Models for fire-driven heat and moisture transport in soils

22 Pages·1996·1.2 MB·English

by  Albini, F. A. (Frank A.)

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Historic,
Do not assume content reflects current
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United States Models for Fire-Driven
Department
ofAgriculture
and
ForestService IHeat l\/loisture
Intermountain
Research Station
Transport Soils
in
General Technical
Report INT-GTR-335
May 1996
Frank Albini
Ms
M. Ruhui Amin
Roger D. Hungerford
William H. Frandsen
Kevin C. Ryan
Soil
Layer
1
C/)
1
The Authors Kevin C. Ryan is a Research Forester in the Pre-
scribed Fire and Fire Effects Research Work Unit at
FrankAlbini is Research Professor of mechanical en- the Intermountain Research Station's Fire Sciences
gineering at Montana State University in Bozeman, Laboratory in Missoula, MT. He received a B.S. de-
MT. He received his B.S., M.S., and Ph.D. degrees in gree in forest biology and an M.S. degree in forest
mechanical engineering from the California Institute of ecology from Colorado State University. He received
Technology in 1958, 1959, and 1962. his Ph.D. degree in forestry from the University of
M. Ruhul Amin is Assistant Professor of mechanical Montana.
engineering at Montana State University in Bozeman,
MT. He received his Ph.D. degree in mechanical engi- Contents
neering from the University of Tennessee in 1989.
Page
Roger D. Hungerford is a Research Forester in the
Prescribed Fire and Fire Effects Research Work Unit Introduction l
Survey of Literature 2
at the Intermountain Research Station's Fire Sciences
Laboratory in Missoula, MT. He received a B.S. de- Models with Soil Science Ancestry 2
Models from Engineering and Geophysics 6
gree in forestry and an M.S. degree in forest pathology
from the University of Idaho. Differences in Approach 7
Computer Programs Exercised 9
William H. Frandsen is a Research Physicist in the Opportunities for Model Improvement 10
Fire Behavior Research Work Unit atthe Intermoun- Possible Important Omissions 1
tain Research Station's Fire Sciences Laboratory in Mis- Possible Simplifications 13
soula, MT. He has a B.A. degree in physics from Lewis Conclusions 14
and Clark College, an M.A. degree from the University Acknowledgments 14
of Oregon, and a Ph.D. degree in forestry from the References 14
University of Montana. Appendix A: The Stefan Correction for
Confined One-Dimensional Diffusion 16
7776 use oftrade orfirm names in ttiispublication is forreaderinformation anddoes not
imply endorsementbythe U.S. DepartmentofAgriculture ofanyproductorsen/ice.
Intermountain Research Station
324 25th Street
Ogden, UT84401
Models for Fire-Driven Heat
and Moisture Transport in Soils
Frank Albini
M. Ruhul Amin
Roger D. Hungerford
William H. Frandsen
Kevin C. Ryan
ofwater inliquid and vapor phases as well as the
Introduction
transport ofheatbythermal conduction. Further-
more, acomplete model mustincludevariations with
Transfer ofheat into the soil beneath a wildland
moisture content and temperature ofthe param-
fire causes a large number ofonsite fire effects
eters that control the transport ofheat, liquid wa-
(Hungerford 1990) that include mortality ofor in-
ter, and watervapor. The dependence ofrate-con-
juryto subsurface parts ofsurface plants orwhole
trollingparameters (such as thermal conductivity,
organisms that live within the soil, thermolysis of vapor dififusivity, and hydraulic conductivity) upon
organic matter, oxidation orvolatilization offree
the dependentvariables means thatthe equations
mineral components, and other physicochemical
are mathematicallynonlinear. This nonlinearity,
changes thatcanbe as extreme as fusion ofmineral
soil constituents. Topredictthe nature and extentof makes it notvalid to solve a series ofsimple prob-
lems and construct more complex cases bylinear su-
such effects itis necessaryto knowthe temperature
perposition ofthe "simple" solutions. Nonlinear sys-
history as a function ofdepth within the soil beneath
temsofequationsdonotgenerally admitto analytical
the fire. solutions. Thus, we need to resortto numerical inte-
To predict the temperature history profile in a soil
gration ofthe model's partial differential equations,
under a fire, we need to knowthe history ofheat in- introducing a whole new realm ofpotential pitfalls.
putto the soil surface orthe surface temperature
Despite these complexities, a fairlyrichliterature
history and to modelthe response ofthe soil to this
stimulus. In this paper we focus on the challenge of on the topic exists.
