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Review of R&D in Drying of RefractoriesZhen-Xiang Gong a & Arun S. Mujumdar ba Simprotek Corporation, Cupertino, California, USAb Mineral, Metal & Materials Technology Centre (M3TC), National University of Singapore,SingaporePublished online: 05 Dec 2007.

To cite this article: Zhen-Xiang Gong & Arun S. Mujumdar (2007): Review of R&D in Drying of Refractories, Drying Technology:An International Journal, 25:12, 1917-1925

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Review of R&D in Drying of Refractories

Zhen-Xiang Gong1 and Arun S. Mujumdar2

1Simprotek Corporation, Cupertino, California, USA2Mineral, Metal & Materials Technology Centre (M3TC), National Universityof Singapore, Singapore

This article reviews the published research and developmentwork on refractory drying. Current practice and potential problemsare analyzed. Some selected important research results are presented.It is shown that significantly improved drying procedures can beachieved through computer simulation of the drying process.

Keywords Calcining; Explosive spalling; Permeability; Refrac-tory drying; Refractory dryout schedules

INTRODUCTION

Refractories are essential construction materials forhigh-temperature installations; for example, in metal-lurgical and chemical industries. While considerable effortshave been dedicated to the development of stronger andbetter refractories such as low cement and cement-freerefractories over the last three decades, people graduallyrealized that drying (initial firing, also known as calcining),as the last operation of refractory manufacturing, is criticalto the quality, even the success, of final refractory products.

Refractory is either prefabricated into pieces of castingsof various shapes or cast into a monolithic lining of a fur-nace. After curing, a refractory casting contains extremelyfine pores filled fully with water. It needs to be carefullydried to remove the contained moisture to avoid explosivespalling when exposed to a rapidly elevated temperature inservice.

The causes of explosive spalling are numerous. Permea-bility, bond strength, particle size distribution, concen-tration of casting water, and ambient curing temperatureare all possible contributing factors (for details, please referto the literature).[1–3] However, drying as the last operationis, without doubt, the most critical and direct cause.

Initial heating of the refractory castings causes the con-tained moisture to evaporate in the pore space and producepore steam pressure. When the temperature of a refractory

casting is raised too fast the contained moisture does nothave enough time to dissipate to the outside surface. Thiscan result in excessive pore steam pressure buildup. Whenthe pore steam pressure exceeds the tensile strength of therefractory casting, explosive spalling will occur. Therefore,the pore pressure is the key parameter that needs to becarefully controlled in the drying process.

Explosive spalling can cause not only enormouseconomic losses, especially for a large monolithic lining,but also sometimes injuries or even death of the field-workers.Each explosion of a large furnace lining may cause losses ofhundreds of thousands, sometimes even millions of dollars.Anytime an explosion occurs, hundreds, even thousands, oftons of waste materials are generated.

In addition to explosive spalling, the drying operationmay also generate other defects such as cracks. Cracksmay also result in unqualified monolithic refractory linings.In general, long parallel cracks may not affect the usabilityof the lining in metallurgical industry. However, largecross-paralleled vertical-horizontal (# shaped) cracks do.When drying generates such cracks on a monolithic liningthe whole cast has to be torn down and rebuilt.

To avoid explosive spalling and defects such as cracks andensure a good quality of the final refractory product, slowheating rates are often required. However, slow heatingmeans not only longer production time, but also more energyconsumption. Some refractory manufacturers insist on con-servative slow heating rates to avoid explosion, while othersprefer relatively rapid heating rates. Every manufacturercannot avoid occasional explosions. This is due to the factthat the drying procedure is often overlooked and dryingschedules are established by purely empirical experience.

An adequate drying procedure is not only necessary butalso much needed in refractory industry. A drying proce-dure requires that the temperature of the heated surfaceof a refractory casting or lining is raised in accordance witha prescribed time-temperature schedule that may consistof several temperature rising-holding (or rising) periods.A typical drying schedule is as displayed in Fig. 1.

