PhD Thesis

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ΕΘΝΙΚΟ ΜΕΤΣΟΒΙΟ ΠΟΛΥΤΕΧΝΕΙΟ ΣΧΟΛΗ ΜΗΧΑΝΟΛΟΓΩΝ ΜΗΧΑΝΙΚΩΝ ΑΘΗΝΑ, Ιούλιος 2012 ΑΝΑΠΤΥΞΗ ΥΠΟΛΟΓΙΣΤΙΚΩΝ ΕΡΓΑΛΕΙΩΝ ΠΡΟΣΟΜΟΙΩΣΗΣ ΦΑΙΝΟΜΕΝΩΝ ΜΕΤΑΦΟΡΑΣ ΣΕ ΣΤΕΡΕΑ ΟΡΙΑ (ΔΟΜΙΚΑ ΥΛΙΚΑ) ΓΙΑ ΣΥΝΘΗΚΕΣ ΚΑΥΣΗΣ/ΦΩΤΙΑΣ ΔΙΔΑΚΤΟΡΙΚΗ ΔΙΑΤΡΙΒΗ ΔΗΜΟΥ Α. ΚΟΝΤΟΓΕΩΡΓΟΥ Διπλωματούχου Μηχανολόγου Μηχανικού Ε.Μ.Π. ΕΠΙΒΛΕΠΟΥΣΑ: Μ. ΦΟΥΝΤΗ Καθηγήτρια Ε.Μ.Π.

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  • , 2012

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  • . . (. 5343/1932, 202)

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    K X B (KXB) ,

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    GPRO (Gypsum PROperties). GPRO

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    HETRAN (HEat TRansfer ANalysis),

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    HETRAN

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    , . , - HETRAN

    -

    , GPRO.

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    600 oC.

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    GPRO

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    , HETRAN, GPRO,

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    Abstract

    Fires in buildings form the main death and destruction cause during fires, despite the fact

    that there are not first in frequency. The latter, creates the necessity for controlling and

    preventing the fire spread inside buildings, firstly for the safety of human life, and secondly

    for the safety of the construction. For that reason, each state establishes fire protection laws

    and regulations, which can be distinguished in two main categories: active and passive fire

    protection measures. Active fire protection measures aim to trace the fire inside a building, to

    inform the inhabitants of the building and to attack the fire, in order to confine it and

    finally quench it. On the other hand, passive fire protection measures aim to confine and

    delay the fire spread inside of an ablaze building, in order to create enough time for building

    evacuation and fire suppression.

    Passive fire protection measures compose not only the modern, but also the necessary way

    for the fire protection of a construction. On the other hand, Light Weight Construction (LWC)

    continuously increases its share in construction due to aesthetic and design versatility, as well

    as due to its very good mechanical, thermal, fire and anti-seismic behavior. Dry Wall Systems

    (DWS), which are part of LWC systems, are widely used in buildings not only due to their

    very good mechanical and anti-seismic behavior, but also due to their very good thermal

    behavior under fire conditions. The latter, is mainly due to the fact that the walls (gypsum

    boards, cement boards etc.), that DWS consist of, contain water in their crystal structure,

    which, under high temperature conditions, is evaporated, absorbing significant heat

    quantities from the fire, and thus, delaying the heat transfer through the assembly.

    The main goal of this dissertation is the development of specialized computational tools,

    in order to accurately predict the variation of the physical properties and the transfer

    phenomena inside porous materials (structural elements), which are exposed to different

    temperature conditions. Moreover, these computational tools are designed in order to be able

    to be combined with detailed Computational Fluid Dynamic (CFD) codes. The frame for the

    development of these tools is based on an integrated study, which is presented for the first

    time in this dissertation, of the thermal behavior of a structural material which is exposed to

    different temperature conditions, and demands the thorough examination of this behavior at

    a micro-scale (micro-structure size level), meso-scale (structural element size level) and

    macro-scale (building size level) size level.

    At first, as part of the micro-scale level study of the thermal behavior of structural

    elements, exposed to different temperature conditions, available computational methods

    from the open literature, which are used for the determination of the kinetic parameters of

    solid state reactions, are programmed. The developed computational tool can be used for post

  • vi

    processing the Differential Scanning Calorimetry (DSC) measurements and for defining the

    kinetic parameters of a solid state reaction that may occur when a structural element is

    exposed to different temperature conditions.

    The connection bond between the micro- and meso-scale size levels, when studying the

    thermal behavior of a structural element exposed to different temperature conditions, is the

    physical properties of the materials, which compose the element and need to be modeled. For

    this purpose, an integrated system of algebraic equations, that defines the physical properties

    of a porous material, is presented. In particular, the physical properties that are related to

    heat and mass transfer through a porous material are modeled, using this system of

    equations, as well as the kinetic parameters, obtained from the micro-scale level analysis. The

    above system is programmed and a computational tool named GPRO (Gypsum PROperties)

    is developed. GPRO is a general computational tool, which is capable of predicting the

    variation of physical properties of a porous material, exposed to different temperature

    conditions.

    The next step of the integrated study of the thermal behavior of a structural element

    exposed to different temperature conditions is the study at a meso-scale level. During this

    dissertation, a computational tool, named HETRAN (HEat TRansfer ANalysis), is developed,

    in order to predict the thermal behavior of a structural element, composed of multilayer

    building materials, exposed to different temperature conditions. HETRAN code has been

    developed to fill in the gap in existing computational tools regarding simultaneous heat and

    mass transfer in multilayered porous materials, as it solves a system of partial differential

    equations, capable of describing the one dimensional simultaneous heat and mass transfer

    through porous materials. Finally, the meso-scale HETRAN code, takes into account the effect

    of the micro-scale level study, by using the physical properties, obtained from the GPRO

    computational tool.

    The developed tools are validated and then used in order to simulate the different

    physical-chemical processes that take place inside commercial gypsum boards, which are

    basic elements of DWS, when they are exposed to high temperatures. Firstly, several DSC

    measurements are performed, through which the theoretical background of these processes is

    verified. Based on the DSC measurements, a simple system of algebraic equations is

    developed, for the determination of the initial composition of a commercial gypsum board

    and the energy absorbed or produced at the end of each process. Moreover, the developed

    computational tool for the definition of the kinetic parameters of a solid state reaction is used,

    in conjunction with the DSC measurements, in order to define the kinetic parameters of the

    most important processes that take place inside a gypsum board at temperatures up to 600 oC.

    Predictions of each reaction progress are compared with experimental data, revealing an

  • vii

    excellent agreement. It is established that the obtained kinetic parameters can accurately

    describe the physical-chemical processes, which take place inside a gypsum board at

    temperatures up to 600 oC.

    Thereinafter, these kinetic parameters are incorporated into GPRO code in order to

    simulate the variation of physical properties of commercial gypsum boards, exposed to

    elevated temperatures. The validation of GPRO is performed with experimental data

    available from the literature and experimental data measured during the dissertation. Results

    showed that the developed computational tool can accurately describe the variation of the

    physical properties of a commercial gypsum board, exposed to elevated temperatures, and

    confirms that it can be used for parametric studies, in order to improve the physical

    properties of a gypsum board.

    Finally, HETRAN code is used, in conjunction with GPRO code, in order to simulate the

    thermal behavior of commercial gypsum board slabs and assemblies, which are exposed to

    elevated temperatures. Predictions of HETRAN code are compared with experimental data

    available from the literature, as well as with experimental data measured during the

    dissertation, revealing the very good accuracy of the numerical results. Furthermore,

    HETRAN code is used in order to assess the effect of several parameters, such as the heat and

    mass transfer mechanisms inside the gypsum board porous structure, the heating rate and the

    water vapor partial pressure, on the thermal behavior of gypsum boards under high

    temperature conditions. Results showed that the developed computational tool can accurately

    describe the thermal behavior of a commercial gypsum board or a DWS composed of gypsum

    boards under fire conditions. Thus, it contributes not only to the theoretical study of the

    different physical-chemical phenomena that take place inside a gypsum board when it is

    exposed to elevated temperatures, but also to the design process, parametric study and

    optimization of the material.

