Computational study of critical moisture and depth of burn in peat fires

Additional keywords: extinction, ignition, modelling, peatland, smouldering, soil moisture, surface fuel, wildfire.

Smouldering combustion is the slow, low-temperature, flameless burning of porous fuels and the most persistent type of combustion – different from flaming combustion in its chemistry, transport processes and time scales (Ohlemiller 1985; Rein 2013). Smouldering is the dominant phenomenon in the burning of natural deposits of peat, which are the largest and longest burning fires on Earth (Page et al. 2002; Turetsky et al. 2015; Rein 2013). Locally, smouldering wildfires cause severe and long-term damage to the soil system (Ryan and Frandsen 1991; Stephens and Finney 2002; Rein et al. 2008). Organic soils and peat store around 25% of the planet’s terrestrial organic carbon – approximately the same mass of carbon as found in the atmosphere – despite peatlands occupying only 3% of the Earth’s surface (Gorham 1994; Turetsky et al. 2015). Globally, these fires contribute greatly to greenhouse gas emissions, and result in widespread destruction of ecosystems and regional haze events, examples being the recent megafires in Southeast Asia, North America and Northern Europe (Rein 2013). During the 1997 extreme haze event in Indonesia, peat fires released the equivalent of 13–40% of global manmade carbon emissions for the same year (Page et al. 2002). More recent figures estimate that the average annual carbon footprint is equivalent to 15% of manmade emissions (Poulter et al. 2006). Moreover, pollutants in smouldering haze substantially increase the risk of cardiopulmonary diseases in the human population (Rappold et al. 2011; Kim et al. 2014).

Peat can hold a wide range of moisture contents (MC¹), from 10% under drought conditions to well in excess of 300% under flooded conditions (Benscoter et al. 2011; Watts 2013). Water represents a significant energy sink and can prevent fire in undisturbed wetlands, but natural or anthropogenic-induced droughts are the leading cause of fires (Turetsky et al. 2015). Therefore, soil moisture is the single most important property governing the ignition, spread and extinction of smouldering wildfires (Frandsen 1987; Frandsen 1997; Rein et al. 2008; Garlough and Keyes 2011; Watts 2013). During an ignition, water evaporates and then the organic content of the peat undergoes pyrolysis until the exothermic char oxidation begins, which can lead to spread of a self-sustaining fire. The critical moisture content for smouldering ignition (MC*_ig) for various peat types has been reported in the range of 40–150% (Frandsen 1987, 1997; Rein et al. 2008; Garlough and Keyes 2011). When drier than this critical content, peat becomes susceptible to smouldering. Other factors affecting soil susceptibility to smouldering include inert content (IC²), bulk density, porosity and chemical composition. The pioneering experiments of Frandsen (1987, 1997) showed that there is a decreasing relationship between MC*_ig and IC: a soil of high IC can only be ignited at low MC. The influence of bulk density was studied experimentally by Hartford (1989) and Garlough and Keyes (2011), who reported contrasting results with respect to smouldering. Hartford (1989) found that a higher bulk density decreases the probability of smouldering, whereas Garlough and Keyes (2011) found that bulk density has no significant effect.

If ignition of the top peat layer occurs, a self-sustaining smouldering front can spread both laterally and in depth (Rein 2013; Huang and Rein 2014). After extinction, the depth of burn (DOB) can be used to estimate the amount of carbon lost in the fire per unit area (Page et al. 2002; Rein 2013; Davies et al. 2013). According to Rein (2013), extinction happens when the vertical spread is quenched by: (i) the presence of the mineral soil layer; (ii) the presence of a thick wet layer; or (iii) the timing of flooding, heavy continuous rains or firefighting. The mechanism of extinction of interest in this work is by a wet layer (ii), which leads to the definition of the critical moisture for extinction (MC*_ex).

Wade et al. (1980) reported experiments where the top layer could only be ignited at MC <65%, but once ignited, the fire continued to burn in depth through wetter layers of MC = 150%, a higher MC than the critical value reported by Frandsen (1987, 1997). More recently, Benscoter et al. (2011) conducted a series of experiments for in-depth spread in field samples with heterogeneous profiles of MC, IC and density. For most of their experiments, the smouldering front did not spread through peat layers with MC >150%, but for one particular sample, the smouldering front spread over a 3-cm thick layer of 295% MC, a much higher value than the MC*_ig expected from Frandsen (1987, 1997). All these experimental studies in the literature suggest that MC*_ex differs from MC*_ig, and that DOB depends on both peat MC and thickness of the layers above and below (heterogeneous profile).

