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J. of Supercritical Fluids 66 (2012) 307 314
Contents lists available at SciVerse ScienceDirect
The Journal of Supercritical Fluids
jou rn al h om epage: www.elsev ier .com
Modeli l wproces
Joo FernSuperwood A/S
a r t i c l
Article history:Received 15 AReceived in reAccepted 5 Ma
ng anood f wooPa aa, woufferints wess. In
and trd, th
The predictions of the model were benchmarked against data
collected during a regular impregnationprocess at the supercritical
wood impregnation plant. It was found that the predictions of the
modelagreed with the measurements.
2012 Elsevier B.V. All rights reserved.
1. Introdu
The use oimpregnaticialized andsupercriticaties comparof the
activecosities andof physical than liquidsconsidered
1.1. The sup
Althoughnation procpressures into structuraof ensuring
CorresponE-mail add
0896-8446/$ doi:10.1016/j.ction
f supercritical carbon dioxide as a carrier uid for woodon has
been successful [1,2]. The technique is commer-
takes advantage of the unusual physical properties ofl uids. At
supercritical conditions the CO2 has densi-able to those of the
liquids, which allows for dissolution
ingredients used in the process; while having low vis- low
surface tensions similar to those of gasses. This setproperties
allows it to ow through wood more easily
and, thus, the impregnation of wood species generallyas
refractory, such as spruce (Picea sp.) is possible.
ercritical wood impregnation process
theoretically simple, the supercritical wood impreg-ess presents
some difculties due to the relatively highvolved (large pressure
gradients can develop and leadl collapse or split of the wood) and
the challenging step
the required transport of actives through the wood.
ding author. Tel.: +45 21690495; fax: +45 76873201.ress:
[email protected] (J. Fernandes).
Generally, the process comprises three steps, a
pressurizationstep, an impregnation step at nearly constant
pressure and nallya depressurization step.
From the saw mill, the wood is received in packages, whose
typi-cal dimensions are 36 m long and 1.1 m squared. The
impregnationvessel is 1.7 m in internal diameter and 6.6 m in
length. The effec-tive volume of the vessel is approximately 8 m3
which correspondsto about 60% of the total volume of the system.
The wood packageis loaded into the impregnation vessel, the vessel
door is closedand pressurization with carbon dioxide starts. The
owrate andtemperature of the CO2 are controlled by a computerized
system.
1.2. Development of pressure gradients in wood
The development of pressure gradients during impregnationis not
conned to SCF processes but is also an issue duringconventional
liquid impregnation. Pressure gradients may have sig-nicant adverse
effects on wood if the material property values areexceeded [3].
Examples of damages occurred during supercriticaltreatment of wood
can be found in [4].
In situ development of pressure difference gradients in
woodduring supercritical impregnation has previously been
measured[57]. In the last paper, Schneider et al. measured the
develop-ment of pressure differentials occurring in four different
species ofwood and noticed a relation between the wood permeability
and
see front matter 2012 Elsevier B.V. All rights
reserved.supu.2012.03.003ng and optimization of the
supercriticasFocus on pressure and temperature
andes , Anders W. Kjellow, Ole Henriksen, Palsgrdvej 3, 7362
Hampen, Denmark
e i n f o
ugust 2011vised form 1 March 2012rch 2012
a b s t r a c t
The present paper deals with modelliIn this process, the
permeability of wand depressurization. The variation opressures
ranging from 0.6 to 15.5 Mwood varies with pressure (at 15.0
MPconditions), suggesting that wood is sThe data obtained in the
measuremesupercritical wood impregnation procwood is considered as
a porous mediaLaw. In the free space outside the boaequations./
locate /supf lu
ood impregnation
d optimization of a supercritical wood impregnation process.is a
key factor that conditions the velocity of pressurizationd
permeability with operating pressure was investigated att 313 K.
The measurements reveal that the permeability ofod permeability is
260% higher than that at near atmosphericng physical or chemical
alterations during the pressurization.as correlated and used has
input for a dynamic model of the
the model, the cross section of a wood board is simulated. Thehe
ow of CO2 in the wood is described by a modied Darcyse ow is
governed by the weakly compressible NavierStokes
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308 J. Fernandes et al. / J. of Supercritical Fluids 66 (2012)
307 314
the magnitude of the pressure differentials, i.e. species that
presenthigher permeabilities develop lower pressure gradients
during thesupercritical impregnation process.