Heat transport and moisture movement within
modelingthe response ofthe soilto boundaryheat-
soilshave been studied in soil science and micro-
ing ortemperature history.
climatology (Al Nakshabandi and Kohnke 1965;
Modelingthe soil's thermal response would be
Bhuiyan and others 1971; Campbell 1985; deVries
relatively simple ifnot for moisture and its move-
1958; deVries andAfgan 1975; Philip and deVries
mentbecause ofspatiallynonuniformheating(Morse
and Feshbach 1953; Steward and others 1990). The 1957). There is a wealth oftheoretical and empirical
knowledge aboutthis phenomenology and the mod-
very large heat ofvaporization ofwater and the ease
with which watervapor can move through a porous eling ofit. Butthe models and relationships are fi-e-
quentlyrestricted to the temperature regimes, heat-
soil matrix cause the transport ofheatto be domi-
ing rates, and spatial gradients oftemperature and
nated by watervapor movement fortemperatures
moisture that occurnaturally in diurnal cycles of
nearthe boiling point ofwater (Aston and Gill 1976;
heating and cooling (and wetting and drying) and
Cheng 1978; Eckert and Faghri 1980; Luikov 1975).
as a resultofprecipitation, drought, and irrigation.
The relative immobility ofwater as aliquid in soil,
Only recently (Hungerford 1990) have investiga-
andthe highvalue ofhquid water'sthermalconduc-
tivity relative to that ofair in the soil pores, make tions been extended to the temperatures, heating
the thermal conductivity ofthe bulk soil medium rates, dryness states, and gradient magnitudes that
sensitive to its liquid water content when liquid wa- characterize the fire environment (Aston and GiU
1976; Campbell and others 1992, 1993, 1994, 1995;
ter occupies a significantvolume fraction within the
medium (Campbell 1985; deVries 1958; Jury 1973; Jury 1973; Peter 1992; Schroeder 1974; Steward
and others 1990). However, none ofthese authors
Peter 1992; Philip and deVries 1957).
have drawn heavily upon parallel literature fi-om
All this complicates the accurate modeling ofheat
the disciplines ofengineering and geophysics.
transport within soils by making it necessary simul-
taneously to model the movement and concentration
1
Inthose research communities, analytical, numerical, density, soil environmental parameters such as tem-
and experimental investigations ofcoupled heat and perature and liquid moisture volume fraction, and
mass transport in porous media have been carried the constitutive parameters describing macroscale
out for more than a century (Catton 1992; Kaviany phenomenology; such as hydraulic conductivity, ef-
1991; Rust and Roberts 1990; Tang and Bau 1992). fective vapor dififusivity, and apparentthermal con-
Engineers view this as a special case in the general ductivity. This approach has had considerable suc-
field ofheat transfer (Bejan 1984). Halfofthis re- cess and is the current paradigm ofthe soil science
centvolume (Kaviany 1991) is devoted to analysis commvmity for modelingheat and moisture move-
ofheat and mass transportin the instance thatthe mentin response to diurnal fluctuations ofthe
interstitial fluid exists in two phases, which is the forces drivingthem.
case ofinterest in fire-heated soils. deVries Formulation—Ina siu-veypaper, deVries
This paper documents a researchjointventure.
(1958) summarized and generalized simultaneous
The objectives:
differential equations forthe transfer ofheat and
1. Survey the literature across several disciplines ofmoisture presented the year before (Philip and
that address heat and mass transport in porous me- deVries 1957) but is available in restricted-circula-
dia, assessing any differences in approach to model- tion publications and in a fragmented form.
ing these processes amongthe different disciplines. We found no derivations ofthe moisture and heat
2. Documenttest exercises oftwo models that are transport equations in either ofthese citations. The
potentially useful for assessing effects ofwildfires. conservation ofmass laws for water vapor and for
3. Identify opportunities for advancing the state of liquid water are used with models for fluxes embed-
the art in modeling fire-driven transport ofheat and ded when they are stated, and an energy conserva-
moisture in soils. tion equation is assembled around the Fourier tran-
sient heat conduction equation. The later paper is
summarized brieflyhere, emphasizing a few confus-
Survey of Literature ing orinconsistent aspects ofthis important work.