The number of computational studies on smouldering peat in the literature is small. Benscoter et al. (2011) modified Van Wagner’s (1972) analytical heat transfer model, and by calibrating the downward heat transfer rate, their predictions of DOB were in good agreement with the experiment measurements. In our previous work (Huang and Rein 2014; Huang et al. 2015), a multi-physics one-dimensional (1-D) model of reactive porous media was developed to investigate the ignition of smouldering peat fire using a five-step chemistry scheme combining drying, pyrolysis and oxidations reactions. The model successfully predicts the experiments of Frandsen (1987, 1997) on small and homogeneous soil samples and revealed the sensitivity of smouldering ignition (MC*_ig) to IC, chemical kinetics and soil properties as well as to the ignition protocol.

In this work, we continue using the existing multi-physics model, and further improve it to consider column samples with heterogeneous profiles of MC and properties that vary with depth. The MC*_ex and DOB are investigated computationally and applied to the experiment of Benscoter et al. (2011).

In-depth smouldering in the vertical direction is best studied in column peat samples as in the experiments of Benscoter et al. (2011), Watts (2013) and Zaccone et al. (2014), which can be approximated as 1-D along the vertical direction of in-depth spread. Fig. 1a shows the computational domain of a peat column with heterogeneous MC and density profiles. The ignition is attempted on the top surface by applying a constant heat flux for a period of time. If the ignition source is weak or MC near the top is high, the smouldering front may not propagate. Once ignited, a smouldering front spreads in depth, drying and consuming the peat below. At the same time, a char layer appears and propagates in depth, and an ash layer gradually accumulates on top, as illustrated in Fig. 1b. The depth at which the fire extinguishes gives the final DOB (Benscoter et al. 2011; Rein 2013).

Fig. 1.  Schematic illustrations of the 1-D computational domain of the peat column with heterogeneous moisture content (MC) and density profiles: (a) before ignition (t = 0) and (b) during self-sustained in-depth spread. DOB, depth of burn.

The open-source code Gpyro for generalised pyrolysis simulations is used to model smouldering peat. Details of Gpyro can be found in Lautenberger and Fernandez-Pello (2009), so only the essentials are presented here. The model solves transient equations for both the condensed and gas phases. The governing equations include Eqn (1) for condensed-phase mass conservation, Eqn (2) for condensed-phase species conservation (assuming thermal equilibrium with the gas phase), Eqn (3) for condensed-phase energy conservation, Eqn (4) for gas-phase mass conservation, Eqn (5) for gas-phase species conservation and Eqn (6) for gas-phase momentum conservation (Darcy’s law):

All symbols are explained in Appendix 1. Subscripts i, j and k refer to the index of condensed-phase species, gas-phase species and reaction, respectively; d and f refer to the destruction and formation of species.

Each condensed-phase species is assumed to have constant properties (e.g. bulk density, specific heat and porosity). All gaseous species are assumed to have a unit Schmidt number and the same specific heat (set to that of nitrogen). The properties in each cell are weighted averages based on mass fraction Y_i or volume fraction X_i (Lautenberger and Fernandez-Pello 2009). As an example, Eqn (7) shows the expression to average four important properties whose format is the same for the other properties (M, K, ϵ and Y):

At the free surface of the top layer (z = 0), the boundary conditions simulate natural convection and no cross-wind for heat transfer (h_c,0 = 10 W m⁻² K⁻¹; radiative emissivity ϵ = 0.95) and mass transfer (h_m,0 ~ h_c,0/c_p,g ~ 0.02 kg m⁻² s⁻¹). The initial pressure and temperature in the domain are atmospheric and 300 K. The ignition source is modelled as an external heat flux () applied at z = 0 for 5 min. Whether the ignition is successful or not depends on MC, IC and properties of the peat layer near the ignition source as well as the ignition protocol, details of which are discussed in depth in Huang et al. (2015). At the bottom of the column (z = H₀), the mass flux is set to be zero (sealed boundary) and heat transfer is purely convective (h_c,L ≈ k_wall/δ_wall = 3W m⁻² K⁻¹) to simulate a small heat loss through an insulating boundary. A fully implicit formulation is adopted for solution of the coupled system of Eqns (1–6). Details about the numerical solution can be found in Lautenberger and Fernandez-Pello (2009). The sample height during spread is equal to the sum of the heights of each cell, , which depends on mass conservation and density. Simulations were run with an initial cell size of Δz_n,0 = 0.2 mm and initial time step of 0.02 s. Reducing the cell size and time step by a factor of two results in no significant difference, so this discretisation is acceptable.