    To sum up, the computational tools, which were developed in this thesis, are capable of

    describing the thermal behavior of commercial gypsum boards, at micro- and meso-scale

    level. Thus, they can be used in order to give a clear picture of how a gypsum board behaves,

    during its exposure to high temperatures conditions.

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  • ix

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    2007 2011.

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    CT-METRE

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  • x

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    , Dr. Ghazi Wakili, EMPA

    Materials Science & Technology,

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    2012

  • xi

    ..................................................................................................................................... I

    ABSTRACT ..................................................................................................................................... V

    ................................................................................................................................ IX

    ..................................................................................................... XI

    .................................................................................................... XVII

    ...................................................................................................... XXVII

    .................................................................................................... XXXVII

    1 ............................................................................................................................... 1

    1.1 ..................................................................................................................... 2

    1.2 ..................................................................................................................... 3

    1.2.1 ................................................................................................ 4

    1.2.2 ................................................................................................... 6

    1.3 .................. 8

    1.4 ........................................................................ 10

    1.5 ................................................................................................ 12

    1.6 .................................................................................................. 13

    1.7 ....................................................................................................................... 16

    2 ... 19

    2.1 ................................................................................................................................ 19

    2.2 - ................................................................................................................... 21

    2.2.1 .................................................................. 22

    2.2.1.1 ............................................................. 23

    2.2.1.2 ............... 24

    2.2.1.3 ........................................... 24

    2.2.1.4 ....................... 25

    2.2.2 ................................................................................................. 25

    2.3 - .................................................................................................................... 26

  • xii

    2.3.1 ................................................................................................... 27

    2.3.2 ............................................................................................. 27

    2.4 - .................................................................................................................. 28

    3 .......................................... 31

    3.1 ................................................................................................................................ 31

    3.1.1 ............................................................................................................... 32

    3.1.2 .................................................................................................... 32

    3.1.3 ................................................................... 33

    3.2 ........................................................ 35

    3.2.1 .................................................................... 37

    3.2.1.1 ...................................................................... 38

    3.2.1.2 .................................................................................................................. 38

    3.2.1.3 ........................................................................................................... 39

    3.2.2 .............................................................. 40

    3.2.2.1 ............................................................................................................... 41

    3.2.2.2 ........................................................................................................ 43

    3.2.3 -

    ................................................................................................ 45

    3.2.3.1 .................................................................................. 45

    3.2.3.2 ......................................................................................... 46

    4 ............................................................................................... 49

    4.1 ................................................................................................................................ 49

    4.2 ........................................................................................... 50

    4.2.1 ........................................................................................................................... 51

    4.2.2 .......................................................................................................................... 51

    4.2.3 ............................................................................................... 51

    4.3 .......................................................................................................... 53

    4.3.1 ........................................................................................................ 53

    4.3.2 .................................................................................................................. 56

  • xiii

    4.3.3 ........................................................................ 59

    4.4 .................................................................................................... 60

    4.5 ................................................................................. 60

    4.6 ........................................................................ 63

    5

    .................................................................................... 65

    5.1 ................................................................................................................................ 65

    5.2

    ............................................................................................................................................. 67

    5.2.1 .......................................................................................... 67

    5.2.2 .......................................................... 69

    5.2.3 ........................................................................................................... 70

    5.3

    ............................................................................................................. 70

    5.3.1 ........................................................................................... 72

    5.3.2 .............................................................................................. 73

    5.3.3 ......................................................................................... 73

    5.4 .............................................................................................................. 73

    5.5 HETRAN ................................................................................... 76

    5.5.1 ........................................................................................................ 76

    5.5.2 ............................................. 77

    5.5.3 ................................................................................. 78

    5.5.4 ........................................................................................... 79

    6 ...... 81

    6.1 ................................................................................................................................ 81

    6.2 ................................................................................................... 82

    6.2.1 .............................................................................................. 84

    6.2.2 ................................................................................................ 86

    6.3 / ...................... 87

  • xiv

    6.3.1 ....................................................................................................... 88

    6.3.2 ....................................................................................... 94

    6.3.3 ............................................................................... 111

    6.4 ................................................................................................. 120

    7

    ..................................................................................................... 123

    7.1 .............................................................................................................................. 123

    7.2 .............................................................. 124

    7.3 ....................................................................... 127

    7.4 .......................................................................................... 128

    7.4.1 .............................................................................................. 128

    7.4.2 ........................................................................................................... 130

    7.5 ................................................................................................. 134

    8

    ..................................................................................................... 137

    8.1 .............................................................................................................................. 137

    8.2 .............................. 138

    8.2.1 .............................................................................................. 138

    8.2.2 ................................................................................... 139

    8.3 GPRO ....................................................................................... 147

    8.3.1 ................................................................................... 151

    8.3.2 ........................................................................... 155

    8.3.3 .................................................................................................... 156

    8.3.4 , , .. 157

    8.3.5 ............................................................................................ 159

    8.4 ................................................................................................. 163

    9

    ......... 165

    9.1 .............................................................................................................................. 165

  • xv

    9.2

    ........................................................................................................................... 166

    9.2.1 ................................................................ 167

    9.2.2 ........................................................................................... 168

    9.2.2.1 ............................................................................................ 171

    9.2.2.2 ............................................................................................. 172

    9.2.2.3 ................................................................................. 175

    9.3

    ...................................................... 177

    9.3.1 ................................................................ 177

    9.3.1.1 ........................................................................................................................... 180

    9.3.2 ........................................................................................... 183

    9.3.3 ............................................................................... 189

    9.4

    ............................................................................................. 194

    9.4.1 ......................................................................... 194

    9.4.2 ................................................................ 196

    9.4.3 ........................................................................................... 197

    9.5 ................................................................................................. 201

    10 ......................................................................... 205

    10.1 .............................................................................................................................. 205

    10.2 .......................................................... 206

    10.3 ............................................................................... 208

    10.4 ................................................. 210

    10.5 ........................................................................................................................ 212

    10.5.1 ............................................................... 212

    10.5.2 ............................................................................... 212

    10.5.3 ......................................................... 213

    ......................................................................................................................... 215

  • xvi

    I .......................................................................................................................... 233

    II ........................................................................................................................ 237

    III ....................................................................................................................... 241

    IV ....................................................................................................................... 245

    V......................................................................................................................... 247

  • xvii

    1

    a

    A - s-1

    fA ..

    a

    b

    iB

    fB ..

    wB

    m-1 s

    c

    C J kg-1 K-1

    0C

    1C

    fC ..

    gC g kg m3

    iC

    Kc Kozeny

    pC J kg-1 K-1

    1 .. .

  • xviii

    d m

    D m2 s-1

    e

    E J m-3

    aE J mol-1

    f ..

    f ..

    F

    .. s-1

    0f

    cf

    f

    G

    g

    ,g

    h J kg-1

    ch W m-2 K

    mh m s-1

    Ph

    j kg s-1 m-2

    aEJ s

    k W m-1 K-1

    K m2

    Tk [s-1]

    L m

    vL ,

    2260000

    J kg-1

  • xix

    m kg

    m / kg s-1

    MW kg kmol-1

    n

    n

    N

    Dn

    FN

    GN

    LN

    Pn

    pN m-3

    RN

    SN

    tn

    o

    p Pa

    P Pa

    DSCP W kg-1

    p

    PDF

    Pr Prandtl

    PSD m-3

    q W m-2

    Q /

    .. m-3

  • xx

    fQ ..

    r s-1

    2R

    gR , 8314 J kmol-1 K-1

    S m2

    Sc Schmidt

    rs %

    0,rs

    ..