Phenomenological equations relate moisture
Aliterature survey was undertaken through the fluxes in liquid and vapor phases to gradients in
technical libraries at Montana State University and temperature and moistxire content. These relation-
at Intermountain Fire Sciences Laboratory, as well ships would supposedly arise from the separation of
as the authors' personal literature collections and the equation expressing conservation ofmomentum
preprints fi"om technical meetings. We found de- for the medium considered as a continuum and then
scriptions ofcomputer simulation models forheat decomposed into its parts: soil particles, liquid wa-
and mass transport in porous media in the litera- ter, watervapor, and interstitial air. This would be
ture ofsoil science and its derivative subdisciplines, the paradigm in an engineering approach.
and inpublications byengineers andbygeophysicists. Two critical assumptions appear earlyinthe paper:
1. The moist soil medium is microscopically iso-
Models with Soil Science Ancestry thermal (all components in the near neighborhood
ofa location are assigned the same temperature) yet
Hungerford (1990) offers a definitive statement of
large temperature gradients can exist across pore
the motivation for modelingheatand moisture trans-
spaces between solid particles. deVries does not dis-
portin soils for the purpose ofpredicting the effects
cuss the contradiction in this two-part assumption.
ofwildland fires and provides a comprehensive sur-
vey ofempirical and interpretive field studies ofthe 2. Watervapor and liquid water are in local vapor
effects offires in forest and rangeland settings. He pressure equilibrium. This assumption allows the
provides anexhaustivelistofthe mathematicalmod- combining ofliquid water content and watervapor
els that had been put forward by mid-1990 for the content to express a water content distribution un-
prediction ofheat and moisture transport in soils ambiguously, in absence ofhysteresis, as the appor-
tioningbetween vapor and liquid, then depends
heated by fires.
The pioneering works by J. R. Philip and D. A. uniquely upon porosity and local temperature.
deVries (deVries 1958; deVries 1975; Phihp 1975; While neithervapor buoyancy nor liquid viscosity
Philip and deVries 1957) explored and analyzed the are found explicitly in the parameters given, the bi-
movement ofmoisture and the transfer ofheat in nary molecular diffusion coefficient ofwatervapor
soils by starting at the size scale ofthe soil particles. in air appears in proportionality constants for both
They soughtto connect soil descriptive parameters thermally induced movementofvaporand movement
such as the relative abundances ofmineral types in ofvapor in response to gradients in water potential.
the soil, particle shapes and size distributions, bulk The rate ofevaporation, expressed as rate ofchange
2
ofmass ofwater (measured as equivalentvolume of sand son, at 20 °C with a constanthorizontalheat
liquid water) perunitvolume perunittime, appears flux of10"^ cal/s cm^ (about 42 W/m^). The moisture
as a source term in the primitive foirn ofthe vapor and temperature distributions in space are not
motion equation and as a sinkterm in the liquid given but can be inferred qualitatively fi-om these
motion equation. Instead ofrelatingthe rate ofevap- graphs to be approximately as follows: Forthe light
oration to the net absorption rate ofenergy, after clay soil, volumetric moisture content rises exponen-
accounting for sensible heat accumulation, the term tiallywith distance fi*omthe plane ofheat applica-
is eliminated by summingthe equation forwaterva- tion, with a characteristic length ofabout 10 cm.
por conservation and the equation forliquid water Whenthe liquidmoisture contentreaches about0.05,
conservation to form an equation for global conser- the slope ofthis curve increases by a factor ofabout
vation ofwater. This step illuminates a difference 15; the moisture content rises abruptly and roiinds
between the soil science approach and thatofthe offto its asymptoticvalue ofabout 0.12. The physi-
investigator ofthe effects offire. cal processes that enforce such avariation ofmois-
The flux ofheat is related to the transportofsen- ture contentwith distance are notextensively dis-
sible and latent heatbywatervapor, transport of cussed. For a medium sand, the moisture content
sensible heat by liquid water movement, and heat varies initiallywith distance fi-om the plane ofheat
conduction through the continuum. At first, conduc- apphcationagainas anexponential, butwith achar-
tion through the continuum is modeled by a "hypo- acteristic length nearer 1 mm. Upon reaching ahq-
thetical" thermal conductivity, X*, understood to uid moisture content ofabout 0.005, the cvirve flat-
characterize soil in which the moisture distribution tens abruptly, the distance scale ofthe exponential
is fixed (deVries 1958, eq. 10). Later, this symbol is growingto about80 cm. This profile would resemble
replaced by the collection: a slightly round-shouldered step function.
