modeling is an important 
 tool in the design and operational control 
 of a plant for biomass thermal conversion processes including combustion , 
 torrefaction , gasification , and liquefaction .
it is also important 
 in the context of storage and handling since self - heating of biomass 
 may lead to self - ignition .
models of the combustion of individual 
 particles of biomass fuel 
 have been developed at a fundamental level , and 
 these have been used as submodels for higher level modeling of furnaces 
 using computational fluid dynamics . while the power 
 of the modeling tools has increased , the usefulness of the models 
 has been limited by detailed and accurate data on the properties and 
 behavior of biomass fuels .
knowledge of fuel properties is understandably 
 challenging because of the vast variability in materials classed as 
 biomass .
in power generation applications , these may include various 
 softwoods , hardwoods , herbaceous energy crops , agricultural residues , 
 and other wastes or industrial byproducts . to effectively model 
 the heat transfer to and within a biomass 
 particle undergoing pyrolysis or combustion ,
the significance of the 
 heat transfer properties of small biomass particles in evaluating 
 the chemical kinetics of pyrolysis and char combustion has been described 
 by hayhurst .
differences in thermal conductivity 
 affect the internal temperatures and heating rates in the particle 
 which , in turn , affect the reaction kinetics .
this is also relevant 
 on the larger scale especially in the phenomenon of self - heating of 
 combustible materials such as the bulk storage of biomass fuel where 
 the risk of self - ignition arising from this is a distinct safety concern .
self - ignition temperatures for biomass materials 
 are dependent on thermal conductivity since this affects the balance 
 between internal heat generation from chemical kinetics and heat dissipation 
 to the external surface .
the risk of self - ignition 
 may be predicted through modeling provided 
 reliable data on thermal conductivity and internal heat generation 
 are available .
published data on thermal conductivity of wood 
 materials are mainly 
 in the context of their use in construction and are generally to inform 
 calculations of building insulation .
well established data from published 
 literature include the crc handbook of physics and chemistry , and the work of austin and eastman .
thermal properties 
 of the bulk mass of biomass materials specifically in the context 
 of wood pellet storage and using transient heat flow measurement methods 
 have been published by guo et al . and 
 sjstrm and blomqvist .
measurements on thermal properties of softwood particles 
 specifically 
 in the context of combustion applications have also been published . 

values for the thermal conductivity and specific heat capacity for 
 samples of softwood , softwood bark , and softwood char are reported 
 by gupta et al .
similar experiments specifically on pine wood and char samples were 
 also undertaken by hanklin et al . while 
 properties of larger specimens ( 300  300  100 mm ) of various hardwoods and softwoods were reported by yu et al . using heat flux sensors with reference to the 
 effects of moisture and temperature . while the aforementioned 
 published data on some types of wood exist , 
 there are little data on herbaceous materials or other nonwoody biomass 
 fuels .
the main reason for this is the difficulty in obtaining a suitably 
 sized uniform sample of material to perform a measurement on .
the 
 techniques used for measuring bulk material properties are not practical 
 on a small particle . both gupta et al . and hankalin et al .
fitch-type 
 apparatus with samples of wood made into regular discs in the order 
 of a few millimeters thickness
. a similar approach can be used for 
 investigating the thermal properties of other biomass materials , but 
 it is clearly not practical to use such a technique on , for instance , 
 raw unprocessed wheat straw .
since biomass is nonhomogeneous and most 
 is distinctly anisotropic , it is difficult to obtain samples which 
 are both large enough for measurement and representative of the material 
 in small particle form . in an attempt to overcome this issue , 
 an experimental method has 
 been developed in which samples of any solid biomass material can 
 be assessed on a comparative basis .
the method requires that the samples 
 are prepared in a consistent way to produce a homogenized disc of 
 material with dimensions and density within a similar range .
the test 
 discs are a simple physical form convenient for thermal conductivity 
 measurement .
it is important to note that this is not the form in 
 which the fuels are normally utilized .
nevertheless , it is contended 
 that the relative thermal conductivity measurements obtained from 
 the discs are a valid and useful representation of the respective 
 materials .
the data may be used to determine the thermal conductivity 
 of various forms of the fuel by applying it to a model of the macrostructure 
 of the material .
modeling of wood by considering the different structural 
 characteristics of different components ( solid matter , moisture , and 
 interstitial gas ) such as that proposed by thunman and leckner is one approach to achieve this .
the objective 
 of this study is to provide thermal conductivity 
 data for accounting for differences between types of biomass fuel 
 in the modeling of thermal conversion , combustion , and self - heating 
 behavior .
all samples 
 were milled using a liquid - nitrogen - cooled impact mill until the entire 
 sample was passed through a 90 m sieve . since moisture from 
 the original bulk sample
is reduced in this process , moisture measurements 
 of the milled samples were obtained using a ta instruments ta5000 
 thermogravimetric analyzer subsequently .
it is noted that moisture 
 content in the samples ranges from 2 to 6% . a correction , described 
 later , to the measurements based on these values is used to compensate 
 for the variation .
all samples were also characterized for volatile 
 content and ash content using standard methods [ en 15148:2009 , en14775:2009 ] . 