    1,rs

    sats

    t s

    T K

    u m s-1

    U m2 K W-1

    V m3

    w

    x m

    X

    BX m

    y

    y y()

    z z()

    0

  • xxi

    m2 s-1

    s-1

    kg kg-1

    H -

    J kg-1

    t s

    m -

    kg kg-1

    Pa s

    kg m-3

    Stefan Boltzmann, 5.66910-8 W m-2 K-4

    l

    aE

    g

    mix

    v

    0

    ph2

    ph3

    AH

  • xxii

    air

    amb

    calc

    cav

    cbw

    CC

    CO

    cond

    conv

    cr

    CS

    cyl

    dc

    dh

    DH

    diff

    ds

    E

    ES

    eff

    eq

    exp

    f

    F

    fire

    fm

    g

  • xxiii

    G

    h

    HH

    i

    in

    j

    kd Knudsen

    l

    L

    m

    M

    MC

    max

    md

    min

    mix

    MO

    O

    out

    p

    par

    pres

    pure

    r

    rad

    ref

    s

  • xxiv

    S

    sl

    sp

    sph

    th

    tot

    d

    CFD Computational Fluid Dynamics

    DWS Dry Wall System

    GPRO Gypsum PROperties

    HETRAN HEat TRansfer ANalysis

    KAS Kissinger-Akahira-Sunose

    LWC Light Weight Construction

    OFW Ozawa-Flynn-Wall

    RSS

    STR Starink

    E

    BA -B

  • xxv

    -

    -

  • xxvi

  • xxvii

    1-1 2010 : ) [KARTER

    M.J., 2011] ) [FIRE STATISTICS GREAT BRITAIN, 2011] ......................... 3

    2-1 ........................................................................ 21

    2-2 - : ) )

    - .......................................................................................... 22

    2-3 ...................... 23

    2-4 - ( ) ............................................................ 27

    2-5 - ........................................................................................... 29

    3-1

    : 1) , 2)

    3) ............................................................................................................ 34

    3-2 ) )

    ( 3-6)

    ........................................................................................................................................................ 42

    4-1 ) ) ................ 50

    4-2 .................................................................... 53

    4-3 :

    ) , ) ) , ................ 55

    4-4

    ............................................................................... 56

    4-5

    ............................................................................................................. 56

    4-6 ............................................................................. 57

    5-1 ...................................................................................................... 68

    5-2 .... 74

    5-3 .............................. 75

    5-4 ...................................................... 77

    5-5 HETRAN ................................. 80

  • xxviii

    6-1 ,

    , : )

    ) ............................................................................................. 89

    6-2 : ) ,

    )

    ) ,

    , ................. 91

    6-3 ( )

    ( ) ,

    40L ( = 2 K MIN-1) : ) )

    ........................................................................................................................................................ 92

    6-4

    ................................................................................................................................ 93

    6-5 : ) , )

    )

    .............................. 95

    6-6 : ) , )

    )

    (

    ) ................................................................................. 96

    6-7 : ) ( =

    5 K MIN-1) ) (=10 K MIN-1) .................... 98

    6-8 : ) )

    .

    (EA,LN(A))

    ,

    ................................................................................................................................... 99

    6-9

    N ,

    - : )

    (5 K MIN-1)

    FRD ) (15 K MIN-1)

    STR ........................................................................... 102

  • xxix

    6-10 Y(): )

    (

    OFW), )

    ( FRD) )

    .............................................................................................................. 103

    6-11 - Y()

    : ) )

    ................................................................................................................. 104

    6-12 RSS N

    : )

    ) ............................ 106

    6-13 ()

    (),

    ,

    ( 6-8): )

    ) (

    ) ..................................................................................................................... 107

    6-14 ()

    (),

    ,

    ( 6-10)

    ( ) ....... 110

    6-15

    : )

    ) .................................................. 113

    6-16

    ( STR) ....................................................................................................... 114

    6-17 ()

    (),

    ,

  • xxx

    ( 6-14)

    ( ) ...... 115

    6-18

    : ) )

    ......................................................................................... 118

    6-19

    ( STR) ....................................................................................................... 118

    6-20 RSS N

    ................................................................................ 119

    6-21 ()

    (),

    ,

    ,

    .... 120

    7-1 GKB: ) )

    ............................................................................................................................................ 124

    7-2 ) , ) )

    (5MM) ........................................................................................................... 125

    7-3 ................................................................... 126

    7-4 ) , ) , )

    )

    ........................................................................................................................ 127

    7-5 ................................................... 127

    7-6 ) CT-METRE

    , ) , )

    ) ..................................................................................... 128

    7-7

    .................................... 130

    7-8 ........................................ 131

    7-9 .. 132

  • xxxi

    7-10 ) )

    ............................................................... 134

    8-1

    ( : MANZELLO ET AL., 2007B) ............................................................ 139

    8-2 [JEULIN ET AL., 2001] .......................................... 140

    8-3 LC/DC

    ,

    ( ) ............................................................................................. 142

    8-4

    ,

    .......................................................................................................... 143

    8-5 (=300C)

    ,

    ( X) ........ 145

    8-6 (T=900OC)

    ,

    ( X) ........ 146

    8-7 ) GKB )

    ...................................... 149

    8-8

    1, ,

    .......................................................... 151

    8-9 : ) )

    2,

    , 8 ............ 152

    8-10 : ) ) ,

    1,

    , , .... 153

  • xxxii

    8-11 ) ) 1,

    ,

    ............................................................................................................................ 154

    8-12 ............... 155

    8-13 1,

    , .............. 156

    8-14 1,

    , , 156

    8-15 1, ,

    , ,

    : ) , ) , ) )

    ..................................................................................... 158

    8-16 KNUDSEN .......................... 159

    8-17 , , 1

    : ) , ) , ,

    ( ), ) ,

    , , (

    ) ) ............. 161

    8-18 , ,

    1, .................................................................. 162

    9-1 ) ISO 834 )

    ............................................................................................................ 166

    9-2 ( GPRO,

    80K MIN-1),

    : ) , )

    ) ....................................... 168

    9-3 (

    HETRAN), ,

    ( GPRO,

    20K MIN-1),

    ,

    [GHAZI WAKILI ET AL., 2007] .......................................................... 170

    9-4 (

    HETRAN), ,

  • xxxiii

    ( GPRO,

    20K MIN-1) ,

    ,

    [GHAZI WAKILI ET AL., 2007] .......................................................... 171

    9-5 ....... 172

    9-6 ( GPRO,

    ), ,

    : ) , ) )

    .............................................................................................................................. 173

    9-7 (

    HETRAN), ,

    ( GPRO,

    ), ,

    ,

    [GHAZI WAKILI ET AL., 2007] .......................................................... 174

    9-8 (

    HETRAN), ,

    ( GPRO,

    80K MIN-1),

    ,

    , [GHAZI WAKILI ET AL., 2007]...................... 176

    9-9 ( GPRO,

    80K MIN-1),

    : ) , )

    , ) )

    ..................................................................................................................................... 179

    9-10

    ................................................................................................................. 183

    9-11 (

    HETRAN), (

    )

    , (

    GPRO,

    80K MIN-1),

    , [GHAZI WAKILI ET AL., 2007]...................... 184

  • xxxiv

    9-12

    , .............................................................. 185

    9-13 : ) -

    ) ,

    , ...................................................................... 186

    9-14 : ) , )

    ) , ,

    ....................................................................................................................... 187

    9-15 : ) , )

    ) , ,

    ........................................................................................................................................ 188

    9-16 (

    ) ............................... 190

    9-17 ( 10K MIN-1): )

    ) [PAULIK

    ET AL., 1992] ................................................................................................................................. 191

