Combustion, Explosion, and Shock Waves, Vol. 42, No. 3, pp. 277–281, 2006
Modeling of Incomplete Combustion of Hydrocarbons in the Presence of Water under High Pressure ´ P. Volchkov1 and N. A. Dvornikov1 E.
UDC 536.46-66.093
Translated from Fizika Goreniya i Vzryva, Vol. 42, No. 3, pp. 37–41, May–June, 2006. Original article submitted February 1, 2005.
Chemical processes proceeding during incomplete oxidation of heavy hydrocarbons in multiphase nonideal systems are modeled. A program is developed for calculating the composition of products of incomplete oxidation of hydrocarbons with the use of equilibrium and kinetic models with allowance for imperfection of the gas phase and solutions. The yield of the product was calculated by the equilibrium and kinetic models to optimize the yield of hydrogen during incomplete oxidation of eicosane (C20 H42 ) in the presence of water in the supercritical domain of state of the system. The data calculated by the kinetic model are compared with experimental data. Key words: combustion, heavy hydrocarbons, equilibrium, kinetics, supercritical state, modeling.
INTRODUCTION Simulation of chemical processes in nonideal systems in the gas and liquid phases and development of efficient calculation algorithms for such processes are important factors for adequate understanding of chemical processes, statement of experimental studies, and design of advanced chemical reactors operating at high pressures. In particular, high pressures are encountered in hypersonic aircraft engines and in technologies based on reactions that proceed in the neighborhood of the critical state of the substance. Since the processes mentioned display some common features in the course of chemical reactions, the present study deals with the process of hydrogen production from heavy hydrocarbons in the presence of water and oxygen. This problem is of academic and applied significance because methods used in hydrogen production become a topical matter in the development of fuel cells. The issues of chemical reactions proceeding in supercritical water, theoretical foundations for modeling the chemical equilibrium and the kinetics of processes in reactors, and relevant experimental data were analyzed in many papers (see, e.g., [1–6]). Consistent equilibrium and kinetic models for calculating systems with a 1
Kutateladze Institute of Thermophysics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090;
[email protected].
nonideal gas phase were proposed in [5]. In the present study, this model is combined with a model of regular solutions for the liquid phase. Optimal conditions for maximizing the yield of hydrogen in reactions of hydrocarbons with water and oxygen are considered.
MODEL FOR CHEMICAL EQUILIBRIUM The method for predicting the equilibrium composition in chemical transformations is based on the fact that the Gibbs energy acquires a minimum value at the point of chemical equilibrium. For actual systems, we can write the specific Gibbs energy as follows [5, 7, 8]: G=
NS
g i ni .
(1)
i=1
Here ni is the number of moles of the substance i in the volume, N S is the number of substances in all phases (substances having identical atomic compositions but residing in different phases have different subscripts i), and gi is the chemical potential per mole of the substance i with allowance for mixing: p ni (2) + ln + ln fi . gi = h0i − T s0i + RT ln p0 nk k
In this equation, the specific enthalpy h0i and the specific entropy s0i under standard pressure p0 = 1 atm are
c 2006 Springer Science + Business Media, Inc. 0010-5082/06/4203-0277
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functions of temperature T for each of the substances, R is the universal gas constant, p is the pressure at which the equilibrium for the gases is sought, p = p0 for liquids and solids, and fi is the fugacity (activity) [8]. In subsequent calculations, the pressure in the system is assumed to be constant. For solutions and gas mixtures, nk is performed over all substances of summation in k
the phase incorporating the substance i; for pure substances, ni = ni . In the case of ideal gases and ideal i
solutions, we have fi = 1. For a real gas, the fugacity is determined with the use of the Redlich–Kwong equation of state d RT − , (3) p= V − b T 0.5 V (V + b) where d and b are constants and V is the molar volume. For Eq. (3), the fugacity can be written as [8] bi dbi V ln fi = ln + − ln Z + 2 V −b V −b b RT 1.5 2 xj dij V +b b V j − , − × ln ln 1.5 V V +b bRT V +b where xi = ni / nk is the number of moles of the k
substance i per mole of the gas mixture, √ Z is the compressibility, and the quantity dij = di dj is to be determined from the coefficients d in the equation of state for the pure substances with the subscripts i and j. To allow for the activity of the substances in solutions, we can use the van Laar model for regular solutions [8] ln fi = Vi (δi − δ)2 ,
(4)
where Vi = Mi /ρi is the volume occupied by one mole of the liquid, Mi is the molar mass, ρi is the density, δi = [(∆hi /(RT ) − 1)/Vi ]1/2 is the parameter of substance solubility in the mixture, ∆hi is the heat of evaporation per mole of the ith liquid at the temperature T , δ= Φi δi is the average parameter of solubility of the mixture, and Φi = xi Vi / xk Vk is the volume fraction k
of the substance j in the mixture. Functional (1) is minimized with the following constraints. 1. Conservation of the number of atoms of the species j: NS
aji ni = ej ,
j = 1, N L.