1.3. Variability of permeability in wood and inuence of ScCO2
onthe permeability of wood
Wood is a largely variable natural material whose propertiesare
determined by factors like species, age of the tree, climate,
geo-graphical origin, etc. [8]. Wood is also a highly anisotropic
material,and its properties vary according to the structural
direction.
Permeability seems to be one of the most important wood
prop-erties variables in the supercritical wood impregnation
process.Permeability data for many species is available at normal
pressure,i.e. close to atmospheric pressure, and temperature
conditions [3]whereas the data at high pressure conditions is
limited to a singlesource [9].
In this paper, permeability measurements at pressures underand
over the critical pressure of CO2 will be presented.
Theexperimental setup and the methodology used to calculate
thepermeabilities is the same as described by Kjellow [9].
1.4. Modeling and process optimization
There have been some attempts to model aspects of the
super-critical wood impregnation process. As examples of modeling
ofphase equilibria can be found the works of Hasan et al. [10]
(whopresented aCO2biocidmodel for taddressed bexamples ca[14].
These in wood ancentration supercriticaview succeactives but
The presnation promanufacturequilibria, t
fast can the process be performed without producing damages
inthe wood. This model provides the manufacturer with a tool to
testdifferent impregnation programs without performing in situ
testswhile allowing creating optimal impregnation programs based
onthe wood characteristics, therefore reducing the costs of the
pro-cess.
2. Mathematical formulation
The model was created using Comsol Multiphysicsv3.5 [17],which
uses the Finite Elements Method (FEM) to solve differen-tial
equations for various physics and engineering applications,and uses
the following Application Modes and Modules: DarcysLaw (Earth
Science Module), Weakly Compressible Navier-Stokes(Chemical
Engineering Module), Convection and Conduction(Chemical Engineering
Module).
The computational domain is 2D and comprises two subdo-mains.
Subdomain 1, which corresponds to the cross-section of awood board,
whereas subdomain 2 corresponds to the free owspace between boards,
see Fig. 1. The input data for the model arethe permeability of the
wood, the temperature of the gas surround-ing the wood and the
pressure inside the impregnation vessel.
The wood is modeled as a porous solid matrix where the
voidvolume formed by the wood cells (tracheids) is initially lled
withgas at normal pressure and temperature. The temperature is
uni-form and hydrostatic equilibrium is established. The
assumptionson Subdomain 1 are:
re is Darcs an
cyan oweousracti
of eparee eno
solid;
permction
ed in t model for the phase behavior of a ternary mixture
ofecosolvent) and Laursen et al. [11] (who presented ahe ternary
system CO2N2-model resin). Other aspecty authors was the deposition
of actives in wood, asn be referred: Sahle-Demessie et al. [12,13];
Kang et al.
authors based their works in the diffusion of the activesd
focused their attention on the retentions and con-proles of
actives. Lucas et al. [15,16] addressed thel impregnation process
from a mass transfer point ofeding in the prediction of the total
retention of theneglecting the existence of concentration
gradients.ent model addresses the supercritical wood impreg-cess
from the point of view of CO2 ow. For theer it is important to be
able to predict not only the phasehe retention and distribution of
the actives but also how
1. The2. The
gaseDarthe geninteumecomlarg
3. Thecess
4. Thedire
Fig. 1. Computational domain and mesh uslocal equilibrium among
the solid and the gas phase;y law holds for the gas phase.
Traditionally the ow ofd liquids has been assumed to obey the
conditions ofow [3]. Several assumptions are taken including:
(1)
is viscous and linear, (2) the porous media is homo-, (3) the
uid is incompressible, and (4) there is noon between the uid and
the porous media. The vol-ach computational element in the
subdomain is smalld to the macroscopic dimensions of the domain but
it isugh to contain many pores and solid matrix elements;
does not suffer any deformation during the whole pro-
eability of the media varies according to structurals in order
to emulate radial and tangential ow in the
he simulations.
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J. Fernandes et al. / J. of Supercritical Fluids 66 (2012) 307
314 309
wood, this situation corresponds to a cross-sectional cut of
avery long board far away from the ends and where axial ownot
occurring;
5. The thermophysical properties of the porous media are
calcu-lated usinthe poro
The owvolume-avedeterminedstructure ofof the medi
u = k( p
In this eability of th(Pa s), p is ttion, is thFor the modthe
Darcy e
u = k( p
Insertingthe general
t() +
t() +
In Eqs. (3porosity. Thand the denpressure.
