ASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERINGAsia-Pac. J. Chem. Eng. (2010)Published online in Wiley InterScience(www.interscience.wiley.com) DOI:10.1002/apj.438

Special Theme Research Article

Modelling air flow and ambient temperature effectson the biological self-heating of compost piles

T. Luangwilai,1* H. S. Sidhu,1 M. I. Nelson1,2 and X. D. Chen3

1School of Physical, Environmental and Mathematical Sciences, University of New South Wales at the Australian Defence Force Academy, Canberra,ACT 2600, Australia2School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522, Australia3Department of Chemical Engineering, Monash University, Clayton, VIC 3800, Australia

Received 30 October 2009; Revised 28 February 2010; Accepted 1 March 2010

ABSTRACT: We formulate and investigate a one-dimensional model for self-heating in compost piles. The self-heating occurs through a combination of biological and chemical mechanisms. Biological heat generation is knownto be present in most industrial processes handling large volumes of bulk organic materials. The heat release ratedue to biological activity is modelled by a function which at sufficiently low temperatures is a monotonic increasingfunction of temperature. At higher temperatures, it is a monotonic decreasing function of temperature. This functionalityrepresents the fact that micro-organisms die or become dormant at high temperature. The heat release due to oxidationreaction is modelled by Arrhenius kinetics. The model consists of mass balance equations for oxygen and energy.Steady-state temperature diagrams are determined as a function of the size of the compost pile and the flow rate of airthrough the pile. We show that there is a range of flow rates for which elevated temperatures, including the possibilityof spontaneous ignition, occur within the pile. We also investigate the effects of variations in the ambient temperature. 2010 Curtin University of Technology and John Wiley & Sons, Ltd.

KEYWORDS: air flow; ambient temperature; combustion; composting; non-linear dynamics; self-heating

INTRODUCTION

The internal heating process that occurs in bulk solids,such as coal, grain, hay, and wool wastes, can causestockpiles of such material to undergo spontaneousignition. These phenomena can be described by thermalexplosion theory.[1,2] In such models, the generation ofheat is represented by a single Arrhenius reaction andspontaneous combustion is initiated when heat lossesare no longer able to balance heat generation.

Industrial compost piles contain large volumes ofbulk organic materials and typically two sources ofheat generation. These are due to oxidation of cel-lulosic materials and to biological activity. The firstof these represents chemical heat generation and maybe modelled by a single Arrhenius reaction. Biolog-ical processes that lead to heat generation include thegrowth and respiration of micro-organisms, such as aer-obic mould-fungi and bacteria. This biological heating,which occurs at lower temperatures than oxidation, may

*Correspondence to: T. Luangwilai, School of Physical, Envi-ronmental and Mathematical Sciences, University of New SouthWales at the Australian Defence Force Academy, Canberra, ACT2600, Australia. E-mail: t.luangwilai@student.adfa.edu.au

increase the temperature sufficiently high to kick-startthe oxidation reactions. Biological heating is known tobe important in large-scale composting operations[3] andin the storage of industrial waste fuels, such as munic-ipal solid waste and landfill.[4] Indeed in compostingself-heating due to biological activity is desirable.[5]

Biological activity is known to work efficientlyin the elevated temperature range 70–90 ◦C. Theseelevated temperatures can be found within a fewmonths or even a few days.[6] It has been recognisedfor almost 30 years that ‘. . . biological heating maybe an indispensable prelude to self-ignition’ [1 : 737].However, mathematical models for the spontaneouscombustion of compost piles due to biological self-heating are very limited.

The classical theory of spontaneous combustion wasfirst extended to include biological heat release byNelson et al .[7] These authors considered the specialcase of a spatially uniform model. Their model did notinclude either oxygen levels within the compost pileor air flow through the pile. Sidhu et al .[8] investigateda spatially distributed model for biological self-heatingthat included oxygen consumption. We extend the lattermodel by including air flow through the compost pile.

2010 Curtin University of Technology and John Wiley & Sons, Ltd.

T. LUANGWILAI ET AL. Asia-Pacific Journal of Chemical Engineering

This supply of oxygen is important for both combustionand micro-organisms.[9] For simplicity, we assume thatthe pile is one dimensional. We take the primarybifurcation parameter to be the size of the compost pileand use the air flow velocity as a secondary bifurcationparameter. In this study, we also analyse variations inthe ambient temperature for different air flow rates.