the average density of particle in the size range 0.54 mm 
 was obtained from measurements on single particles in the context 
 of previous experiments .
the list of 
 materials tested and the results of proximate analysis are presented 
 in table 2 . each material was used to form two 
 test pieces weighing 200 mg 
 ( 10% ) and 400 mg ( 10% ) , respectively .
these were formed 
 using a 13 mm diameter cylindrical steel die in a hydraulic press 
 to a pressure between 360 and 380 mpa .
the resulting pellets were 
 weighed on a digital microbalance to a precision of 1 mg .
the 
 thickness of the pellets was measured using a micrometer to a precision 
 of 0.01 mm .
additional test samples of unprocessed pine 
 wood were prepared 
 with dimensions similar to the pellets and with fiber orientation 
 either parallel or perpendicular to the heat flow .
this was to provide 
 a comparison with the measured thermal conductivity of the pellets 
 and with the published values of other woods ( from table 1 ) .
since the experiment 
 was aimed at small test pieces with relatively low thermal conductivities , 
 it was necessary to design and build a bespoke test apparatus .
the 
 design was based on the  split - bar  method which has 
 been used for measuring thermal conductivity of polymers .
the arrangement of the apparatus is such that 
 the test piece is sandwiched between two reference components of known 
 thermal conductivity .
a heat source is applied to the extremity of 
 one reference piece and a heat sink applied to the opposite end of 
 its counterpart .
the axial temperature gradient across the two reference 
 pieces is measured and the heat flow in each determined . the heat 
 flow through the test piece is taken to be the average of that in 
 the two reference pieces . given the dimensions of the test piece and 
 the measured temperature differential across it , its thermal conductivity 
 is thereby derived .
the system described was implemented using 
 cz121 m engineering brass as the reference 
 material having a thermal conductivity of 123 wmk .
the diameter of the brass rods was made 
 to be coincident with the test pieces at 13 mm .
the lengths of the 
 brass rods were determined mainly by practical considerations of physical 
 support and the required contact area with the heat source and heat 
 sink .
the temperature gradient was measured in the sections of each 
 brass rod adjacent to the test piece between 65 and 5 mm away from 
 the contact interface using 0.5 mm diameter mineral - insulated j - type 
 thermocouples .
these were inserted into holes drilled radially to 
 the center of each brass rod .
the power requirement of the heat 
 source was estimated for a worst 
 case test with high thermal conductivity ( 0.5 wmk ) and thin test piece ( 1 mm ) .
accounting 
 for heat losses along the length of the brass rods , the steady state 
 power requirement was calculated at 3 w. this was provided by a surface - mounted 
  subminiature proportionally controlled 
heater with 
 a nominal rating of 5 w. the heater was mounted on a 50 mm 
 diameter  50 mm length brass cylinder to act as a heat reservoir . 

the opposite  cold  brass rod was extended such 
 that it could be immersed in an ice - bath heat sink formed using a 
 vacuum - insulated steel flask .
diagram of test apparatus in cross - section . a picolog tc-08 thermocouple data acquisition 
 interface and data logging software
the test piece was mounted between the two brass rods and held 
 in place by the moderate pressure from the weight of the upper rod . 

a thermally conductive paste ( proprietary product as used for mounting 
 electronic components with  = 0.19 wmk ) was applied to the contact interfaces . 

