Real Gas Equation of State for Methane

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1 Kaliningrad 2012

1. Commission Regulation (EC) No 692/2008 of 18 July 2008. http://ec.europa.eu/enterprise/sectors/automotive/environment/eurovi/index_ en. htm, p. 130. 2. Payne J. F. B., Skyrme G. Int. J. Multiphase Flow, 1993, Vol.

Moscow, Phyz.- Math. Lit. Publ., 1959. 5. Piskunov V. N. Theoretical models of aerosol formation kinetics. Sarov, Rus. NRC VNIIEF Publ., 2000. 6. Avdeev K. A., Ivanov V. S., Frolov S. М., Basara B.

2 1. Commission Regulation (EC) No 692/2008 of 18 July en. htm, p Payne J. F. B., Skyrme G. Int. J. Multiphase Flow, 1993, Vol. 19? No/ 3, pp Friedlander S. K. Smoke, Dust and Haze: Fundamentals o f Aerosols Dynamics, NY Oxford, Oxford University Press Inc., Levich V. G. Physico-Chemical Flydrodynamics. Moscow, Phyz.- Math. Lit. Publ., Piskunov V. N. Theoretical models of aerosol formation kinetics. Sarov, Rus. NRC VNIIEF Publ., Avdeev K. A., Ivanov V. S., Frolov S. М., Basara B., Priesching P., Suffa M. In: Combustion and Explosion, Moscow, Torus Press, 2012, Issue 5, pp Real Gas Equation of State for Methane C-5 Viktoria V. Kozynda, Alexei V. Dubrovskii, Sergey M. Frolov Semenov Institute of Chemical Physics, 4 Kosigin Str., Moscow, Russia M ethane is one o f the m ost w ide spread fuels and raw m aterials for chem ical industry used for production o f synthetic gas, acetylene, black carbon, etc. D espite its therm ochem ical and physical properties are in general w ell investigated, its num erous novel applications, in particular in transportation engines, require the know ledge o f accurate therm al and calorific equations o f state (EO S). The aim o f this com m unication is to develop the therm al EOS for m ethane in a supercritical param etric dom ain at 250 < 7 < 1000 К and 0.1 < P < M Pa. Figure 1 is the phase equilibrium diagram for m ethane obtained using the data o f [1]. The shaded area in Fig. 1 is the supercritical param etric dom ain o f our interest here. 55

10, Critical point (4.626 MPa; 190.77 K) 0 01 - Triple point (0.01172 MPa; 90.68 K) 1E-3 0 200 400 600 800 1000 т,к Fig. 1. Phase diagram for methane.

com ponent associated only w ith the interaction forces betw een a t om s in the solid (this com ponent depends only on solid volum e) and P, is the therm al pressure com ponent associated w ith

3 10, Critical point (4.626 MPa; K) Triple point ( MPa; K) 1E т,к Fig. 1. Phase diagram for methane. A s is know n from the solid state physics, at relatively low tem peratures the pressure o f solid m atter can be decom posed into tw o parts: P = Pc + Pt, w here Pc is the elastic ( cold ) pressure com ponent associated only w ith the interaction forces betw een a t om s in the solid (this com ponent depends only on solid volum e) and P, is the therm al pressure com ponent associated w ith heating o f the solid (this com ponent depends on both solid volum e and tem perature). A ccording to [2], a sim ilar decom position can be form ally applied to dense gases, how ever the validity o f such an approxim ation should be checked against experim ental data. A pplying the approach o f [2] to m ethane one can approxim ate the therm al EO S as: w here p is the density, ц = g/m ol is the m olecular m ass o f m ethane, R = J/(m ol K ) is the universal gas constant, and f(p ) is the (unknow n) function o f density. The EOS o f Eq. (1) is autom atically valid for the ideal gas since for such a gas Pc (p )= 0 and f(p )= 1. A ccording to [2], the term s Pc(p) and f(p ) are given by: 56 р ( р, т ) = р с(р ) + р К - / ( р ) О )