(5)
i=1
Here aji is the number of atoms of the species j in the substance i, ej is the total number of atoms of the species j, and N L is the number of atomic species in the system.
2. The change in the enthalpy of the system with allowance for losses into the ambient medium: NS
hi ni + DH =
i=1
NS
h0i n0i + DH 0 − Q.
(6)
i=1
Here hi is the enthalpy with no allowance for gas imperfection, DH is the change in enthalpy due to real gas effects, and Q is the heat loss from the system into the ambient medium; the superscript 0 denotes input conditions. Using the Redlich–Kwong equation of state [8], we obtain DH =
bRT d 3d V +b − − . (7) ln V − b T 0.5 (V + b) 2bT 0.5 V
3. Satisfaction of the inequality ni 0.
(8)
Functional (1) under constraints (5), (6), and (8) was minimized using the algorithm described in [5].
KINETIC MODEL The kinetic model for nonideal systems involves the dependence on fugacity and compressibility in the expression for the rate of formation of the ith substance [5] + = (νij − νij )kj+ (Ck fk Z)νkj . (9) wij k
In view of this, the equation for the molar-mass concentration of the substance can be written as νkj −1 ν dσi = (νij − νij )kj+ ρ k σkkj dτ j k
−
(νij
−
j
νij )kj− ρ
k
νkj −1
k
kj+
=
νij + k0j (Z) i
− kj− = k0j (Z) i
νij
ν
σkkj ,
(10)
(fi )νij ,
i
(fi )νij . i
Here τ is the time, σi is the molar-mass concentration, and νij are the stoichiometric coefficients for the νij forward and backward reactions, respectively, Ck is the molar-volume concentration, and + k0j = Aj T nj exp(−Taj /T ) (Aj , nj , Taj = const), − + k0j = k0j
RT (νij −νij ) i
p0
exp
∆j g 0 RT
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are the standard rate constants for the forward and backward reactions ideal system, respectively. in the The quantity (νij − νij )(h0i − T s0i ) = ∆j g 0 is called i
the change in the standard Gibbs energy in the reaction j. The distinctive feature of rate constants in nonideal models is the presence of additional factors that depend on fugacity (activity) and compressibility. Fugacity in kinetic models for nonideal systems has been known for a long time: it has been used in calculations of nonideal systems for more than fifty years. As far as our knowledge goes, compressibility was first introduced into kinetic models in [5] to match the equilibrium coefficients found from the equilibrium model with minimization of the Gibbs energy in the system and the equilibrium coefficients found from the kinetic model with the use of the mass action law. One global reaction of eicosane pyrolysis into methane and carbon [9] and a detailed mechanism of the reaction of the pyrolysis products with oxygen and water [10] were considered in calculations. The pyrolysis reaction is a reaction of hydrocarbon decomposition into the simplest components: Cx Hy + M ⇒ products + M.
Fig. 1. Effect of oxygen flow rate on the hydrogen yield: G = 10 kg/sec for C20 H42 and 20 kg/sec for H2 O; Tin = 650 K for C20 H42 –H2 O and 441 K for O2 .
(11)
This reaction proceeds during breakdown of carbon bonds in hydrocarbon molecules, which is energetically beneficial [9]. According to [11], decomposition of complex hydrocarbons is a first-order reaction with respect to the concentration of the initial hydrocarbon and weakly depends on pressure. According to [9], the specific rate of the decomposition reaction of a complex hydrocarbon molecule is k = 1013 exp(−30,200/T ) [sec−1 ].
(12)
Since the rate of this reaction does not depend on pressure explicitly, only indirect influence of pressure on the pyrolysis reactions is possible, resulting from the change in temperature owing to other reactions that are pressure-dependent.
