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ESTIMATION OF RELATIVE PERMEABILITY

FROM A DYNAMIC BOILING EXPERIMENT

A REPORT

SUBMITTED TO THE DEPARTMENT OF PETROLEUM ENGINEERING

AND THE COMMITTEE ON GRADUATE STUDIES

OF STANFORD UNIVERSITY

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREE OF

MASTER OF SCIENCE

Marilou Tanchuling Guerrero

June 1998

ii

Abstract

Thermal and multiphase flow properties of a Berea sandstone core were estimated by

inverse calculation using temperature, pressure, steam saturation, and heat flux data. The

development of the two-phase flow region was strongly related to the temperature

conditions in the core since heat was the only driving force in the experiment. As a result,

the heat input as well as the thermal properties of the sandstone and insulation materials

were a major consideration in understanding the system behavior. The high sensitivity of

the insulation materials to the observation data and their strong correlation with the other

parameters of interest made it difficult to obtain accurate estimates. Although the linear

relative permeability model gave the best fit in the two cases presented in the paper, all

models yielded similar matches. This indicated that the data did not contain sufficient

information to distinguish the different models, giving a non-unique solution.

Nonetheless, almost all models gave a consistent estimate for Sgr, which was around 0.1-

0.2. In addition, the choice for the capillary pressure model depended on the condition in

the core, whether there was single-phase steam or two phases present. Since the

distribution of steam depended heavily on the capillary pressure, the relative permeability

would have been more accurately estimated had the capillary pressure been known. The

comprehensive analysis of all available data from a transient non-isothermal two-phase

flow experiment provided an insight into relation of processes and correlation of

parameters.

iii

Acknowledgments

I sincerely would like to thank Dr. Cengiz Satik for his patience and understanding while

this project was underway. His insights about the experiment itself and possible solutions

to the inverse problem helped me approach the problem from the proper perspective. I am

also deeply grateful to Dr. Stefan Finsterle, whose guidance, support, and ITOUGH2

expertise were truly valuable. His insightful suggestions helped me understand the

difficulties I encountered in the estimation process. I also would like to thank Prof.

Roland Horne for his guidance, encouragement, and sense of humor. His easy-going

nature made my life as a graduate student more bearable and truly enjoyable.

To my all friends, especially Apu Kumar, thank you for the fond memories. When the

going got tough, you were there to lighten the burden.

To my family, thank you for your love, prayers and support. To Jason, you served as my

inspiration to reach for the stars.

This project was funded by the U.S. Department of Energy under grant number DE-

FG07-95ID13370.

Malou T. Guerrero

June 5, 1998

iv

Table of Contents

Abstract ...............................................................................................................................ii

Acknowledgments ..............................................................................................................iii

Table of Contents ............................................................................................................... iv

List of Figures.....................................................................................................................vi

List of Tables.......................................................................................................................x

Introduction .........................................................................................................................1

Review of Related Literature...............................................................................................3

2.1 Relative Permeability and Capillary Pressure............................................................3

2.2 Heat and Mass Transfer .............................................................................................5

2.3 Previous Work ...........................................................................................................6

Relative Permeability and Capillary Pressure Models ........................................................8

3.1 Linear Model..............................................................................................................8

3.4 Corey Model...............................................................................................................9

3.5 Leverett Model .........................................................................................................10

3.2 Brooks-Corey Model................................................................................................11

3.3 van Genuchten Model ..............................................................................................12

Experimental Apparatus and Procedure ............................................................................14

Numerical Simulation .......................................................................................................18

5.1 Model .......................................................................................................................18

5.2 Forward Calculation.................................................................................................20

5.2.1 Input Data .................................................................................................................................... 205.2.2 Sensitivity Analysis...................................................................................................................... 215.2.3 Initial Guesses.............................................................................................................................. 58

5.3 Parameter Estimation ...............................................................................................58

5.3.1 Inverse Modeling ......................................................................................................................... 585.3.2 Results and Discussion................................................................................................................. 60

Conclusion.........................................................................................................................96

References .........................................................................................................................97

Appendix A .....................................................................................................................100

Appendix A.1.1 TOUGH2 input file. ................................................................................................. 100

v

A.1.2 ITOUGH2 input file.................................................................................................................. 113A.2 Linear model calibration input files ............................................................................................. 118A.2.1 TOUGH2 input file. .................................................................................................................. 118A.2.2 ITOUGH2 input file.................................................................................................................. 130

vi

List of Figures

Figure 2.1 Relative permeability as a function of liquid saturation. ...................................4

Figure 2.2 Relative permeability obtained by Ambusso (1996)..........................................7

Figure 2.3 Relative permeability obtained by Satik (1998).................................................7

Figure 3.1 Linear relative permeability. ..............................................................................9

Figure 3.2 Corey relative permeability. .............................................................................10

Figure 3.3 Brooks-Corey relative permeability. ................................................................12

Figure 3.4 van Genuchten relative permeability. ..............................................................13

Figure 4.1. Schematic diagram of the experimental apparatus (after Satik, 1997b). ........14

Figure 4.2 Experimental temperature data. .......................................................................16

Figure 4.3 Experimental pressure data. .............................................................................16

Figure 4.4 Experimental steam saturation data. ................................................................17

Figure 4.5 Experimental heat flux data. ............................................................................17

Figure 5.1. Schematic diagram of the 4×51 TOUGH2 model. Ring 4 is not shown since it

represents ambient conditions. ..........................................................................................19

Figure 5.2. ITOUGH2 input used to generate the elements and connections. ..................20

Figure 5.3 Base scenario: αs=4.930 W/m2, αb=0.150 W/m2, αi=0.115 W/m2, αh=2.885

W/m2 and αe=0.577 W/m2. ...............................................................................................26

Figure 5.4 αs=4.300 W/m2, αb=0.150 W/m2, αi=0.115 W/m2, αh=2.885 W/m2 and

αe=0.577 W/m2..................................................................................................................27


αe=0.577 W/m2..................................................................................................................28


αe=0.577 W/m2..................................................................................................................29

Figure 5.7 Base case linear model: Slr=0.20, Sgr=0.20, Sls=0.80, Sgs=0.80, Pcmax=105 Pa 30

Figure 5.8 Linear model: Slr=0.02, Sgr=0.10, Sls=0.80, Sgs=0.80, Pcmax=105 Pa................31

Figure 5.9 Linear model: Slr=0.02, Sgr=0.20, Sls=0.80, Sgs=0.70, Pcmax=105 Pa................32

vii

Figure 5.10 Linear model: Slr=0.02, Sgr=0.20, Sls=0.80, Sgs=0.80, Pcmax=104 Pa..............33

Figure 5.11 Base case: Corey relative permeability and linear capillary model: Slr=0.20,

Sgr=0.20, Pcmax=105 Pa......................................................................................................34

Figure 5.13 Corey relative permeability and linear capillary model: Slr=0.20, Sgr=0.10,

Pcmax=105 Pa. .....................................................................................................................36

Figure 5.14 Corey relative permeability and linear capillary model: Slr=0.20, Sgr=0.20,

Pcmax=104 Pa. .....................................................................................................................37

Figure 5.15 Base case: Corey relative permeability and Leverett capillary pressure:

Slr(RP)=0.20, Sgr=0.20, Po=105. Slr (CP)=0.20..................................................................38

Figure 5.16 Corey relative permeability and Leverett capillary pressure: Slr(RP)=0.10,

Sgr=0.20, Po=105. Slr (CP)=0.20. ......................................................................................39


Sgr=0.10, Po=105. Slr (CP)=0.20. ......................................................................................40


Sgr=0.20, Po=104, Slr (CP)=0.20. ......................................................................................41


Sgr=0.20, Po=105, Slr (CP)=0.10. ......................................................................................42

Figure 5.20 Base case: Linear relative permeability and Leverett capillary pressure:

Slr(RP)=0.20, Sgr=0.20, Sls=0.80, Sgs=0.80, Po=105, Slr (CP)=0.20...................................43

Figure 5.21 Linear relative permeability and Leverett capillary pressure: Slr(RP)=0.20,

Sgr=0.10, Sls=0.80, Sgs=0.80, Po=105, Slr (CP)=0.20 ........................................................44


Sgr=0.20, Sls=0.80, Sgs=0.70, Po=105, Slr (CP)=0.2 ..........................................................45





Figure 5.25 Base case: Brooks-Corey model: Slr=0.20, Sgr=0.20, λ=2.0, pe=2000 Pa .....48

Figure 5.26 Brooks-Corey model: Slr=0.10, Sgr=0.20, λ=2.0, pe=2000 Pa.......................49


viii



Figure 5.30 Base case van Genucthen model: Slr=0.2, Sgr=0.2, n=2.0, 1/α=500 ............53

Figure 5.31 van Genucthen: Slr=0.1, Sgr=0.2, n=2.0, 1/α=500........................................54



Figure 5.34 van Genucthen: Slr=0.2, Sgr=0.2, n=2.0, 1/α=1000......................................57

Figure 5.35 Inverse modeling flow chart (after Finsterle et al., 1998). .............................60

Figure 5.36 Measured and calculated temperature after single-phase period calibration. 64

Figure 5.37 Measured and calculated heat flux after single-phase period calibration. .....64

Figure 5.38 Measured and calculated temperature. ...........................................................69

Figure 5.39 Measured and calculated pressure.................................................................70

Figure 5.40 Measured and calculated steam saturation....................................................70

Figure 5.41 Measured and calculated heat flux.................................................................71

Figure 5.42 Temperature with respect to time...................................................................71

Figure 5.43 Pressure with respect to time. ........................................................................72

Figure 5.44 Steam saturation with respect to time. ...........................................................73

Figure 5.45 Heat flux with respect to time. .......................................................................74

Figure 5.46 Temperature with respect to distance from the heater. ..................................74

Figure 5.47 Pressure with respect to distance from the heater. .........................................75

Figure 5.48 Steam saturation with respect to distance from the heater.............................75

Figure 5.49 Heat flux with respect to distance from the heater.........................................76

Figure 5.50 Inverse modeling relative permeability results compared with Ambusso’s

results (1996).....................................................................................................................77

Figure 5.51 Leverett capillary pressure. ............................................................................77

Figure 5.52. Relative permeability estimates compared with Ambusso’s (1996) results. 78

Figure 5.53. Relative permeability estimates compared with Satik’s (1996) results. .......78

Figure 5.54 No Sensor 1 data: Measured and calculated temperature after calibration of

model under single-phase conditions. ...............................................................................79

ix

Figure 5.55 No Sensor 1 data: measured and calculated heat flux after calibration of

model under single-phase conditions. ...............................................................................80

Figure 5.56 No Sensor 1 data: Measured and calculated temperature. .............................84

Figure 5.57 No Sensor 1 data: Measured and calculated pressure. ...................................84

Figure 5.58 No Sensor 1 data: Measured and calculated steam saturation. ......................85

Figure 5.59 No Sensor 1 data: Measured and calculated heat flux. ..................................85

Figure 5.60 No Sensor 1 data: Temperature with respect to time. ...................................88

Figure 5.61 No Sensor 1 data: Pressure with respect to time............................................89

Figure 5.62 No Sensor 1 data: Steam saturation with respect to time...............................90

Figure 5.63 No Sensor 1 data: Heat flux with respect to time. .........................................91

Figure 5.64 No Sensor 1 data: Temperature with respect to distance from heater............92

Figure 5.65 No Sensor 1 data: Pressure with respect to distance from heater. .................92

Figure 5.66 No Sensor 1 data: Steam saturation with respect to distance from heater. ....93

Figure 5.67 No Sensor 1 data: Heat flux with respect to distance from heater. ................93

Figure 5.68 No Sensor 1 data: Relative permeability estimate compared with Ambusso’s

results (1996).....................................................................................................................94

Figure 5.69 No Sensor 1 data: Linear capillary pressure...................................................94

Figure 5.70 No Sensor 1 data: Relative permeability estimates compared with Ambusso’s

results. ...............................................................................................................................95

Figure 5.71 No Sensor 1 data: Relative permeability estimates compared with Satik’s

results. ...............................................................................................................................95

x

List of Tables

Table 4.1. Physical properties of the cores, epoxy, core insulation, and heater insulation.

....................................................................................................................................15

Table 5.1. Observation used for model calibration. ..........................................................61

Table 5.2 Parameter estimates after single-phase calibration period. ...............................62

Table 5.3 Variance-covariance matrix (diagonal and lower triangle) and correlation

matrix (upper triangle) after single-phase period calibration. ....................................63

Table 5.4 Statistical measures and parameter sensitivity after single-phase period

calibration. ..................................................................................................................63

Table 5.5 Total sensitivity of observation, standard deviation of residuals, and

contribution to the objective function (COF) after single-phase period calibration...64

Table 5.6 Parameter estimates for linear relative permeability and Leverett capillary

pressure case. ..............................................................................................................67

Table 5.7 Variance-covariance and correlation matrices. .................................................67

Table 5.8 Statistical measures and parameter sensitivity. .................................................68

Table 5.9 Total sensitivity of observation, standard deviation of residuals, and

contribution to the objective function (COF). ............................................................69

Table 5.10 No Sensor 1 data: Parameter estimates after the single-phase calibration

period. .........................................................................................................................80

Table 5.11 No Sensor 1 data: Variance-covariance and correlation matrices after single-

phase period calibration..............................................................................................81

Table 5.12 No Sensor 1 data: Statistical measures and parameter sensitivity after single-

phase period calibration..............................................................................................81

Table 5.13 No Sensor 1 data: Total sensitivity of observation, standard deviation of

residuals, and contribution to the objective function (COF) after single-phase period

calibration. ..................................................................................................................82

Table 5.14 No Sensor 1 data: Parameter estimates. ..........................................................86

xi

Table 5.15 No Sensor 1 data: Variance-covariance and correlation matrices...................86


residuals, and contribution to the objective function (COF). .....................................87


residuals, and contribution to the objective function (COF). .....................................87

Chapter 1

Introduction

Relative permeability is one of the parameters required in describing multiphase flow in

porous media since it governs movement of one phase or component with respect to

another. It has been studied widely for oil applications (e.g. waterflooding and gas

injection), but less so for geothermal applications, which is the main concern of this

study. So far, relative permeability relations for steam and liquid water have been based

on theoretical methods using field data (e.g. Grant, 1977; Horne and Ramey, 1978), and

laboratory experiments (e.g. Ambusso, 1996; Satik, 1998). Although relative permeability

is best determined through laboratory experiments, it is difficult to measure due to

capillary forces that introduce nonlinear effects on the pressure and saturation distribution

at the core exit (Ambusso, 1996). Also, relative permeability is difficult to measure

directly for steam-water flows due to experimental constraints (Satik, 1997b). Thus, this

study describes a different approach to estimating the relative permeability by matching

data from a transient boiling experiment performed on a Berea sandstone to results

obtained from numerical simulation. This method provides a way to examine the validity

of the relative permeability measurements taken from previous experiments, as well as to

estimate capillary pressure.

Although the focus of this research project is relative permeability, capillary pressure has

also been studied. These two parameters cannot be separated from each other since they

are both important in the behavior of multiphase flow in porous media. However, like

relative permeability, capillary pressure in steam-water systems is unknown. This makes

the estimation process more difficult because the higher number of unknowns in the

2

problem. In addition, other unknown parameters, such as heat input and heat losses,

affect the successful estimation of the relative permeability. To decrease the correlation

between the thermal properties and two-phase parameters of interest, the inversion was

performed in two steps. Several relative permeability and capillary pressure models were

used to solve the inverse problem. The function that best matches the observed data

without over-parameterization can be considered the likely scenario.

This report will begin by discussing the concepts of relative permeability, capillary

pressure, and heat and mass transfer. Results of recent relative permeability experiments

will also be discussed. Following this, a brief summary of the relative permeability and

capillary pressure models used in the study will be given. Then a description of the

experimental apparatus and procedures will be given, followed by a discussion of the

steps involved in the numerical simulation. This report will end with an analysis of results

and conclusion of the study.

3

Chapter 2

Review of Related Literature

In this chapter, relative permeability and capillary pressure will be defined in order to

understand their role in mass flow calculations. Since the system being considered is a

boiling system, a discussion of heat transfer will also be included. Finally, two recent

relative permeability experiments will be reviewed to provide a reference for comparison

for the simulation results.

