Impact of an Oxidative Pyrolysis Model for Charring Wood in Fire Simulations 1 1 1 2 Ragini Acharya Meredith Colket Paul Papas Joseph Senecal

Paper # 070FR-0155 Topic: Fire

8th U. S. National Combustion Meeting Organized by the Western States Section of the Combustion Institute and hosted by the University of Utah May 19-22, 2013

1United Technologies Research Center, East Hartford, CT 2Kidde Fenwal Inc., Ashland, MA

A general method for modeling wood burning within the framework of fire simulations is to apply a specified burning rate on a surface. This burning rate does not depend upon surface temperature. In order to predict mass loss rate of wood and reduction in mass loss rate due to surface cooling provided by watermist, it is required that a closed-loop coupling must exist between the heat feedback from the gaseous flame to solid surfaces, via radiation and convection. A pyrolysis model that couples the burning rate of a solid with the surface temperature via the Arrhenius law can be applied to achieve the closed loop coupling. The Fire Dynamics Simulator (FDS) code contains the entire infrastructure to this complex non-linear feedback and hence provides an excellent modeling environment for implementing an enhanced wood combustion model. While such a model is implemented in the FDS code, the pyrolysis model does not include a char oxidation model, which should account for the effect of oxygen concentration near the surface. In absence of such a model, the char oxidation reaction was treated as a kinetically-controlled reaction that is independent of the local oxygen level, which is in contradiction with the experimental observations for wood-based char oxidation by air (Kashiwagi, Ohlemiller, & Werner, 1987). A single-step reaction scheme with non-reacting char residue was found inadequate for large and medium-scale fire simulations. Therefore, an enhancement was made to FDS (svn no. 10095), to represent the role of oxygen in char oxidation using a power-law based model. In addition, the model for charring wood pyrolysis was compared against the experimental data of Janse et al. (1998) and Santangelo et al. (2012).

1. Introduction Wood-based fire is a major area of research in fire suppression. Wood packages are commonly used to represent solid fuel sources in practical fires and certification tests. For modeling fire suppression by water-based systems, it is imperative to understand and have a capability to accurately simulate the wood burning rate. Introduction of watermist in the wood-based fire can result in flame cooling and quenching, which can reduce the heat feedback from the flame to the burning surfaces of the wood. Reduced heat feedback from the flame can reduce the surface temperatures of wood, and thereby, lower the burning rates. Therefore, the wood burning rate must be coupled with the solid temperature of wood for the purposes of accurate fire suppression modeling, as shown in Fig. 1. A pyrolysis model that couples burning rate of solid with the surface temperature via Arrhenius law can be applied to achieve such closed loop coupling.

Gas-phase Other hot surfaces (via radiation and convection) (via radiation)

via gas-phase Net Heat flux to fuel surface heat release

Calculation of Tsurf

Kinetic parameters for surface reactions Calculation of m& fuel (Tsurf )

Figure 1: Flow chart description of closed-loop coupling between gas-phase and solid surface

Wood burning can be described as a two-step process. The first step is devolatilization of wood (or pyrolysis), which produces combustible gases and char. The second step is the slow oxidative combustion of char. There is significant literature on detailed and reduced reaction kinetics of wood combustion (Di Blasi, 2009). The focus of this work, however, was to implement a model for oxidative pyrolysis of charring wood for wood-based fire simulations within the framework of Fire Dynamics Simulator (FDS) (McGrattan et al., 2012). Fire dynamics simulator has been used widely as a modeling tool by the fire research community over the past decade. This software has successfully provided a framework for providing physical insights into complex large-scale fire simulations with a combination of detailed and reduced order models. FDS has a pyrolysis model implemented; however, the pyrolysis model did not include a char oxidation model that depends upon oxygen concentration near the surface (svn no. 10095). In absence of such a model, the following scenarios were possible:

Wood combustion does not form char Char is formed but not removed Char is formed and removed by a kinetically-controlled process

The above scenarios were not physically viable for large-scale fire scenarios where wood char is formed and also removed by a slow oxidation process. Moreover, if char was formed but not removed, then it formed a physical barrier (see Fig 2) between heat feedback from the gaseous flame and burnable wood fuel, thereby resulting in unphysical extinguishment of fire. It was also found that if wood was modeled as a non-charring material then the predicted wood burning could not reach a steady-state in burning rate as demonstrated by experiments (see Fig. 3), where experiments indicate quasi-steady state conditions can be achieved (shown in Fig. 7 later). Finally, a char removal process by kinetically-controlled process alone is not physically correct.