MATHEMATICAL FORMULATION

We consider an idealised one-dimensional compost pilewith length L. Depletion of cellulosic materials andbiomass is ignored. Interphase (solid particles and gas)temperature gradients are ignored and a single tem-perature is used to describe local behaviour, i.e. thecompost pile is assumed to be at local thermal equilib-rium. This is a common assumption made for porousmedium and packed particle beds.[10] We believe thatthe effects of both the depletion of cellulosic materi-als and temperature gradients are negligible for largecompost piles as well as for the range of temperaturesconsidered in this study. As a result of these assump-tions, the mathematical model contains two equationsfor the distribution of temperature and oxygen withinthe pile. Our model differs from the earlier model usedby Sidhu et al .[8] in that it includes the air flow throughthe compost pile. Our investigation of the effects of airflow through the compost pile is similar to the workof Akgun and Essenhigh[11] and Shamal et al .[12], whoconsidered the flow of air through coal piles. Unlike ourcurrent investigation, the coal models that these authorsexamined did not include heating effects due to biolog-ical activity. Moraga et al .[13] showed explicitly fromtheir experimental data on a sewage sludge pile thatthe model developed by Sidhu et al .[8] (i.e. without airflow) provided reasonable prediction of the tempera-ture increase within the pile. Therefore, we believe thatwe have developed a reasonable model to illustrate thetrends when the flow of air is included.

The governing equations for our model are as follows.Energy balance on 0 ≤ x ≤ L:

(ρC )eff∂T

∂t= keff

(∂2T

∂x 2

)− ερairCairU

∂T

∂x

+ QC(1 − ε)ρCACO2 exp

(−EC

RT

)

+ Qb(1 − ε)ρb

A1 exp

(−E1

RT

)

1 + A2 exp

(−E2

RT

) (1)

Oxygen balance on 0 ≤ x ≤ L:

ε∂O2

∂t= Doeff

(∂2O2

∂x 2

)− εU

∂O2

∂x

− AC(1 − ε)ρCO2 exp

(−EC

RT

)(2)

Algebraic relationships:

keff = εkair + (1 − ε)kC (3)

(ρC )eff = ερairCair + (1 − ε)ερCCC (4)

Doeff = εDoair (5)

The terms that appear in Eqns (1)–(5) are definedin the nomenclature. Physical parameters are consid-ered to be independent of temperature and oxygen con-centration. The second term on the right-hand side ofEqns (1) and (2 models the flow of air through thecompost pile. The heat generated by the oxidation ofcellulosic materials is represented by the third term onthe right-hand side of Eqns (1) and (2). The heat gener-ated by biological activity is represented by the fourthterm on the right-hand side of Eqn (1), and biologicalterm has been used in a number of models for solid-state fermentation processes.[14,15] The parameters A1and E1 in this term model the increase in the metabolicactivity of the biomass with increasing temperature at‘low’ temperatures. At sufficiently high temperatures,the essential proteins, which are sensitive to heat, beginto denature leading to cell death. These processes arerepresented by the biomass deactivation parameters A2and E2. To ensure that the heat release due to thebiological activity has a global maximum, the activa-tion energy for the inhibition process must be largerthan the activation energy for the biomass growth, i.e.E2 > E1. The detailed formulation of the term repre-senting the heat generated by the biomass can be foundelsewhere.[16]

The algebraic expressions (3) and (4) define theeffective thermal conductivity and the effective thermalcapacity of the compost pile in terms of the corre-sponding properties of air and pure cellulosic material.Equation (5) defines the effective diffusion coefficientfor oxygen.

We assume simple boundary conditions for the sys-tem. Both left and right boundaries for temperatureand oxygen are assumed to equal ambient conditions:T = Ta and O2 = O2a at point x = 0 and x = L. Wealso assume that the initial temperature and oxygen dis-tribution within the pile are uniform and equal to theambient conditions.