Correspondence: Zhen-Xiang Gong, Simprotek Corporation,7375 Rollingdell Dr., Suite 41, Cupertino, CA 95014; E-mail:zhenxiang_gong@simprotek.com

Drying Technology, 25: 1917–1925, 2007

Copyright # 2007 Taylor & Francis Group, LLC

ISSN: 0737-3937 print/1532-2300 online

DOI: 10.1080/07373930701727200

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Drying schedules currently used by refractory industry arequite controversial. If you do a Yahoo or Google search withthe ‘‘refractory dryout schedule’’ key words you will findmany Web sites with different drying schedules. Some manu-facturers do not use a holding period. Some others employholding periods. Among the manufacturers that use holdingperiods, some have holding periods at 120, 260, and 540�C,while some others may have only one holding period at150–200�C. In addition, each manufacturer may use differenttemperature-rising rates in the rising period. For example,some use 25�C=h, while some others use 55�C=h. Such incon-sistent situations happen because the drying schedules are notestablished through a scientific approach. A popular rulefollowed by current refractory manufacturers assumes thatthe drying time is proportional to the bulk density of thematerial. Rare manufacturers apparently take permeability,the most important parameter, into direct account as a factorof paramount importance.

An example of a real drying schedule is as follows: Raisesurface temperature from ambient temperature (25�C) to250�F (120�C) at a rate of 100�F (55�C) per hour! holdat 250�F (120�C) 1=2 h per inch thickness! raise from250�F to 500�F (120�C to 260�C) at a rate of 100�F (55�C)per hour! hold at 500�F (260�C) 1=2 h per inch thick-ness! raise from 500�F (260�C) to service temperature ata rate of 100�F (55�C) per hour.

It is obvious that in this schedule only the thickness ofthe refractory decides the total required drying time.

If a refractory slab has a thickness of 20 in., the time-temperature schedule is as shown in Fig. 2.

From the viewpoint of explosive spalling, it is not reason-able to hold the surface temperature at 120�C for 10 h sincethe steam saturation pressure at 120�C is only 1.99 bars (lessthan 2 atm). Due to temperature gradient, the temperatureinside the refractory casting is even smaller than 120�C. At sucha low temperature there is no risk of explosion since any refrac-tory casting has a much higher strength than 1.99 bars.

Holding the surface temperature at 120�C cannot be jus-tified from the viewpoint of moisture transfer as well. Atsuch a low pressure (less than 1.99 bars inside the casting)

moisture transfer is not efficient since pressure difference isthe primary driving force for moisture transport.

Fundamental understanding of the mechanisms of heatand mass transfer during drying of complex shaped refrac-tory objects exposed to time-dependent thermal boundaryconditions is necessary to circumvent the major impedi-ment to the development of a more scientific approach toselecting a priori the optimal drying schedules. Dedicationof research and development to this goal has been limited.Recognition of drying as a key operation in this industry isa prerequisite to reduced cost and enhanced productquality resulting in overall cost-effectiveness.

PRIOR WORK

For lack of space no critical evaluation of earlierliterature is made here. Rather, the intent here is to presentthe level of research devoted to this area so far.[45–53]

Modeling drying of refractories requires a detailed under-standing of the coupled heat and mass transfer processesoccurring within them. Two simple drying theories may beused to model the coupled heat and mass transfer in con-crete-type porous media. One is the liquid diffusion theoryand the other is the evaporation-condensation theory.

Based on the diffusion concept, Bazant and Thonguthai[4]

developed a mathematical model to describe heat and masstransfer in concrete. They solved their model using a finiteelement method and compared the numerically predictedmoisture loss with the experimental data of England andRoss.[5] They also compared the temperature and porepressure distributions with the experimental data ofZhukov et al.[6] and Zhukov and Shevchenko.[7] In anotherarticle Bazant and Thonguthai[8] satisfactorily comparedthe predicted moisture loss with the experiment data ofChapman and England.[9] Bazant et al.[10] further comparedthe numerically predicted cumulative water release with theexperimental results of Postma et al.,[11] McCormack et al.,[12]

and Chen et al.[13] In the same paper they also showed thattheir results compared well with the numerical results ofDavan[14] and Knight and Beck.[15] Dhatt et al.[16] utilizeda finite element method to simulate the temperature and

FIG. 2. A practical drying schedule.FIG. 1. A typical drying schedule.