2.1 Relative Permeability and Capillary Pressure

When two fluids are flowing simultaneously in a porous medium, each fluid has its own

effective permeability, kβ (Dake, 1978). The effective permeability is related to the

absolute permeability, k, a property that is independent of the properties of the single-

phase fluid flowing through the porous medium, by the following equation:

k k krβ β= β = l (liquid), g (gas) ………………………………………… (2.1)

where krβ is the relative permeability of the phase, β. The effective permeabilities are

normally expressed as a function of the saturation of each fluid, and their sum is usually

less than the absolute permeability. For single-component two-phase systems (e.g. liquid

and gas phases in water), the liquid would not flow (kl=0) when the liquid saturation, Sl,

is equal to the residual liquid saturation, Slr. Also, when Sl=1, or when the rock is fully

saturated with water, kl=k. Similarly, the gas would not flow (kg=0) when the gas

saturation, Sg=1-Sl, is equal to the residual gas saturation, Sgr. Also, kg=k when Sg=1. In

terms of relative permeability, krl=0 when Sl=Slr, krl=1 when Sl=1, kgr=0 when Sg=Sgr,

and kgr=1 when Sl=1. A simple illustration of the relative permeability as a function of

4

liquid saturation is shown in Figure 2.1. Apart from saturation, other factors can influence

relative permeability or phase distribution in a porous medium. They include matrix (or

pore) structure, history, interfacial tension, wettability, viscosity ratio, and density ratio

(Dullien, 1992; Kaviany, 1995).

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Sl

kr

Slr Sgr

k r l

k rg

Figure 2.1 Relative permeability as a function of liquid saturation.

Incorporating relative permeability in the generalized Darcy’s law (Dullien, 1992),

( ) ( )δ δµ

ρβ

ββ βQ A

kkp g

r/ n =

∇ −

………………………………………………… (2.2)

where Q is the volumetric flow rate, A is the normal cross sectional area of the porous

medium, n is the unit normal vector of surface area A, µβ is the viscosity of β, ∇pβ is the

pressure drop in β across two points in the porous medium, ρβ is the density of β, and g is

the acceleration due to gravity. The pressures pβ in the two phases are related to each

other by the capillary pressure, pc. Hence, if gas is the non-wetting phase and liquid is the

wetting phase, the two pressure gradients are related to each other by the gradient of the

capillary pressure (Leverett, 1941):

5

∇ = ∇ − ∇p p pc g l ……………………………………………………………………. (2.3)

The general expression for calculating the capillary pressure at any given point on an

interface between liquid and gas is given by the Young-Laplace equation

p p pr r

c g l= − = +

σ 1 1

1 2

…………………………………………………...……… (2.4)

where σ is the interfacial tension between the two liquid and gas phases, and r1 and r2 are

the principal radii of curvature at any point on the interface where the pressures in the

liquid and gas are pl and pg, respectively. Some of the more commonly used relative

permeability and capillary pressure models will be discussed in the next chapter.

2.2 Heat and Mass Transfer

For two phases of a single component in porous media, the conservation of energy can be

simplified as

M C T S uR Rl g

1 1= − +=∑( )

,

φ ρ φ ρβ β ββ

…………………………………………….… (2.5)

where φR is the rock porosity, ρR is the rock grain density, CR is the specific heat of the

rock, T is the temperature, Sβ is the saturation of phase β (liquid or gas), and uβ is the

specific internal energy of β. The first term in Equation 2.1 is the energy of the rock, and

the second term is the summation of the energy of the two phases present. The phase

transition, pressure-work, and viscous dissipation terms are neglected since they are small

in liquid-dominated systems in the absence of an adsorbed phase (Garg and Pritchett,

1977). For a multiphase single component system, the conservation of mass is written as

M S Xl g

2 ==∑φ ρ

ββ β β

,

…………………………………………………………….… (2.6)

Pruess and Narasimhan (1985) expressed the energy-balance and mass-balance equations

in integral form. For an arbitrary flow domain, Vn

d

dtM dv F q dv

n nnVV

( ) ( ) ( ).κ κ κ= +∫ ∫∫

Γ

Γn κ=1:heat and κ=2:water …………….. (2.7)

6

The first term on the right-hand side of Equation 2.7 is the flux term, where the heat flux

is

F K T h Fl g

1 = − ∇ −=∑ β β

β ,

…………………………………………………………….. (2.8)

and the mass flux is

F Fl g

2 ==∑ β

β ,

…………………………………………………………………………. (2.9)

The parameter, K, is the heat conductivity of the rock-fluid mixture, and hβ is the specific

enthalpy of water in β. Equation 2.8 includes conductive and convective heat terms only,

neglecting dispersion. The mass flux in each phase is

F kk

X P g D Xβl g

rg va= − ∇ − − ∇

=∑

β

β

ββ β β β β β βµ

ρ ρ δ ρ,

) ….……………………. (2.10)

The last term in Equation 2.10 represents a binary diffusive flux and contributes only to

gas phase flow (Pruess, 1987).

2.3 Previous Work

A wide range of relative permeability relations has been reported. However, only a few

studies on single-component two-phase systems, particularly steam and liquid water

systems, have been done. In the past, attempts to measure the relative permeability of

single-component two-phase flow directly produced questionable results (Sanchez et al,

1980; Verma, 1986; Clossman and Vinegar) since measurement of the liquid saturation

was inaccurate and the assignment of pressure gradient may have been inappropriate

(Ambusso, 1996). Recently, significant improvements in measuring water and steam

saturation and collecting data from steam-water flow experiments were achieved. Results

of the steady-state experiment conducted by Ambusso (1996) on a Berea sandstone

indicated a linear relationship for steam-water relative permeability (Fig. 2.2). In

attempting to repeat these results, Satik (1998) improved the design of the experimental

apparatus. A successful experiment was conducted and steam-water relative permeability

was obtained. These recent results suggest a more curvilinear relationship (Fig. 2.3) that

7

is different from the results obtained by Ambusso (1996) (linear relationship). Satik

(1998) suggested that the difference in the relative permeability obtained from the two

experiments may have been due to permeability effects. Ambusso used a Berea sandstone

with k=600 md, whereas Satik used another Berea sandstone with k=1200 md. Sanchez

(1987) also reported a relative permeability relation similar to Satik’s results.

Nevertheless, variations in results must be expected since the experimental methods and

cores used differ.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Sl

kr

Figure 2.2 Relative permeability obtained by Ambusso (1996).

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Sl

kr

Figure 2.3 Relative permeability obtained by Satik (1998).

8

Chapter 3

Relative Permeability and CapillaryPressure Models

Several semi-empirical relative permeability and capillary pressure relationships have

been proposed by different authors. However, only four relative permeability and four

capillary pressure models are included in this study. These are the linear, Corey, and

Leverett models, and coupled relative permeability and capillary pressure functions, the

Brooks-Corey and van Genuchten models. The selection of the models was based on the

experimental results obtained by Ambusso (1996) and Satik (1998).

3.1 Linear Model

The linear functions comprise the simplest relative permeability (Fig. 3.1) and capillary

pressure model. They are given by

krl increases linearly from 0 to 1 in the range S S Slr l ls≤ ≤ …………………………. (3.1)

krg increases linearly from 0 to 1 in the range S S Sgr g gs≤ ≤ …….………………….. (3.2)

Pcmax increases linearly from S Sl l= =0 1to ………….……….……………………. (3.3)

where krl is the liquid relative permeability, krg is the gas relative permeability, Sl is the

liquid saturation, Slr is the residual liquid saturation or the liquid saturation at krl=0, Sls is

the liquid saturation at krl=1, Sgr is the residual gas saturation or the gas saturation at

krg=0, Sgs is the gas saturation at krg=1, and Pcmax is the maximum capillary pressure.

9

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

S l

kr

k r l

k rg

Figure 3.1 Linear relative permeability.

3.4 Corey Model

The Corey relative permeability functions (Fig. 3.2), obtained in 1954, are given by

k Srl e= 4 ……………………….……………………………………………………. (3.4)

k S Srg e e= − −( ) ( )1 12 2 ………….………………………………………………….. (3.5)

where

S S S S Se l lr lr gr= − − −( ) / ( )1 …….…………………………………………………. (3.6)

These relationships were determined from experiments with a variety of porous rocks that

had a pore size distribution index of around 2, which is a typical value for soil materials

and porous rocks (Corey, 1994).

10

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

S l

kr

k r l

k rg

Figure 3.2 Corey relative permeability.

3.5 Leverett Model

Leverett (1941) defined a reduced capillary pressure function, which was eventually

named Leverett J function by Rose and Bruce (1949) and used for correlating capillary

pressure data. Expressing the Leverett J function in terms of capillary pressure

pc P T Jo= − σ ( ) …………………………………………………………………… (3.7)

where

J S S S= − − − + −1 417 1 2 120 1 1 263 12 3. ( ) . ( ) . ( )* * * ……………………………….. (3.8)

S S S Sl lr lr* ( ) / ( )= − −1 …………………………………………………………….. (3.9)

σ is the surface tension of water and Po is a scale factor. One limitation of the function is

that it cannot account for the individual differences between the pore structures of various

materials since the scale factor, Po=√k/φ, is inadequate (Dullien, 1992).

11

3.2 Brooks-Corey Model

The Brooks-Corey functions (Fig. 3.3), obtained in 1964, are given by

λλ /)32( −= ekrl Sk .........................................……………………………………………. (3.10)

k S Srg ek ek= − − −( ) ( )( )/1 12 2 3λ λ ...........…........…………………………………….…… (3.11)

where

S S S S Sek l lr lr gr= − − −( ) / ( )1 ......…........…………………………………………. (3.12)

and λ is the pore size distribution index. These relationships are simplifications of the

generalized Kozeny-Carman equations and were verified experimentally by Brooks and

Corey (1964), and Laliberte et al. (1966). Brooks and Corey found that for typical porous

media, λ is 2. Soils with well-developed structures have λ values less than 2, and sands

have λ values greater than 2 (Corey, 1994).

The Brooks-Corey capillary pressure function is given by

( )[ ]( ) ( )[ ]( )

p p S

p S S S

c e lr

e lr l lr

= − −

− − − −

−

−

ε

λ ε ε

λ

λ λ

/

/ /

/

( )/

1

1

1

1 for S Sl wr

< +( )ε (3.13)

p p Sc e ec= − −( ) /1 λ for S Sl wr≥ +( )ε (3.14)

where

S S S Sec l lr lr= − −( ) / ( )1 ...................….....………………………………………. (3.15)

and pe is the gas entry pressure. Equations 3.10 and 3.11 are modified Brooks-Corey

equations. To prevent the capillary pressure from increasing to infinity as the effective

saturation approaches zero, a linear function is used for Sl<(Slr+ε), where ε is a small

number (Finsterle, 1997). The Brooks-Corey capillary pressure function has been

modified for numerical simulation purposes.

12

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

S l

kr

k r l

k rg

Figure 3.3 Brooks-Corey relative permeability.

3.3 van Genuchten Model

The van Genuchten relative permeability (Fig. 3.4) and capillary pressure functions are

given by

[ ]k S Srl ek ekm m= − −1 2 1 2

1 1/ /( ( ) ……………………………………………………… (3.16)

[ ]k S Srg ek ekm m

= − −( ) / /1 11 3 1 2………………………………………………………. (3.17)

[ ]p Sc ecm n

= − −−111 1

α( ) / /

for S Sl wr≥ +( )ε (3.18)

pc = linear model with continuos slope at S Sl wr= + ε for S Sl wr< +( )ε (3.19)

where

m = 1 – 1/n …………………………………………………………………………..(3.20)

The parameter, n is analogous to λ, and α is analogous to pe in the Brooks-Corey

functions. Equations 3.15 and 3.16 are modified versions of the van Genuchten equations.

In order to prevent the capillary pressure from going to infinity as the liquid saturation

approaches zero, a linear function is used for Sl<(Slr+ε), where ε is a small number

(Finsterle, 1997).

13

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

S l

kr

k r l

k rg

Figure 3.4 van Genuchten relative permeability.

14

Chapter 4

Experimental Apparatus and Procedure

The vertical boiling experiment considered in this study was conducted by Satik (1997a).

Figure 4.1 shows a schematic diagram of the apparatus, which consists of a core holder, a

data acquisition system, and a balance. A Berea sandstone core was used in the

experiment. The core had a diameter of 5.08 cm, length of 43.2 cm, absolute permeability

of 780 md, and average porosity of 22% (Table 4.1). Before conducting the experiment,

the core was evacuated and then saturated with pre-boiled water to ensure that there was

no air trapped in the pore space. The core was confined in an epoxy core holder to prevent

fluid from leaking and insulated with a 5.08-cm thick fiber blanket to minimize heat

losses in the radial direction. The heater was attached to the bottom of the core, and was

insulated with ceramic fiberboard. During the experiment, the heating end of the core was

closed to fluid flow while the opposite end was connected to a water reservoir placed on a

balance. The balance was used to monitor the amount of water coming out of the core

during the boiling process (Fig. 4.1).

Figure 4.1. Schematic diagram of the experimental apparatus (after Satik, 1997b).

15

During the experiment, pressure was measured in the core using pressure transducers at

11 locations along the core. Temperature was measured between the epoxy and core

insulation using thermocouples that were located at the same points as the pressure

transducers. In previous experiments, Satik (1997b) found out that the maximum

difference between the temperature in the center of the core and the wall temperature was

less than 2oC. This suggested that the radial temperature gradient along the core was not

significant under these experimental conditions and therefore it would be adequate to

measure wall temperatures only. Similarly, heat flux was measured between the epoxy

and core insulation and at the inlet end of the core holder. Steam saturation was measured

at every 1-cm increment along the core using a CT scanner. The heat flow rate was

increased every time steady-state flow conditions had been reached. At each heat flow

rate increase, steady state conditions were observed when the water production rate

became zero, and the pressure, temperature, and heat flux measurements stabilized during

boiling. Results showed that boiling occurred 118 hours after the start of the experiment

that lasted for 169.5 hours (Figs 4.2-4.5). In the plots shown, T1, P1, Sst1, and H1 are

temperature, pressure, steam saturation, and heat flux data measured at sensor 1 (1 cm

from the heater), T2, P2, Sst2, and H2 are data observed at sensor 2 (5 cm from the

heater), etc.

Table 4.1. Physical properties of the cores, epoxy, core insulation, and heater insulation.

Material φ

%

k

10-15 m2

α

W/m-oC

C

J/kg-oC

ρ

kg/m3

Berea 22 780 4.326 858.2 2163

Epoxy 2.885 1046.6 1200

Core insulation 0.055 104.7 192

Heater insulation 0.065 1046.6 240

16

20

30

40

50

60

70

80

90

100

110

0 25 50 75 100 125 150 175Tim e , hours

Tem

per

atu

re, C

T 1

T 2

T 3

T 4

T 5

T 6

T 7

T 8

T 9

T 10

T 11

Figure 4.2 Experimental temperature data.

15

20

25

30

0 25 50 75 100 125 150 175

T im e , h o u r s

Pre

ss

ure

, k

Pa

P 1

P 2

P 3

P 4

P 5

P 6

P 7

P 8

P 9

P 1 0

P 1 1

Figure 4.3 Experimental pressure data.

17

Figure 4.4 Experimental steam saturation data.

0

50

100

150

200

250

300

350

400

450

0 25 50 75 100 125 150 175Tim e, hours

Hea

t F

lux,

W/m

^2

H F 1

H F 2

H F 3

H F 4

H F 5

H F 6

H F 7

H F 8

H F 9

H F 10

H F 11

Figure 4.5 Experimental heat flux data.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 25 50 75 100 125 150 175

T im e , hours

Ste

am

Sa

tura

tio

n

S s t 1

S s t 2

S s t 3

S s t 4

S s t 5

S s t 6

S s t 7

S s t 8

S s t 9

S s t 1 0

S s t 1 1

18

Chapter 5

Numerical Simulation

Numerical simulation provides a method to visualize or predict the performance of a

system under certain operating conditions. For heat and fluid flow in porous media, the

number and type of equations to be solved depend on the rock properties, characteristics

of the fluids, and process to be modeled. The independent primary variables that

completely define the thermodynamic state of the flow system are pressure, temperature,

and air mass fraction in single-phase flow, and they are temperature, pressure, and gas

saturation in two-phase flow (Pruess, 1987).

In this chapter, the steps involved in modeling the vertical boiling experiment described

in the previous chapter and estimating the two-phase parameters will be discussed. These

steps include constructing a model, and carrying out forward and inverse calculations.

5.1 Model

A two-dimensional radial model of the vertical boiling experiment was constructed in

TOUGH2, a numerical model for simulating the transport of water, steam, air, and heat in

porous and fractured media (Pruess, 1991). The model has four concentric rings and 51

layers, where ring 1 is the innermost ring and layer 1 is the topmost layer (Fig. 5.1). From

layer 1 to layer 44, ring 1 represents the core, ring 2 represents the epoxy, and ring 3

represents the core insulation. Layer 45 in ring 1 is the designated heater grid block, and it

is further divided into five smaller elements to discretize the heat flow rate. Rings 2-3 in

layer 45 represent the epoxy and core insulation, respectively. Layers 46-50, rings 1-3 are

19

core insulation elements. Constant pressure boundary conditions were applied to all rings

in layer 1 to maintain initial conditions at the top of the core, and to simulate water

flowing out from the top of the core during the boiling process. The pressure at the

boundary was equal to the measured pressure at the top end of the core. To model heat

loss to the surroundings, ambient conditions were applied to all elements in ring 4 and

layer 51. Grid blocks associated with constant pressure boundary and ambient conditions

had very large volumes to ensure that their thermodynamic states remained constant in a

simulation. An absolute permeability value was assigned only in the vertical direction

since fluid did not flow out in the radial direction. Initially, each grid block was at

atmospheric temperature and pressure.