Comparison o f predicted (curves) and measured (points [1]) dependencies o f pressure on density for five isotherms: T = 250 К (curve 1), 300 (2), 400 (3), 600 (4) and 1000 К (5) for methane (units o

4 Pc( p ) = Y.{ p ) - r RTH R p ) - i] (2) Y.(p ) = ap 2 + b p 3 + c p 4 + dp* 1+ A p + B p 2 +Cp6 (3) (4) w here Tr is the reference tem perature and a,b,c,d,a,b,c are the coefficients. The values o f these coefficients are: a = ; 6 = ; c = ; ot= ; A = ; Я = ; С = Ф.1* Fig. 2. Comparison o f predicted (curves) and measured (points [1]) dependencies o f pressure on density for five isotherms: T = 250 К (curve 1), 300 (2), 400 (3), 600 (4) and 1000 К (5) for methane (units o f a, b, c, d are in M Pa, cm, g; units o f A, В, С are in cm, g). T hese values w ere obtained by fitting Eqs. (1) and (2) w ith the experim ental data [1] at reference tem perature Tr= 250 K. The accuracy o f the new EO S for m ethane thus derived is illustrated in Fig. 2. Figure 2 co m pares predicted (curves) and m easured (points) dependencies o f pressure on density for five isotherm s: T= 250, 300, 400, 600 and 1000 К at 0.1 < P < M Pa. The approxim ation error in term s o f pressure is in average less than 1.5 %. The m axim um approxim ation error o f 4.2 % is attained at T= 1000 К and P =100 M Pa. 57

Thus, we have developed a new analytical therm al EOS for m ethane providing a good accuracy o f P - p - T data approxim a tion at 250 < T <1000 К and 0.1<.P < 100 M Pa.

V., Vasserman A. A. Thermodynamic properties of methane. Moscow, Standard Publ., 1979. 2. Kuznetsov N. М., Dubrovskii A. V., Frolov S. M. Rus. J. Phys. Chem. B., 2011, Vol. 5, No. 7, pp. 1084 1105.

5 Thus, we have developed a new analytical therm al EOS for m ethane providing a good accuracy o f P - p - T data approxim a tion at 250 < T <1000 К and 0.1<.P < 100 M Pa. Due to sim plicity this EO S can be readily used in C FD sim ulations o f operation p rocesses in various energy conversion plants. T his w ork w as partly supported by RFBR. 1. Sychev V. V., Vasserman A. A. Thermodynamic properties of methane. Moscow, Standard Publ., Kuznetsov N. М., Dubrovskii A. V., Frolov S. M. Rus. J. Phys. Chem. B., 2011, Vol. 5, No. 7, pp To Non-Selfmaintained Discharge Impact on Lean Propane-Air Mixtures C-6 Nikolai V. Ardelyan1, Vladimir L. Bychkov2, Dmitry V. Bychkov1, Sergey V. Denisiuk2, Konstantin V. Kosmachevskii1, Mark N. Sablin1 1Lomonosov Moscow State University, Moscow, Russia 2Moscow Radiotechnical Institute RAS, Moscow, Russia A goal o f the present report is analysis o f the electron-beam in external electric field im pact on ignition o f dry lean flam m able propane-air m ixture. W orks on m odeling o f electron-m olecule processes in propane-air m ixture in external electric field and E- beam at different values o f stoichiom etricity have been realized. A s the basic w e have chosen a sim plified system o f chem ical reactions with added reverse reactions 74 reactions: H ydrogen- O xygen chain, H ydroperoxyl and H ydrogen Peroxide reactions, P ropane reactions, I-Propyl, N -P ropyl and P ropene reactions, E thylene, Ethyl, Vinyl, V inoxy and K etene reactions, M ethyl, M ethoxy, F orm aldehyde, Form yl reactions), standard energy equation 58

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