In SubdoWeakly Cosity of the They contamomentum
t+ (
ut
+ u
where ispressure, body force
The bouboundaries
p = p0 (bou
In the inin subdomainconsistenferent ordewith the trand
nally,between threferred incet al. [19]. Iusing Lagrathe
followin
whereas subscript 2 applies to the conditions in subdomain 2.
Themass conservation across the interface is expressed by:
u1.n1 + u2.n2 = 0 (10)intertively
secothe iting
2) = T(u2
2) = he las
12
(
s, thely fointer
p2) the
n2 the y atsJos21].
j bei
2 the
appluatioblemqs. (ge m
init
1303
= 0 m hean appd wiysicahe eq
sCppo
porol cone u
the for
fluidg the contributions of both the solid and the uid llingus
space.
variables (ow velocity, pressure, density, etc.) areraged. The
Darcy law states that the velocity eld (u) is
by a pressure gradient, the uid viscosity (), and the the porous
medium (represented by k, the permeabilityum):
+ g D) (1)
quation, u is the Darcy velocity (m/s), k is the perme-e porous
medium (m2), is the uids dynamic viscosityhe uids pressure (Pa), g
is the gravitational accelera-e density of the uid and D is
gravitys unitary vector.el in discussion the effects of gravity are
neglected andquation becomes:
) (2)
Darcys Law into the equation of continuity producesized
governing equation:
(u) = 0 (3)
(
k(p)
)= 0 (4)
) and (4), is the density of the uid (kg/m3) and is thee
continuity equation is coupled with a heat equation,sity is made a
function of the local temperature and
main 2, the ow is assumed to be governed by thempressible
Navier-Stokes equations, since the den-uid varies with both the
temperature and pressure.in the compressible formulation of the
continuity and
equations [18]:
u) = 0 (6)
u = p + [( u + ( u)T ) 2
3( u)I
]+ F (7)
the density of the uid, u is the velocity vector, p isis dynamic
viscosity, I is the identity matrix and F is thevector.ndary
conditions for the previous set of equations for
14 are:
ndaries 1, 2, 3 and 4) (8)
ner boundaries [58], the use of different ow modelsin 1 (1) and
subdomain 2 (2) leads to mathematicalcies arising from the coupled
system of equations of dif-rs in different regions. A second
difculty is connectedansmission conditions to be applied at the
interface,
the third difculty that can arise are incompatibilitiese imposed
boundary conditions. In order to solve theonsistencies was used the
method proposed by Laytonn this method the interface conditions are
imposed bynge multipliers and the correct interface conditions.
Ing, subscript 1 applies to the conditions in subdomain 1
in the respec
Theacross 2 ac
t(u2, pwhere
T(u2, p
In tby:
D(u2) =
ThuThe onat the
t(u2,And
p2 2As
velocitBeaverJones [
u2 j =
with kj/
By the eqsubpropling ELagran
Theare:
p = 10
ux, uy
Theductiocouplethe phsure. T1:
(porou
wherethermaand thheat of
And
fluidCpface. u1, u2 are the velocities in subdomains 1 and 2,
whereas n1, n2 are the normal vectors to the interface.nd interface
condition is a balance of normal forcesnterface. By taking the
traction vector t as the force on
on the uid volume inside 2 and that:
n2.T(u2, p2) (11), p2) is the stress tensor associated with
2:
p2I + 2D(u2) (12)t equation, D is the rate deformation tensor
and is given
u2ixj
+ u1jxi
)(13)
force on the interface exerted by the uid volume is t.rce in 1
is the Darcy pressure p1. Continuity of forcesface leads to
n2 = p1 (14) following equation at the interface is
obtained:
D(u2) n2 = p1 (15)uid model is viscous, a condition on the
tangential
the interface must be given. That condition is theephSaffman
law, as proposed by Saffman [20] and
According with Layton [19], it becomes:
kj
22n2 D(u2) j (16)
ng a set of vectors orthonormal to the interface and
friction constant.
ying to the computational domain the weak form ofns it is
possible to split the coupled problem into twos, Layton et al.