Figure 5.2 shows the input file used to generate the elements and the connection between

elements for the first experiment. RZ2D invokes generation of a radially symmetric mesh.

The RADII record gives the radius (cm) of each element (sandstone, epoxy, core

insulation, and air), while the LAYER record gives the thickness (cm) of each layer

(sandstone, heater, heater insulation, and air). The last entries in RADII and LAYER are

much larger than the previous entries because they constitute the ambient grid blocks.

Figure 5.1. Schematic diagram of the 4×51 TOUGH2 model. Ring 4 is not shown sinceit represents ambient conditions.

20

MESHMAKER1----*----2----*----3----*----4----*----5----*----6----*----7----*-----8RZ2DRADII 5 0 0.0254 0.0304 0.0812 5.0812LAYER---------1----*----2----*----3----*----4----*----5----*----6----*----7----*-----8 51 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0050 0.0100 0.0100 0.0100 0.0100 0.0100 5.0000

ENDFILE

Figure 5.2. ITOUGH2 input used to generate the elements and connections.

5.2 Forward Calculation

5.2.1 Input Data

After constructing the grid blocks, simulations were carried out. The following input data

were required in the calculations:

a. properties of the material

i. density

ii. porosity

iii. permeability

iv. thermal conductivity under saturated and desaturated conditions

v. specific heat

vi. compressibility

vii. expansivity

viii. tortuosity

ix. factor for binary diffusion

21

b. process

i. heat injection rate

ii. duration

c. relative permeability relation

i. parameters

d. capillary pressure relation

i. parameters

e. gravity effects

f. initial conditions

i. temperature

ii. pressure

iii. air fraction

g. boundary conditions

i. pressure

ii. temperature

iii. gravity effect

h. computation parameters

5.2.2 Sensitivity Analysis

A sensitivity analysis was carried out in order to make reasonable initial guesses for the

different parameters of interest and to better understand the system behavior. It was

necessary to decouple the thermal parameters from the hydrogeologic parameters since

the production of steam from liquid water in the experiments was highly dependent on the

thermal properties of the materials and heat source. Thus, the thermal properties were

studied under single-phase liquid conditions, while the hydrogeologic properties were

studied under two-phase conditions.

Under single-phase liquid conditions, only temperature and heat flux were used to

determine the effects of the thermal conductivity of each material. Temperature and heat

flux profiles (with respect to the distance from the core) at five different times were

22

generated for a base scenario (Fig. 5.3). These were compared with results obtained from

changing the thermal conductivity of each material one at a time. At lower values of the

thermal conductivity of the sandstone, αs, the temperature and heat flux at the heating end

of the core were slightly greater than at higher values of αs (Figs. 5.3 and 5.4). However,

the temperature and heat flux profiles look almost identical at points farther away from

the heater. If the heat input were greater, the effects of variations in αs would not have

been localized in areas close to the heater only. At lower values of the thermal

conductivity of the base insulation, αb, the temperature and heat flux were greater (Figs.

5.3 and 5.5). The profiles become almost identical at points beyond 15 cm from the

heater. At higher values of the thermal conductivity of the heater insulation, αi, the

temperature was less than at lower values of αi. On other hand, heat flux through the core

wall increased with increasing αi (Figs. 5.3 and 5.6). The temperature and heat flux

profiles show that the system is highly sensitive to variations in αi since changes in

temperature and heat flux were observed in the entire length of the core. Changes in

temperature and heat were not observed as the thermal conductivity values of the epoxy

or heater was varied. Thus, the temperature and heat flux are most sensitive to changes in

αi, followed by αb, then by αs.

Under two-phase conditions, effects of variations in the parameters on temperature,

pressure, steam saturation, and heat flux were studied. However, only the first three

observation types are shown and discussed since the heat flux behaved like the

temperature. Hence, when temperature increased, heat flux at the same point also

increased. Six cases were considered for study: 1) linear relative permeability and

capillary pressure, 2) Corey relative permeability and linear capillary pressure, 3) linear

relative permeability and Leverett capillary pressure, 4) Corey relative permeability and

Leverett capillary pressure, 5) Brooks-Corey relative permeability and capillary pressure,

and 6) van Genuchten relative permeability and capillary pressure.

23

In the linear relative permeability and capillary pressure case, the parameters of interest

were Slr, Sls, Sgr, Sgs, and Pcmax. Figure 5.7 shows a base case for this analysis. Varying Slr

or Sls did not affect the temperature, pressure, and steam saturation distribution in the

two-phase region. The pressure and steam saturation decreased, but the temperature was

not significantly affected, with decreasing Sgr, or Sgs (Figs. 5.8-5.9). The effects of varying

Sgs, however, were not as significant as changing Sgr in the propagation of steam in the

core. The temperature increased considerably in the heating end of the core, but decreased

in the two-phase region with decreasing capillary pressure (Fig. 5.10). Also, the saturation

increased and the pressure decreased significantly with decreasing capillary pressure. The

sudden increase in temperature in the heating end of the core was due to the fact that

superheated steam was present, while the lower temperature in the two-phase region was

due to the lower steam pressure resulting from reduced capillary pressure.

In the Corey relative permeability and linear capillary pressure case, the parameters were

Slr, Sgr, and Pcmax. A base case is shown in Figure 5.11. Results of the sensitivity analysis

showed that the temperature, steam saturation and pressure increased in the two-phase

region with decreasing Slr (Fig. 5.12) On the other hand, the temperature, steam

saturation, and pressure decreased with decreasing Sgr (Fig. 5.13). The effects of varying

Sgr, however, were more significant than the effects of varying Slr. In the two-phase

region, the temperature, pressure, and steam saturation decreased as Pcmax was reduced

(Fig. 5.14). Also, single-phase steam was formed in the heating end of the core as Pcmax

was decreased. Not surprisingly, the two-phase isothermal region shortened with

decreasing capillary pressure since there was less steam pressure to displace the liquid

water.

There were four unknowns considered in the Corey relative permeability and Leverett

capillary pressure case. They were Slr (related to the relative permeability function), Sgr,

Po, and Slr (related to the capillary pressure function). Figure 5.15 shows a base scenario.

As in the previous case, temperature, steam saturation and pressure slightly increased in

the two-phase region with decreasing Slr (relative permeability) (Fig 5.16), and decreased

24

with decreasing Sgr (Fig. 5.17). In the two-phase region, temperature and pressure

decreased while steam saturation increased with decreasing Po (Fig. 5.18). Furthermore,

single-phase steam was formed at the heating end of the core as Po was reduced. The two-

phase region was suppressed as Po was decreased. Pressure and steam saturation slightly

decreased with decreasing Slr (capillary pressure), although temperature remained

constant (Fig. 5.19).

The six unknown parameters considered in the linear relative permeability and Leverett

capillary pressure case were Slr (relative permeability), Sgr, Sls, Sgs, Po, and Sls (capillary

pressure). A base case is shown in Figure 5.20. Results of the sensitivity analysis showed

that variations in Slr and Sls did not have any effect on the temperature, pressure, and

steam saturation. Pressure and steam saturation declined with decreasing Sgr or Sgs (Figs.

5.21 and 5.22). However, temperature remained unchanged. In the two-phase region,

temperature, pressure, and steam saturation decreased, while a superheated steam region

at the heating end of the core was formed as Po was reduced (Fig. 5.23). As in the

previous case, the propagation of steam was deterred by reduced capillary pressure.

Decreasing Slr (capillary pressure) slightly reduced the pressure and increased the

saturation, while keeping the temperature constant (Fig. 5.24).

In the Brooks-Corey model the unknowns were Slr, Sgr, λ, and pe. A base scenario is

shown in Figure 5.25. The temperature, pressure, and steam saturation rose in the two-

phase region with decreasing Slr (Fig. 5.26) but decreased with declining Sgr (Fig. 5.27).

Reducing λ increased the temperature, pressure, and steam saturation in the two-phase

region (Fig 5.28). Due to the more even distribution of pore size, the rate of increase in

steam saturation is faster. Decreasing pe increased the temperature and decreased the

pressure (Fig. 5.29). However, the steam formed at the heating end of the core was not

propagated much farther away from the heater due to reduced capillary pressure.

Finally, the four parameters considered in the van Genuchten model were Slr, Sgr, n, and

1/α. A base scenario is shown in Figure 5.30. The temperature, pressure, and steam

25

saturation decreased in the two-phase region as Slr was reduced (Fig. 5.31). Similarly, the

pressure and steam saturation decreased with declining Sgr (Fig. 5.32). However, the

temperature remained constant. The temperature and steam saturation decreased while the

pressure increased as n decreased or 1/α increased (Fig. 5.33). Reduced capillary pressure

enhanced formation of superheated steam at the heating end of the core.

To summarize, the sensitivity analysis showed that temperature and heat flux were

dependent on the heat losses from the heater, sandstone, and insulation materials under

single-phase liquid conditions. Hydrogeologic parameters affected the system only when

two-phase conditions existed. They determined the temperature, pressure, and saturation

distribution within the core, and the upward propagation of steam. The observations made

in the experiments were more sensitive to the steam relative permeability than to the

liquid relative permeability.

26

0

10

20

30

40

50

60

70

80

90

0 5 10 15 20 25 30 35 40 45

15 hrs

24 hrs

47 hrs

72 hrs

98 hrs

Dis tance from the He ater , cm

Te

mp

era

ture

, C

0

50

100

150

200

250

300

0 5 10 15 20 25 30 35 40 45

15 hrs

24 hrs

47 hrs

72 hrs

98 hrs

Dis tance from the He ate r , cm

He

at

Flu

x,

W/m

^2

Figure 5.3 Base scenario: αs=4.930 W/m2, αb=0.150 W/m2, αi=0.115 W/m2, αh=2.885W/m2 and αe=0.577 W/m2.

27

0

10

20

30

40

50

60

70

80

90

0 5 10 15 20 25 30 35 40 45

15 hrs

24 hrs

47 hrs

72 hrs

98 hrs

Dis tance from the Heater, cm

Te

mp

era

ture

, C

0

50

100

150

200

250

300

0 5 10 15 20 25 30 35 40 45

15 hrs

24 hrs

47 hrs

72 hrs

98 hrs


He

at

Flu

x,

W/m

^2

Figure 5.4 αs=4.300 W/m2, αb=0.150 W/m2, αi=0.115 W/m2, αh=2.885 W/m2 andαe=0.577 W/m2.

28

0

10

20

30

40

50

60

70

80

90

0 5 10 15 20 25 30 35 40 45

15 hrs

24 hrs

47 hrs

72 hrs

98 hrs


Te

mp

era

ture

, C

0

50

100

150

200

250

300

0 5 10 15 20 25 30 35 40 45

15 hrs

24 hrs

47 hrs

72 hrs

98 hrs


He

at

Flu

x,

W/m

^2


29

0

10

20

30

40

50

60

70

80

0 5 10 15 20 25 30 35 40 45

15 hrs

24 hrs

47 hrs

72 hrs

98 hrs


Te

mp

era

ture

, C

0

50

100

150

200

250

300

0 5 10 15 20 25 30 35 40 45

15 hrs

24 hrs

47 hrs

72 hrs

98 hrs


He

at

Flu

x,

W/m

^2


30

0

20

40

60

80

100

120

0 5 10 15 20 25 30 35 40 45

127 hrs

146 hrs

168 hrs

Dis tance from the He ate r, cm

Te

mp

era

ture

, C

0

10

20

30

40

50

60

70

0 5 10 15 20 25 30 35 40 45

127 hrs

146 hrs

168 hrs


Pre

ss

ure

, k

Pa

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25 30 35 40 45

127 hrs

146 hrs

168 hrs


Ste

am

Sa

tura

tio

n

Figure 5.7 Base case linear model: Slr=0.20, Sgr=0.20, Sls=0.80, Sgs=0.80, Pcmax=105 Pa

31

0

20

40

60

80

100

120

0 5 10 15 20 25 30 35 40 45

127 hrs

146 hrs

168 hrs


Te

mp

era

ture

, C

0

10

20

30

40

50

60

70

0 5 10 15 20 25 30 35 40 45

127 hrs

146 hrs

168 hrs


Pre

ss

ure

, k

Pa

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25 30 35 40 45

127 hrs

146 hrs

168 hrs


Ste

am

Sa

tura

tio

n

Figure 5.8 Linear model: Slr=0.02, Sgr=0.10, Sls=0.80, Sgs=0.80, Pcmax=105 Pa.

32

0

20

40

60

80

100

120

0 5 10 15 20 25 30 35 40 45

127 hrs

146 hrs

168 hrs


Te

mp

era

ture

, C

0

10

20

30

40

50

60

70

0 5 10 15 20 25 30 35 40 45

127 hrs

146 hrs

168 hrs


Pre

ss

ure

, k

Pa

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25 30 35 40 45

127 hrs

146 hrs

168 hrs


Ste

am

Sa

tura

tio

n

Figure 5.9 Linear model: Slr=0.02, Sgr=0.20, Sls=0.80, Sgs=0.70, Pcmax=105 Pa

33

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30 35 40 45

127 hrs

146 hrs

168 hrs


Te

mp

era

ture

, C

0

10

20

30

40

50

60

70

0 5 10 15 20 25 30 35 40 45

127 hrs

146 hrs

168 hrs


Pre

ss

ure

, k

Pa

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25 30 35 40 45

127 hrs

146 hrs

168 hrs


Ste

am

Sa

tura

tio

n

Figure 5.10 Linear model: Slr=0.02, Sgr=0.20, Sls=0.80, Sgs=0.80, Pcmax=104 Pa.

34

0

20

40

60

80

100

120

0 5 10 15 20 25 30 35 40 45

127 hrs

146 hrs

168 hrs


Te

mp

era

ture

, C

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40 45

127 hrs

146 hrs

168 hrs


Pre

ss

ure

, k

Pa

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25 30 35 40 45

127 hrs

146 hrs

168 hrs


Ste

am

Sa

tura

tio

n

Figure 5.11 Base case: Corey relative permeability and linear capillary model: Slr=0.20,Sgr=0.20, Pcmax=105 Pa.

35

0

20

40

60

80

100

120

0 5 10 15 20 25 30 35 40 45

127 hrs

146 hrs

168 hrs


Te

mp

era

ture

, C

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40 45

127 hrs

146 hrs

168 hrs


Pre

ss

ure

, k

Pa

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25 30 35 40 45

127 hrs

146 hrs

168 hrs


Ste

am

Sa

tura

tio

n

Figure 5.12 Corey relative permeability and linear capillary model: Slr=0.10, Sgr=0.20, Pcmax=105 Pa.

36

0

20

40

60

80

100

120

0 5 10 15 20 25 30 35 40 45

127 hrs

146 hrs

168 hrs


Te

mp

era

ture

, C

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40 45

127 hrs

146 hrs

168 hrs


Pre

ss

ure

, k

Pa

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25 30 35 40 45

127 hrs

146 hrs

168 hrs

Dis tance fr om the He ate r , cm

Ste

am

Sa

tura

tio

n

Figure 5.13 Corey relative permeability and linear capillary model: Slr=0.20, Sgr=0.10,Pcmax=105 Pa.

37

0

50

100

150

200

250

300

0 5 10 15 20 25 30 35 40 45

127 hrs

146 hrs

168 hrs


Te

mp

era

ture

, C

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40 45

127 hrs

146 hrs

168 hrs


Pre

ss

ure

, k

Pa

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25 30 35 40 45

127 hrs

146 hrs

168 hrs


Ste

am

Sa

tura

tio

n

Figure 5.14 Corey relative permeability and linear capillary model: Slr=0.20, Sgr=0.20,Pcmax=104 Pa.

38

0

20

40

60

80

100

120

0 5 10 15 20 25 30 35 40 45

127 hrs

146 hrs

168 hrs

Distance from the He ater, cm

Te

mp

era

ture

, C

0

10

20

30

0 5 10 15 20 25 30 35 40 45

127 hrs

146 hrs

168 hrs

Distance from the Heater, cm

Pre

ss

ure

, k

Pa

0

0.1

0.2

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0.7

0.8

0.9

1

0 5 10 15 20 25 30 35 40 45

127 hrs

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Ste

am

Sa

tura

tio

n

Figure 5.15 Base case: Corey relative permeability and Leverett capillary pressure:Slr(RP)=0.20, Sgr=0.20, Po=105. Slr (CP)=0.20.

39

0

20

40

60

80

100

120

0 5 10 15 20 25 30 35 40 45

127 hrs

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Dis tance from the He ater, cm

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mp

era

ture

, C

0

10

20

30

0 5 10 15 20 25 30 35 40 45

127 hrs

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168 hrs

Dis tance from the Heate r, cm

Pre

ss

ure

, k

Pa

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0.1

0.2

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0.7

0.8

0.9

1

0 5 10 15 20 25 30 35 40 45

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168 hrs


Ste

am

Sa

tura

tio

n

Figure 5.16 Corey relative permeability and Leverett capillary pressure: Slr(RP)=0.10,Sgr=0.20, Po=105. Slr (CP)=0.20.

