Modeling the Thermal Decomposition of Chlorinated Hydrocarbons in an Ideal Turbulent Incinerator 1

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1 Modeling the Thermal Decomposition of Chlorinated Hydrocarbons in an Ideal Turbulent Incinerator 1 Markus Kraft, Harald Fey, Fachbereich Chemie, Universität Kaiserslautern, Erwin Schrödinger Straße, D Kaiserslautern, FRG mkraft@rhrk.uni-kl.de, fey@mathematik.uni-kl.de Carlo Procaccini, John P. Longwell, Adel F. Sarofim Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 2139, USA cpro@mit.edu Henning Bockhorn Institut für Chemische Technik, Universität Karlsruhe Kaiserstraße 12, D Karlsruhe, FRG bockhorn@ict.uni-karlsruhe.de 1 Keywords reactor model, stochastic differential equations, turbulent mixing, chlorinated hydrocarbons, incineration 1 Introduction Combustion of wastes is an effective disposal technology. Although there are many examples of application in industry, severe environmental concerns are raised regarding the emissons from incinerators. Thermal treatment plants are usually comprised of a primary combustion chamber followed by a second combustion chamber, as schematically described in Fig. 1. During the oxidation of solid and liquid wastes in the primary chamber the mixing and the reaction conditions are inhomogeneous. Thus, the wastes undergo incomplete combustion and the gases traveling to the secondary stage of the reactor are rich in potentially hazardous products of incomplete combustion (PICs) together with unreacted wastes. For instance, incineration of chlorinated hydrocarbons can lead to highly toxic chemical species like polychlorinated dibenzo-p-dioxins (PCDDs) and polychlorinated dibenzofurans (PCDFs). The secondary chamber is the component of the plant which most strongly influences the air quality of the exhaust. Additionally, fuel (usually a waste) is injected to raise the temperature, promote better mixing of the reactants, and thus complete the oxidation of wastes. Formation of large droplets, quenching due to the existence of cold zones, and poor turbulent mixing of the gaseous reactants are examples of faults which may lead to unwanted emissions. In Germany, for instance, the BImSchG law (Bundes-Immissionsschutzgesetz) requires a residence time of 2s at a temperature of 12 o C for the combustion of 1 submitted to Progress in Industrial Mathematics at ECMI96

2 2 chlorinated hydrocarbons to achieve their complete conversion. Nonetheless, the current regulation is not based on an adequate knowledge of the oxidation of halogenated species in the incineration systems [3]. Exhaust to post-processing Primary Feed Solid and liquid phase Complex composition Unsteady feed rate Secondary Feed Steady feed-rate and composition Gases mixing and reactions Reactions of partial oxidation, due to poor mixing of solid and liquid wastes with the gaseous oxidizer Primary Combustion Chamber PCC exhaust Unburned waste PIC's Secondary Combustion Chamber Figure 1: Conversion processes in thermal treatment plants This paper focuses on the effects of turbulent mixing on the formation of trace, potentially toxic, byproducts in the secondary combustion chambers of incinerators. 2 The Partially Stirred Plug Flow Reactor The physical and chemical processes in the secondary combustion chamber of an incinerator can be described in terms of the Navier-Stokes equations and the transport equations for all involved chemical species. Since we are interested in trace byproducts there is a need to employ a detailed chemical model which leads to a high number of chemical species which have to be considered. In this work we use the detailed chemical model given in [1] by Barat et al. This model contains 5 chemical species and 224 reactions. Thus, the resulting system of transport equation is very large. Direct numerical simulations of a typical turbulent high Reynolds number flows exceed the present computational capacities. Therefore, there is a need to use a simpler model. In the present work, a stochastic chemical reactor model, the Partially Stirred Plug Flow Reactor (PaSPFR) [5], is used. This is a modification of the classical Plug Flow Reactor (PFR) scheme, similar to the Partially Stirred Reactor (PaSR) in [2]. 2.1 Governing Equations We consider the composition vector in the PaSPFR φ t = (φ 1 t,..., φ L t ) T = (Yt 1,..., Yt L 1, h ) T to be a stochastic process. The pressure is assumed to be constant at 1 atm and the reactor is assumed to be adiabatic. Y l [, 1] l =