NUMERICAL SOLUTION

In the next section, we present results from our numer-ical investigation of the governing Eqns (1)–(5) andthe corresponding boundary conditions. These wereobtained using the software package FLEXPDE[17]

to determine the steady-state solution by solving the

2010 Curtin University of Technology and John Wiley & Sons, Ltd. Asia-Pac. J. Chem. Eng. (2010)DOI: 10.1002/apj

Asia-Pacific Journal of Chemical Engineering MODELLING AIR FLOW AND AMBIENT TEMPERATURE EFFECTS

time-dependent equations. FLEXPDE is a space- andtime-adaptive finite element package. Due to its adap-tive nature, both time and space errors are minimised toa relative error tolerance of less than 0.1%. The resultsobtained by using FLEXPDE were verified using themethod of lines,[18] in which the governing partial dif-ferential equations (PDEs) and boundary conditions aretransformed into a system of ordinary differential equa-tions (ODEs) using finite differences. The method oflines was coded in MATLAB,[19] so that an efficientODE solver could be used. The results obtained usingFLEXPDE and the method of lines were found to bealmost identical. The maximum steady-state tempera-ture difference was less than 0.5 K. These two meth-ods also predicted the same values of the bifurcationparameter at the limit point bifurcations. In our results,we present only the stable solution branches as thenumerical integration of the PDEs cannot yield unstablesolution branches. The parameters values used in thisinvestigation are based on those used by Sidhu et al .[8]

and are provided in the nomenclature. During our pre-liminary investigation on the sensitivity of the modelparameters, we found that the most sensitive parameterwas the activation energy for the biomass E1. A 3%error in this parameter can lead to a 20% change in thevalue of the ignition limit points.

RESULTS

The effect of air flow

We begin by investigating the case when there is noair flow through the compost pile (U = 0). This casewas analysed by Sidhu et al .[8] For brevity, we onlyhighlight their main results. Figure 1 shows the steady-state temperature and oxygen concentration distribu-tions along the length of the compost pile. In Fig. 1(a),

the maximum temperature is approximately 420 K andis located in the middle of the compost pile. In Fig. 1(b),we see that almost all the oxygen is consumed aroundthe middle of the pile.

Figure 2 shows the variation of the maximum steady-state temperature within the compost pile as a functionof the length of the compost pile when there is no airflow through the pile. There are two stable solutionbranches: the low-temperature branch and the elevatedtemperature branch. On the low-temperature solutionbranch, the maximum temperature within the pile variesfrom approximately 298 to 307 K. This temperaturerange is undesirable for composting as the temperatureis too low for the decomposition processes. The low-temperature ignition limit point (LLP) occurs when thecompost pile length (L) and the maximum steady-statetemperature are approximately 19.11 m and 307.01 K,respectively. If we increase the length of the com-post pile beyond 19.11 m, then the steady-state solution‘jumps’ to the elevated temperature solution branch.

Figure 2. The dependence of the maximum steady-statetemperature within the compost pile upon the length ofthe pile for the case of no air flow through the pile. Thenotations for the critical points are: LLP, low-temperatureignition limit point; ELP, extinction limit point. This figure isavailable in colour online at www.apjChemEng.com.

(a) (b)

Figure 1. (a) Temperature and (b) oxygen concentration distributions within thecompost pile at steady state. The length of the pile is L = 100 m and there is no airflow, U = 0 m s−1. This figure is available in colour online at www.apjChemEng.com.

2010 Curtin University of Technology and John Wiley & Sons, Ltd. Asia-Pac. J. Chem. Eng. (2010)DOI: 10.1002/apj

T. LUANGWILAI ET AL. Asia-Pacific Journal of Chemical Engineering

Figure 3. Maximum temperature–time for differentcompost lengths. The compost lengths are L = 19.1 m(red curve) and L = 19.5 m (blue curve). The flow rate isU = 0 m s−1. This figure is available in colour online atwww.apjChemEng.com.

Figure 4. Maximum temperature–time for differentcompost lengths. The compost lengths are L = 9.9 m(red curve) and L = 9.8 m (blue curve). The flow rate isU = 0 m s−1. This figure is available in colour online atwww.apjChemEng.com.

This ‘jump’ is shown in the time-profile plot in Fig. 3.When L = 19.1 m, the temperature increases from theambient condition of 298 to 307 K (red curve). How-ever, when the length of the compost pile is increasedto L = 19.5 m, we can see that the temperature pro-file gradually rises to a certain point and then sud-denly ‘increases’ or ‘jumps’ to the steady-state valueof 360 K.