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pore pressure responses to various heating rates for anaxisymmetrical refractory concrete furnace wall.

The first attempt to simulate kiln drying of refractoryconcrete was carried out by Gong and Mujumdar.[17] Theydeveloped a one-dimensional finite element model andsimulated various time-temperature schedules for refrac-tory concrete slabs of different thicknesses. New realisticdrying schedules for kiln drying of refractory concrete weresuggested on the basis of the simulation results. At a latertime Gong and Mujumdar[18] extended their model to simu-late more complex two-dimensional geometries for kiln dry-ing of refractory concrete. Gong and Mujumdar[19] alsoinvestigated the influence of an impermeable surface onthe buildup of pore steam pressure during drying of refrac-tory concrete slabs. Gong and Mujumdar[20] performed acomprehensive modeling study on one-sided heating-dryingof refractory concrete slabs. They found that permeability,heating rate, slab thickness, holding temperature, and hold-ing time of a drying schedule all affect the accumulation ofpore steam pressure. They also concluded that relative per-meability of the refractory is the major parameter that con-trols that drying process and has a major influence on themaximum steam pressure generated in a drying process.

A long-term research project[21,22] was carried out byMoore’s group at the University of Missouri, Rolla, duringthe 1990s to study the effect of drying of on the quality ofrefractories. Moore’s work led to a computer model thatshowed that heat transfer is mainly by conduction andthere is a sharp moving drying front during drying of arefractory castable. It also further verified the predictionof Gong and Mujumdar[20] that permeability is the primaryparameter that controls the drying process.

Valuable experiments[23–26] have also been performed atthe University of Sao Carlos, Brazil, to understand the dewa-tering mechanisms and affecting parameters in the heat andmass transfer process. These experiments have gainedincreased knowledge about the heat=mass transfer mech-anism for the drying of refractories, especially for the newhigh-density and low-permeability refractories. Research bythe same research group has also been devoted to the develop-ment of fiber additives that can increase the permeability toimprove the dryability of low cement refractories.

Franco[27] developed a control volume finite differencemodel to predict the heat and mass transfer processfor the drying of refractories. He later joined Calderys tocontinue his modeling work.

Compared with explosive spalling, research attentionpaid to thermal and shrinkage-induced stress analysis forthe drying of refractories is relatively rare. Several workshave been carried out on general concrete for thermaland shrinkage stress analysis.[28–30] These works can bereferenced in modeling the stress in refractory castablesdue to the combined effects of shrinkage and thermal strainfor refractory drying.

MATHEMATICAL MODELS

Heat and Mass Transfer

Although several mathematical models based on eitherliquid diffusion theory or evaporation-condensationtheory[30–42] are available for the coupled heat and masstransfer in concrete type porous media, only Bazant andThonguthai’s[4,8] formulations are easily applicable tomodeling refractory drying since the other models do notinclude the effects of dehydration in the drying process.

Following Bazant and Thonguthai,[4] the governingequations of the heat and mass transfer in concrete are asfollows:

@W

@t¼ �div Jþ @Wd

@tð1Þ

J ¼ � a

ggrad P ð2Þ

qC@T

@t� Ca

@W

@t¼ �div qþ Cw J � grad T ð3Þ

q ¼ �k grad T ð4Þwhere W is free water content; Wd is the water liberated bydehydration during initial heating; a is relative permeability(in m=s); g is gravity acceleration (9.806 m=s2); P is poresteam pressure; t is time; q and C are the mass densityand the isobaric specific heat of the concrete, respectively;Ca is the evaporation heat of free water; Cw is the specificheat of water; k is the thermal conductivity of the concrete;and T is temperature.