initial measurements omitted this , and significant variations in repeat 
 measurements were noted owing to imperfect surface contact ( i.e. , 
 air gaps ) . with the heater and the heat
sink applied , the apparatus 
 was left 
 until the temperatures indicated on the measurement thermocouples 
 had stabilized .
the thermocouple measurements were then logged at 
 a rate of one sample per second for a period of at least 30 min .
the 
 logged data were checked for stability ( i.e. , gradient of less than 
 0.001 ks ) and the mean averages recorded 
 for calculation .
the axial heat flow in 
 the upper rod is calculated from the ideal heat flow and a correction 
 for the radial heat loss .
the calculation is approximated in the expression1where t1 and t2 are the temperatures 
 measured by thermocouples 
 tc1 and tc2 , respectively ; tamb is the 
 ambient temperature ( 23 c ) ; brass is 
 the thermal conductivity of brass ( 123 wmk ) ; acs is 
 the cross - sectional area of brass rod ( 133 mm ) ; ltc is the axial distance between the two thermocouples 
 tc1 and tc2 ( 60 mm ) ; ains is the effective 
 surface area of the insulation layer ( 5.5  10 m ) ; dins is the thickness 
 of the insulation layer ( 40 mm ) ; and ins is the 
 thermal conductivity of insulation ( 0.065 wmk ) . the axial heat flow in the lower 
 rod , q2 , is calculated with a similar 
 expression substituting t1 and t2 with t3 and t4 , respectively .
the axial heat flow through 
 the sample is approximated as the average 
 of the heat flows in the upper and lower brass rods:2the temperature differential across the sample , 
 ts , is derived from the difference 
 of t2 and t3 with a correction for the 5 mm of brass rod between the thermocouples 
 and interface surface as3the thermal conductivity of a sample with 
 axial length ls is then calculated from4a correction to the calculated 
 value of s based on the moisture content can be 
 estimated by assuming 
 the moisture content contributes uniformly to the measured value and 
 the contribution is directly proportional to the moisture content 
 by weight . the corrected ( dry basis ) thermal conductivity , s is then5where  is the proportion 
 of moisture 
 by weight in the sample and w is the thermal conductivity 
 of water at 300 k , taken as 0.61 wmk .
thermal conductivity and the density of wood are 
 strongly correlated 
 as shown by austin and eastman .
this 
 correlation is the basis of modeling the thermal properties of woody 
 materials  for example , the model for thermal conductivity described 
 by thunman and leckner .
the relationship 
 is also consistent for bulk quantities of wood pellet as shown in 
 the study by sjstrm and blomqvist .
examination of the relationship between material 
 density and thermal 
 conductivity is therefore useful for deriving or validating models 
 of biomass in various applications including single - particle combustion , 
 self - heating in bulk storage , and in dust layer combustion behavior . 