40

0

20

40

60

80

100

120

0 5 10 15 20 25 30 35 40 45

127 hrs

146 hrs

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Te

mp

era

ture

, C

0

10

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30

0 5 10 15 20 25 30 35 40 45

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ss

ure

, k

Pa

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0.1

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0.7

0.8

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1

0 5 10 15 20 25 30 35 40 45

127 hrs

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168 hrs


Ste

am

Sa

tura

tio

n

Figure 5.17 Corey relative permeability and Leverett capillary pressure: Slr(RP)=0.20,Sgr=0.10, Po=105. Slr (CP)=0.20.

41

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30 35 40 45

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Te

mp

era

ture

, C

0

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ss

ure

, k

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0.8

0.9

1

0 5 10 15 20 25 30 35 40 45

127 hrs

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168 hrs


Ste

am

Sa

tura

tio

n

Figure 5.18 Corey relative permeability and Leverett capillary pressure: Slr(RP)=0.20,Sgr=0.20, Po=104, Slr (CP)=0.20.

42

0

20

40

60

80

100

120

0 5 10 15 20 25 30 35 40 45

127 hrs

146 hrs

168 hrs


Te

mp

era

ture

, C

0

10

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30

0 5 10 15 20 25 30 35 40 45

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ss

ure

, k

Pa

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0.1

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0.7

0.8

0.9

1

0 5 10 15 20 25 30 35 40 45

127 hrs

146 hrs

168 hrs


Ste

am

Sa

tura

tio

n

Figure 5.19 Corey relative permeability and Leverett capillary pressure: Slr(RP)=0.20,Sgr=0.20, Po=105, Slr (CP)=0.10.

43

0

20

40

60

80

100

120

0 5 10 15 20 25 30 35 40 45

127 hrs

146 hrs

168 hrs


Te

mp

era

ture

, C

0

10

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30

0 5 10 15 20 25 30 35 40 45

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ss

ure

, k

Pa

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0.7

0.8

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1

0 5 10 15 20 25 30 35 40 45

127 hrs

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168 hrs


Ste

am

Sa

tura

tio

n

Figure 5.20 Base case: Linear relative permeability and Leverett capillary pressure:Slr(RP)=0.20, Sgr=0.20, Sls=0.80, Sgs=0.80, Po=105, Slr (CP)=0.20.

44

0

20

40

60

80

100

120

0 5 10 15 20 25 30 35 40 45

127 hrs

146 hrs

168 hrs


Te

mp

era

ture

, C

0

10

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30

0 5 10 15 20 25 30 35 40 45

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ss

ure

, k

Pa

0

0.1

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0.3

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0.7

0.8

0.9

1

0 5 10 15 20 25 30 35 40 45

127 hrs

146 hrs

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Ste

am

Sa

tura

tio

n

Figure 5.21 Linear relative permeability and Leverett capillary pressure: Slr(RP)=0.20,Sgr=0.10, Sls=0.80, Sgs=0.80, Po=105, Slr (CP)=0.20

45

0

20

40

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120

0 5 10 15 20 25 30 35 40 45

127 hrs

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era

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, C

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, k

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46

0

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, C

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47

0

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, C

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ure

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48

0

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0 5 10 15 20 25 30 35 40 45

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mp

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, C

0

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, k

Pa

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0 5 10 15 20 25 30 35 40 45

127 hrs

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168 hrs

Dis tance from the Heate r , cm

Ste

am

Sa

tura

tio

n

Figure 5.25 Base case: Brooks-Corey model: Slr=0.20, Sgr=0.20, λ=2.0, pe=2000 Pa

49

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30 35 40 45

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Te

mp

era

ture

, C

0

10

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30

0 5 10 15 20 25 30 35 40 45

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ss

ure

, k

Pa

0

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0.7

0.8

0.9

1

0 5 10 15 20 25 30 35 40 45

127 hrs

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Ste

am

Sa

tura

tio

n

Figure 5.26 Brooks-Corey model: Slr=0.10, Sgr=0.20, λ=2.0, pe=2000 Pa

50

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30 35 40 45

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mp

era

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, C

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ure

, k

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51

0

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, C

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52

0

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, C

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ure

, k

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53

0

50

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mp

era

ture

, C

0

10

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40

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ure

, k

Pa

0

0.1

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0.7

0.8

0.9

1

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Ste

am

Sa

tura

tio

n

Figure 5.30 Base case van Genucthen model: Slr=0.2, Sgr=0.2, n=2.0, 1/α=500

54

0

50

100

150

200

0 5 10 15 20 25 30 35 40 45

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Te

mp

era

ture

, C

0

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ure

, k

Pa

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0.8

0.9

1

0 5 10 15 20 25 30 35 40 45

127 hrs

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Ste

am

Sa

tura

tio

n

Figure 5.31 van Genucthen: Slr=0.1, Sgr=0.2, n=2.0, 1/α=500

55

0

50

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0 5 10 15 20 25 30 35 40 45

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era

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, C

0

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56

0

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57

0

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, C

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58

5.2.3 Initial Guesses

To avoid time consuming inverse calculations, forward calculations were carried out and

initial guesses were made. The initial guesses for αs, αi, and αb were estimated by trial-

and error, by changing each parameter one at a time. A rough fit of the temperature and

heat flux data under single-phase conditions were obtained at αs=4.930 W/m-C, αi=0.150

W/m-C, and αb=0.115 W/m-C, indicating heat losses. The linear relative permeability

initial guesses were taken from the results obtained by Ambussso (1996). They are:

Slr=0.30, Sgr=0.10, Sls=0.80 and Sgs=0.80. On the other hand, the initial guesses for the

Brooks-Corey relative permeability parameters were obtained by trial-and-error, based on

Satik’s results (1998). Slr=0.3, Sgr=0.1, and λ=1.5. For the Corey and van Genuchten

relative permeability functions, the initial guesses for the residual saturations in the

Brooks-Corey functions were used. Finally, the initial guesses for Pcmax, pe, po, and 1/α

were at 105 Pa, 2000 Pa, and 105, and 500 Pa, respectively.

5.3 Parameter Estimation

This section will briefly discuss the inverse modeling process. Also, the various steps

involved in estimating the thermal parameters and two-phase parameters using the

different relative permeability and capillary pressure models will be outlined. Finally,

results of the inverse calculation will be discussed.

5.3.1 Inverse Modeling

ITOUGH2 (Finsterle, 1997) provides inverse modeling capabilities for the TOUGH2

codes and solves the inverse problem by automatic model calibration based on the

maximum likelihood approach. Figure 5.35 shows a flow chart of the inverse modeling

process. TOUGH2 solves the forward problem and submits the results to ITOUGH2

during the calibration phase, when simulated data are compared with real data and the

59

weighted difference between them is minimized. A higher accuracy of the model

prediction can be achieved by a combined inversion of all available data since the

different data types contribute to parameter estimation in different degrees (Finsterle et al,

1997). In this study, the observation data used were temperature, pressure, steam

saturation, and heat flux. To obtain an aggregate measure of deviation between the

observed and calculated system response, an objective function is introduced. In this case,

the objective function is based on the standard weighting least square criterion, and it is

given by

S CTzz= −r r1 ………………………………………………………………………. (5.1)

where r is the residual vector with elements ri = zi* - zi(p), zi

* is an observation

(temperature, pressure, steam saturation, or heat flux) at a given point in time, zi is the

corresponding prediction that depends on the unknown parameters vector p, and Czz is the

covariance matrix. The ith diagonal element of Czz is the variance representing the

measurement error. The objective function is minimized to be able to reproduce the

observed system behavior more accurately. One way to reduce the objective function is

to update p repeatedly to overcome the nonlinearity in zi(p). Finally a detailed error

analysis of the final residuals and the estimated parameters is conducted, under the

assumption of normality and linearity (Finsterle et al., 1998). To compare the competing

models, the a posteriori variance so2, a goodness-of-fit measure, was used as a basis. It is

given by

sM No

Tyy2

1

=−

−r C r ……………………………………………………………………. (5.2)

where M is the number of observations, and N is the number of parameters.

In preparing the ITOUGH2 input file, various information was required to describe the

unknown parameters, measured data, and computational data. Successful inverse

calculations depend on the data provided both in the TOUGH2 and ITOUGH2 input files.

Details of the TOUGH2 file format can be found in Pruess (1987) and Pruess (1991), and

details of the ITOUGH input file format can be found in Finsterle (1997).

60

priorinformation

updatedparameter

modeltrue

systemresponse

stopping criteria

measured system

response

calculated system

response

minimizationalgorithm

objective function

bestestimate

maximumlikelihood

erroranalysis

uncertaintypropagation

analysis

Figure 5.35 Inverse modeling flow chart (after Finsterle et al., 1998).

5.3.2 Results and Discussion

To reduce the correlation between parameters, the estimation process was divided into

two parts: single-phase and two-phase periods. As already demonstrated in Section 5.2.2,

thermal properties must be estimated in the absence of boiling, and hydrogeologic

parameters must be estimated under two-phase conditions. In the first half of the

parameter estimation process, the heat flow rates (measured at five heat changes) H2-H6

were included with αs, αi, and αb. The numerical model was calibrated against

temperature and heat flux only since there were no pressure gradient and steam present.

All temperature and heat flux data sets measured at 11 locations along the core were used

61

in the single-phase period calibration. The TOUGH2 and ITOUGH2 input files for this

process are found in Appendix A.1.

The standard deviation values given in Table 5.1 reflect the uncertainty associated with

the measurement errors. For heat flux, it is the standard deviation of the measured data

only at Sensor 1, where the measurement uncertainty is larger than at any other

observation point. The standard deviation at all other observation points was 10 W/m2.

Table 5.2 shows a summary of the estimated parameter set. The covariance and

correlation matrices are given in Table 5.3, where the diagonal elements give the square

of the standard deviation of the parameter estimate, σp. σp takes into account the

uncertainty of the parameter itself and the influence from correlated parameters. In Table

5.4, the conditional standard deviation, σp* reflects the uncertainty of one parameter if all

the other parameters are known. Hence, σp*/σp (column 3) is a measure of how

independently a parameter can be estimated. A value close to one denotes an independent

estimate, while a small value denotes strong correlation to other uncertain parameters.

The total parameter sensitivity (column 4) is the sum of the absolute values of the

sensitivity coefficients, weighted by the inverse of individual measurement errors and

scaled by a parameter variation (Finsterle et al, 1997). As shown in Table 5.4, αi and αb

are the most sensitive parameters. Except for H2 and H3, and perhaps H4, all parameters

cannot be determined independently because they are correlated to one or more of the

other parameters.

Table 5.1. Observation used for model calibration.

Data Type Standard Deviation

Temperature 1 oC

Pressure 1000 Pa

Steam Saturation 0.01

Heat Flux 20 W/m2

62

Table 5.2 Parameter estimates after single-phase calibration period.

Parameter Initial Guess Best Estimate

αs, W/m-C 4.930 4.989

αι, W/m-C 0.115 0.115

αb, W/m-C 0.150 0.163

H2, W 0.234 0.190

H3, W 0.515 0.464

H4, W 0.972 0.994

H5, W 1.240 1.345

H6, W 1.510 1.679

Table 5.5 gives the statistical parameters related to the residuals. Comparing the total

sensitivity of the two observation types, accurate measurements of temperature are

sufficient to solve the inverse problem, i.e. heat flux data are much less sensitive. Also,

the standard deviation values of the final residual are of the same order of magnitude as

the measurement errors (Table 5.1). However, in the heat flux match in Figure 5.37, the

random scattering around the diagonal line suggests that the matches to the individual

sensors are not optimal in the least-square sense. The vertical distance of the symbol to

the diagonal line represents the residual. The heat flux data show a systematic over- or

under-prediction. Since this pattern is not observed in the temperature data (Figure 5.36),

it is suspected that the heat flux sensors exhibit systematic trends. Moreover, the

contribution of each observation type to the final value of the objective function (COF) is

evenly distributed between temperature and heat flux, indicating that the choice of

weighting factor is reasonable (Table 5.5). Although the a posteriori variance of 3 is not

so much greater than one, the match could be improved by discarding some data,

specifically at Sensor 1. The data at this location dominated the inverse calculation

process that the estimates were such that they reflect more the observation at the boiling

front, rather than the average two-phase condition in the core. Results of eliminating

Sensor 1 data will be shown and analyzed later in this section.

63

Table 5.3 Variance-covariance matrix (diagonal and lower triangle) and correlationmatrix (upper triangle) after single-phase period calibration.

αs αb αI H2 H3 H4 H5 H6

αs 1.37E-02 -3.87E-01 5.15E-01 1.25E-01 2.83E-01 5.42E-01 6.31E-01 6.49E-01

αb -1.32E-04 8.51E-06 -7.36E-01 -2.83E-01 -2.02E-01 -2.58E-01 -3.10E-01 -3.15E-01

αi 9.00E-05 -3.20E-06 2.23E-06 1.25E-01 2.77E-01 5.27E-01 6.18E-01 6.27E-01

H2 1.43E-04 -8.05E-06 1.81E-06 9.50E-05 -1.07E-02 3.70E-02 4.12E-02 4.26E-02

H3 3.27E-04 -5.80E-06 4.07E-06 -1.03E-06 9.73E-05 1.32E-01 2.35E-01 2.37E-01

H4 7.27E-04 -8.61E-06 8.99E-06 4.12E-06 1.49E-05 1.31E-04 4.61E-01 4.95E-01

H5 1.01E-03 -1.23E-05 1.25E-05 5.46E-06 3.15E-05 7.17E-05 1.85E-04 5.58E-01

H6 1.27E-03 -1.53E-05 1.56E-05 6.90E-06 3.89E-05 9.43E-05 1.26E-04 2.77E-04

Table 5.4 Statistical measures and parameter sensitivity after single-phase periodcalibration.

Parameter σ σ*/σ Parameter Sensitivity

αs 0.1172 0.6150 340

αb 0.0029 0.5716 11872

αi 0.0015 0.4380 43367

H2 0.0097 0.9468 1726

H3 0.0099 0.9410 1787

H4 0.0114 0.7604 1971

H5 0.0136 0.6602 1770

H6 0.0166 0.6415 1198

64

Table 5.5 Total sensitivity of observation, standard deviation of residuals, andcontribution to the objective function (COF) after single-phase periodcalibration.

Sensitivity Standard

Deviation

COF

%

Temperature 2129 1.8 53.86

Heat Flux 567 16.6 45.93

0

20

40

60

80

100

0 20 40 60 80 100

T1

T2

T3

T4

T5

T6

T7

T8

T9

T10

T11

M e as ure d Te m pe rature , C

Ca

lcu

late

d T

em

pe

ratu

re,

C

Figure 5.36 Measured and calculated temperature after single-phase period calibration.

0

50

100

150

200

250

300

350

0 50 100 150 200 250 300 350

HF1

HF2

HF3

HF4

HF5

HF6

HF7

HF8

HF9

HF10

HF11

M e as ure d He at Flux, W/m ^2

Ca

lcu

late

d H

ea

t F

lux

, W

/m^

2

Figure 5.37 Measured and calculated heat flux after single-phase period calibration.

65

In the second part of the estimation process, the model was calibrated against

temperature, pressure, steam saturation, and heat flux to estimate permeability,

parameters of the different relative permeability and capillary pressure functions, and heat

rate (H7 and H8) at the heat changes during the two-phase period. As observed in the first

half of the estimation process, the heat rate estimates do not indicate a trend that only a

fraction of the heat was actually going into the core (Table 5.2). If this were not so, the

heat rate could have been discarded in the second half of the estimation process,

eliminating the correlation between the heat input and the two-phase parameters. The

absolute permeability was included as an unknown since it is also a fluid flow property.

Whereas all 11 sets of temperature, pressure, and heat flux were employed, only six sets

of steam saturation data were used. This was because the two-phase region was confined

within the first 7 cm from the heater. Considering only these data reduced the error in the

calculation. The apparent two-phase region observed under single-phase conditions was

probably due to density differences in the liquid water, with the liquid closer to the heater

having a smaller density, and not because steam was actually present. Thus, a simple

linear correction was applied to minimize unreasonable steam saturation values during

the single-phase period. To reduce the error variance both single- and two-phase data

were employed in the second half of the inversion process. However, many calibration

points were wasted in that the model had already been previously calibrated using single-

phase data. The TOUGH2 and ITOUGH2 input files for each case are presented in

Appendices A.2-A.7.

Subjecting all competing models to the two-phase parameter estimation process, the

model that gave the smallest error variance, So2, was the linear capillary relative

permeability and Leverett capillary pressure case. However, So2=6.4 is significantly

greater than one and it reflects the fact that the match is not as good as expected. This is

partly due to the inaccurate estimates of the thermal properties and heat rates in the first

part of the estimation process, and partly because of the constraints posed by the large

number of parameters being estimated at the same time. The error variance of the other

estimates were of the same order of magnitude as the error variance of the linear relative

66

permeability and Leverett capillary pressure case, although the models differ from each

other. Thus, using the error variance as a goodness-of-fit criterion, none of the cases

performs significantly better than the others. However, as suggested earlier, the function

that matches the data without over-parameterization is the most likely scenario.