Since W is a function of both temperature T and porepressure P (W ¼W(P,T)) we can write:

@W

@t¼ @W

@P

@P

@tþ @W

@T

@T

@tð5Þ

Substitution of Eq. (5) into Eqs. (1) and (3) yields:

A1@P

@tþ A3

@T

@t¼ �div Jþ @Wd

@tð6Þ

A2@P

@tþ A4

@T

@t¼ �div q� Cw J � grad T ð7Þ

where

A1 ¼@W

@P; A2 ¼�Ca

@W

@P; A3 ¼

@W

@T; A4 ¼ qC�Ca

@W

@T

ð8Þ

The boundary conditions arefor pressure

� a

g

@P

@n¼ BwðP� PenÞ ð9Þ

or

P ¼ Pw ð10Þand for temperature

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�k@T

@n¼ BTðT � TenÞ þ CaBwðP� PenÞ ð11Þ

or

T ¼ Tw ð12Þwhere Bw and BT are convective transfer coefficients formoisture and heat, respectively; Ten and Pen are ambienttemperature and ambient steam partial pressure, respec-tively; Pw and Tw are the steam pressure and temperatureat the boundary, respectively; and n is the outward normalto the boundary.

Permeability Model and State Equation

Research shows that permeability a is one of the mostimportant parameters that controls the accuracy of themathematical model. Permeability is a function of moisturecontent and is strongly dependent on temperature. Accordingto Bazant and Thonguthai[4,8] and Song,[43] the followingempirical formula may be employed to calculate thepermeability of concrete:

a ¼ a0 f1ðh;TÞf2ðTÞ ðT � 95�CÞ5:6a0 f3ðTÞ ðT > 95�CÞ

�ð13Þ

in which a0 is the permeability at the temperature 25�C;h is the relative humidity in the pore, h ¼ P=Ps(T); and

f1ðh;TÞ¼1:28929�0:013571T

1þ½4ð1�hÞ�4 þ 0:031571T�0:28929 ðh<1Þ1 ðh�1Þ

(

ð14Þ

f2ðTÞ ¼ exp 27001

273þ T0� 1

273þ T

� �� �ð15Þ

f3ðTÞ ¼ expT � 95

0:881þ 0:214ðT � 95Þ

� �ð16Þ

It was noted that permeability jumps by about twoorders of magnitude in a small temperature range frombelow to above 100�C (see Bazant and Thonguthai[4]).

To solve Eqs. (6) and (7), a state equation, W ¼W(P,T),is necessary. Following Bazant and Thonguthai[4,8] andSong[43] the state equation is as follows:

W ¼

WcW0

Wch

� � 1mðTÞ ðh � 0:96Þ

W1 þ 0:08W2 �W1

h� 0:96ð0:96 < h < 1:04Þ

Wc 0:037ðh� 1:04Þ½

þ0:3335 1� T2

3:6� 105

� �� ðh � 1:04Þ

8>>>>>>>><>>>>>>>>:

ð17Þ

in which Wc and W0 are the anhydrous cement content andsaturation water content at 25�C per cubic meter ofconcrete, respectively (in this model, Wc ¼ 300 kg=m3,

W0 ¼ 100 kg=m3); W1 and W2 are the free water contentcorresponding to h ¼ 0.96 and 1.04, respectively; m(T) isa coefficient related to temperature.

mðTÞ ¼ 1:04� ðT þ 10Þ2

ðT þ 10Þ2 þ 22:3ðT0 þ 10Þ2ð18Þ

Dehydration Curve

Wd in Eq. (1) is the water liberated into the pores bydehydration (removal of bound water) when the refractorycasting is heated. Initial, free moisture and dehydratedwater Wd are the only sources of free moisture in the poresthat induce the pore steam pressure. Rapid dehydrationsometimes releases a fair amount of moisture into the poresin a short time, which may cause explosive spalling in thecase of rapid temperature elevation. The dehydration rateis another important parameter that controls the accuracythe model. Here shown in Fig. 3[16] is an example of a dehy-dration curve for one type of refractory concrete. Differenttypes of refractories have different compositions. Each typehas its own dehydration characteristics. The dehydrationcurve of a refractory can be determined by thermo-gravimetric analysis (TGA).