    9-18 (

    GPRO, 10K MIN-1) (

    PAULIK ET AL. [PAULIK ET AL., 1992], 10K MIN-1)

    : ) , )

    , )

    , ) , ) , )

    , ) ) ....................... 191

    9-19 (

    HETRAN),

    10K MIN-1,

    ( GPRO) ( PAULIK

    ET AL. [PAULIK ET AL., 1992]) ,

    , .................. 193

    9-20 ................................................................................................. 195

    9-21

    ........................................................................................................................ 195

    9-22 .............................................................................. 197

  • xxxv

    9-23 (

    HETRAN), ,

    ( GPRO,

    , 30K MIN-1

    FC=1.58),

    : ) )

    , ....................................................................... 198

    9-24 (

    HETRAN), ,

    ( GPRO,

    , 30K MIN-1

    FC=1.58),

    ,

    : ) ) ,

    ...................................................................................................... 199

    9-25 (

    HETRAN), ,

    ( GPRO,

    , 30K MIN-1

    FC=1.58),

    ,

    : ) ) ,

    ........................................................................................................... 200

  • xxxvi

  • xxxvii

    1-1

    2010 ..................................................................................................................... 2

    1-2 ................................................ 13

    3-1 ................................................................................................. 33

    3-2 ( 3-16) ...................... 44

    4-1 [HAMMILTON & CROSSER, 1962] .... 50

    4-2 A P ............ 54

    5-1 ................................ 77

    6-1 ................................................................ 89

    6-2 ................. 93

    6-3 ............................................... 94

    6-4

    ................................................................................................................................... 97

    6-5

    ( 3-20) ............................................................................................................................... 99

    6-6 - N

    .............................................. 100

    6-7 - N

    Y() .............................................. 105

    6-8

    ................................................................................... 106

    6-9 -

    ......................................................................................................... 108

    6-10

    ,

    ............................................................................................................. 109

  • xxxviii

    6-11

    ,

    [BROWN ET AL., 2000] ............................................................................................ 111

    6-12

    ,

    [HURST, 1991] ........................................................................................................ 111

    6-13

    ......................................................... 112

    6-14

    ,

    ............................................................................................................. 114

    6-15

    ................................................................................................................................... 116

    6-16

    ,

    ....................................................... 119

    8-1 ....... 139

    8-2 [GHAZI

    WAKILI & HUGI, 2009] ................................................................................................................ 140

    8-3 ........................................................ 141

    8-4 LC/DC .............................. 143

    8-5

    ............................................................................ 146

    8-6

    ................................................................................................ 147

    8-7 ............................. 148

    8-8 ................. 148

    8-9 .............................................................................................. 150

    8-10 ............................................................................................ 150

  • 1

    1

    1

    1

    , .

    ,

    1050000 [, 2006]. ,

    ,

    . ,

    . , ,

    [Quintiere, 2006].

    .

    1%

    () [Founti & Cox, 2000, , 2006, Quintiere,

    2006]. :

    , ,

    .

    (.. ),

    .

    2007, 2688340

  • 2

    2, 63 3,

    5 4.

    ,

    ,

    .

    1.1

    ,

    [Yeoh & Yuen, 2009]. 1-1

    ,

    ( ), (.. ),

    [Karter, 2011] [Fire

    Statistics Great Britain, 2011], 2010. , 1-1,

    1-1.

    ,

    , .

    , ,

    , , ,

    . ,

    ,

    ,

    [, 2006].

    1-1 2010

    (109)

    482000 2755 15420 9.7$

    215500 310 1590 1.4$

    634000 55 710 0.5$

    1331500 3120 17720 11.6$

    2 " ". on Line. 28/08/2007.

    3 " ". in.gr. 27

    2007.

    4 "Griechenland atmet auf". n-tv.de. 28/08/2007. 28 2007.

  • 1

    3

    69600 325 10142 -

    32500 44 520 -

    216900 19 472 -

    319000 388 11134 -

    1-1 2010 : ) [Karter M.J., 2011] )

    [Fire Statistics Great Britain, 2011]

    1.2

    ,

    (). ,

    , ,

    , .

    , :

    .. 71/88 ( 32/17.2.1988) .

    5905/15/839/1995 ( 611 /12.7.1995)

    ,

    .

    .. 6/96 ( 150 13.3.96) .

    .. 3/81 .

  • 4

    .. 3/81 3/19.1.1981

    .

    .. 36/95 3/1981

    .

    ,

    , [Purkiss,

    1996, , 2006]:

    ,

    , , ,

    ,

    (), ,

    ,

    (stability) (integrity)

    , , ,

    ,

    : () .

    ,

    () , ,

    , .

    1.2.1

    ,

    , .

    , ,

    , , ,

  • 1

    5

    .

    :

    (, , ..)

    ( ,

    ..)

    (sprinklers)

    ,

    (, ..) ..

    /

    (sprinkler),

    (wet), (dry), (preaction), (deluge)

    (water spray) (fog)

    (foam)

    , ,

    (halon), ..

    ( )

    ( , ..)

  • 6

    ( ,

    )

    1.2.2

    , ,

    .

    , , ,

    .

    , , .

    :

    .

    ,

    .

    :

    ,

    ,

    , .

    , , :

    :

    ,

    , . (

    ) , :

    ,

    (, ..)

    ,

  • 1

    7

    :

    .

    (

    ):

    ,

    ,

    ..

    :

    . ( )

    , ,

    , , ,

    :

    : ,

    .

    ,

    : ,

    ,

    .

    : ,

    . , 140oC

    180oC

    :

    ,

    ().

    ,

  • 8

    .

    :

    :

    ,

    .

    :

    ,

    1.3

    (numerical simulation)

  • 1

    9

    ,

    . , (modeling)

    . ,

    , , .. ,

    , .. , ,

    ,

    [, 2000].

    ,

    ,

    . ,

    ,

    . , ,

    ,

    ,

    . , ,

    ,

    .

    ,

    , . ,

    , ,

    [, 2000].

    [, 2000, , 2005]. ,

    , , ,

    .. ,

    , , ,

    , ,

    .. ,

    , ,

    , , , .. [,

    2005]. ()

    .

  • 10

    1.4

    , ()

    (light weight constructions) .

    ,

    , ,

    ,

    . (),

    , ,

    ,

    [Henkel et al., 2010].

    .

    , ,

    , , ,

    [Ghazi Wakili et al., 2007].

    (.. ),

    ( ) .

    , ,

    .

    , ,

    ,

    .

    ,

    ,

    , .

    .

    .

    ,

    :

    ()

  • 1

    11

    ,

    .

    ,

    , . ,

    ,

    . ,

    ,

    . ,

    , ,

    .

    ,

    , . ,

    ,

    ,

    .

    . , ,

    .

    ,

    . ,

    . ,

    ,

    .

  • 12

    1.5

    , .

    ,

    , ,

    ,

    .

    :

    ( 4).

    -

    .

    .

    ( 6).

    , , (

    ), ,

    ,

    ( 7).

    .

    , ,

    . , ,

    ,

    , ( 8).

    .

    .

    ,

    ,

    ( 9).

  • 1

    13

    1.6

    10

    . ,

    . ,

    ,

    . 2 5

    , 6 9

    , ,

    ,

    ,

    .

    .

    , ,

    ,

    . 1-2 ,

    .

    1-2

    &

    2

    6

    2 2

    &

    3 4 5

    &

    &

    6 7

    8

    7

    9

    2

    ,

    .

  • 14

    (-, - -),

    .

    3

    (, ). ,

    ( , -

    ) .

    , ,

    .

    , ,

    4.

    . , ,

    ,

    .

    5. ,

    ,

    . ,

    , . ,

    HETRAN (HEat TRansfer ANalysis)

    ,

    .

    6

    . ,

    ,

    , . ,

    ,

    ,

    ,

    , .