Table 5.6 shows a summary of the estimated parameter set for the linear relative

permeability and Leverett capillary pressure case. Results show that Sgr and Sgs are the

most sensitive parameters. Except for k, Sls, and H7, all parameters cannot be determined

independently because they are correlated to one or more of the other parameters (Table

5.8). Of particular interest are the very low values of σ*/σ for Sgr, Sgs, and Po. This

implies that they are highly correlated with one another or with the other parameters.

Comparing the total sensitivity of all observation types (Table 5.9), accurate

measurements of temperature, pressure, and steam saturation are sufficient to solve the

inverse problem. Although the standard deviation values of the final residual are of the

same order of magnitude as the measurement errors (Table 5.1), the assumed accuracy of

the match was overestimated. The standard deviation of the steam saturation residual is

greater than the error measurement by an order of magnitude. This shows clearly that

there was a systematic deviation in the steam saturation match. This could be due to the

fact that the steam saturation was measured only three times during the two-phase period.

During the calibration phase, steam saturation data were just interpolated between the

three measured data points. Since the parameters are highly sensitive to the steam

saturation, slight errors in the steam saturation data could be translated to greater errors in

the predictions. Also, the corrections applied to the steam saturation data may have a

great bearing on the estimates. As in the first half of the estimation process, the heat flux

match in Figure 5.41 has random scattering around the diagonal line, suggesting that the

matches to the individual sensors are not optimal in the least-square sense. Since the

under- and over-prediction pattern is not observed in the temperature data (Figure 5.38),

the heat flux sensors may exhibit systematic trends. Furthermore, the pressure during the

two-phase period is under-predicted (Fig. 5.39). It may be due to the insufficient capillary

pressure predicted by the Leverett function. The contribution of each observation type to

67

the final value of the objective function (COF) is well balanced (Table 5.9). Figures 5.42-

5.45 show the predicted and measured temperature, pressure, steam saturation, and heat

flux in terms of time, respectively. Figures 5.46-5.49 show the predicted and measured

temperature, pressure, steam saturation, and heat flux in terms of distance from the

heater.

Table 5.6 Parameter estimates for linear relative permeability and Leverett capillarypressure case.


Slr (RP) 0.30 0.33

Sgr 0.10 0.16

Sls 0.80 0.82

Sgs 0.80 0.92

Po 100,000 92,941

Slr (CP) 0.30 0.12

k, md 780 3080

Table 5.7 Variance-covariance and correlation matrices.

k Slr (RP) Sgr Sls Sgs

k 3.04E-06 -4.60E-02 6.98E-02 -2.82E-03 -2.83E-02

Slr (RP) -5.79E-07 5.21E-05 -5.91E-01 -3.16E-01 -3.16E-01

Sgr 3.77E-07 -1.32E-05 9.56E-06 -3.51E-02 4.69E-01

Sls -6.16E-07 -2.86E-04 -1.36E-05 1.57E-02 4.56E-02

Sgs -1.45E-07 -6.68E-06 4.24E-06 1.67E-05 8.56E-06

Po -2.18E-06 2.61E-05 -2.16E-05 1.52E-04 1.81E-05

Slr (CP) -3.20E-07 -8.43E-06 -1.01E-05 -1.25E-05 6.79E-06

HR7 -1.04E-07 4.23E-06 -2.85E-06 4.61E-06 -5.16E-07

HR8 6.01E-08 1.04E-05 -3.99E-06 8.99E-06 -1.84E-06

68

Po Slr (CP) HR7 HR8

k -9.70E-02 -2.26E-02 -2.54E-02 1.26E-02

Slr (RP) 2.80E-01 -1.44E-01 2.50E-01 5.24E-01

Sgr -5.44E-01 -4.03E-01 -3.94E-01 -4.70E-01

Sls 9.43E-02 -1.23E-02 1.57E-02 2.62E-02

Sgs 4.82E-01 2.86E-01 -7.53E-02 -2.29E-01

Po 1.66E-04 6.57E-01 3.19E-01 2.79E-01

Slr (CP) 6.85E-05 6.58E-05 1.98E-01 -5.45E-02

HR7 9.61E-06 3.75E-06 5.48E-06 2.03E-01

HR8 9.86E-06 -1.21E-06 1.31E-06 7.53E-06

Table 5.8 Statistical measures and parameter sensitivity.


k 0.0017 0.9893 8109

Slr (RP) 0.0072 0.5025 6222

Sgr 0.0031 0.0820 40215

Sls 0.1253 0.7989 152

Sgs 0.0029 0.0866 30669

Po 0.0129 0.0835 9632

Slr (CP) 0.0081 0.5144 7579

HR7 0.0023 0.9097 7172

HR8 0.0027 0.7366 8964

69

Table 5.9 Total sensitivity of observation, standard deviation of residuals, andcontribution to the objective function (COF).

Observation Sensitivity Standard

Deviation

COF

%

Temperature 1041 1.9 C 14.54

Pressure 3383 1740 Pa 16.98

Saturation 6783 0.09 37.84

Heat Flux 311 28.1 W/m2 30.64

0

20

40

60

80

100

120

0 20 40 60 80 100 120M e as ure d Te m pe rature , C

Ca

lcu

late

d T

em

pe

ratu

re,

C

Figure 5.38 Measured and calculated temperature.

70

0

5

10

15

20

25

30

0 5 10 15 20 25 30M e as ure d Pre s s ure , k Pa

Ca

lcu

late

d P

res

su

re,

kP

a

Figure 5.39 Measured and calculated pressure.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

M e as ure d Ste am Saturation

Ca

lcu

late

d S

tea

m S

atu

rati

on

Figure 5.40 Measured and calculated steam saturation.

71

0

100

200

300

400

500

0 100 200 300 400 500M e as ure d He at Flux, W/m ^2

Ca

lcu

late

d H

ea

t F

lux

, W

/m^

2

Figure 5.41 Measured and calculated heat flux.

20

30

40

50

60

70

80

90

100

110

120

0 25 50 75 100 125 150 175Tim e , hours

Te

mp

era

ture

, C

T1 dat

T1 s im

T2 dat

T2 s im

20

30

40

50

60

70

80

90

100

110

120

0 25 50 75 100 125 150 175

Tim e , hours

Te

mp

era

ture

, C

T3 dat

T3 s im

T4 dat

T4 s im

20

30

40

50

60

70

80

90

100

110

120

0 25 50 75 100 125 150 175

Tim e , hours

Te

mp

era

ture

, C

T5 dat

T5 s im

T6 dat

T6 s im

20

30

40

50

60

70

80

90

100

110

120

0 25 50 75 100 125 150 175

Tim e , hours

Te

mp

era

ture

, C

T7 dat

T7 s im

T8 dat

T8 s im

Figure 5.42 Temperature with respect to time.

72

0

10

20

30

40

0 25 50 75 100 125 150 175Tim e , hours

Pre

ss

ure

, k

Pa

P1 dat

P1 s im

P2 dat

P2 s im

0

10

20

30

40

0 25 50 75 100 125 150 175Tim e, hours

Pre

ss

ure

, k

Pa

P3 dat

P3 s im

P4 dat

P4 s im

0

10

20

30

40

50

60

0 25 50 75 100 125 150 175Tim e, hours

Pre

ss

ure

, k

Pa

P5 dat

P5 s im

P6 dta

P6 s im

Figure 5.43 Pressure with respect to time.

73

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 25 50 75 100 125 150 175Tim e , hours

Ste

am

Sa

tura

tio

n

Ss t1 dat

Ss t1 s im

Ss t2 dat

Ss t2 s im

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 25 50 75 100 125 150 175Tim e , hours

Ste

am

Sa

tura

tio

n

Ss t3 dat

Ss t3 s im

Ss t4 dat

Ss t4 s im

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 25 50 75 100 125 150 175Tim e , h ours

Ste

am

Sa

tura

tio

n

Ss t5 dat

Ss t5 s im

Ss t6 dat

Ss t6 s im

Figure 5.44 Steam saturation with respect to time.

74

0

50

100

150

200

250

300

350

400

450

500

0 25 50 75 100 125 150 175T im e , h ou r s

He

at

Flu

x,

W/m

^2

HF1 d at

HF1 s im

HF2 d at

HF2 s im

0

50

100

150

200

250

300

0 25 50 75 100 125 150 175T im e , h o u rs

He

at F

lux,

W/m

^2

HF3 d at

HF3 s im

HF4 d at

HF4 s im

0

5 0

10 0

15 0

20 0

25 0

0 2 5 50 75 10 0 12 5 1 50 1 75T im e , h o u r s

He

at

Flu

x,

W/m

^2

HF5 d a t

HF5 s im

HF6 d at

HF6 s im

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

0 2 5 5 0 7 5 1 0 0 1 2 5 1 5 0 1 7 5T im e , h o u r s

He

at

Flu

x, W

/m^

2

HF7 d a t

HF7 s im

HF8 s im

HF8 s im

Figure 5.45 Heat flux with respect to time.

20

40

60

80

100

120

0 10 20 30 40 50

127 h r s s im

127 h r s d at

146 h r s s im

146 h r s d at

168 h r s s im

168 h r s d at

Te

mp

era

ture

, C

Dis tan ce fr o m the he ate r , cm

Figure 5.46 Temperature with respect to distance from the heater.

75

10

15

20

25

30

35

40

0 10 20 30 40 50

127 hrs s im

127 hrs dat

146 hrs s im

146 hrs dat

168 hrs s im

168 hrs datP

res

su

re,

kP

a

Dis tance from the he ate r , cm

Figure 5.47 Pressure with respect to distance from the heater.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4 5 6 7

127 hrs s im

127 hrs dat

146 hrs s im

146 hrs dat

168 hrs s im

168 hrs dat

Ste

am

Sa

tura

tio

n


Figure 5.48 Steam saturation with respect to distance from the heater.

76

0

100

200

300

400

500

0 10 20 30 40 50

127 hrs s im

127 hrs dat

146 hrs s im

146 hrs dat

168 hrs s im

168 hrs dat

He

at

Flu

x,

W/m

^2


Figure 5.49 Heat flux with respect to distance from the heater.

Figure 5.50 shows the linear relative permeability curves based on the two-phase

parameter estimates and Figure 5.51 shows the corresponding Leverett capillary pressure.

The liquid relative permeability agrees well with Ambusso’s results. On the other hand,

Sgl does not coincide with the measured Sgl, although there is a good agreement between

the estimated Sgr and Ambusso’s kgr. Figure 5.52 shows the relative permeability

estimates obtained from the estimation process. Although the relative permeability

relations of the models are different, they all seem to agree in terms of Sgr. The Sgr value

is around 0.15-0.20. Since the observations made during the boiling experiment were

more sensitive to the steam relative permeability, inverse modeling at least made Sgr

consistent. A comparison of the different relative permeability estimates with the results

obtained by Satik is also shown in Figure 5.53. Although Corey’s relative permeability

(estimates from the Corey relative permeability and linear capillary pressure case) best

mimic Satik’s curves, the fit was worse than that obtained from the linear relative

permeability and Leverett capillary pressure case.

77

0

0 . 1

0 . 2

0 . 3

0 . 4

0 . 5

0 . 6

0 . 7

0 . 8

0 . 9

1

0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1

L i q u i d sa tu r a ti o n , S l

Re

lati

ve

Pe

rme

ab

ilit

y

Figure 5.50 Inverse modeling relative permeability results compared with Ambusso’sresults (1996).

1 . E + 0 2

1 . E + 0 3

1 . E + 0 4

0 0 . 2 0 . 4 0 . 6 0 . 8 1

Sl

log

Pc

, P

a

Figure 5.51 Leverett capillary pressure.

78

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1

Liquid Saturation

Rel

ativ

e P

erm

eab

ility

krl (linear)

krg (linear)

krl (Ambusso)

krg (Ambusso)

krl (Corey-linear)

krg (Corey-linear)

krl (Brooks-Corey)

krg (Brooks-Corey)

krl (Corey-Leverett)

krg (Corey-Leverett)

krl (linear-Leverett)

krg (linear-Leverett)

krl (van Genuchten)

krg (van Genuchten)

Figure 5.52. Relative permeability estimates compared with Ambusso’s (1996) results.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1

Liquid Saturation

Rel

ativ

e P

erm

eab

ility

krl (linear)

krg (linear)

krl (Satik)

krg (Satik)

krl (Corey-linear)

krg (Corey-linear)

krl (Brooks-Corey)

krg (Brooks-Corey)





krl (van Genuchten)

krg (van Genuchten)

Figure 5.53. Relative permeability estimates compared with Satik’s (1996) results.

The error variance, So2, can be improved by discarding some observation data. Since data

at Sensor 1 dominated the estimation process, it is practical to eliminate them. By doing

so, the error caused by the heat input, boundary effects, and adsorption can be minimized.

79

Also, the effects of the poorly understood capillary pressure of superheated steam can be

reduced. Going through the same parameter estimation process, So2 was reduced to 1.9

after the single-phase calibration period. Although this is still greater than one, it gave a

better fit than the previous estimates (with Sensor 1 data) (Figs 5.54 and 5.55). Table 5.10

shows the parameter estimates after the single-phase calibration period. As expected, the

estimates for the thermal properties and heat input are lower than in the previous case

since data from Sensor 1 were not included in the calibration period. The most sensitive

parameters are αi and αb, which concurs with the finding in the previous estimation

process. Except for H4, H5, and H6, none of the parameters can be estimated

independently without high uncertainty (Table 5.12). Comparing the total sensitivity of

the different observation types (Table 5.13), accurate measurements of temperature are

sufficient to solve the inverse problem. Moreover, the standard deviation values of the

final residual (Table 5.13) are of the same order of magnitude as the measurement errors,

although the heat flux matches to the individual sensors are not optimal in the least square

sense (Fig. 5.55). Finally, the contribution of temperature and heat flux to the final value

of the objective function is well balanced (Table 5.13).

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80 90 100

T2

T3

T4

T5

T6

T7

T8

T9

T10

T11

M e as ure d Te m pe rature , C

Ca

lcu

late

d T

em

pe

ratu

re,

C

Figure 5.54 No Sensor 1 data: Measured and calculated temperature after calibration ofmodel under single-phase conditions.

80

0

50

100

150

200

0 50 100 150 200

HF2

HF3

HF4

HF5

HF6

HF7

HF8

HF9

HF10

HF11

M e as ure d He at Flux, W/m ^2

Ca

lcu

late

d H

ea

t F

lux

, W

/m^

2

Figure 5.55 No Sensor 1 data: measured and calculated heat flux after calibration ofmodel under single-phase conditions.

Table 5.10 No Sensor 1 data: Parameter estimates after the single-phase calibrationperiod.


αs 4.930 4.826

αb 0.150 0.066

αi 0.115 0.100

HR2 0.235 0.141

HR3 0.515 0.482

HR4 0.972 0.802

HR5 1.237 1.079

HR6 1.510 1.357

81

Table 5.11 No Sensor 1 data: Variance-covariance and correlation matrices after single-phase period calibration.

αs αb αi HR2 HR3 HR4 HR5 HR6

αs 1.48E-02 -5.69E-01 4.01E-01 1.14E-01 1.54E-01 2.32E-01 2.94E-01 2.85E-01

αb -3.29E-04 2.26E-05 -5.86E-01 -7.74E-01 -2.45E-01 -3.81E-02 -5.21E-02 -5.46E-02

αi 6.95E-05 -3.98E-06 2.04E-06 1.91E-01 3.06E-01 5.03E-01 6.14E-01 5.55E-01

HR2 1.08E-04 -2.89E-05 2.14E-06 6.15E-05 -2.56E-01 -2.38E-01 -2.83E-01 -2.55E-01

HR3 1.56E-04 -9.74E-06 3.65E-06 -1.68E-05 7.00E-05 1.26E-01 1.56E-01 1.42E-01

HR4 2.61E-04 -1.68E-06 6.64E-06 -1.72E-05 9.78E-06 8.55E-05 4.44E-01 3.37E-01

HR5 4.18E-04 -2.91E-06 1.03E-05 -2.60E-05 1.53E-05 4.81E-05 1.37E-04 4.69E-01

HR6 4.44E-04 -3.33E-06 1.01E-05 -2.57E-05 1.53E-05 3.99E-05 7.04E-05 1.64E-04

Table 5.12 No Sensor 1 data: Statistical measures and parameter sensitivity after single-phase period calibration.


αs 0.1215 0.0656 1129

αb 0.0048 0.0231 74231

αI 0.0014 0.1163 74700

HR2 0.0078 0.0295 34257

HR3 0.0084 0.0695 14404

HR4 0.0092 0.7539 2081

HR5 0.0117 0.6369 1758

HR6 0.0128 0.7040 1080

82

Table 5.13 No Sensor 1 data: Total sensitivity of observation, standard deviation ofresiduals, and contribution to the objective function (COF) after single-phaseperiod calibration.