Heat feedback + external heat flux Heat loss via (if any) radiation Surface location

Residue layer { Non reacting char

Burnable material {

Figure 2: Schematic description of the effects of non-reacting char during the wood pyrolysis process.

Figure 3: A schematic comparison of non-charring wood pyrolysis model and char formation without removal models and hypothesis on the effect of char oxidation model on mass loss rate prediction from

2 Therefore, it was desired to implement a model that included a char oxidation model that depends upon oxygen concentration near the surface as well as solid temperature of char. The objectives of this work are:

• Implement an oxidative char combustion model within FDS; and • Step-wise validation of the above model with (a) combustion of char and (b) combustion of charring wood

Two sets of measured data were used for testing the predictive capability of two-step charring wood pyrolysis model. The first validation test consisted of pyrolysis of char only. The second case consisted of a wood crib freeburn, where char formed following wood devolatilization and then slowly burned as a result of oxidative pyrolysis. A stepwise validation tested the added model component separately as well as coupled with the wood devolatilization step.

2. Description of Charring Wood Pyrolysis Model Charring wood pyrolysis is a complex process with many reactions. The simplest model for this phenomenon requires at least three reactions to be modeled. They are described as following.

Wood ⎯⎯→k1 ν Fuel +ν Char + ΔH (R-1) (s) F Char (s) r1 wood Char +ν O →ν CO +ν CO − ΔH (R-2) (s) O2 2(g) CO2 2(g) CO (g ) r1 solid CO + 0.5 O → CO − ΔH (R-3) ( g ) 2( g ) 2( g ) r2 gas

The reaction rate expressions for reactions (R-1) and (R-2) are given as following.

nT 1 ns1 r1 = A1Ts exp(− Ea1 RuTs )Y f (1) n r = A exp()− E R T (1− X ) s 2 p nT 2 (2) 2 2 a2 u s O2

where

Conversion factor: X ≡ 1− M (t) M 0 (3)

In the above equations, r1 and r2 are rates of reaction, A1 and A2 are the pre-exponential factors, Ea1, Ea2 are the activation energies, nT1, nT1, ns1 are the exponents, Ru is the universal gas constant, Ts is the solid temperature, Yf is the wood mass fraction, po2 is the partial pressure of oxygen present next to the char surface, and M (t), M0 are the mass of char as at time t and at time = 0, respectively. The kinetic parameters used for Eqs. (1) and (2) are given in Table 1. The kinetic parameters for reaction (R-1) were obtained from McGrattan et al. (2012) and for the reaction (R-2) from Janse, Jonge, Prins, & van Swaaij (1998).

Table 1: Kinetic parameters for two-step reactions for wood combustion A1 [1/s] nT1 [-] Ea1 ns1 [-] A2 [1/s] Ea2 ns2 [-] nT2 [-] [J/mol] [J/mol] 5.36×1012 0.0 1.88×105 1.0 5.3×105 1.25×105 0.49 0.53

Reaction (R-1) and (R-2) are heterogeneous reactions. Fuel produced in reaction (R-1) burns in gas-phase. The third reaction occurs in gas-phase and can be modeled as mixing controlled reaction, which means that mixing rate of fuel and oxidizer determines the rate of reaction. In FDS (svn no. 10095), for mixing-controlled reaction option, only three lumped species were tracked. These lumped species are FUEL, OXIDIZER (mixture of 21% O2 and 79% N2, by mol/mol) and PRODUCTS (mixture of CO2 and H2O, based upon complete oxidation of fuel). As a consequence, CO and CO2 were not explicitly tracked. Therefore, CO and CO2 can be replaced from reactions (R-2) and (R-3) by “PRODUCTS” and “FUEL” in such a way (see Reactions R-4 and R-5) that that the net energy generated in (R-2) and (R-3) remains the same as (R-4) and (R-5), respectively. Mass should also remain conserved. With these two constraints, the reaction steps for char oxidation (reactions R-2 and R-3) were modeled as following.