SELECTED RESULTS

In the following selected results from Gong andMujumdar[18,20] both one-side heating and kiln drying ofrefractory concrete castings are presented. Different dryingschedules are simulated and analyzed based on a finiteelement model developed from the mathematical modelEqs. (1)–(4).

Drying of Refractory Concrete Slabs by Heatingfrom One Side

Suppose that initially a slab has a uniform temperatureof 25�C and a relative humidity of P=Ps (25�C) ¼ 90% inthe pore. When the slab is dried by one-side heating, theheated surface is exposed to the hot air (e.g., combustion).

FIG. 3. Dehydration curve.

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The unheated surface exchanges both moisture and heatwith the environment.

A large concrete slab can be approximated by a one-dimensional model. The moisture flux on both the heatedand unheated sides is described by Eq. (9). The moisturetransfer coefficient Bw and the ambient steam partial pressurePen are taken to be 10�6 s=m and 2850 N=m2, respectively.The heat flux on the unheated side is described by Eq. (11).The heat transfer coefficient BT and the ambient temperatureTen are taken to be 1.0 W=m2s and 25�C, respectively.

The following physical properties are assumed constant:

q ¼ 2200 kg=m3;C ¼ 1100 J=kg K;

k ¼ 1:67 W=m K;Cw ¼ 4100 J=kg K

Ca is calculated from the following equation:

Ca ¼ 3:5� 105 ð374:15� TÞ1=3 ðT � 374:15�CÞ0 ðT > 374:15�CÞ

�

Ad is calculated with the aid of the following equation:

Ad ¼@Wd

@t¼ @Wd

@T

@T

@tð19Þ

in which @Wd=@T is obtained from the dehydration curvedisplayed in Fig. 3.

Effects of Permeability

To investigate the effects of permeability on the dryingprocess, four permeability values as listed in Table 1 weretested for a slab of 100 mm thickness heated at a rate of15�C=h. In the drying process the temperature in the con-crete slab rises with the elevation of the temperature ofthe heated surface. The temperature rise in the slab resultsin a rise of the pore pressure. At every instant there is onepeak in the pore pressure along the thickness of the slab.The magnitude and the location of this peak pore pressurevary with the progress of the drying process. In otherwords, this peak pore pressure is time-dependent. The peakpore pressure has one maximum in the drying process. Thismaximum is called maximum pore pressure. Table 1 showsthe maximum pore pressures corresponding to differentpermeability values for a concrete slab of 100 mm thicknesswhen it is dried at a heating rate of 15�C=h.

Figure 4 displays the peak pore pressure history curvescorresponding to the computed cases in Table 1. The solid,dashed, dotted, and dash-dot lines present cases 1, 2, 3, and4 (this notation will be followed in the subsequent figures),respectively. As expected, the lower the permeability thehigher the maximum pore pressure. One can see from boththe table and the figure that the increasing rate of themaximum pore pressure goes up rapidly with decrease ofthe permeability. When the permeability is 3.0� 10�13 m=sthe maximum pore pressure is 3.72� 105 N=m2. As thepermeability of the slab decreases to 1.5� 10�13 m=s themaximum pore pressure increases to 6.33� 105 N=m2.

It should be noted that in Fig. 4 there is a second peak inthe peak pore pressure history. This second peak resultsfrom the release of free water into the pores by dehydrationdue to temperature elevation in the temperature range of200–350�C. The magnitude of the second peak dependson both the heating rate in this temperature range andthe residual water content at the location of this peak.