The critical point on the left-hand side of the elevatedtemperature solution branch is called the ‘extinctionlimit point (ELP)’. If the length of the compost pileis reduced beyond that corresponding to the ELP (inthis case, the value is approximately 9.86 m), then thesolution ‘drops off’ the elevated temperature branchback to the low-temperature branch. Again the ‘dropoff’ behaviour is shown in the time-profile plot in Fig. 4.When L = 9.9 m, the temperature of the compost heapstay at the elevated steady-state temperature of 342 K(red curve). However, when the length of the compostpile is decreased to L = 9.8 m, then the temperature

profile ‘drops’ from the elevated temperature to the lowsteady-state value of 300 K.

In Fig. 2, between the two limit points (LLP andELP), there is an unstable solution branch whichcannot be detected in our numerical scheme as weare integrating the PDE (1) and (2) with the associatedboundary and initial conditions. As a result, the solutionbranches appear to be disjointed. From the steady-state plot of Fig. 2, we see that at the beginning ofthe elevated solution branch, the maximum steady-state temperature within the compost pile increasesrapidly as the length of the compost pile is increased.The rate of temperature rise decreases significantlyafter the maximum steady-state temperature reaches410 K. This makes physical sense as along the elevatedtemperature branch both the oxidation and biologicalreactions generate heat. However, once the maximumtemperature becomes sufficiently high, the contributionfrom biological self-heating decreases as the micro-organisms begin to die (or become dormant). Thecontribution from chemical heating also decreases asthere is insufficient oxygen within the pile. As a result ofthese mechanisms, the rate of change in the maximumtemperature is dramatically reduced.

When there is no air flow, the steady-state diagram,shown in Fig. 2, possesses two notable features. First,the maximum steady-state temperature on the elevatedtemperature solution branch gradually increases as thelength of the compost pile is increased. As compostmaterials generally ignite at about 423 K (150 ◦C)[3], wesee that ignition occurs only for very long (very wide)piles, that is for piles greater than 110 m. Furthermore,the transition from the elevated temperature solutionto the flaming combustion solution is ‘smooth’ and isnot characterised by a bifurcation. From the operationalviewpoint, the elevated temperature branch is desirableas the composting process is enhanced at such temper-atures. However, ignition of the compost pile must alsobe avoided.

We now investigate the effect of air flow throughthe compost pile. Figure 5 shows the maximum steady-state temperature within a compost pile for two extremeair flow velocities: U = 1 × 10−6 and U = 0.1 m s−1,respectively. In Fig. 5(a), there is very little flow of airthrough the pile and the solution behaviour is almostidentical to the case with no flow shown in Fig. 2.The only significant difference is that the elevatedtemperature branch is higher in Fig. 5(a) than whenthere was no flow. This is because the flow of airthrough the pile increases, the oxygen supply in theinterior of the compost pile which in turn increases theoxidation reaction within the pile. However, when theflow rate was set to U = 1 × 10−7 m s−1, the resultswere identical to the case with no air flow. That is thesupply of oxygen is too low to make any impact on theoxidation reaction within the pile.

2010 Curtin University of Technology and John Wiley & Sons, Ltd. Asia-Pac. J. Chem. Eng. (2010)DOI: 10.1002/apj

Asia-Pacific Journal of Chemical Engineering MODELLING AIR FLOW AND AMBIENT TEMPERATURE EFFECTS

(a) (b)

Figure 5. The dependence of the maximum steady-state temperature within thecompost heap upon the length of the pile for two extreme air flow rates:(a) U = 1 × 10−6 m s−1 and (b) U = 0.1 m s−1. This figure is available in colour onlineat www.apjChemEng.com.

In Fig. 5(b), the flow of air through the pile isrelatively high. The solution branch is continuous andthere are no longer any limit points (LLP and ELP). Thepractical consequence of having an air flow rate U =0.1 m s−1 is that very long compost piles are required togenerate elevated temperatures. Physically, this makessense as although the higher flow rate supplies moreoxygen into the piles, the flow also acts to cool thecompost piles. At high flow rates, the latter mechanismdominates. Consequently, larger compost lengths arerequired to achieve an elevated temperature increase.Comparing Figs 2 and 5, we conclude that to obtainelevated temperature for a shorter compost length, therehas to be a balance between having too little flow ofoxygen through the pile, which means that oxygen israpidly depleted, and having too great a flow whichresults in the cooling down of the compost pile. Wenow analyse the cases when the flow rates vary betweenthese extreme cases.