Sensitivity StandardDeviation

COF%

Temperature 10350 1.4 54.42Heat Flux 2684 13.1 44.54

Subjecting all competing models to the two-phase parameter estimation process, the

model that gave the smallest error variance, So2, was the linear capillary relative

permeability and capillary pressure model. Although the error variance was reduced as a

result of not including data at Sensor 1, So2=5.2 is still significantly greater than one.

Thus, the match is not as good as expected. This is in part due to the inaccurate estimates

of the thermal properties and heat rates in the first part of the estimation process, and

partly because of the constraints posed by the large number of parameters being estimated

at the same time. The error variance values of the other estimate were of the same order

of magnitude as the error variance of the linear relative permeability and capillary

pressure case. This indicates that none of the cases performs significantly better than the

others, although each model is different from another.

Table 5.14 shows a summary of the estimated parameter set for the linear model. Results

show that k, HR8, HR7, and Sgr are the most sensitive parameters, and Slr and Sls are not

sensitive parameters at all (Table 5.16). This means that Slr and Sls can assume any value

and not affect the inversion process. Except for k, Slr, and Sls, all parameters cannot be

determined independently because they are correlated to one or more of the other

parameters. Although the standard deviation values of the final residual (Table 5.17) are

of the same order of magnitude as the measurement errors (Table 5.1), the assumed

accuracy of the match was overestimated. The large standard deviation of the steam

saturation residual shows that there was a systematic mismatch to in the steam saturation

measurements. Furthermore, the pressure during the two-phase period is under-predicted

(Fig. 5.58). It may be due to the insufficient capillary pressure predicted by the linear

function, although it is greater than the one predicted in the previous case. The heat flux

83

matches in Figure 5.59 has an under- and over-prediction pattern that is not observed in

the temperature match (Figure 5.56). This indicates that the heat flux sensors may exhibit

systematic trends. In addition, the contribution of each observation type to the objective

function is well balanced. Figures 5.60-5.63 show the predicted and measured

temperature, pressure, steam saturation, and heat flux in terms of time, respectively.

Figures 5.64-5.67 show the predicted and measured temperature, pressure, steam

saturation, and heat flux in terms of distance from the heater. Clearly, the fit is better than

in the previous case.

Figure 5.68 shows a comparison of the relative permeability obtained by Ambusso (1996)

and by inverse calculation. As in the previous case, the two relative permeability relation

agree on Sgr. Slr and Sls can be manipulated to coincide with Ambusso’s results since the

observation data are not sensitive to them. Figures 5.68 and 5.69 show a comparison of

all the models with Ambusso’s results and Satik’s measurements, respectively. Except for

the van Genuchten model, all models agree on the value of Sgr which is around 0.1.

In general, the inverse problem that was formulated here was ill-posed since too many

parameters were estimated at the same time. This could not be avoided, however, since

the thermal parameters, including the heat input, were strongly correlated with the

hydrogeologic properties. This was due to the fact that the two-phase flow was driven

only by boiling, and not by, say, fluid injection. Thus, it was necessary to divide the

estimation process into two parts: single-phase and two-phase period estimation. This

reduced the dependence between the multiphase and thermal parameters, although not

completely. If the thermal parameters and capillary pressure were known, a more accurate

estimate of the relative permeability could be achieved. However, this was not possible

under the given operating conditions. Consequently, the results of the estimation process

were ambiguous, making the determination of the appropriate relative permeability as

well as the capillary pressure function difficult.

84

0

20

40

60

80

100

120

0 20 40 60 80 100 120M e as ure d Te m pe rature , C

Ca

lcu

late

d T

em

pe

ratu

re,

C

Figure 5.56 No Sensor 1 data: Measured and calculated temperature.

0

5

10

15

20

25

30

0 5 10 15 20 25 30M e as ur e d Pr e s s u r e , k Pa

Ca

lcu

late

d P

res

su

re,

kP

a

Figure 5.57 No Sensor 1 data: Measured and calculated pressure.

85

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

M e as ure d Ste am Saturation

Ca

lcu

late

d S

tea

m S

atu

rati

on

Figure 5.58 No Sensor 1 data: Measured and calculated steam saturation.

0

50

100

150

200

250

0 50 100 150 200 250M e as ure d He at Flux, W/m ^2

Ca

lcu

late

d H

ea

t F

lux

, W

/m^

2

Figure 5.59 No Sensor 1 data: Measured and calculated heat flux.

86

Table 5.14 No Sensor 1 data: Parameter estimates.


k, md 780 518

Slr 0.30 0.31

Sgr 0.10 0.10

Sls 0.80 0.80

Sgs 0.80 1.00

Pcmax, Pa 100000 12,788

HR7, W 1.790 1.729

HR8, W 2.083 2.005

Table 5.15 No Sensor 1 data: Variance-covariance and correlation matrices.

k Slr Sgr Sls Sgs Pcmax HR7 HR8

k 3.65E-07 5.38E-05 -4.48E-05 5.82E-05 4.82E-03 -7.75E-03 -1.38E-03 -1.90E-03

Slr 3.70E-09 1.30E-02 1.68E-02 -6.57E-04 -5.68E-03 1.16E-02 -7.99E-03 -1.71E-03

Sgr -4.49E-10 3.17E-05 2.76E-04 1.70E-02 -3.75E-03 4.33E-01 -7.52E-01 -7.18E-01

Sls 4.00E-09 -8.52E-06 3.21E-05 1.30E-02 -6.18E-03 1.62E-02 -5.38E-03 -4.11E-03

Sgs 2.67E-07 -5.94E-05 -5.72E-06 -6.46E-05 8.44E-03 8.61E-01 1.57E-01 2.13E-01

Pcmax -2.24E-07 6.33E-05 3.43E-04 8.80E-05 3.78E-03 2.28E-03 -1.51E-01 -3.21E-02

HR7 -2.46E-09 -2.69E-06 -3.69E-05 -1.81E-06 4.27E-05 -2.13E-05 8.71E-06 6.33E-01

HR8 -3.03E-09 -5.13E-07 -3.14E-05 -1.23E-06 5.16E-05 -4.04E-06 4.92E-06 6.95E-06

87

Table 5.17 No Sensor 1 data: Total sensitivity of observation, standard deviation ofresiduals, and contribution to the objective function (COF).


k 0.0006 0.9986 13396

Slr 0.1139 0.9992 5

Sgr 0.0166 0.2869 3598

Sls 0.1139 0.9982 6

Sgs 0.0919 0.2552 596

Pcmax 0.0478 0.2141 1536

HR7 0.0030 0.6208 7057

HR8 0.0026 0.5513 11425

Table 5.18 No Sensor 1 data: Total sensitivity of observation, standard deviation ofresiduals, and contribution to the objective function (COF).

Sensitivity Standard

Deviation

COF

%

Temperature 4.79E+02 1.67 21.11

Pressure 2.48E+03 1410 13.36

Saturation 2.41E+03 0.067 40.64

Heat flux 1.39E+02 19.8 24.67

88

20

30

40

50

60

70

80

90

100

110

0 25 50 75 100 125 150 175Tim e , hours

Te

mp

era

ture

, C

T2 dat

T2 s im

T3 dat

T3 s im

20

30

40

50

60

70

80

90

100

110

120

0 25 50 75 100 125 150 175

Tim e , hours

Te

mp

era

ture

, C

T4 dat

T4 s im

T5 dat

T5 s im

20

30

40

50

60

70

80

90

100

110

120

0 25 50 75 100 125 150 175

Tim e , hours

Te

mp

era

ture

, C

T6 dat

T6 s im

T7 dat

T7 s im

Figure 5.60 No Sensor 1 data: Temperature with respect to time.

89

0

10

20

30

40

0 25 50 75 100 125 150 175Tim e , hours

Pre

ss

ure

, k

Pa

P2 dat

P2 s im

P3 dat

P3 s im

0

10

20

30

40

0 25 50 75 100 125 150 175Tim e , hours

Pre

ss

ure

, k

Pa

P4 dat

P4 s im

P5 dat

P5 s im

0

10

20

30

40

50

60

0 25 50 75 100 125 150 175Tim e , hours

Pre

ss

ure

, k

Pa

P6 dat

P6 s im

P7 dat

P7 s im

Figure 5.61 No Sensor 1 data: Pressure with respect to time.

90

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 25 50 75 100 125 150 175Tim e , hours

Ste

am

Sa

tura

tio

n

Ss t2 dat

Ss t2 s im

Ss t3 dat

Ss t3 s im

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 25 50 75 100 125 150 175T im e , h o u r s

Ste

am

Sa

tura

tio

n

Ss t4 d at

Ss t4 s im

Ss t5 d at

Ss t5 s im

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 25 50 75 100 125 150 175Tim e , hour s

Ste

am

Sa

tura

tio

n

Ss t6 dat

Ss t6 s im

Figure 5.62 No Sensor 1 data: Steam saturation with respect to time.

91

0

50

100

150

200

250

0 25 50 75 100 125 150 175T im e , hour s

He

at

Flu

x,

W/m

^2

HF2 dat

HF2 s im

HF3 dat

HF3 s im

0

50

100

150

200

250

0 25 50 75 100 125 150 175T im e , h o u r s

He

at F

lux,

W/m

^2

HF4 d at

HF4 s im

HF5 d at

HF5 s im

0

5 0

10 0

15 0

20 0

25 0

0 25 50 7 5 1 00 12 5 15 0 1 75T im e , h o u r s

He

at

Flu

x,

W/m

^2

HF6 d at

HF6 s im

HF7 d at

HF7 s im

0

50

100

150

200

250

0 25 50 75 100 125 150 175T im e , h o u r s

He

at

Flu

x,

W/m

^2

HF8 d at

HF8 s im

HF9 s im

HF9 s im

Figure 5.63 No Sensor 1 data: Heat flux with respect to time.

92

20

40

60

80

100

120

0 10 20 30 40 50

127 hrs s im

127 hrs dat

146 hrs s im

146 hrs dat

168 hrs s im

168 hrs dat

Te

mp

era

ture

, C


Figure 5.64 No Sensor 1 data: Temperature with respect to distance from heater.

10

15

20

25

30

35

40

0 10 20 30 40 50

127 hrs s im

127 hrs dat

146 hrs s im

146 hrs dat

168 hrs s im

168 hrs dat

Pre

ss

ure

, k

Pa


Figure 5.65 No Sensor 1 data: Pressure with respect to distance from heater.

93

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4 5 6 7 8

127 h rs s im

127 h rs d at

146 h rs s im

146 h rs d at

168 h rs s im

168 h rs d at

Ste

am

Sa

tura

tio

n

Dis tance fr om the he ate r , cm

Figure 5.66 No Sensor 1 data: Steam saturation with respect to distance from heater.

0

50

100

150

200

250

0 10 20 30 40 50

127 hrs s im

127 hrs dat

146 hrs s im

146 hrs dat

168 hrs s im

168 hrs dat

He

at

Flu

x,

W/m

^2


Figure 5.67 No Sensor 1 data: Heat flux with respect to distance from heater.

94

0

0 . 1

0 . 2

0 . 3

0 . 4

0 . 5

0 . 6

0 . 7

0 . 8

0 . 9

1

0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1

L i q u i d sa tu r a ti o n , S l

Re

lati

ve

Pe

rme

ab

ilit

y

Figure 5.68 No Sensor 1 data: Relative permeability estimate compared with Ambusso’sresults (1996).

1 . E + 0 2

1 . E + 0 3

1 . E + 0 4

1 . E + 0 5

0 0 . 2 0 . 4 0 . 6 0 . 8 1

Sl

log

Pc

, P

a

Figure 5.69 No Sensor 1 data: Linear capillary pressure.

95

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1

Liquid Saturation

Rel

ativ

e P

erm

eab

ility

krl (linear)

krg (linear)

krl (Ambusso)

krg (Ambusso)

krl (Corey-linear)

krg (Corey-linear)

krl (Brooks-Corey)

krg (Brooks-Corey)





krl (van Genuchten)

krg (van Genuchten)

Figure 5.70 No Sensor 1 data: Relative permeability estimates compared with Ambusso’sresults.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1

Liquid Saturation

Rel

ativ

e P

erm

eab

ility

krl (linear)

krg (linear)

krl (Satik)

krg (Satik)

krl (Corey-linear)

krg (Corey-linear)

krl (Brooks-Corey)

krg (Brooks-Corey)





krl (van Genuchten)

krg (van Genuchten)

Figure 5.71 No Sensor 1 data: Relative permeability estimates compared with Satik’sresults.

96

Chapter 6

Conclusion

1) Thermal and multiphase flow properties of a Berea sandstone core were estimated by

inverse calculation using temperature, pressure, steam saturation, and heat flux data.

The development of the two-phase flow region was strongly related to the temperature

conditions in the core since heat was the only driving force in the experiment. As a

result, the heat input as well as the thermal properties of the sandstone and insulation

materials played a major role in understanding the system behavior. In addition, the

high sensitivity of the insulation materials to the observation data and their strong

correlation with the other parameters of interest made it difficult to obtain accurate

estimates.

2) Although the linear relative permeability model gave the best fit in the two cases

presented in the paper, all models yielded similar matches. This indicated that the data

did not contain sufficient information to distinguish the different models, making the

solution non-unique. Nonetheless, almost all models gave a consistent estimate for

Sgr, which was around 0.1-0.2.

3) The choice for the capillary pressure model depended on the condition in the core,

whether there was single-phase steam or two phases present. Since the distribution of

steam depended heavily on the capillary pressure, the relative permeability would

have been more accurately estimated had the capillary pressure been known.

4) The comprehensive analysis of all available data from a transient non-isothermal two-

phase flow experiment provided an insight into the relation of processes and

correlation of parameters. This information will be useful in the design of future

experiments.

97

References

[1] W.J. Ambusso, 1996. Experimental Determination of Steam-Water Relative

Permeability Relations, MS Thesis, Stanford University, Stanford. Calif.

[2] R.H. Brooks and A.T. Corey, 1964. “Hydraulic Properties of Porous Media”,

Colorado State University, Hydro paper No.5.

[3] A. T. Corey, 1954. “The Interrelations Between Gas and Oil Relative Permeabilities”,

Producers Monthly Vol. 19 pp 38-41.

[4] A. T. Corey, 1994. Mechanics of Immiscible Fluids in Porous Media, Water

Resources Publications.

[5] L. P. Dake, 1978. Fundamentals of Petroleum Engineering, Elsivier Science B. V.

[7] F. A. Dullien, 1992. Porous Media Fluid Transport and Pore Structure, Academic

Press.

[8] S. Finsterle, 1997. ITOUGH2 Command References Version 3.1, Lawrence Berkeley

National Laboratory, Berkeley, Calif.

[9] S. Finsterle, K. Pruess, D.P. Bullivant, and M.J. O’Sullivan, 1997. “Application of

Inverse Modeling to Geothermal Reservoir Simulation”, Proc. of 22rd Workshop on

Geothermal Reservoir Engineering, Stanford, Calif.

[10] S. Finsterle, C. Satik, and M. Guerrero, 1998. “Analysis of Boiling Experiments

Using Inverse Modeling, Proc. of 1st ITOUGH2 Workshop, Berkeley, California.

98

[11] S. K. Garg and J. Pritchett, 1977. “On Pressure-Work, Viscous Dissipation and

Energy Balance Relation fro Geothermal Reservoirs, Advances in Water Resources, 1,

No. 1, 41-47.

[12] M. Grant, 1977. “Permeability Reduction Factors at Wairakei”, Proc. of

ASME/AIChe Heat Transfer Conference, Salt Lake City, Utah, 77-HT-52, 15-17.

[13] R. N. Horne and H Ramey, 1978. “Steam/Water Relative Permeabilities From

Production Data”, GRC Trans. (2), 291.

[14] N. Kaviany, 1995. Principles of Heat Transfer in Porous Media, Mechanical

Engineering Series, Springer.

[15] M. C. Leverett, 1941. “Capillary behavior in Porous Solids”, Petroleum Technology,

No. 1223, 152-169.

[16] K. Pruess and T. N. Narasimhan, 1985. “A Practical Method for Modeling Fluid and

Heat Flow in Fracture Porous Media, SPE Journal, Vol. 25, No. 1, 14-26.

[17] K. Pruess, 1987. TOUGH User’s Guide, Lawrence Berkeley National Laboratory,

Berkeley, Calif.

[18] K. Pruess, 1991. TOUGH2-A General Purpose Numerical Simulator for Multiphase

Fluid and Heat Flow, Report LBL-29400, Lawrence Berkeley National Laboratory,

Berkeley, Calif.

[19] C. Satik (1997a), Stanford Geothermal Program Quarterly Report June-September

1997, Stanford University.

99

[20] C. Satik (1997b), “A Study of Boiling in Porous Media”, Proc. 19th New Zealand

Geothermal Workshop, Auckland, NZ.