-L The parametervalues used by deVries are repre-
X, pi
sentative ofthe concerns ofsoil scientists in quanti-
where Xis identified as the "apparent conductivity fying phenomenology associated with irrigating, the
ofthe medium includingthe effect ofvapor distilla- drying ofsoils heated by sunshine, and evaporation
tion due to temperature gradient,"L is the latent ofsoil moisture into a dry atmosphere. The heating
heat ofvaporization ofwater, pi the densityofliquid rates and temperature levels ofinterest in soils un-
water, andDtvthe thermal diffusivityofwatervapor der fires are, ofcourse, substantially different. Some
within the soil medium. The reader is cautioned ofthe features ofthe model presented by deVries
thatthe two quantities are not equal because the are confusing or surprising probably due to the dif-
heat fluxes in different parts ofthe medium are not ferences in technical backgrounds and in motivation
additive. for addressingthis complex phenomenology. Had an
An investigation ofsteady state heat conduction engineer specializing in fluid mechanics orin heat
concludes the paper and illustrates the model's non- transfer described the processes, the terms used and
A
linear character. plot ofisothermal moisture con- the emphasis would be much different. An engineer
ductivity(velocityofliquid watermovementperimit would have selected different ranges ofparameters,
gradient ofwaterpotential, with potential expressed ifthe perturbation ofsoil temperature and moisture
as hydraulic head) and isothermal moisture diffu- profiles were to be inferred due to heatingby a fire
sivities (as vapor and liquid) in relation to gradients in the surface mantle.
in moisture content show strong sensitivityto water Most modem engineering audiences would find
content. Another plot similarly shows isothermal the deVries (1958) formulation deficient in at least
liquid water potential as a function ofliquid mois- two respects: First, the model contains no equation
ture content and moisture diffusivities in response forthe conservation ofmomentum. Because there is
to thermal gradients as strongly dependentupon no explicitexpression ofa force balance, one is left
liquid moisture content. to ponder: Does the watervaporgo up or down when
Usingthe mathematicalrelationships illustrated the soil is heated on the upper surface? The vapor
inthese two figures, deVries, found steady state tends to move from high temperature toward low
equations for temperature gradient and liquid mois- temperature, but also to move from high toward low
ture gradientby settingto zero the time dependent moisture concentration. The mechanical forces are
terms (local temperature rise rate and moisture ac- not identified except in limiting forms, nor does the
cumulation rate) and the moisture flux. He then acceleration ofgravity appear in the model. Thus,
solves these steady state equations forthe steady the phenomenon that nonuniform pressure acceler-
state spatial temperature and moisture gradients ates a fluid toward lower pressure is omitted, so wa-
as a function ofliquid moisture content. The final tervaporhas no buoyancy ortendencyto rise. Con-
two figures in the paper displaythe results ofthese ditions under which the neglect ofbuoyancy is valid
manipulations for a light clay and for a medium need to be established.
3
Second, the energy conservation equation is not The movement ofliquid water is modeled by the
derived from the energy transport equation ofcon- continuityequation, the speed ofliquid water mo-
tinuum mechanics, so the transfer ofenergy by tion beinggiven bythe product ofthe gradient of
mass movement is "added on"to the Fourier heat hydraulic potential and the hydraulic conductivity.
conduction equation. Such a derivation taxes com- Asource term is included, being the local rate of
prehension because the heat conduction equation condensation ofwatervapor. We believe that the
employs an apparent thermal conductivity thatin- "hydraiilic potential" described here is rather the
cludes the transport ofheatbyvapor movement. water (matric) potential expressed as equivalent
This contribution is then subtracted from conductiv- water depth at standard gravity.