[19]. According with Layton, the cou-
10) and (15) are viewed as constraints and imposed
viaultipliers.ial conditions throughout the computational
domain
Pa
/s
t transfer was modeled using the convection and con-lication
mode. The heat transfer in the system is fullyth the momentum
equations through the variation ofl properties of the uid with the
temperature and pres-uations governing the heat transfer are, for
subdomain
rous)T
t+ fluid Cpfluid u T = (porous T) (17)
us, Cpporous and porous are the density, specic heat
andductivity of the porous media (accounting for the solidid
parts), uid and Cpuid are the density and specicuid,
respectively.subdomain 2:(
T
t+ u T
)= (fluid T) (18)
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310 J. Fernandes et al. / J. of Supercritical Fluids 66 (2012)
307 314
The boundary conditions for the heat transfer equations are:
T = T0 (for boundaries 1, 2, 3 and 4) (19)
n1 (q1 q2) (for boundaries 5, 6, 7 and 8) (20)n1 is the unitary
vector perpendicular to the boundary conditions,q1 and q2 are the
uxes from both sides of the boundary condition.
The initi
T = 303 K
The ther
i. The den
porous =
The ping the dthe emp(21). Thethe comcorrespouration between
ii. The specway as fthe specof woodplus a cand an addition
Cpwood,d
Cpwood =
The ad
Ac = M(
with b1 =with T in
Thus t
Cpporous
iii. The ther
porous =
For momal conlinear eq
wood =
where Gume at aC are con0.00406
iv. The varisure andwith valsure andtables aorder tothermopNIST
the
3. Numerical solution
The governing equations are solved numerically with
ComsolMultiphysics v3.5 [17] which allows simulating systems of
cou-pled non-li(PDE) in onten in parti
itial genctionse sol
to bts m
teria
rmea
ce ond anabilit. Thre, ac
lcula
percatiooxide
P
k is tengte oalculod driategrat
tion a
mpe a reg
rdern theoard
press In thboardm h
In thIn eaith
ed toe g
Fig. tubee impntialide oter ae dionne
the al condition for the whole computational domain is:
mophysical properties in the model are as follows:
sity of the porous media is given by (kg/m3):
(1 ).ske 100+ M
100 100 (M/Msat)
100+ .fluid (21)
orous media density (porous) is calculated by weight-ensity of
the solid with the density of the uid lling
ty volume (-fraction of empty volume), as shown in Eq. skeletal
density of wood, ske, is 1500 kg/m3, and this ismonly accepted
value for this property [22], M and Msatnd to the wood moisture
content and to the ber sat-
point (FSP) in percent value, establishing a dependence the
solids density and its moisture content.ic heat for the porous
media is calculated in the sameor density by weighting the specic
heat of wood withic heat of the uid. According to [23], the specic
heat
is calculated with basis on the dry wood specic heatontribution
due to the water moisture content (Cpw)additional adjustment factor
Ac that accounts for theal energy in the wood-water chemical
bound:
ry = 0.1031 + 0.003867T (oC) (22)Cpwood,dry + 0.001M.Cpw
1 + 0.01M + Ac (23)
justment factor, Ac, can be derived from:
b1 + b2T + b3M) (24)
0.06191, b2 = b 2.36 104, and b3 = 1.33 104 Kelvins.he specic
heat for the porous media yields:
= (1 ) Cpwood + Cpfluid (25)
mal conductivity of the porous media is given by [23]:
(1 ) wood + fluid (26)
isture content levels below 25%, the approximate ther-ductivity
() across the grain can be calculated with auation of the form
[23]:
G(B + CM) + A (27)
is specic gravity based on oven-dry weight and vol- given
moisture content M in percentage and A, B, andstants. A, B, and C
take the values 0.01864, 0.1941 and
4 (with wood in W/(m K)), respectively.ation in the
thermophysical properties of CO2 with pres-
temperature is accounted by using a series of tablesues for each
physical property as a function of the pres-
temperature. Comsol Multiphysicsv3.5 consults thesend if
necessary performs interpolations of the data in
obtain the corresponding values of the properties. Thehysical
data used to construct the tables was taken fromrmodynamic database
[24].
and inconversimulaand thsideredelemen
4. Ma
4.1. Pe
Sinof woopermeformedpressu
4.2. Ca
Themodibon di
k = qLAI
whereis the lA is thence cthe woappropcal intecorrec
4.3. Teduring
In osures iwood bential vessel.wood two 3 mbored.tubes. 0.1 K)
wwas usthe samvessel,
Theexit thdiffereother sthat enBoth thwere cside ofbath.near and
time dependent partial differential equationse-, two- or three
dimensions. The equations are writ-al differential form in line
with the program denitions,and boundary conditions are determined.
