolation produces an undesired curvature on the UEL curve, near the apex of the explosion area. It has a slight effect on the MAl, MXC, and ICR values - as it is shown in Table 2. In the second example, in the case of the Methane/CO:c'Air-system with the traditional Spline interpolation, the undesired curvature appears on the LEL curve, again, near the apex of the explosion area. In this case the curvature causes a considerable error in the MXC point and in the slope of the ICR line. By using comonoton vector splines both above mentioned errors can be avoided. It needs to be mentioned that traditional spline approximation had been found to produce similar errors in five out of the about twenty investigated systems. On the programming side the new parametric vector splines required changes in 3 of the 4 worksheets, 3 of the 7 diagrams, 8 of the 11 modules and 3 of the 5 forms of the original TRIANGLE (Visual Basic for Excel) program. 145 Table 3 Comparison of ditierent interpolation methods Methane/C02/ Air-System (T=297 K; P=O, I MPaJ Traditional Comonoton Linear Spline Spline Inte~lation MAl 31,02 31,02 31,02 MOC 13,52 13,54 1355 MXC 16,95 17,39 17,39 JAR 0,45 0,45 0,45 ICR 4,9 4,75 4,75 80~~~--~~~~--~~~~ 70~~~~-r~--,---~ 60+-~~~~--r-----~~ 50+--+--~~~~~~--~ 40+--+--T-~~~~~--~----~-; 30+--+--+-~~~~~--,-~--~-i 20+--+--+-------~j 10+-~--~~--~~ 10 20 30 40 50 60 70 80 90 100 L_ ________________________________ _ Fig.6 Isothermal level curves ofH2/C02/Air J 3D visualisation- examples of the extended TRIGON application The TRIGON program was created for visualisation of triangular (ternary) vapour-liquid equilibrium (VLEJ surfaces [7, 11]. As we recognized the interesting possibility to visualize the temperature or pressure dependence in the explosion areas of ternary systems containing flammable gas, we tried to utilize TRIGON and its embedded Bezier surfaces. Although < lUr minimal energy Bezier surfaces have many useful properties [2, 6-8], we could not directly apply t~em. for the Ternary Explosion Surface (TES) approxtmauon. because their computational algorithm needs the whole triangle as domain for the surfaces. A simila: proble~ occurred with the application of Shepard s metnc interpolation [3]. . After investigating the above problems, we dec~ded to use the 2D comonoton spline level curves comb1~ed by bilinear interpolation. The comonoton sphne (isothermal) level curves of Hydrogen/Carbon dioxide! Air-system are shown in Fig.6 as an example. The five data sets belonging to the temperatures ~0. I 00~~ 200, 300 and 400 C are from the CHL~iS.~FE· database. The bilinear interpolation allowed ,1 Mmple restriction of the whole triangle domain. using the inner and the outer level rurves 146 Extended units of TRIGON Without new routines Extension: DIAGR: 8 new routines Helper: 1 new routine Development In the future: MOTION (reading co-ordinates from the figures) t~-i~~~i<;, Fig. 7 Extensions necessary for TRIGON visualizing TES (L(20) and L(400) in Fig.6) as boundaries in the restricting inequalities. Parametric comonoton vector splines were used for the (isothermal or isobaric) level curves and a bilinear interpolation was used for the trapezoid inner part between the level curves. To accomplish this, we had to extend the VLE TRIGON software according to Fig. 7. The TES TRIGON program version contains the MENU and HPEMU units [11] unchanged, but in the DIAGR unit we had to develop 8 new routines, and one in the HELPER unit. The output of the TES-TRIGON software for two example ternary systems (Hydrogen I Carbon dioxide I Air-system defined by isothermal level curves and Ethene I Nitrogen I Air-system defined by isobaric level curves) are shown in Figs.8 and 9. In the approximation