ity measurement data so the effect can be added in The movement ofwatervapor is modeled by a con-
to the vapormovementmodel. This formulation does tinuity equation, with local velocity ofwatervapor
notreadilypermitdifferences intemperaturebetween modeled as being equal to the product ofthe gradi-
liquid, vapor, andmineral constituents, whichwould ent ofvaporpressure and "vapor conductivity" in
be relatively simple to accommodate in a model de- analogy to hydraulic conductivity forthe liquid
rived from the perspective ofcontinuum mechanics. phase. This parameter is proportional to the binary
Although these aspects ofdeVries' (1958) formula- molecular diffusion coefficient and includes an em-
tion are not discussed in later literature, this water- pirical correction factorto be chosen bythe model
shed work gave us a model forthe coupled transport user.
processes that has persisted largelyunchanged, ex- The vaporpressure, e, is derived from the tem-
planatory power must be acknowledged despite any perature-dependent saturation vapor pressure, e^,
uncertainties raised here. scaled by a temperature sensitive exponential factor:
FireHeatingModel ofAston and Gill—Another ele^ = e^^i-^MJRT)
early and important model is that ofAston and Gill where
(1976), who addressed the problem for conditions of <D = "hydraulic potential" (must be converted
heating by a surface fire. These authors address the to erg/gm)
modeling ofheat and moisture transport in soils in - molecular weight ofwater, gm/mol
the vertical direction only, but generalization of R = universal gas constant, erg/molK
their equations should be straightforward. T = absolute temperature,K
Compared to deVries' complicated formulation, Note the conflictin dimensions ofthe parameters
that ofAston and Gill embodies simplicity even stemming from the factthat the unit ofthe "hydrau-
though it rests upon three coupled diffusion equa- lic potential" is given as length. Ifthe acceleration of
tions, each with a source term. Equations are pos- gravity is added as a factor in the numerator ofthe
ited as phenomenological descriptions ofsensible
exponent, it becomes dimensionless. This is consis-
heattransport, liquid water transport, and water tent with the formulation ofBhuiyan and others
vapor transport. Not emphasized is the assumption (1971), cited byAston and Gill as the source for the
that all components share a local temperature. liquid water motion model used. Bhuiyan and others
The transport ofsensible heat is modeled without use the same symbol, O, butidentifyitas the sum of
mass transport except that the rate ofcondensation the "pressure potential" and the "gravitational po-
ofwatervapor, multiplied by the latentheat ofva-
tential," the latterhavingthe units ofacceleration
porization, appears as a source term in the tran-
times length.
sient Fourier equation forheat conduction. In this The authors did notuse the vaporpressiire formal-
equation, the specific heat capacity per unitvolume ism in the numerical examples theypresented. In-
is a function ofthe porosity and liquid water content stead, e/Cg was assumed to be independent oftem-
ofthe soil, and the conductivity ofthe medium as a perature and was taken from an empirical equation
continuum is related empirically to the same pa- relating it to volumetric water content for a particu-
rameters, followingAl Nakshabandi and Kohnke lar soil. Again a source term was included in the liq-
(1965). Transport ofsensible heat by moisture (as uid water continuity equation, being the negative of
liquid orvapor or both) is incorporated through use the watervapor source term.
ofan empirical thermal conductivity (deVries' "ap- Boundary conditions used for the computer imple-
parent" thermal conductivity), for which measure- mentation ofthis modelare inthe form ofa specified
ments usually exist only at low temperatures. The surface temperature history. The moisture bound-
authors used a linear function oftemperature as an ary condition is unspecified at the heated surface,
empirical correction factor ofthe thermal conductiv- but temperature and moisture content are held
ity, allowing them to match measured histories of constant at a "deep" boundary, where their gradi-
temperature atvarious depths beneath a surface ents vanish. Numerical results generated from the
exposed to radiant heating.
4
computer code ofAston and Gill (1976) showed CampbelFs Model—Prominent soil scientist,
agreementwith soil temperatures measured vmder Professor Gaylon Campbell ofWashington State
a spreading grass fire (Scotter 1970). The tempera- University, led a research team in developing a
ture predictions ofthe model range from roomtem- model forheat and moisture transport in soils appli-
perature to over 400 °C, moisture contents treated cable atthe heatingrates and temperature levels
range from bone dry to near saturation, and simu- ofsoils underwildland fires. This model (Campbell
lated time extended well beyond 200 minutes. These and others 1992, 1995) embodies several significant
results are impressive consideringthat the model extensions ofdeVries' formulation. It includes equa-
equations are mathematically "stiff" (Press and oth- tions for predicting apparent soil thermal conductiv-
ers 1986), and especially in light ofthe questionable ity as a function ofmoistiu*e content and tempera-
features noted in the model for heat transport. Al- ture (Campbell and others 1994) and a new water
though this model's predictions agreed well with the content-humidity relationship for soils (Campbell
data ofScotter (1970), the model has not performed and others 1993). It incorporates the advances in
well when applied under other conditions, and it ap- theoretical and empirical modeling oftransport
pears to lack generality. properties overthe past 20 years (Campbell 1985).