  • 1

    15

    7

    . ,

    ,

    ,

    .

    8

    . ,

    . ,

    GPRO (Gypsum PROperties), 4

    6 ,

    .

    , 7 .

    , 9

    ,

    , HETRAN,

    GPRO. ,

    ,

    . ,

    ,

    , ,

    . ,

    , ,

    HETRAN

    .

    10

    ,

    ,

    ,

    .

    I

    . II

  • 16

    HETRAN. III

    . IV

    . , V

    , 7 ,

    9 .

    1.7

    :

    .. , . , . , .. , . ,

    ,

    , , , 5-8 2007, . 229.

    . , . , .,

    , 1 , Divani

    Caravel, , 21-23 2008, : . 843-854.

    . , . , .,

    , 1

    , Divani Caravel, , 21-23 2008, : . 1473-1484.

    . , . , . , . , . ,

    , 2008, 6

    , , 28 , 2008.

    :

    D. Kontogeorgos, E. Keramida, M. Founti, Radiative heat transfer modeling of natural gas

    diffusion flames, in: Proceedings of 3rd European Combustion Meeting, Chania, Crete,

    Greece, 11-13 April 2007.

    D. Kontogeorgos, D. Kolaitis, M. Founti, Numerical modeling of heat transfer in gypsum

    plasterboards exposed to fire, in: Proceedings of 6th International Conference on Heat

    Transfer, Fluid Mechanics and Thermodynamics, Pretoria, South Africa, 27 June to 2 July

    2008, paper number: KD1.

  • 1

    17

    I. Mandilaras, D. Kontogeorgos and M. Founti, Effects of PCMs on Gypsum Board

    Properties at Elevated Temperatures, in: Proceedings of 9th IIR Conference on Phase-

    Change Materials and Slurries for Refrigeration and Air Conditioning, Sofia, Bulgaria, 29

    September to 1 October 2010, p. 123-130.

    I. Mandilaras, D. Kontogeorgos and M. Founti, Implementation of the Heat Capacity Method

    for Modelling the Thermal Performance of Agglomerate Stones Containing PCM, in:

    Proceedings of 9th IIR Conference on Phase-Change Materials and Slurries for

    Refrigeration and Air Conditioning, Sofia, Bulgaria, 29 September to 1 October 2010, p.

    133-141.

    D.A. Kontogeorgos and M.A. Founti, Heat and mass transfer phenomena occurring in a

    gypsum board exposed to fire conditions, in: Proceedings of First Middle East Conference on

    Smart Monitoring, Assessment and Rehabilitation of Civil Structures, Dubai, UAE, 8 10

    February 2011, paper number 160.

    :

    Kontogeorgos, D.A., Keramida, E.P., Founti, M.A., Assessment of simplified thermal

    radiation models for engineering calculations in natural gas fired furnace, Int. J. Heat

    Mass Transfer 50 (2007) 5260 5268.

    D. Kontogeorgos and M. Founti, Numerical investigation of simultaneous heat and

    mass transfer mechanisms occurring in a gypsum board exposed to fire conditions,

    Applied Thermal Engineering 30 (2010) 1461-1469.

    D. Kontogeorgos, I. Mandilaras and M. Founti, Scrutinizing Gypsum Board Thermal

    Performance at Dehydration Temperatures, Journal of Fire Sciences 29 (2010) 111-130.

    D. Kontogeorgos, K. Ghazi Wakili, E. Hugi and M. Founti, Heat and moisture transfer

    through a steel stud gypsum board assembly exposed to fire, Construction and Building

    Materials 26 (2012) 746-754.

    D.A. Kontogeorgos and M.A. Founti, Gypsum Board Reaction Kinetics at Elevated

    Temperatures, Thermochimica Acta 529 (2012) 6-13.

  • 18

  • 2

    19

    2

    2

    2.1

    , ,

    .

    , ,

    : 5

    .

    ,

    , ,

    .

    , ,

    () . ,

    , ,

    () [Zalba et al.,

    2003]. ,

    5 .

  • 20

    ,

    .

    , , ,

    6 ( ),

    , ,

    , , [Kaasinen, 1992]. ,

    ,

    [Peippo et al., 1991].

    ,

    , .. ,

    . ,

    ,

    , [Novozhilov,

    2001]. , ,

    ,

    , ,

    .

    [Feng et al., 2003 , ,

    2006].

    , ,

    . ,

    , , ,

    -

    , ,

    , .

    , ,

    : -,

    - -.

    ( 2-1).

    ,

    , .

    6 ().

  • 2

    21

    ,

    ,

    ,

    .

    .

    2-1

    2.2 -

    - (micro-scale), nm m,

    ( 2-2).

    :

    -

    .

    ,

    .

    ,

    ,

    . ,

    - , . ,

    ,

    ,

    ( 2-2).

    3 ,

    4 .

    ,

  • 22

    . ,

    . ,

    , -

    ,

    6 .

    2-2 - : ) ) -

    2.2.1

    .

    / ,

    - ,

    . ,

    , , , ,

    , . , ,

    ,

    , ,

    . , -

    ,

    . ,

    . ,

    (thermal analysis)

    (calorimetry),

    ,

    [Haines, 2002].

  • 2

    23

    , [Mackenzie, 1983,

    Hemminger & Sarge, 1998]:

    ()

    ,

    .

    ()

    - , , ..

    .

    .

    2.2.1.1

    [Christian & OReilly,

    1985, Skoog & Leary, 1992, Haines, 2002] ( 2-3):

    2-3

    .

    , .

    ,

    (.. , , ).

    , ,

    , ,

    .

  • 24

    2.2.1.2

    ,

    [Doyle, 1961, Coats &

    Redfern, 1964, Paulik et al., 1992, Haines, 1995, Haines, 2002], ..

    ,

    ..

    (reproducibility) .

    (Sample): ,

    .

    (Crucible):

    . ,

    , . ,

    .

    (Rate of heating):

    .

    (thermal lag)

    . , ,

    .

    (Atmosphere):

    . ,

    (.. ) ,

    (.. ).

    (Mass of the sample):

    , . , ,

    .

    2.2.1.3

    ()

    , .

    . , ,

  • 2

    25

    , ,

    .

    , ,

    .

    (), .

    ,

    .

    2.2.1.4

    () ()

    .

    , .

    , ,

    , .

    .

    ,

    . , ,

    ,

    . , ,

    , ,

    .

    2.2.2

    . ,

    .. , ,

    ..

    . , ,

    ,

    .

    .

  • 26

    .

    :

    , ,

    ,

    .

    , .

    , . ,

    ,

    . ,

    ,

    .

    ,

    ,

    .

    2.3 -

    - (meso-scale),

    ,

    , ( 2-4).

    , ,

    7,

    . (

    / ),

    . :

    .

    -. ,

    7 ,

    ,

    .

  • 2

    27

    -,

    . , ,

    ,

    .

    2-4 - ( )

    2.3.1

    - .

    , ( -),

    , , ,

    . ,

    ,

    ,

    , . ,

    ,

    ,

    .

    2.3.2

    ,

    -,

    , .

  • 28

    . ,

    , -,

    . , -

    -.

    - .

    Navier-Stokes -,

    . ,

    , ,

    -, - ,

    , ,

    .

    2.4 -

    - (macro-scale), ,

    ,

    ( 2-5). , -

    ,

    , , ,

    .

    . , ,

    - , .

    , , -

    , , ,

    , .

    ,

    , .

  • 2

    29

    2-5 -

  • 30

  • 3

    31

    3

    3

    3.1

    ,

    -

    /, .

    ,

    .

    : , T, (conversion

    fraction), , , P, :

    PhfTkdt

    dr

    3-1

    3-1, ,

    0 1 (=0 =1

    ). k(T) (reaction

    rate constant), .

    f() (reaction model function)

  • 32

    . , h(P) (pressure term)

    .