3 3 1,..., L 1 are mass fractions of L 1 chemical species and h = T T c p dt, h IR is the enthalpy contribution due to the heat of the gas mixture in the volume element of the reactor. The time evolution of the stochastic process {φ t, t T } is given by the vector stochastic differential equation (SDE) with initial condition ψ t = ψ. The l-th component the SDE is given by ( see Ref. [7]) dψ l t = ( A l (ψ t ) + S l (ψ t ) ) dt + L B lm (ψ t )dw bin l t, (1) where W bin = {W bin t, t } is L- dimensional normalized binomial process with components W bin 1 t,..., W bin L t which are independent scalar binomial processes with respect to a common family of σ algebras. Then A : IR L IR L, S : IR L IR L, and B : IR L IR L L are given by: A l (ψ) = 1 [ ( 1 + k 1 D(φ )] l) Cφ 2 ψl 2 τ (ψ l E(φ l )) (2) [ ] B lm k 1 (ψ l E(φ l )) 2 C φ (ψ) = D(φ ψl 2 τ l) : l = m (3) : l m m=1 { (ψ max l E(φ ψ l = l )) : (ψ l E(φ l )) (ψl min E(φ l )) : (ψ l E(φ l )) <. (4) The empirical constant k is set to be.1 and C φ = 2. as suggested in, e.g., Ref. [6]. The chemical source term is S l = ρ 1 ω l (ψ)w l (l = 1,..., L 1) where ω l (ψ) is the molar production rate and W l is the molar weight of the l-th species. Source term for the enthalpy is S L = ρ 1 L 1 l=1 h lw l ω l (ψ) where h l is the formation enthalpy of the l -th species. To obtain statistical moments of the stochastic process information on its probability density, f(ψ, t), is required. Here, the mean of the random variable φ l is denoted as E(φ l ) and its variance as D(φ l ). In a variable density flow the quantity which is usually studied is the mass probability density function (MDF) F(ψ; t) = ρ(ψ)f(ψ, t). To calculate F(ψ; t) at time t we approximate the initial condition MDF F(ψ; ) m δ(ψ ψ n ) by N particles with weight m. Each particle serves as initial condition with ψ n t = ψ n of equation (1). The ensemble of particles at time t, ψ n, approximate the MDF F(ψ, t). Details of the numerical t procedure are given in Ref. [5]. 2.2 Initial Conditions The PaSPFR model accounts for two of the processes which take place in a combustion chamber. The first one is a set of chemical reactions, the second one is the mixing of chemical species due to turbulence. The PaSPFR is a tubular reactor in which a statistically stationary, isotropic, homogeneous turbulent flow exists. The evolution of a small volume of gas, moving downstream at a speed equal to the mean velocity, can be described through the spatial changes of the relevant physical quantities along the reactor axis. The relaxation constant τ represents different degrees of turbulent mixing intensity. For τ =, ideal mixing takes place inside

4 4 the reactor, and the PaSPFR model is equivalent to a homogeneous PFR model. For τ =, no mixing occurs. In the present study, we assume that two initially separated streams, V 1 and V 2, mix and react inside the PaSPFR. V 2 represents the hot products of fuel-lean combustion, coming from the primary chamber. V 1 is a stream of CH 3 Cl, chosen as a typical waste surrogate. The ratio between the volume flow rates, V 1 / V 2, is fixed at.5. The only parameter varied in this study is the characteristic turbulent mixing time τ. Numerical simulations are performed for τ = s,.25s,.5s, and.1s. For τ =.1s, the characteristic mixing and chemical times are of the same order of magnitude. The perfectly premixed inlet composition and temperature, when τ =, are shown in table 1 as PFR inlet conditions. As initial condition for the MDF transport equation, we have chosen the joint composition mass density function at time t = t. F(ψ; t ) = F (ψ) = 1 2 ρ(ψ) ( δ(ψ ψ (1) ) + δ(ψ ψ(2) )) (5) In equation (5) the vectors ψ (1) and ψ (2) are the mass fraction and enthalpy composition vectors of stream V 1 and stream V 2 respectively. Waste Exhaust PFR V 1 V 2 X(H 2 O) X(O 2 ) X(CO 2 ) X(CH 3 Cl) X(N 2 ) Temp. 11 K 135 K 1334 K Table 1: Inlet conditions to the PaSPFR ( V 1, V 2 ) and the PFR as used in this study. X(k) are mole fractions of the chemical species and the ratio of the volume streams between V 1 and V 2 is set to be V 1 / V 2 =.5. 3 Results and Discussion In order to investigate the influence of different degrees of mixing (i.e.different values of τ) on the chemical reaction pathways during the ignition process, we have first studied the perfectly premixed case (τ = ). Here, the PFR model can be used because both streams V 1 and V 2 are homogeneously mixed at the time t = s. Later, different degrees of mixing intensity, represented by different values of the parameter τ, have been studied in the model. A special focus of the study is on the effect of unmixedness on the mechanism of chlorine inhibition. Chlorine is know to inhibit the hydrocarbon oxidation by depleting the H radical, used to produce HCl, and consequently causing a decrease in OH available for the burnout of CO [1].