AModel IgnoringMoisture Movement—In Campbell and others (1992, 1995) model sensible
using a model ofheat transport in soil, one common heat accumulation as the difference between the di-
vergence ofthe heat flux and the rate ofheat ab-
predictionis whethercertainplantcomponents are
sorption perunitvolume by moisture evaporation.
killed bythe thermal impactofafire. Mostplanttis-
This is a fundamental difference from the approach
sue (exceptingseed) is killed once its temperature is
raised to 60 °C for a short time (Levitt 1980). How taken byAston and Gill. The heat flux is modeled
asthe product ofapparentthermal conductivity and
farbelow the surface ofthe mineral soil at a fire site
is this maximum temperature achieved? The sim- temperature gradient, and all soil components are
assumed to have the same temperature atthe same
plest model for predictingthat maximal depth dur-
"point" in the continuum. Liquid wateris treated as
ing a spreading fire is one that ignores moisture
movementwithin the soil and treats the moistme- fi-ozen in place, with its concentration changingbe-
dium as an inert solid with constant constitutive pa- cause ofevaporation. This simplification isjustified
on the grounds that liquid water movement is too
rameters. Modelingthe fire as a movingline heat
slowto maintain equilibrium with the rapid tem-
source at the soil surface, Richon (1987) found that
perature changes that are to be expected in the
for the soil surrogate material properties explored,
the problem could be simplified by idealizing the heating environment under a fire.
The flux density ofwatervapor is calculated as
analysis to a one-dimensional transient situation.
thenegative oftheproductofvaporconductivity £md
Steward and others (1990) extended this idealiza-
the gradient ofp, the partial pressure ofwaterva-
tion to include coolingofthe heated surface using
a constEintNewtonian film heat transfer coefficient. por, allmultipliedbythe "Stefan correction"P/iP-p),
They found analytical solutions in dimensionless whereP is total atmospheric pressure. (This factor
may or maynot be appropriate over some range of
form forfour differentprofiles ofheattransferrate
as a function oftime, with Newtonian cooling occur- watervapor partial pressure but is certainly not
valid near the boiling point ofwater, wherep = P
ring either at £ill times or only afterheatinghad
and the equation forvapor flux becomes singular.
ceased.
Soil canbe treated as a medium with fixed prop- See appendixAfor discussion ofthis factor). Ifwe
assume that the liquid water doesn't move, and ne-
erties and the fire treated as a transientbovmdary
glectthe rate ofaccumulation ofwatervapor, with
heating rate (to the extentthat such approximations
respectto the otherterms in the equation, the con-
do not impose intolerable error), a treatment such as
servation ofmass applied to water in the soil yields
this is highly desirable. Using dimensionless vari-
an equation linkingthe time rate ofchange ofliquid
ables, aU situations ofanentire class canbe described
watervolume firaction to the divergence ofthe water
by a single equation.
We cannot solely rely on models using moist soil vaporflux density. The liquid water fraction is in
as a medium with constant thermophysical proper- turn equated to a compact empirical function ofthe
water (matric) potential that includes only two pa-
ties. However, one must assume that, eventhough
rameters: the water potential ofovendry soil and an
all the assumptions ofthe model are notvalid, it
mayhave adequate predictive power. Nevertheless empirical constant found to be approximately six
times the air dry moisture fraction (Campbell and
extensive empiricaljustification is notyet available
forthis model. others 1993). This relationship alone is an impor-
tant simplifying advance in the modelingprocess.
5
The apparentthermal conductivity model is an Jury's thesis remainsvaluable for the physical con-
extension ofdeVries' (1963) model and is fully docu- cepts behind the mathematical expressions in these
mented forthe first time in Campbell and others complicated models.