of the apex of explosion surfaces we had to solve a "apex accumulation" problem. As it is shown in Fig.8, in the first solution we slightly broke the "level curves condition''. Even though in the real explosion of surface plots this is unnoticeable, we continue to work on a solution that does not break the condition of the level curve system. The different rotation and view angle changing features of TRIGON show the properties of the ternary explosion areas very \Veil. In the case of the Ethene!NitrogeniAir~system. given by isobaric level curves, in the Fig.9, the lower pressure part between 0.1 and 1 MPa is interesting, because the dangerous part is wider than in higher pressure, between 1 and 10 MPa. Conclusions For correct 2D visualisation of isothermal or isobaric explosion areas of ternary gas mixtures containing flammable gas. we extended the TRIANGLE software (created by BAM. Berlin). To reach the desired accuracy for the approximation of explosion characteristics we used parametric comonoton vector Splines. The software and the method had already been tested on many systems in chemical safety engineering. ~~~~ ,, ............................................................. . Fig.8 3D Explosion areas of Hydrogen/Carbon dioxide/Air- System given by isothermal level curves, plotted by TESTRIGON Fig.9 3D Explosion areas ofEthene/Nitrogen/Air-System given by isobaric level curves, plotted by TES TRIGON In some cases, when 3D visualisation is necessary, the extended TES TRIGON software (created by BUTE, Budapest) gives good results. In this program the base of the numerical surface approximation was comonoton vector Spline, the same as in the 2D visualisation. Between the isobaric or isothermal explosion level curves we used bilinear interpolation that made the necessary domain restriction also easy to implement. Acknowledgements The authors wish to express their gratitude to Thomas Bendrich and to Michael Bulin (BAM), to Dr. Prof. Norbert Herrmann (Univ. of Hannover) and to Dr. Marta Lang-Lazi (BUTE). The work has been supported by the Hungarian National Research Foundation (OTKA, grant # T023258/97), by the BAM (Berlin) and by the Varga J6zsef Foundation of the Chemical Engineering Faculty, BUTE. SYMBOLS IAR Minimum Inert gas I Air (Oxidising gas) ratio ICR Minimum Inert gas I Combustible Ratio LEL Lower Explosion Limit L(T) Isothermal level curve of TES MAl Minimum required Amount of Inert gas MOC Maximum Oxidising gas Content MXC MaXimum permissible Amount of Combustible gas P Pressure, ~a S Arc length parameter T Temperature, K or C TES Ternary Explosion Surface UEL Upper Explosion Limit (x,y) Cartesian co-ordinates VLE Vapour Liquid Equilibrium REFERENCES 1. CHEMSAFE®-Database For Safety Characteristics, BAM, Berlin, PTB, Braunschweig, DECHEMA, Frankfurt am Main, v1.4, 2001 147 2. F~SSHAUER G. E. and SCHUMAKER L. L.: Computer Aided Geometric Design, 1996, 13, 45 3. GORDON W. J. and WIXOM J. A.: Math. and Comput., 1998, 32, 253 4. GRONEWOLD G.: Hung. J. Ind. Chern., 1996,25,59 5. HERRMANN N.: Hung. J. Ind. Chern., 1996, 25, 263 6. KOLIA.R-HUNEK K., LANG-LAzi M., HERRMANN N., MIKLOS D. and KovAcs I.: Hung. J. Ind. Chern., 1998,26,269 7, KOLIAR-HUNEK K., VICZIAN Zs. and LANG-LAzi M.: Hung. J. Ind. Chern., 1999, 27, 6 8 .. LANG-LAzi M., DIOSPATONYI I., VICZIAN G. and HESZBERGERJ.: Hung. J. Ind. Chern., 1999,21,317 9. SHIKIN E. V. and Pus A. I.: Handbook on Splines for the User; CRC Press, Boca Raton, FL, USA, 1995 10. SPATH H.: Algorithmen zur Konstriktion glatter Kurven und Flachen, Oldenburg, Mlinchen, Wien, 1983 11. VICZrAN G., LANG-LAzi M., HESZBERGER, J., DIOSPATONYI I. and KoLLAR-HUNEK K.: Hung J. Ind. Chern., 2000, 28, 311 Page 143 Page 144 Page 145 Page 146 Page 147