    3.1.1

    .

    ,

    ,

    / . ,

    [Sestak, 1984, Sestak, 2005, Vyazovkin, 2008].

    . ,

    ,

    .

    ,

    3-2 [Burnham et al., 2007].

    PnPPh

    3-2

    (reversible) ,

    (AsolidBsolid+Cgas),

    .

    3-3 [Vyazovkin, 2011], P Peq

    , .

    eqP

    PPh 1

    3-3

    3.1.2

    Arrhenius:

    TRE

    g

    a

    AeTk

    3-4

    A Ea - ,

    , Rg .

  • 3

    33

    3.1.3

    , f(),

    [Malek, 1992, ,Vyazovkin & Dollimore, 1996, Vyazovkin & Wight, 1999,

    Brown, 2001, Vyazovkin et al., 2011]. 3-1

    8.

    3-1

    f() g()

    (Power Law)

    Pn n(n-1)/n 1/n

    (Reaction order)

    Rn (1-)n -ln(1-), n=1

    [(1-)(1-n)-1]/(n-1), n1

    Avrami-Erofeev An n(1-)[-ln(1-)](n-1)/n [-ln(1-)]1/n

    -

    (One-dimensional

    diffusion)

    D1 1/2-1 2

    -

    (Two-dimensional

    diffusion)

    D2 [-ln(1-)]-1 (1-)ln(1-)+

    -

    (Three-dimensional

    diffusion)

    D3 3/2(1-)2/3[1-(1-)1/3]-1 [1-(1-)1/3]2

    (Contracting model)

    Cn n(1-)(n-1)/n 1-(1-)1/n

    n=2, (contracting cylinder)

    n=3, (contracting sphere)

    , ,

    : ,

    ( ) [Vyazovkin et al., 2011],

    , , , d/dt, ,

    8 ,

    .

  • 34

    .

    ,

    . , k(T),

    , h(P), 3-1,

    ,

    , f().

    , , k(T), ,

    f(), ,

    , h(P).

    3-1

    .

    3-1

    : 1) , 2) 3)

    , ,

    , ,

    (Power Law) ( 3-1). ,

    ,

    . (Reaction Order)

    (Diffusion) ( 3-1). , ,

    , .

    , ,

    .

  • 3

    35

    Avrami-Erofeev ( 3-1)

    .

    3.2

    [Brown et al., 2000]:

    ( Arrhenius )

    , Arrhenius, A Ea

    , f(),

    . ,

    3-1 (Hemminger & Sarge, 1998, Galwey

    & Brown, 1999]. , 3-1

    , ,

    , [Brown et al., 2000].

    , ,

    [Brown et al., 2000,

    Vyazovkin et al., 2011] 3-5:

    RN

    r

    rrdt

    dw

    dt

    d

    1

    3-5

    NR ,

    , wr r

    , (wr=1, r=).

    3-1 :

    fAedt

    dr

    TR

    E

    g

    a

    3-6

    (differential kinetic methods), :

    tTR

    E

    dteAf

    dg g

    a

    00

    3-7

  • 36

    (integral kinetic methods). g(),

    ( 3-1).

    , , [Doyle, 1962, Coats & Redfern, 1964, Ozawa, 1965,

    Abdel Aziz Khalil, 1982, Elder, 1985, Strydom et al., 1995, Hudson-Lamb et al., 1996, Aybers,

    1998, Erdogan et al., 1999, Sanders & Gallagher, 2002, Demir et al., 2003, Seungdo et al., 2004,

    Elbeyli & Piskin, 2004].

    ( 3-6 3-7)

    ,

    [Vyazovkin et al., 2011]. ,

    , ()

    (),

    ( ). , ,

    ,

    , ,

    9 .

    ,

    , :

    (model-fitting method)

    (model-free method).

    Arrhenius, ,

    Arrhenius

    . ,

    . ,

    . ,

    ,

    =0.1-0.9 =0.05-0.95.

    9

    , .

  • 3

    37

    .

    3.2.1

    (model-fit method) ,

    .

    , Arrhenius

    .

    ,

    .

    , . ,

    : .

    Arrhenius (A Ea),

    , . ,

    , ,

    .

    ,

    , ,

    Arrhenius.

    , ..

    () (

    ). ,

    , . , ,

    Arrhenius

    [Vyazovkin & Dollimore, 1996,

    Vyazovkin, 1997, Vyazovkin, & Wight, 1999, Vyazovkin et al., 2011].

    10 [Brown et al., 2000, Vyazovkin et al., 2011].

    ,

    10 3-5.

  • 38

    .

    3.2.1.1

    .

    ,

    Arrhenius.

    (.. , ,

    ..).

    ,

    .

    ,

    :

    ;

    (

    ) (

    ), ,

    .

    .

    , Ea,

    , (. );

    : , (.

    3.1.3);

    , , ,

    ( 3-1).

    3.2.1.2

    (linear model-fitting method)

    ,

    ( 3-6) .

  • 3

    39

    3-6

    , 1/.

    [Vyazovkin et al., 2011]:

    oncf 1

    3-8

    3-8

    ( 3-1),

    c, n o [Perez-Maqueda et al., 2006]. , ,

    3-8 3-6

    :

    TR

    EcA

    dt

    d

    g

    a

    on

    ln

    1

    1ln

    3-9

    3-9

    (

    ) n

    o

    .

    ,

    n o.

    ,

    , Ea, ln(cA),

    ,

    . n o

    , c, n o

    . , c,

    - , A. n o

    , c A

    . , c ,

    - , ln(cA)ln(A).

    3.2.1.3

    (non-linear model-fitting

    method)

    .

  • 40

    Arrhenius, ,

    (residual sum of squares), RSS,

    ,

    3-10.

    min1

    2

    exp

    N

    jcalcjj

    yyRSS

    3-10

    y

    , exp calc

    , . RSS

    ( ) .

    3.2.2

    (model-

    free isoconversional method) ,

    ,

    [Friedman, 1964, Ozawa, 1965, Flynn & Wall, 1966].

    3-6

    , 1/T, :

    111

    lnlnln

    T

    f

    T

    Tk

    T

    dtd

    3-11

    .

    3-11 , ,

    (. =.), f() ,

    ,

    :

    g

    a

    R

    E

    T

    dtd

    1

    ln

    3-12

    3-12,

    , ,

  • 3

    41

    11,

    , , .

    ,

    ,

    : (differential isoconversional methods)

    (integral isoconversional methods) .

    ,

    ( )

    (). 3-12,

    .

    , ,

    , =0.05-0.95, 0.05

    [Vyazovkin et al., 2011].

    ,

    .

    , ,

    ,

    3-6 .

    .

    ,

    .

    3.2.2.1

    Friedman [Friedman, 1964],

    3-13:

    TR

    EAf

    dt

    d

    g

    alnln

    3-13

    3-13 3-6

    11 , , ,

    .

  • 42

    . 3-2

    , , , T,

    , .

    , =0.

    ln(d/dt) 1/T ( 3-13), ,

    , 3-2.

    (ln(d/dt),1/T)

    .

    ( 3.2.2)

    .

    ,

    .

    3-2 ) )

    ( 3-6)

    ,

    , , ,

    (. 3.2.2.2). , , ,

    . ,

    (.. ),

    , , ,

    [Starink,

    2003]. ,

    [Sbirrazzuoli, 2007]. ,

    (.. )

    , ()

  • 3

    43

    . , ,

    .

    3.2.2.2

    3-7.

    ,

    , :

    tAeg TRE

    g

    a

    3-14

    3-14, 3-16:

    TR

    E

    A

    gt

    g

    alnln

    3-15

    , , , =0 (

    3-2), ln(t) 1/ ( 3-15),

    , ,

    3-1. (ln(t),1/T)

    .