TABLE 1Effects of permeability on pore pressure

Thickness ¼ 100 mm, heating rate ¼ 15�C=h

CasePermeability

a0 (m=s)Maximum pore pressure

(1.0� 105 N=m2)

1 1.0� 10�12 1.692 5.0� 10�13 2.573 3.0� 10�13 3.724 1.5� 10�13 6.33

FIG. 4. Peak pore pressure history curves (for Table 1).

TABLE 2Effects of heating rates on pore pressure

Thickness ¼ 100 mm, a0 ¼ 1.0� 10�12 m=s

CaseHeating rate

(�C=h)Maximum pore pressure

(1.0� 105 N=m2)

1 20 1.852 40 2.313 60 2.664 100 3.16

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The effects of permeability on pore pressure are obvious.Different types of refractory concrete have different valuesof permeability. Therefore, when different types of concreteare dried, different time-temperature schedules should beprescribed.

Effects of Heating Rate

To investigate the effects of heating rate on themaximum pore pressure, four cases were computed aslisted in Table 2. Table 2 shows the maximum porepressures corresponding to different heating rates for aconcrete slab of 100-mm thickness with a permeability of1.0� 10�12 m=s. As expected, the larger the heating rate,the higher the maximum pore pressure. This is becausethe faster the heating rate, the less time for the moistureto be driven to the outside surface, the more buildup ofthe pore steam pressure in the slab.

Effects of Slab Thickness

To investigate the effects of slab thickness on themaximum pore pressure, a total of three cases were com-puted as listed in Table 3. Table 3 shows the maximumpore pressures corresponding to different thicknesses fora concrete slab with a permeability of 1.0� 10�12 m=swhen it is dried at heating rates of 30�C=h. It is clear thatthe thicker the slab, the higher the pore pressure.

This is easy to understand since the thicker the slab, thelonger the moisture transfer path, and the more difficultfor the moisture to be transported to the slab surface.

Simulation of Drying Schedules for a Slabof 400 mm Thickness

Table 4 shows the simulated schedules for a concreteslab of 400-mm thickness. Schedule 1 is cited fromthe Handbook of Mechanical Engineering[44] in China. Thisschedule is used as a guideline for the drying of refractoryconcrete castings or monolithic refractory concrete installa-tions of 400-mm thickness. Simulation results indicate thatboth the holding temperature and the time of the two hold-ing temperature periods in schedule 1 are irrational.Although this schedule takes more than 100 h to completethe drying process, the maximum pore pressure is still ashigh as 3.9� 105 N=m2. From this table one can see thatschedule 2, designed by the author based on many simula-tion experiments, requires only 62.1 h to complete thedrying process. However, the maximum pore pressure isonly 2.36 � 105 N=m2, which is only 61% of the pressureproduced by schedule 1.

TABLE 3Effects of slab thickness on pore pressure

a0 ¼ 1.0� 10�12 m=s, heating rate ¼ 30�C=h

CaseThickness

(mm)Maximum pore pressure

(1.0� 105 N=m2)

1 100 2.102 150 2.753 200 3.32

TABLE 4Simulated schedules for a slab of 400-mm thickness

a0 ¼ 1.0� 10�12 m=s, thickness ¼ 400 mm

Case Temperature scheduleMaximum pore pressure

(1.0� 105 N=m2)

1 25�C15�C=hr

8:33 hrs150�C

0�C=hr

36 hrs150�C

20�C=hr

10 hrs350�C

0�C=hr

36 hrs350�C

20�C=hr

12:5 hrs600�C

3.90 (102.8 h)

2 25�C15�C=hr

13:33 hrs225�C

0�C=hr

30 hrs225�C

20�C=hr

18:75 hrs600�C 2.36 (62.1 h)

FIG. 5. Peak pore pressure history curves.