5 5 3.1 Chemical System Figure 2 schematically represents, the final stage of the hydrocarbon combustion,i.e. the CO oxidation. The reaction numbers refer to the reactions in Ref. [1]. The oxidation of CO takes place mainly through reaction No. 62, which is driven by the chainbranching reaction No For this reaction as well as others (Nos. 135,147,137) the H radical is an important starting species. O 21 CO CO 2 19 H 2 O OH H +H H 2 + O 2 H 2 O 1 8 HO H +O 11 2 OH OH + O 2 O O x H 2 O 2 +O 2 12 OH Figure 2: Reaction paths for the oxidation of CO. In Figure 3 the formation paths of HCl are displayed. The numbers on the arrows represent the net specific mole fluxes of the corresponding species which are converted to HCl. Each path is comprised of a certain number of elementary reactions. These reactions are listed in the same Figure on the right hand side. The percentage of how much each reaction contributes to the formation of HCl are also given. The reactions which are responsible for the H abstraction are mainly Nos. 152 and 178. CH Cl 2 CH 3 Cl : production of HCl 176 : CH 3 Cl+Cl= HCl+CH 2 Cl 23.1 % 178 : CH 3 Cl+H = HCl+CH % CH Cl *E *E *E-4 HCl 9.48 *E *E-4 Cl CH 2 Cl : 188 : CH 2 Cl+CH 3 = C 2 H 4 +HCl 7.34 % Cl : 152 : H +Cl+M = HCl +M 22.3 % 176 : 192 : CH 2 O+Cl =HCO+HCl 13.3 % 23 : C 2 H 4 +Cl = HCl+C 2 H % 27 : C 2 H 6 +Cl =HCl+C 2 H % 29 : ClO : 195 : CH 3 +ClO = HCl+CH 2 O 3.12 % C H Cl 2 5 ClO C 2 H 5 Cl : 29 : Cl+C 2 H 5 Cl = HCl+CH 2 ClC.H % Figure 3: Reaction paths for the HCL production

6 6 3.2 Influence of Mixing In Figures 4 and 5 the time evolution of mean and standard deviation for the OH radical and HCl is shown. The distribution of the mean mass fraction of OH radical is strongly influenced by the mixing intensity. A rapid increase in the OH concentration signals that ignition takes place. Due to the reduction of the mixing intensity (higher τ), the presence of OH radical is shifted to an earlier point in time. Moreover, the sharp peak present in the diagram of the mean OH concentration for τ = is broadened, meaning that the ignition process is distributed over a longer interval..1.3 E(Y(OH)) τ =. s τ =.5 s τ =.25 s τ =.5 s τ =.1 s std.dev. (Y(OH)) τ =.5 τ =.25 τ =.5 τ = t[s] t[s] Figure 4: Time evolution of estimated mean and standard dev. of OH mass fraction in the PFR and PaSPFR for different turbulent times. At t =.7s the ignition phase is finished an the system can be considered to be in equilibrium. The turbulence time τ =.5s in the PaSPFR corresponds to the PFR because mixing is completed before the chemical reactions can take place. The time evolution of the standard deviation for τ =.5s illustrates this point. The different ignition process leads to a slight acceleration of CH 3 Cl degradation and HCl formation. As indicated by the mean mass fraction of HCl in Figure 5. E(Y(HCl)) τ =. s τ =.5 s τ =.25 s τ =.5 s τ =.1 s std.dev. (Y(HCl)) τ =.5 τ =.25 τ =.5 τ = t[s] t[s] Figure 5: Time evolution of estimated mean and standard dev. of HCl mass fraction in the PFR and PaSPFR for different turbulent times.