The heterogeneous reaction k of condensed species A in mass basis is given as:

where v_B,k = 1 + (ρ_B/ρ_A – 1)χ_k and χ_k quantifies the shrinkage or expansion. The destruction rate of species A in the reaction k is expressed by the Arrhenius equation given in Eqns (9) and (10):

The formation rates of the condensed species B and all gases from reaction k are and , respectively. The corresponding condensed-phase heat of reaction is .

In our previous work (Huang and Rein 2014), various chemical kinetic schemes for smouldering combustion were investigated using thermogravity data from four peat samples from Scotland (SC), Siberia (SI-A and SI-B) and China (CH). The best kinetics scheme was found to include one drying step (Eqn 11), one pyrolysis of peat (Eqn 12) and three oxidations of peat (Eqn 13), β-char (Eqn 14), and α-char (Eqn 15).

where, v_w,dr = MC and the subscripts w, p, α, β and a represent the five condensed species (water, peat, α-char, β-char and ash). Four gaseous species are considered: oxygen (O₂), nitrogen (N₂), water vapour (H₂O) and combustion products (Gas). The composition of the gaseous combustion products in peat fire was discussed further in Rein et al. (2009).

For the model implementation, the vertical profile is discretised in N number of layers (i = 1, 2, 3, … N) of varying thickness (δ_i), moisture content (MC_i), properties (e.g. ρ_i, k_i, c_p,i) and chemistry, as shown in Fig. 1a. This discretisation is convenient to simulate field samples that typically include heterogeneous profiles with depth for the properties. For example, in the experiment of Benscoter et al. (2011), the 20–30 cm tall peat columns were divided into multiple layers, each of 3 cm in thickness.

We first study in detail a simple and ideal column with a heterogeneous profile made of three layers: a top layer (δ_t), a middle wet layer (δ_w) and a bottom dry layer (δ_b). Fig. 2 shows the computational domain, with a fixed height of h₀ = δ_t + δ_w + δ_b = 20 cm, while the thickness of each layer varies for different cases. The top layer has an MC lower than the critical value for ignition (MC_t < MC*_ig) so it can be ignited by external heating. The middle layer (MC_w) is much wetter, and the bottom layer is air-dried peat, which is in equilibrium with the ambient MC_b = 10% (Cancellieri et al. 2012; Huang and Rein 2014). The function of this dry layer is to create a consistent boundary and to minimise its influence on extinction and DOB.

Fig. 2.  Schematic illustration of the 1-D computational domain of the peat column with heterogeneous moisture and density profiles made of three layers.

If MC_w is below a threshold, the smouldering front arriving from the top is able to propagate through it and to burn to the bottom layer, eventually consuming the whole sample (i.e. DOB = h₀ = 20 cm). This threshold is the critical MC for extinction (MC*_ex) and can be found by continuously increasing MC*_w in different simulations until it results in DOB = h₀.

The thermo-physical properties of each condensed-phase species (i) are listed in Table 1. The bulk densities ρ_i,0 are taken from Benscoter et al. (2011) or Hadden et al. (2013). The properties of the solid (non-porous) material ρ_s,i, k_s,i, c_p,i for peat, char and ash are taken from Jacobsen et al. (2003). The porosity is calculated as:

Table 1.  Physical parameters of the condensed-phase species: ρ_s,i, k_s,i and c_p,i are from Jacobsen et al. (2003), and ρ_i,0 is from Benscoter et al. (2011) or Hadden et al. (2013)

The effective thermal conductivity includes the radiation across pores as:

where γ_i ~ 10⁻⁴ m depends on the pore sized as γ_i = 3d_p,i (Yu et al. 2006). The average pore size relates to the particle specific surface area S as d_p,j = 1/S_iρ_i where S_p = S_c = 0.05 m² g⁻¹ and S_a = 0.2 m² g⁻¹ (de Jonge et al. 1996). The absolute permeability can be calculated from the empirical expression of Punmia and Jain (2005) as:

where K_i varies from 10^–12 to 10⁻⁹ m² and decreases with the bulk density. Because of the high porosity of peat (ψ_p = 0.973) and its low volumetric water content (Benscoter et al. 2011), water can be assumed to stay in the pores without causing volume expansion. The bulk density of moist peat is ρ = (1 + MC)ρ_p. The properties of α-char and β-char are assumed to be the same.