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Corresponding to the computed cases in Table 4, Fig. 5displays the peak pore pressure history curves. In Fig. 5 thesolid and dashed lines corresponds to schedules 1 and 2in Table 4. From this figure one can see that schedule 1generates a global maximum pressure at around 57 h. Acomparison of the two peak pore pressure history curvescorresponding schedules 1 and 2 shows that the two hold-ing periods in schedule 1 are not appropriate. In contrast,the holding period of schedule 2 is more rational.

From this figure one can also see that even after over44 h of drying according to schedule 1 the pore pressurecan still shoot up when further increasing the temperatureafter the first holding period. That means that even aftersuch a long time of drying if the first holding period (bothtemperature and time) is not appropriate there is still thepossibility of explosion.

Kiln Drying

When a casting is dried in a kiln all the surfaces of thecasting are exposed to the hot air (e.g., combustion). Themoisture flux on the heated surfaces can be describedby Eq. (9). The moisture transfer coefficient Bw and theambient steam partial pressure Pen are taken to be the sameas those used in the one-side heating drying.

A long casting can be approximated by a two-dimensional model. A square section as illustrated inFig. 6a is taken as the model geometry. The four sides ofthe square can be approximated as having the same tempera-ture and moisture boundary conditions (in practice, there issome difference for different sides). Such a simplification ismade not because the numerical model cannot simulate thenonuniform temperature and moisture boundary but becauseof the lack of needed information since there is no experi-mental data available about the nonuniformity. Due to thesymmetry of the geometry and the boundary conditions,one half of a quarter of the square is used as the computa-tional domain. The finite element mesh is demonstratedin Fig. 6b. Sides AB and AC are insulated for heat as wellas moisture. The temperature on side BC is elevated accord-ing to a prescribed time-temperature schedule.

Computations are carried out for a concrete castable of400-mm thickness (L ¼ 400 mm). The schedule listed inTable 5 is used. Figure 7 shows the peak pore pressurehistory curves for the computed problem. In this figureone can see that the predicted maximum pore pressurefrom the 2-d model is 2.69� 105 N=m2. There is a secondand a third peak in the peak pore pressure history. Thesecond and third local maximum pore pressures are dueto the two temperature elevation periods of 200–300�Cand 300–600�C in the schedule and the dehydration atthe temperature range of 200–350�C.

CONCLUDING REMARKS

Extensive R&D efforts in refractory technology haveled to much stronger and more durable refractories. Thesenew refractories have much higher density and lowerpermeability. Low permeability means not only muchlonger drying time and more thermal energy consumptionbut also a greater tendency to explosive spalling.

Due to increased use of large monolithic castablelinings, the economic loss of any drying failure for a largemonolithic castable is very costly. It is not only necessarybut also much needed to have a scientific method to design

FIG. 6a. Model geometry; 6b. Finite element mesh.

TABLE 5Simulated schedules for a slab of 400-mm thickness

a0 ¼ 1.0� 10�12 m=s, thickness ¼ 400 mm

Case Temperature scheduleMaximum pore pressure

(1.0� 105 N=m2)

400 mm 25�C20�C=hr

6:25 hrs150�C

0�C=hr

26 hrs150�C

15�C=hr

3:33 hrs200�C

0�C=hr

3 hrs200�C

15�C=hr

6:67 hrs300�C

0�C=hr

5 hrs300�C

30�C=hr

10 hrs600�C

2.69 (60.25 h)

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drying schedules that are not only safe but also time-savingand less energy-consuming.

Computer simulation combined with certain experi-mental verification is a feasible way to design dryingschedules. As is illustrated in the selected research results,all the major contributing factors can be taken intoconsideration into a simulation model. As long as the per-meability, dehydration curve, and strength of a refractoryare available, simulations can predict the pore steampressure and optimize the drying procedure.

The following URLs have useful information for thebenefit of readers:

http://www.ablerefractory.com/index.htmhttp://www.ceramicbulletin.org/refractory01.asp

ACKNOWLEDGMENT

The authors are grateful to Dr. Wu Zhonghua of theNational University of Singapore for valuable commentsand additional references included in this article.

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