The meshe was veried with successively rened meshes. The
were conducted in transient mode and the time stepsver was
allowed to choose the time steps. It was con-e appropriate an
geometry with 4265 nodes and 7694esh size.
ls and methods
bility measurements
e of the input data of the model is the permeabilityd its
variation with pressure, measurements of woody at pressures ranging
from 0.6 to 15.0 MPa were per-ose measurements were performed, at
each measuringcording with the method described by Kjellow [9].
tions
meabilities were calculated using Eq. (28), which is an of
Darcys Law, accounting for the non-ideality of car-, whose
derivation can be found in [9]:
(28)
he permeability in m2, q is the mass ow rate (kg/s), Lh of the
dowel (m), is the viscosity of the uid (Pa s),w area (m2) and IP is
the integral of pressure differ-ated between inlet and outlet
pressures on the ends ofowel, and is calculated using an equation
of state (EOS)
for the uid used in the measurements. The numeri-ion of IP was
done using Simpsons rule with n = 10. Thisllows measuring the
permeabilities for non-ideal gases.
rature and pressure measurements inside a boardular impregnation
program
to gather data on the temperatures and internal pres- wood
during the supercritical impregnation process, a
with temperature probes and connected to two differ-ure meters,
was put at the bottom of the impregnatione following is descried
the preparation of the board. A
with 6 m length and 32 mm thickness was taken andoles, 50 mm
deep and with a separation of 150 mm wereese holes were inserted
two 3 mm external diameterch tube was introduced a temperature
probe (accuracy1 mm diameter. At the surface and inside the board,
glue
seal the holes. This setup is shown in Fig. 2a and b. Inure is
also presented the setup nearby the impregnation2c.s were connected
to 1/16 in. high pressure tubes thatregnation vessel and are
connected to one side of two
pressure meters (SMAS 301, with 0.1 bar accuracy). Thef the
differential pressure meters is connected to tubesgain in the
impregnation vessel and have open ends.
fferential pressure meters and the temperature probescted to the
online acquisition system in the plant. Out-impregnation vessel the
tubes were heated by a water
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J. Fernandes et al. / J. of Supercritical Fluids 66 (2012) 307
314 311
tup ne
5. Results
During tto know thcenter of thlow a tempto condensaexplosions)be
used to acontrol themodel is ab
The chodomain is ato a certain is viscous apath is conttion
betweeis not and hdependent;ible gas; thmedia, in twood and Cwith
CO2 ptionally appsimplest momedia regio
In the lito model t[25,26], theeled by usinux and visbecause
themuch largepath of thelarly at hig
densen diypotow
forcproa
een Fig. 2. Test board (a); scheme of the holes in the board
(b); se
and discussion
he high pressure impregnation of wood, it is importante
magnitude of the pressure differences between thee boards and its
surfaces, and the temperatures (tooerature during the venting part
of the process can leadtion of the carbon dioxide inside the boards
leading to, and how they change with time. This information can
of the Knudsow hof the pits orthis aplaw.
As s
djust the treatment parameters and, consequently, to
quality of nal product more effectively. The presentle to
successfully predict these proles.ice of Darcys Law as the ow model
for the porousrguable since the assumptions of Darcy ow are
violatedextent, for example: Darcys Law assumes that the ownd
linear, the ow in wood is not linear since the owinuously
obstructed by pits or forced to change direc-n tracheids; the
porous media is homogeneous, woodomogeneous material and its
properties are direction
the uid is incompressible, CO2 is a very compress-ere is no
interaction between the uid and the poroushis paper we show that
there is interaction betweenO2 otherwise the permeability of wood
would not varyressure. Nevertheless, the Darcy Law has been
tradi-lied to the description of ow in wood and it is also thedel
hence its choice to describe the ow in the porousn of the
model.terature it is possible to nd other approaches usedhe ow of
ScCO2 in porous media. For example, in
ow of ScCO2 in nanoltration membranes is mod-g a combination of
equations for the Knudsen diffusioncous ow. This approach cannot be
applied to wood
lumens of the tracheids, rays and resin canals haver dimensions
(in the range of 2050 m) than the mean
CO2 molecules (in the order of 1 109 m), particu-her pressures
since the mean ow path is a function
determinescenter and shape of thto develop necessary
tvariability onumber of at ambientabilities of anot giving isure)
or at hpaper). To oat high preKjellow [9]
In orderpermeabilitdowel wasvalues for th
The resumeability iinteractionexpected tothe permea
In Fig. 4 ments at setwo differenduced fromarby the impregnation
vessel (c).
