Modeling and Optimization of the Supercritical Wood Impregnation

J. of Supercritical Fluids 66 (2012) 307 314

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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

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.

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)


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


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


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.


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

References

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[5] M. Dresccharactercritical u. Example of impregnation program created by the model.

ions

osure of wood to supercritical carbon dioxide leads tos physical properties. One of the properties that changes

permeability. In this paper is presented data for woody at different pressure conditions. Moreover, the data

the permeability tends to increase with the working2 density. Attaining values that are 260% higher thanrmeabilities measured at low pressure. It is hypothe-he increased permeabilities result from the softening ofaspirated inter-tracheid bordered pits. In the softenedhould act as semi-permeable membranes and allow-

of CO2. The increased permeability at higher pressurestions for the supercritical impregnation of wood pro-wood permeability is a key factor in determining howan be pressurized and depressurized without suffer-l damages resulting from excessive internal pressure

conomic performance of the process it is important tohe overall impregnation times. If the limits of pressur-

depressurization are calculated based on permeabilitysured at atmospheric pressure, then the process will

its full economic potential.el presented is able to qualitatively and quantitativelyo a standalone computational tool to produce possibleon programs.

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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

Documents

Modeling and Optimization of the Supercritical Wood Impregnation