The smouldering chemistry corresponding to the Scotland (SC) samples of subshrub and sphagnum high-moor peat (Rein et al. 2008; Cancellieri et al. 2012; Huang and Rein 2014) is selected for all three peat layers. Table 2 lists the kinetic and stoichiometric parameters. The heat of oxidation is related to the organic content as ΔH_k = C_k(1 – v_B,k). The surface peat reported in Benscoter et al. (2011) has a low bulk density and a low degree of decomposition, so the heat of combustion is set to a lower value than the high-density peat with high degree of decomposition reported in Frandsen (1987) and Leroy-Cancellieri et al. (2014). By integrating the heat flow measurements for peat samples (see Bergner and Albano 1993; Chen et al. 2011), we estimate that C_po = 7.5 MJ kg⁻¹ and C_ao = C_bo = 15 MJ kg⁻¹. The oxygen consumption coefficients in Eqns (13–15) are related to the heat of oxidation as v_O2,k = ΔH_k/13.1, where ΔH_k is given in MJ kg⁻¹ (Huggett 1980).

Table 2.  Reaction parameters and gas yields of the five-step scheme for a Scotland (SC) peat sample (Huang and Rein 2014)

We arbitrarily choose a base case to investigate the smouldering process and front structure in detail (δ_t = 6 cm, δ_w = 3 cm and δ_b = 11 cm). The peat sample has a uniform bulk density of 40 kg m⁻³ and a wet layer of MC_w = 180%. Air-dried peat is chosen for both the top and bottom layers (MC_t = MC_b = 10%). Using the method in Huang et al. (2015), the weakest ignition protocols required to ignite the dry top layer are 8.3 kW m⁻² for 5 min, or 5.0 kW m⁻² for 30 min. Based on this result and to ensure a successful ignition, a strong heating source ( kW m⁻², similar to a flame) for 5 min is chosen as the ignition protocol. The predicted mass evolution of each species m_i and the evolution of DOB and spread rate are shown in Figs 3(a) and (b). The instantaneous DOB is calculated by the deepest location at which most peat has been consumed (i.e. Y_p < 5%). The spread rate is obtained by tracking the position of the peak temperature.

Fig. 3.  Predicted evolution of (a) the species mass, m_i; and (b) the depth of burn and spread rate for the base case: δ_t = 6 cm (MC_t = 10%), δ_w = 3 cm (MC_w = 180%), δ_b = 11 cm (MC_b = 10%).

Four different stages can be seen during propagation across each of the three different peat layers and at burnout: (I) t < 15 min, (II) 15 < t < 60 min, (III) 60 < t < 170 min and (IV) 170 < t < 270 min. When the smouldering front propagates through the wet layer (Stage II), the drying becomes fast while the peat consumption slows down. The spread rate decreases due to the heat sink of water, increasing the residence time for the exothermic char oxidation to drive the smouldering front in depth to the bottom layer. Once the bottom dry layer is burning (Stage III), the spread rate increases rapidly and the char layer grows. The original peat is degraded into char within 170 min, and afterwards, the char oxidation dominates the spread (Stage IV).

The temperature evolution with depth and time is shown in Fig. 4, along with the regression of the top surface. The peak temperature is found at 1–2 cm below the top surface. Although the peak temperature in the dry layers (Stage I and III) is predicted to be around 850°C – higher than the peak values (500–600°C) measured by Rein et al. (2008) – the peak temperatures across the wet layer (Stage II) is 550–600°C and agrees well with measurements. Fig. 4 also qualitatively shows the size of the reaction zones. The thickness of the high-temperature (exothermic oxidation) region grows in the dry layers (Stage I & III), whereas it decreases in the wet layer (Stage II) as well as near fuel burnout (Stage IV). The thickness of the lower temperature (drying) region follows a similar trend. At ~130 min, the smouldering front reaches the bottom and the boundary affects the fire propagation; burnout takes place at 270 min.