7 7 The time evolution of the standard deviation indicates that two main processes superimpose. Chemical reactions lead to a strong increase of the standard deviation of the mass fraction of OH and HCl and molecular mixing reduces this variance because of the drift term in equation 1. The less the mixing the slower the decrease in the variance. Since the decay of the variance is slowed down, radicals like OH and H are present for a longer time interval, but at lower concentrations. This change of the radical mass fraction influences the reaction paths. Figure 6 shows the estimated mean specific conversion of reactions that consume H radicals. Reactions 135 and 133, the chain branching reactions, are important for the oxidation of CO and reactions 152 and 178 contribute to the formation of HCl. These two reactions are responsible for approximately 45 % of the HCl production and because of the consumption of the H radical, they slow down the overall CO oxidation. Figure 6 shows that the reactions 152 and 178 decrease their mean specific molar production as τ increases. On the other hand, reaction 135 and 133 increase the production of H radical. The H radical contributes to the oxidation of CO rather than to the formation of HCl. As a consequence, the chlorine inhibition is less strong and the degradation of methyl chloride is accelerated as exhibited in the mean mass fraction profiles. The faster formation of hydrogen chloride indicates that the formation paths, as displayed in Figure 3, are shifted. Figure 7 illustrates how the mean of the specific production of HCl by the main contributing reactions varies according to different turbulence mixing times τ. The overall production of HCl remains constant over the time interval considered because after.1s the oxidation is fully completed. As indicated in Figure 6, the contribution of reactions 152 and 178 is not as strong as in the case of perfect mixing (τ = s). Instead, reactions 176 and 192 increase their production. These reactions do not compete for the H radical but capture additional chlorine radicals and accelerate the formation of HCl. H + O 2 + M = HO 2 + M 135 O + OH = O 2 + H 133 H + Cl + M = HCl + M CH 3 Cl + H = HCl + CH τ=.s τ=.25s τ=.5s τ=.1s E( Q i ) [moles g -1 ] Figure 6: Estimated mean specific conversion of reactions 135, 133, 152, and 178 for varying turbulence times τ. The integration time is.1s.

8 8 E(w HCl ) [moles g- 1] τ [s] reaction 152 H+Cl+M = HCl+M 178 CH 3 Cl+H = HCl+CH CH 3 Cl+Cl = HCl+CH 2 Cl 188 CH 2 Cl+CH 3 = C 2 H 4 +HCl 192 CH 2 O+Cl = HCO+HCl 195 CH 3 +ClO = HCl+CH 2 O 23 C 2 H 4 +Cl = HCl+C 2 H 3 27 C 2 H 6 +Cl = HCl+C 2 H 5 29 Cl+C 2 H 5 Cl = HCl+CH 2 ClC.H 2 Figure 7: Estimated mean of the specific overall production of HCl for different turbulence mixing times τ. The integrated time interval is set to be [,.1]s. References [1] Barat R.B., Sarofim A.F., Longwell J.P., Bozelli J.W. : Inhibition of a Fuel Lean Ethylene/Air Flame in a Jet Stirred Combustor of Methyl Chloride: Experimental and Mechanistic Analysis Combust. Sci. and Tech., Vol.74, pp ,199 [2] Chen J.-Y. : Stochastic Modeling of Partially Stirred Reactors submitted to Combust. Sci. and Tech. 3/1995 [3] Christill M., Kolb Th., Seifert H., Leukel W., Kufferath A. : Untersuchungen zum termischen Abbauverhalten chlorierter Kohlenwasserstoffe VDI Berichte Nr. 1193, pp , 1995 [4] Kee R.J., Rupley F.M., Miller J.A.: Chemkin-II: A Fortran Chemical Kinetics Package for the Analysis of Gas Phase Chemical Kinetics Sandia Report SAND89-89B UC-76, 1993 [5] Kraft M., Fey H., Schlegel A., Chen J.-Y., Bockhorn H.: A Numerical Study on the Influence of Mixing Intensity on NOx Formation. 3rd Workshop on Modelling of Chemical Reaction Systems Proceedings, to appear 1997 [6] Pope S. B.: PDF Methods for Turbulent Reactive Flows Progress in Energy and Combustion Science, Vol.11, pp , 1985 [7] Valiño L., Dopazo C.: A binomial Langevin model for turbulent mixing Phys. Fluids, A3(12), pp , 1991