[21] C. Satik (1998), “A Measurement of Steam-Water Relative Permeability”, Proc. of

23rd Workshop on Geothermal Reservoir Engineering, Stanford, Calif.

[22] M.L. Sorey, M.A. Grant and E. Bradford, 1980. Nonlinear Effects in Two Phase

Flow to Wells in Geothermal Reservoirs. Water Resources Research, Vol. 16 No. 4, pp

767-777.

[23] M. van Genuchten, 1980. “A Closed-Form Equation for Predicting the Hydraulic

Conductivity of Unsaturated Soils”, Soil Sci. Soc. Am. J, 44(5), 892-898.

100

Appendix A

A.1 Single-phase period calibration input files.

Appendix A.1.1 TOUGH2 input file.

ROCKS----1----*----2----*----3----*----4----*----5----*----6----*----7----*----8BEREA 2 2163. 0.210 0.0E-20 0.0E-20 8.487E-13 4.930858.240.0000E+000.0000E+000.2163E+010.1000E+01 5 0.200 0.200 0.000 1 0.0000 0.000 1.000000HEATE 0 2200. 0.010 0.0E-15 0.0E-15 0.0E-15 2.885246.6HEATB 0 240. 0.010 0.0E-15 0.0E-15 0.0E-15 0.1501046.6EPOXY 0 1200. 0.010 0.0E-15 0.0E-15 0.0E-15 0.5771046.6INSUL 0 192. 0.010 0.0E-15 0.0E-15 0.0E-15 0.115104.7BOUND 0 2163. 0.990 0.0E-15 0.0E-15 0.0E-15 0.642-1611.0AMBIE 1.293 0.990 0.0E-20 0.0E-20 1.0E-10 0.055-1611.0

START----1----*----2----*----3----*----4----*----5----*----6----*----7----*----8PARAM 123456789012345678901234 -31200 1200100000100101000400001000 2.130E-05 1.0 6.1020E5 1.00E+03 9.8100 1.E-5 1.0065E5 24. 0.0MESHMAKER1----*----2----*----3----*----4----*----5----*----6----*----7----*----8RZ2DRADII 5 0 0.0254 0.0304 0.0812 5.0812LAYER----1----*----2----*----3----*----4----*----5----*----6----*----7----*----8 51 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.01000.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.01000.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.01000.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.01000.0100

101

0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.01000.0100 0.0100 0.0100 0.0100 0.0100 0.0050 0.0100 0.01000.0100 0.0100 0.0100 5.0000

ELEME --- 4 5 0 0 0.00000 5.132BOU 1 BOUND .2027E+540.2027E-02 0.1270E-01 -.5000E-02A2 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.1500E-01A3 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.2500E-01A4 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.3500E-01A5 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.4500E-01A6 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.5500E-01A7 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.6500E-01A8 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.7500E-01A9 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.8500E-01AA 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.9500E-01AB 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.1050E+00AC 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.1150E+00AD 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.1250E+00AE 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.1350E+00AF 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.1450E+00AG 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.1550E+00AH 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.1650E+00AI 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.1750E+00AJ 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.1850E+00AK 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.1950E+00AL 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.2050E+00AM 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.2150E+00AN 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.2250E+00AO 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.2350E+00AP 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.2450E+00AQ 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.2550E+00AR 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.2650E+00

102

AS 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.2750E+00AT 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.2850E+00AU 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.2950E+00AV 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.3050E+00AW 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.3150E+00AX 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.3250E+00AY 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.3350E+00AZ 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.3450E+00B1 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.3550E+00B2 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.3650E+00B3 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.3750E+00B4 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.3850E+00B5 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.3950E+00B6 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.4050E+00B7 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.4150E+00B8 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.4250E+00B9 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.4350E+00BA1 1 HEATE2.0260E-060.0000E+00 0.1270E-01 -.4425E+00BA2 1 HEATE2.0260E-060.0000E+00 0.1270E-01 -.4425E+00BA3 1 HEATE2.0260E-060.0000E+00 0.1270E-01 -.4425E+00BA4 1 HEATE2.0260E-060.0000E+00 0.1270E-01 -.4425E+00BA5 1 HEATE2.0260E-060.0000E+00 0.1270E-01 -.4425E+00BB 1 HEATB .2027E-040.0000E+00 0.1270E-01 -.4500E+00BC 1 HEATB .2027E-040.0000E+00 0.1270E-01 -.4600E+00BD 1 HEATB .2027E-040.0000E+00 0.1270E-01 -.4700E+00BE 1 HEATB .2027E-040.0000E+00 0.1270E-01 -.4800E+00BF 1 HEATB .2027E-040.0000E+00 0.1270E-01 -.4900E+00AMB 1 AMBIE .1013E+540.2027E-02 0.1270E-01 -.2995E+01A2 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.1500E-01A3 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.2500E-01

103

A4 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.3500E-01A5 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.4500E-01A6 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.5500E-01A7 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.6500E-01A8 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.7500E-01A9 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.8500E-01AA 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.9500E-01AB 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.1050E+00AC 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.1150E+00AD 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.1250E+00AE 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.1350E+00AF 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.1450E+00AG 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.1550E+00AH 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.1650E+00AI 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.1750E+00AJ 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.1850E+00AK 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.1950E+00AL 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.2050E+00AM 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.2150E+00AN 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.2250E+00AO 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.2350E+00AP 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.2450E+00AQ 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.2550E+00AR 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.2650E+00AS 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.2750E+00AT 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.2850E+00AU 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.2950E+00AV 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.3050E+00AW 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.3150E+00AX 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.3250E+00

104

AY 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.3350E+00AZ 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.3450E+00B1 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.3550E+00B2 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.3650E+00B3 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.3750E+00B4 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.3850E+00B5 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.3950E+00B6 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.4050E+00B7 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.4150E+00B8 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.4250E+00B9 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.4350E+00BA 2 EPOXY .4383E-050.0000E+00 0.2790E-01 -.4425E+00BB 2 HEATB .8765E-050.0000E+00 0.2790E-01 -.4500E+00BC 2 HEATB .8765E-050.0000E+00 0.2790E-01 -.4600E+00BD 2 HEATB .8765E-050.0000E+00 0.2790E-01 -.4700E+00BE 2 HEATB .8765E-050.0000E+00 0.2790E-01 -.4800E+00BF 2 HEATB .8765E-050.0000E+00 0.2790E-01 -.4900E+00A2 3 INSUL .1781E-000.0000E+00 0.5580E-01 -.1500E-01A3 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.2500E-01A4 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.3500E-01A5 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.4500E-01A6 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.5500E-01A7 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.6500E-01A8 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.7500E-01A9 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.8500E-01AA 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.9500E-01AB 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.1050E+00AC 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.1150E+00AD 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.1250E+00AE 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.1350E+00

105

AF 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.1450E+00AG 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.1550E+00AH 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.1650E+00AI 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.1750E+00AJ 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.1850E+00AK 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.1950E+00AL 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.2050E+00AM 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.2150E+00AN 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.2250E+00AO 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.2350E+00AP 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.2450E+00AQ 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.2550E+00AR 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.2650E+00AS 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.2750E+00AT 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.2850E+00AU 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.2950E+00AV 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.3050E+00AW 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.3150E+00AX 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.3250E+00AY 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.3350E+00AZ 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.3450E+00B1 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.3550E+00B2 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.3650E+00B3 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.3750E+00B4 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.3850E+00B5 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.3950E+00B6 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.4050E+00B7 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.4150E+00B8 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.4250E+00B9 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.4350E+00

106

BA 3 INSUL .8905E-040.0000E+00 0.5580E-01 -.4425E+00BB 3 HEATB .1781E-030.0000E+00 0.5580E-01 -.4500E+00BC 3 HEATB .1781E-030.0000E+00 0.5580E-01 -.4600E+00BD 3 HEATB .1781E-030.0000E+00 0.5580E-01 -.4700E+00BE 3 HEATB .1781E-030.0000E+00 0.5580E-01 -.4800E+00BF 3 HEATB .1781E-030.0000E+00 0.5580E-01 -.4900E+00

CONNEA2 1A2 2 10.1270E-010.2500E-020.1596E-02A3 1A3 2 10.1270E-010.2500E-020.1596E-02A4 1A4 2 10.1270E-010.2500E-020.1596E-02A5 1A5 2 10.1270E-010.2500E-020.1596E-02A6 1A6 2 10.1270E-010.2500E-020.1596E-02A7 1A7 2 10.1270E-010.2500E-020.1596E-02A8 1A8 2 10.1270E-010.2500E-020.1596E-02A9 1A9 2 10.1270E-010.2500E-020.1596E-02AA 1AA 2 10.1270E-010.2500E-020.1596E-02AB 1AB 2 10.1270E-010.2500E-020.1596E-02AC 1AC 2 10.1270E-010.2500E-020.1596E-02AD 1AD 2 10.1270E-010.2500E-020.1596E-02AE 1AE 2 10.1270E-010.2500E-020.1596E-02AF 1AF 2 10.1270E-010.2500E-020.1596E-02AG 1AG 2 10.1270E-010.2500E-020.1596E-02AH 1AH 2 10.1270E-010.2500E-020.1596E-02AI 1AI 2 10.1270E-010.2500E-020.1596E-02AJ 1AJ 2 10.1270E-010.2500E-020.1596E-02AK 1AK 2 10.1270E-010.2500E-020.1596E-02AL 1AL 2 10.1270E-010.2500E-020.1596E-02AM 1AM 2 10.1270E-010.2500E-020.1596E-02AN 1AN 2 10.1270E-010.2500E-020.1596E-02AO 1AO 2 10.1270E-010.2500E-020.1596E-02AP 1AP 2 10.1270E-010.2500E-020.1596E-02AQ 1AQ 2 10.1270E-010.2500E-020.1596E-02AR 1AR 2 10.1270E-010.2500E-020.1596E-02AS 1AS 2 10.1270E-010.2500E-020.1596E-02AT 1AT 2 10.1270E-010.2500E-020.1596E-02AU 1AU 2 10.1270E-010.2500E-020.1596E-02AV 1AV 2 10.1270E-010.2500E-020.1596E-02AW 1AW 2 10.1270E-010.2500E-020.1596E-02AX 1AX 2 10.1270E-010.2500E-020.1596E-02AY 1AY 2 10.1270E-010.2500E-020.1596E-02AZ 1AZ 2 10.1270E-010.2500E-020.1596E-02B1 1B1 2 10.1270E-010.2500E-020.1596E-02B2 1B2 2 10.1270E-010.2500E-020.1596E-02B3 1B3 2 10.1270E-010.2500E-020.1596E-02B4 1B4 2 10.1270E-010.2500E-020.1596E-02B5 1B5 2 10.1270E-010.2500E-020.1596E-02B6 1B6 2 10.1270E-010.2500E-020.1596E-02B7 1B7 2 10.1270E-010.2500E-020.1596E-02B8 1B8 2 10.1270E-010.2500E-020.1596E-02B9 1B9 2 10.1270E-010.2500E-020.1596E-02BA1 1BA 2 10.1270E-010.2500E-021.5960E-04BA2 1BA 2 10.1270E-010.2500E-021.5960E-04BA3 1BA 2 10.1270E-010.2500E-021.5960E-04BA4 1BA 2 10.1270E-010.2500E-021.5960E-04

107

BA5 1BA 2 10.1270E-010.2500E-021.5960E-04BB 1BB 2 10.1270E-010.2500E-020.1596E-02BC 1BC 2 10.1270E-010.2500E-020.1596E-02BD 1BD 2 10.1270E-010.2500E-020.1596E-02BE 1BE 2 10.1270E-010.2500E-020.1596E-02BF 1BF 2 10.1270E-010.2500E-020.1596E-02A2 2A2 3 10.2500E-020.2540E-010.1910E-02A3 2A3 3 10.2500E-020.2540E-010.1910E-02A4 2A4 3 10.2500E-020.2540E-010.1910E-02A5 2A5 3 10.2500E-020.2540E-010.1910E-02A6 2A6 3 10.2500E-020.2540E-010.1910E-02A7 2A7 3 10.2500E-020.2540E-010.1910E-02A8 2A8 3 10.2500E-020.2540E-010.1910E-02A9 2A9 3 10.2500E-020.2540E-010.1910E-02AA 2AA 3 10.2500E-020.2540E-010.1910E-02AB 2AB 3 10.2500E-020.2540E-010.1910E-02AC 2AC 3 10.2500E-020.2540E-010.1910E-02AD 2AD 3 10.2500E-020.2540E-010.1910E-02AE 2AE 3 10.2500E-020.2540E-010.1910E-02AF 2AF 3 10.2500E-020.2540E-010.1910E-02AG 2AG 3 10.2500E-020.2540E-010.1910E-02AH 2AH 3 10.2500E-020.2540E-010.1910E-02AI 2AI 3 10.2500E-020.2540E-010.1910E-02AJ 2AJ 3 10.2500E-020.2540E-010.1910E-02AK 2AK 3 10.2500E-020.2540E-010.1910E-02AL 2AL 3 10.2500E-020.2540E-010.1910E-02AM 2AM 3 10.2500E-020.2540E-010.1910E-02AN 2AN 3 10.2500E-020.2540E-010.1910E-02AO 2AO 3 10.2500E-020.2540E-010.1910E-02AP 2AP 3 10.2500E-020.2540E-010.1910E-02AQ 2AQ 3 10.2500E-020.2540E-010.1910E-02AR 2AR 3 10.2500E-020.2540E-010.1910E-02AS 2AS 3 10.2500E-020.2540E-010.1910E-02AT 2AT 3 10.2500E-020.2540E-010.1910E-02AU 2AU 3 10.2500E-020.2540E-010.1910E-02AV 2AV 3 10.2500E-020.2540E-010.1910E-02AW 2AW 3 10.2500E-020.2540E-010.1910E-02AX 2AX 3 10.2500E-020.2540E-010.1910E-02AY 2AY 3 10.2500E-020.2540E-010.1910E-02AZ 2AZ 3 10.2500E-020.2540E-010.1910E-02B1 2B1 3 10.2500E-020.2540E-010.1910E-02B2 2B2 3 10.2500E-020.2540E-010.1910E-02B3 2B3 3 10.2500E-020.2540E-010.1910E-02B4 2B4 3 10.2500E-020.2540E-010.1910E-02B5 2B5 3 10.2500E-020.2540E-010.1910E-02B6 2B6 3 10.2500E-020.2540E-010.1910E-02B7 2B7 3 10.2500E-020.2540E-010.1910E-02B8 2B8 3 10.2500E-020.2540E-010.1910E-02B9 2B9 3 10.2500E-020.2540E-010.1910E-02BA 2BA 3 10.2500E-020.2540E-010.9550E-03BB 2BB 3 10.2500E-020.2540E-010.1910E-02BC 2BC 3 10.2500E-020.2540E-010.1910E-02BD 2BD 3 10.2500E-020.2540E-010.1910E-02BE 2BE 3 10.2500E-020.2540E-010.1910E-02BF 2BF 3 10.2500E-020.2540E-010.1910E-02A2 3AMB 1 10.2540E-011.0000E-110.5102E-02A3 3AMB 1 10.2540E-011.0000E-110.5102E-02A4 3AMB 1 10.2540E-011.0000E-110.5102E-02A5 3AMB 1 10.2540E-011.0000E-110.5102E-02A6 3AMB 1 10.2540E-011.0000E-110.5102E-02A7 3AMB 1 10.2540E-011.0000E-110.5102E-02