Fig. 4.  Predicted contour of temperatures in depth v. time for the base case: δ_t = 6 cm (MC_t = 10%), δ_w = 3 cm (MC_w = 180%), δ_b = 11 cm (MC_b = 10%). (For colour figure, see online version of this paper available at http://www.publish.csiro.au/paper/WF14178.htm.)

Fig. 5 shows results of the predicted temperature, reaction rates, MC and species profiles at different instants of time. During Stage I and II, the smouldering front is thin – around 2 cm thick. The thickness then increases to 5 cm in Stage III due to the growth of char layer (from 1 cm to 3 cm as seen in Fig. 5e), and then decreases to a thinner zone in Stage IV. The thickness of ash layer (Fig. 5f) continues to increases from zero to δ_a,max ≈ 2 cm at the bottom. After burnout, the residue left is very small in mass, and made of ash at the top and char below. This is the typical composition of the residue found after smouldering wildfires in the field (Moreno et al. 2011) and experiments (Zaccone et al. 2014).

Fig. 5.  Predicted profiles of (a) temperature, T; (b) reaction rate, ω^k_; (c) moisture content (MC) and species mass fraction, Y_i; (d) peat, (e) char and (f) ash for the base case: δ_t = 6 cm (MC_t = 10%), δ_w = 3 cm (MC_w = 180%), δ_b = 11 cm (MC_b = 10%).

As peat MC increases, it requires more heat to dry the fuel, thus slowing down the spread rate (see Fig. 3b) and eventually, extinction occurs. This event defines the critical MC for extinction (MC*_ex). The value of MC*_ex depends on the properties across the vertical heterogeneous profile. This is shown in Fig. 6 where MC*_ex is predicted to vary with the thicknesses of the top layer (δ_t, MC_t = 10%) and the wet layer (δ_w). Above a critical line in Fig. 6, extinction occurs in the wet layer; below the line, no extinction occurs before burnout.

Fig. 6.  Predicted critical moisture content (MC*_w) in the wet layer v. thicknesses of the top dry layer (δ_t), (MC_t = 10%) and the wet layer (δ_w).

Fig. 6 shows that a smouldering fire is able to spread across very wet layers above 250% MC as the thickness of the top dry layer increases. On the other hand, the heat sink of water increases with δ_w, thus reducing MC*_ex. For example, with δ_t = 8 cm, the MC*_ex decreases from 256% to 195%, as the wet layer thickness δ_w increases from 2 to 8 cm.

If there is no top layer (δ_t = 0), the case becomes an ignition problem. Frandsen (1987, 1997) conducted a series of ignition experiments on multiple small and homogeneous peat samples of 4–5 cm thick, which had been successfully predicted in the previous work (Huang et al. 2015). For the current ignition protocol and peat properties, MC*_ig is found to be 117% based on the method in Huang et al. (2015). The maximum critical value for ignition MC*_ig,max reported by Frandsen (1987, 1997) is 145%. This value is included for reference in Fig. 6. The predictions show that MC*_ex is always higher than MC*_ig and explain for the first time the experimental observation in Wade et al. (1980) where the measured MC*_ig of 65% was much lower than the MC*_ex of 150%.

After extinction, the final DOB is obtained. Fig. 7 shows the DOB v. MC_w for several possible profiles. MC*_ex is indicated as a jump in DOB: below MC*_ex, the whole peat column (20 cm) is burnt, whereas above it, only the top dry layer (δ_t) plus 1–2 cm of the wet layer are consumed.

Fig. 7.  Predicted final depth of burn (DOB) v. the moisture content of the wet layer (MC_w). The top layer is dry (MC_t = 10%).

The moisture of the top layer (MC_t) controls the possibility of ignition, and serves as an upstream condition to control the spread in the wet layer below. Fig. 8a shows the predicted MC*_ex v. MC_t for several cases. The value of MC*_ex slowly decreases with the increasing MC_t until it is near the critical value for ignition (MC*_ig). Afterwards, MC*_ex quickly drops to 117%, converging to MC*_ig, and the system becomes an ignition problem. In addition, as δ_w increases, the curve becomes flatter (i.e. MC*_ex becomes less sensitive to MC_t). For example, in the base case (δ_t = 6 cm, δ_w = 3 cm ), when MC_t increases from 10% to 100%, MC*_ex only decreases from 192% to 173%.