ity. Therefore it is unlikely that the contribution of
theffusion ux to the total ow is important. The Poiseuilleheses
would also be violated due to the non-linearity
within a piece of wood (the CO2 is obstructed in theed to change
direction between tracheids). Thereforech also possesses some of
the limitations of the Darcy
in the denition of the model, the permeability of wood
the magnitude of the pressure difference between thethe surface
of the board. Therefore it can determine thee pressure curve in an
impregnation program. In ordermore adequate and faster impregnation
programs it iso know the permeabilities of the raw material. Since
thef wood is so large, the measurements involve a large
wood samples. These measurements can be performed pressure (this
process allows to measure the perme-
large number of samples in an expedite way althoughnformation on
the permeability dependence with pres-igh pressure conditions (the
approach presented in thisur knowledge, the only available data on
permeabilitiesssures (supercritical conditions) was that produced
by.
to validate the experimental setup for measurement ofies
measurement, the permeability of a sintered metal
measured, in Fig. 3 are presented the permeabilitiese range of
0.915.0 MPa and at the temperature of 41 C.lts presented in Fig. 3
were expected since the per-s an intrinsic property of the porous
media and no
between the CO2 and the steel of the dowel was happen. Having
validated the setup, we proceeded withbility measurements in
wood.are presented the results of the permeability measure-veral
pressures. The measurements were carried out int wood dowels (D1
and D2). The two dowels were pro-
the same wood board, nevertheless the permeabilities
-
312 J. Fernandes et al. / J. of Supercritical Fluids 66 (2012)
307 314
Fig. 3. Variation of permeability with pressure in the sintered
steel dowel.
measured differ in nearly one order of magnitude. Such
differencescan arise from the enormous variability that wood
presents.
From the plot it can be seen that the permeability increaseswith
CO2 pressure what indicates that an interaction is occurringbetween
the CO2 and the wood. At 15.0 MPa, the permeability mea-sured is
260% higher than that measured for the lowest pressure.
In Fig. 5 aof CO2, the density of Calso corroboof permeab
If adsorpadsorb in siit will causwhich has should leadthe
reducticontraries ohigher presavailable atamount of to penetratThe
tori conwhich are ehave shown
Fig. 4. Permeand triangles temperature obut normalize
Fig. 5. Permeability variation with CO2 density. Circles
correspond to dowel 1 (D1)and squares to dowel 2 (D2). The
measurements were performed at an averagetemperature of 41 C. In
the small plot are presented the permeabilities measuredbut
normalized to the lowest value.
pressures [31]. In spruce, the majority of these pits are
aspiratedwhich accoimpregnati
natithe icess
polymrder
dow metncesriticaata w
impr the boarand ttatio
was was
wasn Figfferere plotted the permeabilities as a function of the
densityplots show an increase of permeability value with theO2.
This relation seems to be linear in nature, which israted to some
extent by the sigmoid shape of the plots
ility as a function of pressure.tion of CO2 is occurring, and
CO2 has been shown to
gnicant amounts to many polymers [27], it is likely thate some
swelling of the wood. However, such swelling,been noticed in plant
material by other authors [28];
to a reduction of the permeability of wood due toon of the
porous space within the solid matrix, whichur observations.
Therefore, the data indicates that atsures the CO2 is able to ow
through paths that are not
lower pressure. A likely explanation for the increasedow paths
at higher pressures can be that the CO2 is ablee the aspirated tori
of the inter-tracheid bordered pits.sist of a network of cellulose
and hemicellulose brilsmbedded in a pectin matrix [29,30], and
these polymers
to suffer modication in contact with CO2 at higher
impregwhen the proof the
In owhereing thedifferesupercgram, dof the board;of the board
compumodelwhichulation[6,7]. Isure diability variation with
pressure. Circles correspond to dowel 1 (D1)to dowel 2 (D2). The
measurements were performed at an averagef 41 C. In the small plot
are presented the permeabilities measuredd to the lowest value.