    , 3-7

    .

    (.. Taylor) .

    3-7

    ,

    [Starink, 2003]:

    TR

    ECConst

    T g

    aiBi

    ln

    3-16

    Bi Ci

    3-7. 3-2

    3-16, .

    Ozawa-Flynn-Wall (OFW) , Kissinger-Akahira-

    Sunose (KAS) Starink (STR) .

  • 44

    3-2 ( 3-16)

    Bi Ci

    Ozawa-Flynn-Wall (OFW) 0.00 1.0520 [Ozawa, 1965, Flynn & Wall, 1966]

    Kissinger-Akahira-Sunose

    (KAS)

    2.00 1.0000 [Akahira & Sunose, 1971]

    Starink (STR) 1.92 1.0008 [Starink, 2003]

    3-7. , , 3-7

    [Vyazovkin & Dollimore, 1996, Vyazovkin, 1997, Vyazovkin, 2001].

    , , (

    )

    :

    N

    i

    N

    ij ja

    iaa

    tTEJ

    tTEJE

    1 ,

    ,

    3-17

    i j ,

    J12 :

    ttTR

    E

    a dtetTEJg

    a

    0

    ,

    3-18

    3-17

    ( 3.2.2), ,

    , .

    3-7

    . , ,

    [Vyazovkin &

    Sbirrazzuoli, 2006, Vyazovkin, 2008],

    20-30%,

    [Vyazovkin, 2001].

    Friedman,

    12 J .

  • 3

    45

    :

    t

    t

    tT

    a dttTEJ

    -

    g

    a

    R

    E-

    e,

    3-19

    3-19 , ,

    .

    3.2.3 -

    ,

    ,

    - .

    ,

    3-6.

    .

    ,

    3-5, .

    . ,

    ,

    - :

    .

    3.2.3.1

    (compensation effect)

    (.. ).

    ,

    3-10,

    - , Ei Ai, .

    (..

    ), ,

    (Ei,Ai).

  • 46

    3-20,

    [Vyazovkin et al., 2011].

    baEA ii ln

    3-20

    (Ei,Ai)

    3-20. ,

    (. 3.2.2), Ea,

    3-20 - , A ( 3-21),

    .

    baEA a ln

    3-21

    - ,

    ( 3-22)

    ( 3-23) .

    tTR

    E

    dteAg ga

    0

    3-22

    TR

    E

    g

    a

    Aedt

    df

    1

    3-23

    3-22 3-23

    t (d/dt), ,

    , g() f().

    g() f() ( 3-1)

    .

    3.2.3.2

    (master plots) :

    y() z() [Malek, 1992].

    ,

    (. 3.2.2), y()

    z():

  • 3

    47

    Afedt

    dy RT

    Ea

    3-24

    gfTdt

    dz

    2

    3-25

    y() z(), , ,

    g() f() ( 3-1).

    y(), - ,

    .

    , -

    3-26.

    max

    max2max

    TR

    E

    g

    a g

    a

    efTR

    EA

    3-26

    max

    , .

  • 48

  • 4

    49

    4

    4

    4.1

    , ,

    , , ,

    .

    13 , ,

    .

    , , ,

    , ,

    ( 4-1). 14

    ( )

    ( 4-1).

    , .. , , ..

    ,

    - ,

    13 , .

    14 3.510-4m,

    >1m.

  • 50

    . , , ,

    , ,

    .

    ,

    , .

    4-1 ) )

    4.2

    , ,

    ,

    , , :

    par

    sph

    S

    S

    4-1

    . 4-1

    [Hammilton & Crosser, 1962].

    4-1 [Hammilton & Crosser, 1962]

    ,

    1.00

    5:1 0.68

    10:1 0.57

    , .. [Jeulin et al., 2001],

  • 4

    51

    , Lcyl dcyl,

    [Korte & Brouwers, 2010]. , , ,

    4-2.

    2

    1

    1

    4

    632

    cyl

    cylcyl

    cyl

    d

    Ld

    L

    4-2

    4.2.1

    (porosity)

    ( ), VF, , V, .

    V

    VF

    4-3

    ,

    4-4, VS

    sr .

    r

    N

    s s

    s

    S

    sV

    m

    V

    VV

    S

    11

    V

    V

    0

    1F

    4-4

    4.2.2

    (saturation)

    , VL, , VF.

    F

    Lsat

    V

    Vs

    4-5

    4.2.3

    (, Probability Density Function) ,

    (, Pore Size Distribution) [Assouline &

    Rouault, 1997, Rouault & Assouline, 1998].

    , [Beck & Schultz, 1972, Collins & Ramirez, 1979,

  • 52

    Nakao & Kimura, 1981, Deen et al., 1983, Tam & Tremblay, 1993, Krajewska & Olech, 1996,

    Assouline & Rouault, 1997, Rouault & Assouline, 1998],

    [Du Bois & Stoupel, 1976, Deen et al., 1983, Aimar et al., 1990, Tam & Tremblay, 1993,

    Mochizuki & Zydney, 1993, Assouline & Rouault, 1997, Rouault & Assouline, 1998, Bowen &

    Welfoot, 2002], [Mochizuki & Zydney, 1993], ,

    Weibull Rayleigh [Deen et al., 1983, Derjani-Bayeh & Rodgers, 2002]

    [Wendt et al., 1976, Mason et al., 1980, Wendt & Klein, 1984].

    ,

    , ,

    .

    ,

    , ,

    [Bowen & Welfoot, 2002, Derjani-

    Bayeh & Rodgers, 2002].

    4-6, dp,m l

    .

    2

    2

    ,

    2

    log

    2

    1l

    mp

    p

    d

    d

    lp

    p ed

    dPDF

    4-6

    , l,

    4-7, , l, dp,th

    (maximum pore diameter threshold) .

    thp

    mpthp

    l

    l

    dC

    ddC

    C

    C

    ,5

    1

    2,,

    0

    21

    1

    0

    210

    2

    loglog

    ln

    4-7

    dp dp-

    dp dp+dp, dp0 4-8.

    ppp dPDFNdPSD

    4-8

    Np

    , 4-9.

  • 4

    53

    max,

    min,

    max,

    min,

    p

    p

    p

    p

    d

    d

    ppFp

    p

    d

    d

    ppFpF

    dddVdPDF

    VNdddVdPSDVV

    4-9

    4.3

    :

    .

    , : ,

    .

    4.3.1

    (tortuosity factor)

    , Lsl, , L,

    4-10 [Dias et al., 2006, Matyka et al., 2008].

    1L

    Lsl

    4-10

    4-2

    .

    ,

    : ( 4-11) [Iversen & Jorgensen, 1993, Koponen et al., 1996,

    Salem & Chilingarian, 2000, Blondeau et al., 2003], ( 4-12) [Archie, 1942,

  • 54

    Millington & Quirk, 1961, Klusacek & Schneider, 1981, Huizenga & Smith, 1986, Zhang &

    Bishop, 1994, Mota et al., 1998, Mota et al., 2001, Dias et al., 2006]

    ( 4-13) [Weissberg, 1963, Ho & Strieder, 1981, Tsai & Strieder, 1986, Comiti & Renaud,

    1989, Barrande et al., 2007, Matyka et al., 2008] .

    pa

    4-11

    p

    4-12

    ln1 p

    4-13

    4-2 a p

    a p

    ( 4-11)

    3 -2 Iversen & Jorgensen, 1993

    4 -3 Iversen & Jorgensen, 1993

    2.2271 -1.12 Blondeau et al., 2003

    ( 4-12)

    1/3 Millington & Quirk, 1961

    0.5 Zhang & Bishop,1994

    Mota et al., 1997

    0.4 Mota et al., 1998

    ( 4-13)

    0.5 Weissberg, 1963

    Ho & Strieder, 1981

    1 Tsai & Strieder, 1980

    2/3 Tsai & Strieder, 1980

    0.86 Comiti & Renaud, 1989

    1.66 Barrande et al., 2007

    0.77 Matyka et al., 2008

    a p

    . 4-2 a p

    .