From Fig. 5(b), we can conclude that for very highflow rates, the solution branch contains no limit pointsand is continuous. From a practical perspective, wecan define flaming combustion as occurring when themaximum steady-state temperature exceeds 423 K, asdiscussed earlier.

From Fig. 6, we see that for high flow rates, verylarge piles are required to obtain elevated temperature.As we decrease the value of the flow rate, there is a crit-ical value at which a limit point bifurcation occurs thatgenerates a high-temperature limit point (HLP). Curves(a) and (b) in Fig. 6 show steady-state diagrams con-taining such a point. Increasing the size of the compostpile past that associated with the HLP results in thenumerical solution failing to converge due to the verysudden and large increases in temperature (blow up).Physically, this corresponds to the ignition of the cellu-losic materials followed by flaming combustion withinthe pile. The location of these critical lengths are L =148 m in curve (a) and L = 117 m in curve (b) which

Figure 6. The dependence of the maximum steady-state temperature within the compost heap upon thelength of the pile. The notations for the critical pointsare: LLP, low-temperature ignition limit point; HLP,high-temperature ignition limit point; ELP, extinctionlimit point. The flow rates are: (a) U = 5 × 10−4 m s−1,(b) U = 4 × 10−4 m s−1, (c) U = 3 × 10−4 m s−1, (d) U =2 × 10−4 m s−1 and (e) U = 1 × 10−5 m s−1. This figure isavailable in colour online at www.apjChemEng.com.

correspond to flow rates of U = 5 × 10−4 m s−1 andU = 4 × 10−4 m s−1.

As we decrease the flow rate further, a secondlimit point bifurcation occurs in the range 3 × 10−4 <U < 4 × 10−4 m s−1 [between curves (b) and (c)]. Thisbifurcation generates both a low-temperature ignitionlimit point (LLP) and an ELP. As mentioned earlier,the temperature ‘jumps’ or ‘drops’ between solutionbranches when the length of compost pile increases ordecreases beyond LLP and ELP. These solution curvesstill contain the HLP. In these systems, the elevatedtemperature branch is associated with the LLP while theflaming combustion branch is associated with the HLP.

The maximum temperature profile is shown inFig. 7(a) and the minimum oxygen concentration pro-file in Fig. 7(b) for different sizes of compost pile. Inthese figures, we use air flow rate U = 3 × 10−4 m s−1

which corresponds to the curve (c) in Fig. 6 and vary

2010 Curtin University of Technology and John Wiley & Sons, Ltd. Asia-Pac. J. Chem. Eng. (2010)DOI: 10.1002/apj

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(a)

(b)

Figure 7. (a) Maximum temperature–time and (b) minimum oxygenconcentration–time profiles for different compost lengths. The compostlengths are L = 40 m (red curve), L = 60 m (blue curve) and L = 85 m (blackcurve). The flow rate is U = 3 × 10−4 m s−1. This figure is available in colouronline at www.apjChemEng.com.

the lengths of the compost pile L = 40, 60 and 85 m.When compost length is fixed at L = 40 m (i.e. a valueless than the LLP value of 48.8 m), the maximumtemperature profile [red curve in Fig. 7(a)] converges tothe low steady-state temperature branch (approximately307 K). The temperature in this case is too low forcomposting. The oxygen concentration within the com-post heap for this case [red curve in Fig. 7(b)] remainsalmost at the same value as the initial condition.

When the length of the compost is taken to bebetween LLP and HLP values (HLP occurs for L ≈79.8 m), the heat generation is more effective than theprevious case. As a result, the temperature profile [bluecurve in Fig. 7(a)] for L = 60 m converges to the ele-vated steady-state temperature branch (approximately373 K). The oxygen concentration within the compostheap for this case [blue curve in Fig. 7(b)] drops slightlyfrom the initial value.

However, choosing a value of the compost lengthgreater than the HLP value, the temperature profileinitially ‘jumps’ slightly from the ambient temperatureto the elevated temperature value and then increasesgradually until it reaches a certain point where thereis a second, bigger ‘jump’ in temperature. This case isillustrated by the black curve in Fig. 7(a) for L = 85 m.The second ‘jump’ represents spontaneous ignitionwithin the pile as the temperature increases beyond theignition value of 423 K. Here, we see that all oxygenwithin compost heap is consumed by biological andoxidation processes as shown in the black curve inFig. 7(b).