(1994). It is complicated but straightforward, and in- Peter(1992) directly attacked one ofthe situations
corporates latent heat transport by vapor fl\ix. that motivate the entire realm ofstudy here: heat
The vapor conductivity model follows the formula- transfer in soil beneath a spreading fire. Peter docu-
tion ofPhilip and deVries (1957), includingthe con- ments four major areas ofstudy:
catenation ofempirical factors multiplyingthebinary
1. Heat transferwithin fires in a fuel bed
diAffnusiimopnocrotefafnitciceonnttorfibwuattieornvianptohrisinmoadire.l is its nu- 32.. HHeeaatt tarnadnsmfaesrswittrhainnsfderrywmiithnienramloisositlsoil
merical integration scheme, which uses temperature
4. Heat and mass transfer within an organic layer
and water potential as independent variables in ex-
undergoing smoldering combustion above mineral
pressions for the correction ofthe errors in the heat
soil
and mass conservation equations at each node. The
integration scheme is fast and numerically stable Peter's work also includes codingofa computer sim-
over a wide range oftestconditions. ulation. The basis forthe model is the formulation
This model represents an important advance and ofdeVries (1958), despite the reservations noted and
willbetestedinfield appUcationswhen itis available. the observations ofdeficiencies made byJury(1973).
Othermodels—Three other models, taken from The workleaves little room for conjecture. Awork-
ing personal computerversion ofthe simiilation code
graduate theses, are firmly in the family ofmodels
could not be obtained for testing for this study. The
from soil science, and the influence ofthe pioneering numerical integration algorithm it contains was a
works is evident.
supercomputer-based utility routine that is being
Schroeder(1974) developed an optimized computer
replaced.
simulation model forheat and moisture transfer in
soils for a Ph.D. degree in computer science at Texas Luikov's Formulation—No survey ofthis field
A&M University. In selecting a formulation to be would be complete without acknowledgingthe broad
implemented as the computer simulation, Schroeder contributions ofthe Russian scientist, A. V. Luikov,
summarizedthe equations describingmoisture move- head ofthe Heat and Mass Transfer Institute ofthe
ment found in five publications. The only model that Belorus Academy ofSciences. His major works are
included heattransport was the model ofPhilip and summarized in a survey paper (Luikov 1975), pub-
deVries (1957) and deVries (1958). The deVries(1958) lished posthumously.
model is the one he chose to implement. Emphasis LuikoVs surveycovers research contributions from
was on the efficiency ofthe computer code imple- the former Soviet Union to the field ofheat and
menting the model, and not the model itself There masstransportin porous media, byproviding amath-
was no extension, development, or experimental ematical synopsis ofmodels developed at the Heat
verification ofthe model. and Mass Transfer Institute. While it should have
In contrast, the dissertation ofJury (1973), docu- worldwide research community backing, little ofthe
ments the writing and testing ofa computer simula- background workis accessible in English and the
tion, also discusses the physics underlyingthe pro- svu-vey is not sufficiently detailed to permit replica-
cesses modeled, and compares model predictions tion ofthe computations exhibited. Our unsatisfying
with experimental results. Cited as motivation for and inescapable conclusion is thatthe supporting
investigating the workings ofthe deVries' model work mustbe duplicated, but that Luikov's sum-
(which is essentiallythe model he used) was in dis- mary guidance should be valuable in that process.
agreement between experiment and theory(Jury
Models from Engineering and Geophysics
1973, p. 4):
.Severalexperimentshavecastseriousdoubton Engineering and geophysics literature (see cita-
..
thepresenttheoreticalmodelsofthecoefficients tions in Introduction) shows contrast between ap-
usedfordescribingthethermaltransportofwater proaches to the formulation ofmodels forheat and
intheliquidphase. Noneofthemodelshasyetbeen
mass transport in porous media. Engineering ap-
abletopredictdetailedbehaviorinthevaporphase.
proaches to modeling include Kansa and others
Jury presented a flowchart and FORTRAN listing (1977) who employed a model for heat and mass
ofthe program developed, but this particular model transport within a moist wood element undergoing
was not implemented for testing because it was not pyrolysis to infer the theoretical influence offuel
directed toward the temperature and heatingregime moisture on the rate ofpyrolysis. Moallemi and
associated with a fire environment. Nonetheless,
6