Fig. 8.  Predicted (a) critical moisture content for extinction in the wet layer (MC*_ex) and (b) final depth of burn (DOB) for the base case (δ_t = 6 cm, δ_w = 3 cm), v. moisture for the top layer (MC_t).

Fig. 8b shows the corresponding DOB v. MC*_ex and MC_t for the base case, where four different regions (A–D) can be seen. If the top layer is very wet (Region A: MC_t > MC*_ig), no ignition occurs. If the moisture anywhere in the sample is less than the ignition threshold (Region B: MC_i < MC*_ig), no extinction occurs before burnout. These two zones were identified in the experiments of Frandsen (1987, 1997) and in the simulations of Huang et al. (2015). However, once ignited (MC_t < MC*_ig), there is an additional region of wetter conditions (Region C: MC*_ig < MC_w < MC*_ex), where the whole peat column is also burnt but this has not been identified or explained before. Moreover, in Region D (MC*_ex < MC_w), only the top layer and a short depth of the wet layer burn, which was observed in the experiment of Benscoter et al. (2011).

Fig. 9 shows that the bulk density of peat (ρ_p) affects the ignition and extinction criteria. The critical moisture for extinction is shown to be much larger than that for ignition (MC*_ex > MC*_ig) across the whole density range. For MC*_ex, it first increases with ρ_p until reaching a peak around ρ_p = 100 kg m⁻³, and then slowly decreases. This result agrees with the duff experiment of Garlough and Keyes (2011), who found that MC*_ex and DOB for lower density samples ( kg m⁻³) were smaller than higher density samples in depth ( kg m⁻³). The peak in MC*_ex implies that the sample density affects two competing mechanisms in the extinction of smouldering: heat transfer (via energy conservation in Eqn (3)) and oxygen supply (via energy conservation in Eqn (3) and permeability in Eqn (18)). On the other hand, the marked decrease in MC*_ig in the high-density range is caused by the increase in thermal inertia (via energy conservation in Eqn (3)), as previously observed in Hartford (1989) and modelled in Huang et al. (2015). In addition, for this short 5-min ignition protocol, the results for MC*_ex do not change for an external heat flux level  kW m⁻², whereas the curve of MC*_ig significantly drops in value as the external heat flux level decreases.

Fig. 9.  Predicted critical moisture contents MC*_ig and MC*_ex v. peat bulk density, ρ_p for different columns. The top layer is dry (MC_t = 10%).

Benscoter et al. (2011) extracted cores from six different peat types in the Athabasca Bog, Canada (dominated by Sphagnum fuscum and Pleurozium schreberi) and divided them into column samples. Each peat type was treated differently for drying, according to three methods: field moisture (no drying); 2-week air drying; and 2-week air drying plus 48-h oven drying at 40°C – producing a total of 18 samples. The central portion of each column was tested inside a vertical box made of 1.3-cm ceramic fibreboard with the top open to the air.

Prior to testing, the columns were sliced into 3-cm layers, and the average values of MC, IC and bulk density were measured to capture the vertical profiles (similar to Fig. 1a). The bulk density of peat samples ranged from 2 to 90 kg m⁻³ with an average value of ~40 kg m⁻³, much lower than the samples in Frandsen (1987, 1997) and Rein et al. (2008). These profiles are used as inputs to the model. Other physical parameters are shown in Table 1; these are assumed to be independent of temperature. The ignition source in Benscoter et al. (2011) was a propane-fired radiator, placed above the top surface for 5 min. This is modelled by a heat flux of 30 kW m⁻² for 5 min as a boundary condition, which is high enough to accommodate the flaming ignition of the top layer observed in the experiment. It is acceptable to model a strong ignition source this way because as shown in Fig. 6, MC*_ex increases only slightly for δ_t < 1 cm, implying the influence of ignition protocol is limited to the top 1 cm.

We choose one representative case, the oven-dried mixed-species hollow sample 2 (Oven Hol 2), to study in detail the smouldering process. This sample is 21 cm high, and Table 3 lists the measured profiles of ρ_p, MC, and IC for each of seven 3-cm layers. The corresponding measurements for all 18 columns are available in Benscoter et al. (2011). In general, ρ_p increases with depth due to soil compaction and aging. The MC also increases with depth due to the proximity of the watertable. The average IC of the column is relatively high (), so for simulations we use the decomposition chemistry of a Siberian scheuchzeria and sphagnum transition peat, IC_SI–B ≈ 8.8% (Cancellieri et al. 2012), the kinetic parameters of which were found in Huang and Rein (2014).