3 Char(s) +ν O O2( g ) →ν P Products (g ) +ν F Fuel( g ) − ΔH r (R-4) 2 1 142 43 123 1 solid Represents CO2 Represents but consists of CO and other CO2 and H2O unburnt HC

Fuel( g ) +ν O′ O2 →ν P Products( g ) − ΔH r′ (R-5) 2 2 142 43 2 gas Represents CO2 but consists of CO2 and H2O

The mass balance and energy balance between reactions R-2/R-3 and reactions R-4/R-5, was maintained via following equations:

Mass balance: ν Mw +ν Mw =ν Mw +ν Mw (4) CO2 CO2 CO CO P1 P F F Energy balance: ν Mw ΔH =ν Mw ΔH ′ (5) CO CO r2 F F r2

In the above equations, νi are the stoichiometeric coefficients, and Mwi are the molecular weights.

For example, if Fuel = Propane then “PRODUCTS” consists of 3×CO2 and 4×H2O. In that case, Mw = 3× Mw + 4× Mw (6) P CO2 H 2O Mw = Mw (7) F C3H8

3. Results and Discussion

3.1. Code Verification In order to test the implementation of the char oxidation model in FDS, four cases were run. In each of these cases, gas- phase processes were turned off and only solid-phase calculations were performed on a surface. A description of these cases is provided in Table 2.

k1 Wood(s) ⎯⎯→ Char(s) (R-6)

k2 Char(s) ⎯⎯→ Ash(s) (R-7) The above reactions can be represented by the following ordinary differential equations: dY dY dY wood = −r ; char = r − r ; Ash = r (8) dt 1 dt 1 2 dt 2 A comparison of calculated results from FDS with 4th order Runge-Kutta integration of Eq. (8) is shown in Figure 4. Note that the kinetic parameters for cases shown in Table 2 are for code verification purpose only and were not used for validation. The numbers shown in Table 2 are not the experimentally obtained kinetic parameters.

Table 2: List of parameters for 4 verification cases

Figure 4: Verification of char oxidation model implementation in FDS

3.2. Validation: With Char Combustion As mentioned earlier, a stepwise validation was performed. In this section, the validation for oxidation of only char is described. The kinetic parameters for char oxidation reaction have been obtained from experimental work of Janse, Jonge, Prins, & van Swaaij (1998) and are shown in Table 1. They measured the evolution of conversion factor X with time by burning char in a controlled environment with 18 vol% oxygen by using thermogravimetric analysis. In these measurements, char produced by flash pyrolysis of wood and then heated in oxidizing environment. Wood is not part of the validation data.

A certain amount of cold char (less than 0.5 mg) was put into the small sample basket of the TGA. At the start of an experiment, the hot tube furnace was positioned quickly around the sample holder for heating the char sample, after which the weight decrease in time was recorded. A gas consisting of a mixture of a specified ratio of oxygen and nitrogen was supplied to the furnace tube. The sample was heated to different temperatures in presence of oxygen- nitrogen mixture, and conversion factor X vs. time was recorded for each of these four conditions. Based upon this information, similar conditions were modeled in an FDS input file and a conversion factor vs. time data was calculated for each of the four temperatures. A comparison of calculated results by using the char oxidation model in FDS with measured data is shown in Fig. 5. Calculated results can predict the trends shown by measurements. However, there is more than 20% difference between calculations and measurements at some conditions. This difference could result from (a) numerical inaccuracy, and/or (b) dependence of kinetic parameters of char oxidation reaction on operating conditions. In the simulation, constant values for A and E have been used; however, experimental results have indicated that these parameters are strongly dependent upon conversion factor X, oxygen concentration, and surface temperature.

k2 Char(s) + O2 ⎯⎯→ Fuel (R - 2)

5 Symbols – Expt. Data Solid curves – Model Results

Figure 5: Comparison of calculated conversion factor and measured data for char oxidation coupled with gas-phase physics.

3.3. Validation: With Wood + Char Combustion In this section, results from application of charring wood pyrolysis model on a realistic geometry are discussed. A wood crib geometry is used for certification tests by UL (e.g., UL2167) for nozzles and sprinklers. The details of the computational domain are described below and also shown in Fig. 6:

• Room dimensions : 2 m × 2 m × 2.56 m • Ceiling : Sloped with open hood (similar but not same as experimental set up) • Mesh : 4 cm each direction • Bar dimensions : 38.1mm x 508mm x 38.1mm (25 bars total) • Material : Cellulose • Boundary conditions: Open all surfaces except floor • Igniter : Heptane pool under the crib up to 137 s

Sloped hood with open ceiling

Wood crib

Igniter

Figure 6: Description of the computational domain with wood crib placed in center.