a plot of density against thermal conductivity is also a useful means 
 of visualizing the similarities and differences between the materials 
 measured in this study . before presenting the data for the homogenized 
 biomass pellets , 
 the measurement method should be validated by comparing the measured 
 properties of materials against known published values for similar 
 materials . for this purpose , a set of test pieces made from poly(tetrafluoroethylene ) 
 ( ptfe ) were made and the thermal conductivity was measured in the 
 same manner as that for the biomass samples .
the resulting measurements 
 showed an average thermal conductivity within 3% of the published 
 value for ptfe and with a standard deviation 
 of less than 3% .
in addition , test samples made of bulk pieces of 
 pinewood were formed both with perpendicular and parallel fiber orientation 
 ( cross - grain and parallel grain ) .
the resulting measurements showed 
 strong agreement with the published data for wood with similar density .
figure 2 shows a plot of 
 the measured thermal conductivity versus the material density for 
 the ptfe and pinewood reference samples together with the respective 
 published data for comparison .
measured thermal conductivity of cross - grain 
 ( open circle ) and 
 parallel grain ( solid circle ) pine samples compared to published values 
 ( + and  , respectively ) for woods [ reference table 1 ] .
measured thermal conductivity 
 of ptfe samples ( open square ) compared to published value ( solid square ) .
having shown the measurement method to be consistent with 
 published 
 data , the measured values for the homogenized biomass pellets , which 
 fall between the values of the reference materials , can be reported 
 with a high level of confidence .
each material was measured using 
 at least two test samples and at two different heater settings ( 70 
 and 60 c ) .
the calculated standard deviation of the data obtained 
 for each material was , on average , only 3.5% .
this value is close 
 to that evaluated for the reference measurements for the ptfe test 
 pieces .
the measured thermal conductivity of the materials tested 
 is presented 
 in table 3 .
the plot in figure 3a also includes the published 
 data from selected biomass materials as listed in table 1 for comparison .
figure 3b shows the data for the homogenized 
 biomass in more detail along with indications of the type of biomass 
 for each data point .
measured thermal conductivity of homogenized - densified 
 biomass 
 plotted against density : ( a ) measurements ( open circles ) compared 
 with published values ( + ) for cross - grain thermal conductivities of 
 wood ; ( b ) measurements with indication of type of biomass ( error bars 
 indicate 1 sd in measurements ) .
key differences between the various biomass material types can 
 be identified from the data presented in figure 3 .
it is clear from this plot that the torrefied 
 materials ( torrefied pine and black pellet ) have a significantly higher 
 thermal conductivity compared to the natural wood materials .
there 
 is less of a difference between the woody and herbaceous materials 
 although , on average , the latter show slightly lower thermal conductivities 
 than the former .
olive residue has a slightly higher conductivity 
 than the woody and herbaceous materials but not as high as the torrefied 
 materials .
examination of the results of the experiment show 
 that the expected 
 relationship between density and thermal conductivity for wood conforms 
 to a linear function . considering the wood pellet data alone , the 
 average measured
thermal conductivity for the three samples is 0.184 
 wmk and their 
 average density (  ) is 1152 kgm .
a 
 linear regression function for the cross - grain thermal conductivity  density 
 relations can be derived from the published data for wood ( figure 3a ) as6evaluating 
 this for the average wood pellet 
 properties gives a thermal conductivity value of 0.187 wmk : less than 3% difference 
 from the average measured value .
this suggests that the thermal conductivity 
 of the homogenized pellets is directly related to that of the bulk 
 wood perpendicular to the fiber orientation ( i.e. , cross - grain ) .
since 
 this relationship is confirmed by the measurements , it is not unreasonable 
 to assume that the other biomass materials examined also show a linear 
 relationship with respect to density .
a simple model can therefore 
 be proposed whereby the coefficients in eq 6 are determined for each material type from 
 the data points plotted in figure 3b .
this would allow a thermal conductivity value to 
 be derived for a lower density sample .
to illustrate this , figure 4 shows a plot of 
 the thermal conductivity of each of the tested samples recalculated 
 according to the density of the original material ( see table 2 ) .
the following observations 
 are made concerning the thermal conductivity 
 of these materials in their original form . both olive residue and 
 black pellet , having high  as - received  densities ( similar 
 to that of the test samples ) show values of 0.25 and 0.23 wmk , respectively . wood pellets 
 show a value of between 0.11 and 0.12 wmk .
miscanthus and willow are slightly lower 
 at 0.11 and 0.10 wmk , respectively , while wheat straw and rape straws can be as low as 
 0.05 wmk .
interestingly , 
 torrefied wood shows a high value in the compressed pellet form but 
 an uncompressed torrefied wood particle has a value similar to that 
 of an uncompressed , untorrefied wood particle the increase 
 in conductivity of the solid matter is compensated for by reduction 
 in density of the structure .
it should be noted that these derived 
 values apply to the conductivity 
 in the direction perpendicular to the fiber orientation of fibrous 
 materials .
as shown in figure 2 , the conductivity parallel to fiber orientation may be 2.53 
 times higher than the perpendicular direction .
while the measurement 
 method does not allow verification of this for herbaceous materials , 
 for the purposes of modeling , this multiplier may be assumed to account 
 for the anisotropy of straw and miscanthus in the same way as for 
 woods .
this does not apply to olive residue and black pellet since 
 their structure is more isotropic .
a measurement method for determining the relative thermal conductivity 
 of various biomass fuels has been presented .
the method has been shown 
 to be effective by comparison with existing published data .
the experiment 
 has provided data on the thermal properties of small particles of 
 both woody biomass , herbaceous and other nonwoody biomass , and also 
 torrefied biomass .
while there are a considerable amount of published 
 data on thermal properties of wood , there are little , if any , comparable 
 data available for the other materials investigated .
analysis 
 of the data has confirmed that woody biomass fuels conform 
 to a general relationship between material density and thermal conductivity . 
 the compressed solid matter in torrefied wood
olive 
 residue pellets and black pellet are shown to have higher thermal 
 conductivities than wood while herbaceous materials tend to have lower 
 values than wood .
a means of deriving useful values of thermal 
 conductivity from 
 the measured data for the purposes of modeling biomass thermal processing 
 and single particle combustion has been presented .
further investigation 
 on herbaceous materials would be required to validate the assumption 
 that particles of such materials show thermal anisotropy similar to 
 that of wood .
the data are also useful in the assessment of 
 the self - ignition 
 risk in bulk storage of biomass .
further investigations utilizing 
 measured thermal conductivity together with additional experimental 
 data may be used to develop and validate 
 self - ignition modeling for different biomass materials .
 the 
 thermal conductivity of solid biomass fuels is useful information 
 in the investigation of biomass combustion behavior and the development 
 of modeling especially in the context of large scale power generation . 
 
 there are little published data on the thermal conductivity of certain 
 types of biomass such as wheat straw , miscanthus , and torrefied woods . 
 
 much published data on wood is in the context of bulk materials . 
 a 
 method for determining the thermal conductivities of small particles 
 of biomass fuels has been developed using a custom built test apparatus . 
 
 fourteen different samples of various solid biomass fuel were processed 
 to form a homogenized pellet for analysis . 
 the thermal conductivities 
 of the pelletized materials were determined and compared against each 
 other and to existing data . 
Introduction
Experiment
Results
Discussion
Conclusions