As we continue to decrease the flow rate, Fig. 6shows that the elevated temperature branch occursfor increasingly shorter compost lengths, which in

practice is very useful. However, the size of the com-post pile corresponding to the HLP point is alsoreduced. Thus, the possibility of ignition in the pileis also increased. Decreasing the flow rate furtherfrom U = 1 × 10−5 m s−1, curve (e) in Fig. 6, to U =1 × 10−6 m s−1, Fig. 5(a), we deduce that there is athird limit point bifurcation which results in the HLPbeing ‘destroyed’. As a consequence, the system corre-sponds to the case in which there is too little oxygenflowing through the pile and the value for compostlength to reach the elevated solution branch increasesdramatically.

Figure 8 shows steady-state temperature and oxy-gen concentration distributions within the compost pilewith air flow. Figure 8(a) and (b) corresponds to thecase when L = 100 m and U = 1 × 10−6 m s−1. InFig. 8(a), the maximum temperature occurs slightly tothe left compared to the case when U = 0 m s−1 inFig. 1(a). As more oxygen is supplied into the compostpile from the left boundary, the oxidation reaction gen-erates more heat in that area. Also the maximum tem-perature within the pile increases from approximately420 K in Fig. 1(a) to 433 K in Fig. 8. In Fig. 8(b), theoxygen concentration distribution is almost identical tothe case when U = 0 m s−1.

In Fig. 8(c) and (d), the air flow rate is increasedto U = 4 × 10−4 m s−1. The maximum temperaturedecreases from 433 K in Fig. 8(a) to 381 K in Fig. 8(c) and the location of the maximum temperature movestowards the right boundary. This is because the air flowcools the temperature more in the area closer to theleft boundary, and consequently the maximum tempera-ture point is ‘pushed’ to the right-hand side. Figure 8(d)shows that there is a lot more oxygen supply within the

2010 Curtin University of Technology and John Wiley & Sons, Ltd. Asia-Pac. J. Chem. Eng. (2010)DOI: 10.1002/apj

Asia-Pacific Journal of Chemical Engineering MODELLING AIR FLOW AND AMBIENT TEMPERATURE EFFECTS

(a) (b)

(c) (d)

Figure 8. (a) Temperature and (b) oxygen concentration distributions within compost pilewhen L = 100 m and U = 1 × 10−6 m s−1. (c) Temperature and (d) oxygen concentrationdistributions within compost pile when L = 100 m and U = 4 × 10−4 m s−1. This figure isavailable in colour online at www.apjChemEng.com.

pile than the case U = 1 × 10−6 m s−1 in Fig. 8(b).The minimum oxygen concentration point is locatedclose to the right boundary.

The effect of varying the ambient temperature

In this section, we will investigate the effect ofvarying the ambient temperature. Due to seasonality,the average ambient temperature is changing all yearround. From the Bureau of Meteorology (AustralianGovernment),[20] depending on the location and timeof the year, the temperature of 313 K is not uncom-mon and in some cases extreme values of 320 K canoccur. Furthermore, United Nations IntergovernmentalPanel on Climate Change also predicts that the aver-age temperature around the globe would increase by2–5 K in 40 years due to the factors causing globalwarming.[21] As a consequence, an understanding of theeffect of the variation of ambient temperature upon thethermal behaviour of compost piles is crucial to pre-vent incidents of fires in compost facilities. Therefore,in this section, we will investigate the compost pilebehaviour when the ambient temperature is increasedby 10 and 20 K (i.e. from 298 to 308 and 318 K). Inthis analysis, we will present the results of varying theambient temperature for three different air flow ratesshown in Fig. 6: two extreme air flow rates of U =5 × 10−4 m s−1 [curve (a)] and U = 1 × 10−5 m s−1

[curve (e)], and one intermediate air flow rate ofU = 3 × 10−4 m s−1 [curve (c)]. In this way, we willbe able to obtain the whole spectrum of differentbehaviour.

Figure 9 shows the results of the comparison betweenthe ambient temperature 298 K (in red solid curves)and a higher ambient temperature value of 308 K (inblue dash curves). From the results, we can see that theoverall behaviour of the steady-state curves for thesetwo ambient temperature values are similar except thatthe solution branches for the higher ambient temperatureis shifted to the left. In other words, the locations ofall the limit points (LLP, ELP and HLP) are locatedat shorter lengths for the higher ambient temperature.The ambient temperature has a more significant effecton both solution branches (the low- and high- solutionbranches) in Fig. 9(b) and (c) and only the low-temperature branch in Fig. 9(a).