6 The calculated mass loss rate is shown in Figure 7. In this figure, the measured mass loss rate from a wood crib and heptane pool used as igniter are also shown. These measurements were obtained by Santangelo et al. (2012). In a separate experiment from the same authors, mass loss rate from the heptane pool igniter was characterized without the wood crib. This defined mass loss rate was used to characterize the heptane pool igniter in our simulation. As shown in Fig. 7, predictions show quantitative match with measurement data up to ~500 s. There is difference between measured data and calculation results with char oxidation between 150-200 s. This difference could be attributed (but not certainly) to the uncertainty in igniter burning rates. Numerical results from a calculation where char was formed but not removed are also shown in this plot. It is evident that the case without char removal results in unphysical extinguishment, thereby showing the significance of oxidative char combustion reaction in the modeling of the wood pyrolysis process. Use of the more conventional prescribed heat release method can result in a much closer simulation of the experimental mass loss rate data; however, such empirical fitting does not lend itself to the feedback necessary for the fire suppression modeling.

Figure 7: Comparison of net mass loss rate from solid as a function of time with charring without removal, and charring wood pyrolysis models.

Various stages of wood crib pyrolysis are shown in Figures 8 and 9. Figure 8 shows the flame height and solid temperature of wood at various physical instances. Figure 9 shows gas temperature profiles and the solid temperature of wood at same times. These two plots show that this simulation is able to reproduce the phenomenological behavior of wood crib freeburn as observed by Santangelo et al. (2012). Figures 8 and 9 show that up to 72 second, the flame is sustained by the igniter below the wood crib since the majority of the wood members of the crib are below the wood decomposition temperature. The flame height reduces slightly as the igniter burns out at 147 second. Figure 8 shows that the wood crib starts to burn from the inside as demonstrated by the higher solid temperatures from 147 second onwards. The outer wood members of the crib do not burn out till 550 second as they are heated more slowly than the internal wood members. The gas temperature continues to increase until complete burnout of the internal wood members of the crib occurs. After this, the flame height is reduced and gas temperatures decrease.

Figure 8: Calculated flame height and solid temperature profiles at various instances for wood crib combustion with 2- step reaction scheme for oxidative wood pyrolysis.

Figure 9: Calculated gas temperature and solid temperature profiles at various instances for wood crib combustion with 2-step reaction scheme for oxidative wood pyrolysis.

4. Summary & Future Work This work presents a description of a 2-step charring wood combustion model. The model utilizes the oxygen concentration near the surface for the calculation of char oxidation rates. The char oxidation model was verified with theoretical solutions. Impact of the char oxidation model on charring wood combustion and its ability to predict directional trends was demonstrated. The char oxidation model was validated with two cases of increasing physical complexity. Having a validation model for oxidative pyrolysis of charring wood should have impact on the predictive capability of numerical code for fire suppression with watermist. In the future, additional validation can be performed with experimental data. Physical cracking of the wood structure, which increases porosity, and could play a role in larger fires, was not included in the current model.

8 References

1. Di Blasi, C. (2009), Combustion and Gasification Rates of Lignocellulosic Chars, Progress in Energy & Combustion Science, vol. 35, pp. 121-140. 2. McGrattan, K., Mell, W., McDermott, R., Hostikka, S., and Floyd, J., Fire Dynamics Simulator: Technical Reference Guide, Volume 1: Mathematical Model, NIST SP-1018, National Institute of Standards and Technology, Gaithersburg, MD, 2012. 3. Janse, A. M. C., de Jonge, H. G., Prins, W., & van Swaaij, W. P. M., Combustion Kinetics of Char Obtained by Flash Pyrolysis of Pine Wood, Ind. Eng. Chem. Res. (1998), 37 (10), pp. 3909-3918. 4. Kashiwagi, T. , Ohlemiller, T. J., and Werner, K., Effects of External Radiant Flux and Ambient Oxygen Concentration on Nonflaming Gasification Rates and Evolved Products of White Pine, Combustion and Flame (1987), Vol. 69, pp. 331-345. 5. Santangelo, P. E., Jacobs, B. C., Ren, N., Sheffel, J. A., Corn, M. L., and Marshall, A. W., Suppression Effectiveness of Water Sprays on Accelerated Wood-Crib Fires, SUPDET 2012.