Fig. 6. Compacontinuous linunts for the low permeability of this
species making itson using the common impregnation methods
(vacuumon, pressure impregnation) nearly impossible
thoughmpregnation is carried out at supercritical conditions
becomes possible, the reason can be the plasticizationers that
form the tori in the bordered pits [9].
to validate the computational model, the board fromels D1 and D2
were produced was prepared accord-hod for the measurement of
temperature and pressure
inside the impregnation vessel, and submitted to al impregnation
program. During the impregnation pro-as collected on the
temperatures at the top and bottom
egnation vessel, on the surface and in the center of thepressure
in the vessel and the pressures in the centerd. From this data, the
temperature at the surface of thehe pressure inside the vessel were
used as input to thenal model presented in this paper. Another
input to the
the data obtained in the permeability measurementscorrelated as
a function of CO2 density. A transient sim-
performed and the results are presented in next gures. 6 are
compared the experimental and predicted pres-nces between the
center and surface of the test board.rison between measured and
predicted pressure differences. The dis-e shows the system pressure
variation with time.
-
J. Fernandes et al. / J. of Supercritical Fluids 66 (2012) 307
314 313
Fig. 7. Compathose measure
The guthe magnitudecrease ofsystem presnation progdifference
csure increasIn the deprperform as wood propesured tempproperties
cneverthelespressure di
In Fig. 7 the board arelatively wa decouplinobserved tothe end
temthe temperto the surfaboard this mused as inp
In the mdecrease thswitching cimpregnatiare the maxof the
boardimum tempThe objectia wood boaence that wis shown onpressure
di
The greacreating anperform coto the fact tmeasured, tdone in a
facomputatiobe tailored different dimatch the n
Fig. 8
clus
exp of itst isabilit
thatre/COof pehat ti of hey s
owplicaince ood cernants.
the eize t
and meattain
moduce the temperatures and pressures inside a board duringlar
impregnation. By extending the model by adding pres-nd temperature
increase/decrease routines the model canrison between predicted
temperature in the center of the board andd.
re shows that the model is able to predict not onlyde of the
pressure differences but also the increase or
the pressure gradients. For instance, the uctuations insure
occurring between 50 and 105 min of the impreg-ram are correctly
translated in the calculated pressureurve, the same after 105 min,
where the system pres-es more rapidly leading to higher pressure
differences.essurization part of the program the model does
notwell, this may be explained by insufcient data on therties and
to differences between the modeled and mea-eratures (deviation on
the values of the thermophysicalalculated by the model and those in
the real system),s the model is still able to predict the magnitude
of thefferences and the general tendencies.is compared the
predicted temperature in the center ofnd those measured, the
predicted temperature agreesell with the measured temperatures.
Although againg in the predicted vs measured temperatures can
bewards the end of impregnation process, nevertheless,peratures are
very close. It is interesting to notice that
ature prole given by the model responds much morece temperature
than the measured temperatures in theay be related to the estimates
of wood property values
ut to the simulation.odel were also introduced routines to
increase ande operating pressure and temperature with time,
andonditions transforming it in a standalone calculator ofon
programs. The inputs for this version of the modelimum allowed
pressure difference between the center
and its surface, the maximum pressure and the max-
6. Con
Thechangethe mopermeshowspressuthose sized tthe torstate ting
thehas imcess. Sfast wing intgradie
Forminimizationvaluesnever a
Thereproda regusure aeratures for each step of the impregnation
program.ve was to create the fastest impregnation program forrd
without exceeding the maximum pressure differ-ood can withstand
without suffering damages. In Fig. 8e example of an impregnation
program for a constant
fference of 1.0 MPa.test advantage of using the model is that it
allows
d testing impregnation programs without the need tostly tests at
the supercritical impregnation plant. Duehat the model requires as
input data that can be easilyhe optimization of impregnation
programs can also bester and easier way. Another advantage of using
thisnal tool resides in the fact that the model can easilyto create
impregnation programs for wood pieces withmensions, if the
computational domain is rescaled toew dimensions.
be turned timpregnati
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Modeling and optimization of the supercritical wood impregnation
processFocus on pressure and temperature1 Introduction1.1 The
supercritical wood impregnation process1.2 Development of pressure
gradients in wood1.3 Variability of permeability in wood and
influence of ScCO2 on the permeability of wood1.4 Modeling and
process optimization
2 Mathematical formulation3 Numerical solution4 Materials and
methods4.1 Permeability measurements4.2 Calculations4.3 Temperature
and pressure measurements inside a board during a regular
impregnation program
5 Results and discussion6 ConclusionsReferences