When the ambient temperature is increased, the heatlost to the surrounding environment process becomes‘ineffective’. Therefore, the overall compost tempera-ture is increased for the same size of the compost heap.The effect of increasing the ambient temperature hasthe advantage of increasing the performance by achiev-ing elevated temperature regions for shorter piles, but atthe same time, it also increases the risk of spontaneouscombustion as the HLP also decreases.

It is clear from our previous analysis that the locationsof the three critical points (HLP, ELP and LLP) arecrucial in determining the type of behaviour within the

2010 Curtin University of Technology and John Wiley & Sons, Ltd. Asia-Pac. J. Chem. Eng. (2010)DOI: 10.1002/apj

T. LUANGWILAI ET AL. Asia-Pacific Journal of Chemical Engineering

(a) (b) (c)

Figure 9. The dependence of the maximum steady-state temperature within thecompost heap upon the length of the pile. The ambient temperature values areas follows: red solid curves, 298 K and blue dash curves, 308 K. The notationused here is the same as in Fig. 6. The flow rates are (a) U = 1 × 10−5 m s−1,(b) U = 3 × 10−4 m s−1 and (c) U = 5 × 10−4 m s−1. This figure is available incolour online at www.apjChemEng.com.

(a)

(b)

(c)

Figure 10. The locations of various critical points as functions of thelength of the compost pile. The notation used here is the same as inFig. 6. The symbols are as follows: triangle, HLP; square, ELP and circle,LLP. The flow rates are (a) U = 1 × 10−5 m s−1, (b) U = 3 × 10−4 m s−1

and (c) U = 5 × 10−4 m s−1. This figure is available in colour online atwww.apjChemEng.com.

pile. More importantly, the locations of the LLP andHLP are of particular interest as their locations indicatehow to achieve the elevated temperature and whetherflaming combustion can occur for a particular compostsize. In this section, we analyse the locations of theselimit points further when the ambient temperatures arevaried. We use three different ambient temperatures(298, 308 and 318 K) for the same air flow rates usedin our previous analysis (U = 1 × 10−5, 3 × 10−4 and5 × 10−4 m s−1). From the overall results shown inFig. 10, we can see that the ambient temperature hasa significant effect on the locations of all the criticalpoints, that is they are located at lower compost lengths.However, when the ambient temperature is increasedto 318 K for the air flow rates U = 1 × 10−5 and3 × 10−4 m s−1 (Fig. 10(a) and (b)), the steady-state

solution behaviour has changed. This means that theLLP and ELP bifurcation points have coalesced fora value of ambient temperature slightly larger than308 K. Hence, the steady-state solution becomes asingle continuous solution [similar to curves (a) and(b) in Fig. 6] and there are only HLPs.

As can be seen from Table 1, small increase inambient temperature 3–7% can have significant effecton the location of the LLP up to 70.5% for U =3 × 10−4 m s−1. This implies that elevated tempera-ture can be obtained for moderately sized compostpiles – gain in performance. More importantly, for thesame change in ambient temperature, the location ofthe HLP (the bifurcation point that signifies the criticalpoint before flaming combustion occurs in a pile) candecrease by approximately 48%. This can have serious

2010 Curtin University of Technology and John Wiley & Sons, Ltd. Asia-Pac. J. Chem. Eng. (2010)DOI: 10.1002/apj

Asia-Pacific Journal of Chemical Engineering MODELLING AIR FLOW AND AMBIENT TEMPERATURE EFFECTS

Table 1. The comparison of the changes in ambienttemperature and the locations of LLP and HLP.

Air flowrate (m s−1)

Changein ambienttemperature

(%)

Decreasein LLP

location (%)

Decreasein HLP

location (%)

U = 1 × 10−5 3.4 46.2 3.06.7 – 6.0

U = 3 × 10−4 3.4 70.5 34.76.7 – 38.3

U = 5 × 10−4 3.4 – 38.76.7 – 48.0

The dash indicates that the steady-state solution curve is continuousand the LLP no longer exists.

implications for composting facilities as piles that weredeemed ‘safe’ may now be in danger of spontaneouslyigniting.