Table 3.  Measured profiles of peat bulk density (ρ_p), moisture content (MC), and inert content (IC) for the Oven Hol 2 sample in Benscoter et al. (2011)

Fig. 10 shows the predicted evolutions of the temperature and moisture for the Oven Hol 2 sample. The modelled smouldering fire lasts for ~110 min, close to ~90 min observed in the experiment. The column does not burn completely due to the very high moisture at z > 9 cm and the predicted DOB is 11.5 cm, in agreement with the experimental measurement of 9±3 cm. It can be seen in Fig. 10a that the temperature trends to decrease with the depth as the peat MC increases, and it drops rapidly after 90 min when the drying front reaches the wetter layer of MC = 373% at z = 12 cm where extinction occurs. After extinction, the high-temperature front is able to continue drying the peat until the residual column cools down completely.

Fig. 10.  Predicted evolution of (a) the temperature, T and (b) moisture content, MC v. depth, for the Oven Hol 2 sample. DOB, depth of burn.

All 18 samples in Benscoter et al. (2011) were simulated. For the low-mineral peat types (), the smouldering chemistry of a Scotland subshrub and sphagnum high-moor peat, IC_SC ≈ 2% (Cancellieri et al. 2012; Huang and Rein 2014) is used (see Table 2). For the high-mineral peat type (), the same Siberia (SI–B) peat as the Oven Hol 2 sample is used. Fig. 11 compares our predicted DOB to the measurements in Benscoter et al. (2011). The degree of agreement is measured by the R² coefficient, which is 0.87. Despite the model limitations due to the 1-D assumption and the approximation of heat and mass transfer boundary conditions at the top surface (h_c and h_m), and considering the complexity of the fire process and the field samples, the predictions reported here are very good and outperformed any other peat fire model in the literature, e.g. Benscoter et al. (2011).

Fig. 11.  Comparison of predicted and measured depth of burn for the 18 natural samples in Benscoter et al. (2011). The horizontal error bar is the uncertainty from experimental observations, and the vertical error bar is the calculated uncertainty in the model.

In general, the chemical and physical properties of peat (e.g. the heat of smouldering ΔH_sm, heat capacity c_p, conductivity k) vary with the depth and from site to site, which translates to a degree of uncertainty in model predictions. We have studied this uncertainty and found that both MC* and DOB increase with ΔH_sm, but decrease with c_p and k. In order to quantify how these variations (uncertainties) in these properties propagate into the modelling results (in particular the predicted DOB), we investigate ranges of parameter values for these peat properties taken from the literature: ΔH_sm ∈ [9.5, 15] MJ kg⁻¹ (Bergner and Albano 1993; Leroy-Cancellieri et al. 2014), c_p,p ∈ [1500, 2000] J kg⁻¹ K⁻¹, and k_s,p ∈ [0.8, 1.2] W m⁻¹ K⁻¹ (Jacobsen et al. 2003). The resulting ranges of predictions are shown as vertical error bars in Fig. 11. In comparison with the effect of peat MC, these properties have a small influence on DOB. Both for very dry peat (points in upper-right corner) and very wet peat (points in lower-left corner), the vertical uncertainty bars are too small to be seen. Only for the peat layer with moderate moisture (near MC*) do these properties have a significant influence on DOB (by 5–10 cm). In short, the main mechanism driving the in-depth spread of surface peat fires over high MC layers is heat transfer to dry the peat.

We developed a comprehensive 1-D model of a reactive porous media to investigate the in-depth spread of smouldering fires in vertical peat columns with heterogeneous profiles of density, MC and IC. The critical MCs and DOB are predicted. It is found that the smouldering combustion can spread over peat layers of very high moisture (MC > 250%) if the top dry layer is thick and the lower wet layer is thin. The critical moisture for extinction is found to be higher than that for ignition (MC*_ex > MC*_ig). The model simulates the experiments of all 18 natural peat samples in Benscoter et al. (2011), and the predicted DOB agrees well with experimental measurements. The influence on key thermo-physical properties of peat is investigated and found to be less important than the peat moisture, IC and bulk density. This study provides a physical understanding of the role of moisture in ignition and extinction in smouldering peat fires, and explains for the first time the phenomenon of smouldering in very wet peat layers.

Appendix 1.  Nomenclature