    4-3

    , .

    , ,

    , . ,

  • 4

    55

    ,

    (0 1). ,

    ,

    ,

    , (, Least Square

    Method). .

    4-3 : ) , )

    ) ,

    4-4

    ,

    4-14, calc exp

    , , N .

    N

    i

    calctote1

    2exp

    4-14

  • 56

    4-4

    ,

    , p=0.601859,

    , .

    4-5

    ( 4-13, p=0.601859), .

    4-5

    4.3.2

    (permeability)

    .

    .

    , ,

  • 4

    57

    , , , Ssp,

    [Koponen et al.,

    1997, Matyka et al., 2008].

    :

    2

    ,

    spS

    gK

    4-15

    Kozeny ( 4-16) Kozeny ( 4-17),

    [Bear, 1972].

    2

    3

    spKScK

    4-16

    22

    3

    spK ScK

    4-17

    cK Kozeny

    (capillaries) ( 4-2),

    2 12 [Scheigegger, 1957, Han, 1969, Bear, 1972].

    4-6

    ,

    (interconnected

    pores) ( 4-6). ,

  • 58

    ( dead-end pore)

    ( occluded pore)

    ( 4-6).

    ,

    (percolation threshold), th , ,

    Kozeny.

    .

    (effective porosity), eff ,

    15

    [Koponen et al., 1997]:

    xxx thefftheffeffeff 12 ,2,3,

    4-18

    ththx 1 eff,

    . : 1 dd effeff 1

    0eff th .

    , , 4-15 4-16

    :

    2

    3

    spK

    eff

    ScK

    4-19

    22

    3

    spK

    eff

    ScK

    4-20

    , ,

    [Koponen et al., 1997]:

    ln,parh

    Dsp

    d

    nS

    4-21

    15 (>0.6) ,

    .

  • 4

    59

    dh,par=nDVpar/Spar , nD

    , Vpar Spar ,

    .

    ,

    4-22, Kref=(Vpar/Spar)2/cK.

    2

    2

    ln

    effeffrefKK

    4-22

    (>0.6)

    , 4-22 :

    2ln

    refKK

    4-23

    ,

    Kref.

    Kref=(dcyl)2/cK.

    4.3.3

    (diffusion)

    , , Knudsen

    [Treybal, 1981, Ruthven, 1984, Incropera &

    DeWitt, 1985, , 1993, Masel, 1996].

    , .

    , Knudsen

    . ,

    ,

    10-7-10-9 m2/s [Treybal, 1981].

    Knudsen

    .

    Knudsen , ,

    ,

    (effective diffusion coefficient) [, 1993]:

    effkdeffmdeff DDD ,,

    111

    4-24

  • 60

    Dmd,eff Dkd,eff

    Knudsen, .

    4-25 [Weissberg, 1963, Mota et al., 1998, Blondeau et al., 2003]. Dm

    .

    meffmd DD ,

    4-25

    Knudsen

    4-26 [, 1993].

    mfpeffkd udD ,,3

    1

    4-26

    dp uf,m

    f, 4-27.

    21

    ,,

    8

    g

    g

    mgmfMW

    TRuu

    4-27

    4.4

    (effective density) ,

    ,

    , .

    ,

    . , ,

    , ( ),

    .

    r

    N

    s

    s

    N

    l

    l

    r

    SLeff

    sV

    mm

    sV

    mm

    V

    m

    SL

    11 0

    11

    0

    4-28

    4.5

    (effective thermal conductivity)

    , , , ,

  • 4

    61

    , ,

    .. [Horai & Simmons, 1969, Hsu et al., 1994, Hsu et al., 1995,

    Clauser & Huenges, 1995, Kaviany, 1995]. (..

    , ..),

    ,

    , .

    ( 23 )

    . , ,

    , ,

    ,

    [Ahmed & Hurst, 1997, Korte & Brouwers, 2010].

    Ahmed & Hurst

    [Ahmed & Hurst, 1997] ( 4-29), kS, kL kG

    , , , ssat

    ( 4-5), nt ,

    .

    tttt nnGsatnLsatnSpheff kskskk1

    3, 11

    4-29

    , ,

    , ( S-G)

    ( S-L). ,

    4-30 [Somerton et al., 1974].

    GSpheffLSpheffsatGSpheffpheff kkskk ,2,,2,,2,3,

    4-30

    ,

    [Hamilton & Crosser, 1962, Zehner & Schlunder, 1970, Hsu et al., 1994,

    Hsu et al., 1995, Kaviany, 1995, Cernuschi et al., 2004, Carson et al., 2005, Cote & Konrad,

    2005, Yu et al., 2006, Do et al., 2007, Cote & Konrad, 2009].

    Maxwell [Maxwell, 1873], ,

    ( )

    ( ).

    [Carson et al.,

  • 62

    2005], .

    , Maxwell [Hadley, 1986] (

    4-31).

    12

    2112

    111

    11

    2

    0

    00

    0002,

    FS

    FSFS

    FS

    FSFpheff

    ff

    ffkk

    4-31

    S-F

    , kS/kF, 0 (degree of consolidation) f0

    .

    4-32.

    580.0298.0,298.0778.6084.1log

    298.00827.0,0827.0154.3405.0log

    0827.00,898.4log

    0

    0

    0

    4-32

    4-33 [Korte &

    Brouwers, 2010] 4-34 [Verma et al., 1991].

    3

    2

    12

    2

    3

    20

    FS

    FSf

    4-33

    31

    3

    0ln

    FS

    f

    4-34

    ,

    .

    [Burgoyne & Weinberg, 1953, Mathur et al., 1967],

    4-35, Xf f.

    F

    F

    N

    f f

    f

    N

    f

    ffF

    k

    XkXk

    1

    1

    15.0

    4-35

    , ,

    ( 4-36)

    ( 4-37) ( 4-38)

  • 4

    63

    [Clauser & Huenges, 1995, Cote & Konrad, 2005].

    ,

    .

    SN

    s

    ssS kXk1

    4-36

    SN

    s s

    s

    S

    k

    Xk

    1

    1

    4-37

    S

    s

    N

    s

    XsS kk

    1

    4-38

    ,

    . ,

    [Kingery et al., 1976, Harmathy, 1988, Ahmed & Hurst, 1997, Szelagowski et

    al., 1999, Yu et al., 2006, Do et al., 2007].

    , keff,rad, 4-39, G

    (2/3 1

    ).

    pradeff dTGk3

    , 4

    4-39

    ,

    , 4-40.

    radeffpheffeff kkk ,3,

    4-40

    4.6

    ()

    r :

  • 64

    rrr rH

    dt

    dh

    4-41

    Hr

    r, rr r.

    :

    rrrrr

    rrr

    r rH

    dT

    dhrH

    dt

    dT

    dT

    dhrH

    dt

    dh

    4-42

    4-42 , Cr, r,

    (effective specific heat),

    :

    dTCdh rr

    4-43

    , ,

    :

    rrr

    rHC

    4-44

    ,

    ,

    [Harmathy, 1983]:

    RR N

    r

    rrref

    N

    r

    rrefeff

    rHCCCC

    11

    4-45

  • 5

    65

    5

    5

    5.1

    ,

    , , .

    , , ,

    , ,

    . ,

    , , ..,

    , -16

    ,

    , .

    ,

    ,

    , ,

    , .

    16 ,

    .

  • 66

    ( )

    . -

    , / ,

    ,

    [Pham, 2006].

    .

    :

    .

    ,

    (

    ), .

    ,

    , 17. , ,

    ,

    - ,

    , ,