CALCULATED EQUILIBRIUM COMPOSITIONS We simulated pyrolysis and partial oxidation of eicosane (C20 H42 ) with joint injection of oxygen and water. The effect of system parameters on the hydrogen yield was examined. The data prove it possible to optimize the reactor in terms of pressure, temperature of reacting species, and composition of initial substances to raise the yield of the desired product, which is hydrogen in the case under consideration. Some results are plotted in Figs. 1–4.
Fig. 2. Effect of water flow rate on the hydrogen yield for GC20 H42 = 10 kg/sec and GO2 = 5 (1), 8 (2), and 12 kg/sec (3); Tin = 650 K for C20 H42 –H2 O and 441 K for O2 ; the dotted curve shows content of H2 in the fuel.
Figure 1 shows the hydrogen yield versus the rate of oxygen supply (G ) for fixed water and eicosane flow rates (20 and 10 kg/sec, respectively). The temperature at the reactor input was 650 K for eicosane and water vapor and 441 K for oxygen. It is seen that the maximum yield of hydrogen is reached at the rate of oxygen supply equal to 12 kg/sec. Figure 2 shows the hydrogen yield versus the flow rate of water for fixed oxygen and eicosane flow rates (5,
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Fig. 3. Effect of reactor pressure on the hydrogen yield: G = 10 kg/sec for C20 H42 , 20 kg/sec for H2 O, and 12 kg/sec for O2 ; Tin = 650 K for C20 H42 –H2 O and 441 K for O2 .
Volchkov and Dvornikov
Fig. 5. Time variation of the concentration of reaction products for a reactor temperature of 983.15 K.
At pressures in the system above 100 atm, the hydrogen yield decreases markedly and the temperature goes down and reaches a minimum at p = 250 atm (Fig. 3). An increase in the input temperature of eicosane and water results in a higher yield of hydrogen and the reactor temperature (Fig. 4). The hydrogen concentration in the reactor reaches a maximum value at a temperature of 1550 K and varies insignificantly with a further increase in temperature.
KINETIC MODELING OF EICOSANE OXIDATION
Fig. 4. Effect of reactor temperature on the hydrogen yield: G = 10 kg/sec for C20 H42 , 20 kg/sec for H2 O, and 12 kg/sec for O2 ; Tin = var for C20 H42 –H2 O and 441 K for O2 .
8, and 12 kg/sec for oxygen and 10 kg/sec for eicosane). The temperature at the reactor input was 650 K for eicosane and water vapor and 441 K for oxygen. As the flow rate of oxygen increases from 5 to 12 kg/sec, the hydrogen yield also increases, and the yield maximum is shifted toward higher flow rates of water. The hydrogen yield can exceed the initial content of hydrogen in eicosane (dotted curve in Fig. 2).
To verify the model for predicting the kinetics of chemical reactions, we compared the calculated results with experimental data obtained in tests aimed at determining the products of eicosane oxidation in the presence of water [6]. The experiment was performed by placing weighed specimens of substances in a thermostatted bomb, followed by a subsequent analysis of reaction products on a mass-spectrometer. The calculations and experiments were performed under the following conditions: 10 kg of C20 H42 , 20 kg of H2 O, and 2.7 kg of O2 ; p = 30 MPa. Figure 5 shows the predicted composition versus the reaction time for a fixed temperature in the reactor. A comparison of these data with experimental results also plotted in Fig. 5 shows that the predicted methane concentrations almost coincide with the experimental values, whereas the predicted concentration of hydrogen is greater than the experimental value by a factor of 1.5–3.
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REFERENCES
Fig. 6. Concentrations of reaction products versus the reactor temperature for a reaction time of 300 sec.
Figure 6 shows the predicted composition in the reactor at a fixed reaction time versus the reactor temperature and the corresponding experimental data. Similarly to Fig. 5, the predicted methane content is closer to its experimental value, and the predicted hydrogen content is higher than the experimental one. The discrepancy in terms of hydrogen can be attributed both to insufficient accuracy of the kinetic scheme and to errors in the method of mass spectrometry used to determine the concentrations of substances in the experiment. Nonetheless, the experimental tendency of hydrogen concentration to increase with temperature and a weak effect of the reaction time on the hydrogen yield in the examined time interval agree well with the predicted data. This work was supported by the Russian Foundation for Basic Research (Grant No. 04-02-08015).
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