CONCLUSIONS

In this paper, we have undertaken an investigation ofa one-dimensional spatially dependent model for self-heating of a compost pile with different air flow andambient temperature. This model incorporates termsthat account for self-heating due to both biological andoxidative mechanisms with the presence of air flow.These conditions and reactions are known to occurwithin normal compost heap.

The value of the air flow velocity is crucial indetermining the behaviour of the compost pile. It actsboth to increase the rate of heat generation by supplyingoxygen for oxidation reaction and to decrease it byremoving heat from the cooling compost pile. Whenthe velocity is too high, heat loss predominates andvery large pile sizes are required to reach the desiredtemperature. When the velocity is too low, there isinsufficient oxygen within the pile to generate hightemperatures. As a result, internal heat generation fromoxidation reaction ceases at the elevated temperatures.For intermediate values of the flow rate, elevatedtemperatures can be achieved by moderately sizedcompost piles. However, this gain in performance iscountenanced by the possibility that the compost pilewill spontaneously ignite.

As one would expect, ambient temperature is anotherimportant factor that increase the overall compost heaptemperature. The effect of ambient temperature changesis more pronounced for higher air flow rates. If theambient temperature is increased, the elevated steady-state temperature can be easily achieved for smaller sizeof compost pile, which is ideal. However, this impliesthat the location of the critical point associated withspontaneous ignition is also decreased which in turn

means that the probability of spontaneous combustionis also increased. Therefore, a full understanding ofthe effects of both the air flow rate and the ambienttemperature is very important in practical industrialcomposting. In the near future, we plan to extendour one-dimensional analysis presented here to twodimensions.

It has long been suspected that the initiation ofhaystack fire is due to the biological heating underthe influence of water content or air humidity, whichacts to increase the temperature sufficiently to triggersignificant chemical reaction or oxidation of cellulosicmaterial.[1] We hope to extend our model to includethese features at a later date, and only after the inclusionof moisture into the full model, a validation of the modelcan be made via a sequence of experiments.

NOMENCLATURE

AC Pre-exponential factor for the oxidation of thecellulosic material (s−1); 1.8 × 104

A1 Pre-exponential factor for the oxidation of thebiomass growth (s−1); 2.0 × 106

A2 Pre-exponential factor for the inhibition ofbiomass growth (−); 6.86 × 1030

Cair Heat capacity of air (J kg−1 K−1); 1005CC Heat capacity of the cellulosic material

(J kg−1 K−1); 3320Doair Diffusion coefficient for oxygen; 1.0 × 10−5

Doeff Effective diffusion coefficient for oxygen;3.0 × 10−6

EC Activation energy for the oxidation of thecellulosic material (J mol−1); 110 × 103

E1 Activation energy for the biomass growth(J mol biomass−1); 100 × 103

E2 Activation energy for the inhibition of biomassgrowth (J mol biomass−1); 200.0 × 103

L Length of the compost pile (m)O2 Oxygen concentration within the pile (kg m−3)O2a Ambient oxygen concentration (kg m−3); 0.272Qb Exothermicity for the oxidation of biomass per

kg of dry cellulose (J kg−1); 6.66 × 106

QC Exothermicity for the oxidation of the cellu-losic material (J kg−1); 1.7 × 107

R Ideal gas constant (J K−1 mol−1); 8.31441T Temperature within the compost pile (K)Ta Ambient temperature (K); 298U Air velocity (m s−1)kair Effective thermal conductivity of air

(W m−1 K−1); 0.026kC Effective thermal conductivity of cellulose

(W m−1 K−1); 0.3keff Effective thermal conductivity of the bed

(W m−1 K−1)t Time (s)

2010 Curtin University of Technology and John Wiley & Sons, Ltd. Asia-Pac. J. Chem. Eng. (2010)DOI: 10.1002/apj

T. LUANGWILAI ET AL. Asia-Pacific Journal of Chemical Engineering

x Spatial distance along the length of the pile (m)ε Void fraction (−); 0.3(ρC )eff Effective thermal capacity per unit volume of

the bed (J m−3 K−1)ρair Density of air (kg m−3); 1.17ρb Density of bulk biomass within the compost

pile (kg m−3); 0.5 × ρCρC Density of pure cellulosic material (kg m−3);

1150

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2010 Curtin University of Technology and John Wiley & Sons, Ltd. Asia-Pac. J. Chem. Eng. (2010)DOI: 10.1002/apj