108

A8 3AMB 1 10.2540E-011.0000E-110.5102E-02A9 3AMB 1 10.2540E-011.0000E-110.5102E-02AA 3AMB 1 10.2540E-011.0000E-110.5102E-02AB 3AMB 1 10.2540E-011.0000E-110.5102E-02AC 3AMB 1 10.2540E-011.0000E-110.5102E-02AD 3AMB 1 10.2540E-011.0000E-110.5102E-02AE 3AMB 1 10.2540E-011.0000E-110.5102E-02AF 3AMB 1 10.2540E-011.0000E-110.5102E-02AG 3AMB 1 10.2540E-011.0000E-110.5102E-02AH 3AMB 1 10.2540E-011.0000E-110.5102E-02AI 3AMB 1 10.2540E-011.0000E-110.5102E-02AJ 3AMB 1 10.2540E-011.0000E-110.5102E-02AK 3AMB 1 10.2540E-011.0000E-110.5102E-02AL 3AMB 1 10.2540E-011.0000E-110.5102E-02AM 3AMB 1 10.2540E-011.0000E-110.5102E-02AN 3AMB 1 10.2540E-011.0000E-110.5102E-02AO 3AMB 1 10.2540E-011.0000E-110.5102E-02AP 3AMB 1 10.2540E-011.0000E-110.5102E-02AQ 3AMB 1 10.2540E-011.0000E-110.5102E-02AR 3AMB 1 10.2540E-011.0000E-110.5102E-02AS 3AMB 1 10.2540E-011.0000E-110.5102E-02AT 3AMB 1 10.2540E-011.0000E-110.5102E-02AU 3AMB 1 10.2540E-011.0000E-110.5102E-02AV 3AMB 1 10.2540E-011.0000E-110.5102E-02AW 3AMB 1 10.2540E-011.0000E-110.5102E-02AX 3AMB 1 10.2540E-011.0000E-110.5102E-02AY 3AMB 1 10.2540E-011.0000E-110.5102E-02AZ 3AMB 1 10.2540E-011.0000E-110.5102E-02B1 3AMB 1 10.2540E-011.0000E-110.5102E-02B2 3AMB 1 10.2540E-011.0000E-110.5102E-02B3 3AMB 1 10.2540E-011.0000E-110.5102E-02B4 3AMB 1 10.2540E-011.0000E-110.5102E-02B5 3AMB 1 10.2540E-011.0000E-110.5102E-02B6 3AMB 1 10.2540E-011.0000E-110.5102E-02B7 3AMB 1 10.2540E-011.0000E-110.5102E-02B8 3AMB 1 10.2540E-011.0000E-110.5102E-02B9 3AMB 1 10.2540E-011.0000E-110.5102E-02BA 3AMB 1 10.2540E-011.0000E-110.2551E-02BB 3AMB 1 10.2540E-011.0000E-110.5102E-02BC 3AMB 1 10.2540E-011.0000E-110.5102E-02BD 3AMB 1 10.2540E-011.0000E-110.5102E-02BE 3AMB 1 10.2540E-011.0000E-110.5102E-02BF 3AMB 1 10.2540E-011.0000E-110.5102E-02BOU 1A2 1 31.0000E-100.5000E-020.2027E-021.A2 1A3 1 30.5000E-020.5000E-020.2027E-021.A3 1A4 1 30.5000E-020.5000E-020.2027E-021.A4 1A5 1 30.5000E-020.5000E-020.2027E-021.A5 1A6 1 30.5000E-020.5000E-020.2027E-021.A6 1A7 1 30.5000E-020.5000E-020.2027E-021.A7 1A8 1 30.5000E-020.5000E-020.2027E-021.A8 1A9 1 30.5000E-020.5000E-020.2027E-021.A9 1AA 1 30.5000E-020.5000E-020.2027E-021.AA 1AB 1 30.5000E-020.5000E-020.2027E-021.AB 1AC 1 30.5000E-020.5000E-020.2027E-021.AC 1AD 1 30.5000E-020.5000E-020.2027E-021.AD 1AE 1 30.5000E-020.5000E-020.2027E-021.AE 1AF 1 30.5000E-020.5000E-020.2027E-021.AF 1AG 1 30.5000E-020.5000E-020.2027E-021.AG 1AH 1 30.5000E-020.5000E-020.2027E-021.AH 1AI 1 30.5000E-020.5000E-020.2027E-021.AI 1AJ 1 30.5000E-020.5000E-020.2027E-021.

109

AJ 1AK 1 30.5000E-020.5000E-020.2027E-021.AK 1AL 1 30.5000E-020.5000E-020.2027E-021.AL 1AM 1 30.5000E-020.5000E-020.2027E-021.AM 1AN 1 30.5000E-020.5000E-020.2027E-021.AN 1AO 1 30.5000E-020.5000E-020.2027E-021.AO 1AP 1 30.5000E-020.5000E-020.2027E-021.AP 1AQ 1 30.5000E-020.5000E-020.2027E-021.AQ 1AR 1 30.5000E-020.5000E-020.2027E-021.AR 1AS 1 30.5000E-020.5000E-020.2027E-021.AS 1AT 1 30.5000E-020.5000E-020.2027E-021.AT 1AU 1 30.5000E-020.5000E-020.2027E-021.AU 1AV 1 30.5000E-020.5000E-020.2027E-021.AV 1AW 1 30.5000E-020.5000E-020.2027E-021.AW 1AX 1 30.5000E-020.5000E-020.2027E-021.AX 1AY 1 30.5000E-020.5000E-020.2027E-021.AY 1AZ 1 30.5000E-020.5000E-020.2027E-021.AZ 1B1 1 30.5000E-020.5000E-020.2027E-021.B1 1B2 1 30.5000E-020.5000E-020.2027E-021.B2 1B3 1 30.5000E-020.5000E-020.2027E-021.B3 1B4 1 30.5000E-020.5000E-020.2027E-021.B4 1B5 1 30.5000E-020.5000E-020.2027E-021.B5 1B6 1 30.5000E-020.5000E-020.2027E-021.B6 1B7 1 30.5000E-020.5000E-020.2027E-021.B7 1B8 1 30.5000E-020.5000E-020.2027E-021.B8 1B9 1 30.5000E-020.5000E-020.2027E-021.B9 1BA1 1 30.5000E-020.5000E-030.2027E-021.BA1 1BA2 1 30.5000E-030.5000E-030.2027E-021.BA2 1BA3 1 30.5000E-030.5000E-030.2027E-021.BA3 1BA4 1 30.5000E-030.5000E-030.2027E-021.BA4 1BA5 1 30.5000E-030.5000E-030.2027E-021.BA5 1BB 1 30.5000E-030.5000E-020.2027E-021.BB 1BC 1 30.5000E-020.5000E-020.2027E-021.BC 1BD 1 30.5000E-020.5000E-020.2027E-021.BD 1BE 1 30.5000E-020.5000E-020.2027E-021.BE 1BF 1 30.5000E-020.5000E-020.2027E-021.BF 1AMB 1 30.5000E-021.0000E-110.2027E-021.BOU 1A2 2 31.0000E-100.5000E-020.8765E-031.A2 2A3 2 30.5000E-020.5000E-020.8765E-031.A3 2A4 2 30.5000E-020.5000E-020.8765E-031.A4 2A5 2 30.5000E-020.5000E-020.8765E-031.A5 2A6 2 30.5000E-020.5000E-020.8765E-031.A6 2A7 2 30.5000E-020.5000E-020.8765E-031.A7 2A8 2 30.5000E-020.5000E-020.8765E-031.A8 2A9 2 30.5000E-020.5000E-020.8765E-031.A9 2AA 2 30.5000E-020.5000E-020.8765E-031.AA 2AB 2 30.5000E-020.5000E-020.8765E-031.AB 2AC 2 30.5000E-020.5000E-020.8765E-031.AC 2AD 2 30.5000E-020.5000E-020.8765E-031.AD 2AE 2 30.5000E-020.5000E-020.8765E-031.AE 2AF 2 30.5000E-020.5000E-020.8765E-031.AF 2AG 2 30.5000E-020.5000E-020.8765E-031.AG 2AH 2 30.5000E-020.5000E-020.8765E-031.AH 2AI 2 30.5000E-020.5000E-020.8765E-031.AI 2AJ 2 30.5000E-020.5000E-020.8765E-031.AJ 2AK 2 30.5000E-020.5000E-020.8765E-031.AK 2AL 2 30.5000E-020.5000E-020.8765E-031.AL 2AM 2 30.5000E-020.5000E-020.8765E-031.AM 2AN 2 30.5000E-020.5000E-020.8765E-031.AN 2AO 2 30.5000E-020.5000E-020.8765E-031.AO 2AP 2 30.5000E-020.5000E-020.8765E-031.AP 2AQ 2 30.5000E-020.5000E-020.8765E-031.

110

AQ 2AR 2 30.5000E-020.5000E-020.8765E-031.AR 2AS 2 30.5000E-020.5000E-020.8765E-031.AS 2AT 2 30.5000E-020.5000E-020.8765E-031.AT 2AU 2 30.5000E-020.5000E-020.8765E-031.AU 2AV 2 30.5000E-020.5000E-020.8765E-031.AV 2AW 2 30.5000E-020.5000E-020.8765E-031.AW 2AX 2 30.5000E-020.5000E-020.8765E-031.AX 2AY 2 30.5000E-020.5000E-020.8765E-031.AY 2AZ 2 30.5000E-020.5000E-020.8765E-031.AZ 2B1 2 30.5000E-020.5000E-020.8765E-031.B1 2B2 2 30.5000E-020.5000E-020.8765E-031.B2 2B3 2 30.5000E-020.5000E-020.8765E-031.B3 2B4 2 30.5000E-020.5000E-020.8765E-031.B4 2B5 2 30.5000E-020.5000E-020.8765E-031.B5 2B6 2 30.5000E-020.5000E-020.8765E-031.B6 2B7 2 30.5000E-020.5000E-020.8765E-031.B7 2B8 2 30.5000E-020.5000E-020.8765E-031.B8 2B9 2 30.5000E-020.5000E-020.8765E-031.B9 2BA 2 30.5000E-020.2500E-020.8765E-031.BA 2BB 2 30.2500E-020.5000E-020.8765E-031.BB 2BC 2 30.5000E-020.5000E-020.8765E-031.BC 2BD 2 30.5000E-020.5000E-020.8765E-031.BD 2BE 2 30.5000E-020.5000E-020.8765E-031.BE 2BF 2 30.5000E-020.5000E-020.8765E-031.BF 2AMB 1 30.5000E-021.0000E-110.8765E-031.BOU 1A2 3 31.0000E-100.5000E-020.1781E-011.A2 3A3 3 30.5000E-020.5000E-020.1781E-011.A3 3A4 3 30.5000E-020.5000E-020.1781E-011.A4 3A5 3 30.5000E-020.5000E-020.1781E-011.A5 3A6 3 30.5000E-020.5000E-020.1781E-011.A6 3A7 3 30.5000E-020.5000E-020.1781E-011.A7 3A8 3 30.5000E-020.5000E-020.1781E-011.A8 3A9 3 30.5000E-020.5000E-020.1781E-011.A9 3AA 3 30.5000E-020.5000E-020.1781E-011.AA 3AB 3 30.5000E-020.5000E-020.1781E-011.AB 3AC 3 30.5000E-020.5000E-020.1781E-011.AC 3AD 3 30.5000E-020.5000E-020.1781E-011.AD 3AE 3 30.5000E-020.5000E-020.1781E-011.AE 3AF 3 30.5000E-020.5000E-020.1781E-011.AF 3AG 3 30.5000E-020.5000E-020.1781E-011.AG 3AH 3 30.5000E-020.5000E-020.1781E-011.AH 3AI 3 30.5000E-020.5000E-020.1781E-011.AI 3AJ 3 30.5000E-020.5000E-020.1781E-011.AJ 3AK 3 30.5000E-020.5000E-020.1781E-011.AK 3AL 3 30.5000E-020.5000E-020.1781E-011.AL 3AM 3 30.5000E-020.5000E-020.1781E-011.AM 3AN 3 30.5000E-020.5000E-020.1781E-011.AN 3AO 3 30.5000E-020.5000E-020.1781E-011.AO 3AP 3 30.5000E-020.5000E-020.1781E-011.AP 3AQ 3 30.5000E-020.5000E-020.1781E-011.AQ 3AR 3 30.5000E-020.5000E-020.1781E-011.AR 3AS 3 30.5000E-020.5000E-020.1781E-011.AS 3AT 3 30.5000E-020.5000E-020.1781E-011.AT 3AU 3 30.5000E-020.5000E-020.1781E-011.AU 3AV 3 30.5000E-020.5000E-020.1781E-011.AV 3AW 3 30.5000E-020.5000E-020.1781E-011.AW 3AX 3 30.5000E-020.5000E-020.1781E-011.AX 3AY 3 30.5000E-020.5000E-020.1781E-011.AY 3AZ 3 30.5000E-020.5000E-020.1781E-011.AZ 3B1 3 30.5000E-020.5000E-020.1781E-011.B1 3B2 3 30.5000E-020.5000E-020.1781E-011.

111

B2 3B3 3 30.5000E-020.5000E-020.1781E-011.B3 3B4 3 30.5000E-020.5000E-020.1781E-011.B4 3B5 3 30.5000E-020.5000E-020.1781E-011.B5 3B6 3 30.5000E-020.5000E-020.1781E-011.B6 3B7 3 30.5000E-020.5000E-020.1781E-011.B7 3B8 3 30.5000E-020.5000E-020.1781E-011.B8 3B9 3 30.5000E-020.5000E-020.1781E-011.B9 3BA 3 30.5000E-020.2500E-020.1781E-011.BA 3BB 3 30.2500E-020.5000E-020.1781E-011.BB 3BC 3 30.5000E-020.5000E-020.1781E-011.BC 3BD 3 30.5000E-020.5000E-020.1781E-011.BD 3BE 3 30.5000E-020.5000E-020.1781E-011.BE 3BF 3 30.5000E-020.5000E-020.1781E-011.BF 3AMB 1 30.5000E-021.0000E-110.1781E-011.

TIMES----1----*----2----*----3----*----4----*----5----*----6----*----7----*----8 2 4.320E+05 6.048E+05INDOM----1----*----2----*----3----*----4----*----5----*----6----*----7----*----8BOUND 1.1861E5 24.AMBIE 1.0065E5 24.

GENER----1----*----2----*----3----*----4----*----5----*----6----*----7----*----8BA1 1HTR 1 9 HEAT 0.0000000E+00 0.2988000E+04 0.8701200E+05 0.1800000E+06 0.2688120E+06 0.3528000E+06 0.4403880E+06 0.5256600E+06 0.6134400E+06 0.1728000E-03 0.2354920E+00 0.5151800E+00 0.9724400E+00 0.1237280E+01 0.1509900E+01 0.1789780E+01 0.2083600E+01 0.2083600E+01BA2 1HTR 2 9 HEAT 0.0000000E+00 0.2988000E+04 0.8701200E+05 0.1800000E+06 0.2688120E+06 0.3528000E+06 0.4403880E+06 0.5256600E+06 0.6134400E+06 0.1728000E-03 0.2354920E+00 0.5151800E+00 0.9724400E+00 0.1237280E+01 0.1509900E+01 0.1789780E+01 0.2083600E+01 0.2083600E+01BA3 1HTR 3 9 HEAT 0.0000000E+00 0.2988000E+04 0.8701200E+05 0.1800000E+06 0.2688120E+06 0.3528000E+06 0.4403880E+06 0.5256600E+06 0.6134400E+06 0.1728000E-03 0.2354920E+00 0.5151800E+00 0.9724400E+00 0.1237280E+01 0.1509900E+01 0.1789780E+01 0.2083600E+01 0.2083600E+01BA4 1HTR 4 9 HEAT 0.0000000E+00 0.2988000E+04 0.8701200E+05 0.1800000E+06 0.2688120E+06 0.3528000E+06 0.4403880E+06 0.5256600E+06 0.6134400E+06 0.1728000E-03 0.2354920E+00 0.5151800E+00 0.9724400E+00 0.1237280E+01 0.1509900E+01 0.1789780E+01 0.2083600E+01 0.2083600E+01BA5 1HTR 5 9 HEAT 0.0000000E+00 0.2988000E+04 0.8701200E+05 0.1800000E+06 0.2688120E+06 0.3528000E+06 0.4403880E+06 0.5256600E+06 0.6134400E+06 0.1728000E-03 0.2354920E+00 0.5151800E+00 0.9724400E+00

112

0.1237280E+01 0.1509900E+01 0.1789780E+01 0.2083600E+01 0.2083600E+01

ENDCY----1----*----2----*----3----*----4----*----5----*----6----*----7----*----8

113

A.1.2 ITOUGH2 input file.

> PARAMETERS >> heat CONDUCTIVITY >>> MATERIAL: BEREA >>>> VALUE >>>> RANGE: 3.0 6.0 >>>> DEVIATION: 0.2 >>>> STEP :0.05 <<<< >>> MATERIAL: HEATB >>>> VALUE >>>> RANGE: 0.001 2.0 >>>> DEVIATION: 0.05 <<<< >>> MATERIAL: INSUL >>>> VALUE >>>> RANGE: 0.01 2.0 >>>> DEVIATION: 0.05 <<<< <<< >> RATE >>> SOURCE: HTR_1 +4 >>>> ANNOTATION : H2 >>>> PARAMETER No.: 2 >>>> DEVIATION : 0.1 >>>> VALUE >>>> STEP : 0.1 <<<< >>> SOURCE: HTR_1 +4 >>>> ANNOTATION : H3 >>>> PARAMETER No.: 3 >>>> DEVIATION : 0.1 >>>> VALUE >>>> STEP : 0.1 <<<< >>> SOURCE: HTR_1 +4 >>>> ANNOTATION : H4 >>>> PARAMETER No.: 4 >>>> DEVIATION : 0.1 >>>> VALUE >>>> STEP : 0.1 <<<< >>> SOURCE: HTR_1 +4 >>>> ANNOTATION : H5 >>>> PARAMETER No.: 5 >>>> DEVIATION : 0.1 >>>> VALUE >>>> STEP : 0.1 <<<< >>> SOURCE: HTR_1 +4 >>>> ANNOTATION : H6 >>>> PARAMETER No.: 6 >>>> DEVIATION : 0.1 >>>> VALUE >>>> STEP : 0.1 <<<< <<< <<> OBSERVATIONS

114

>> TIMES: 30 EQUALLY spaced in [DAYS] between 0.140 4.900 >> TIMES: 5 in SECONDS at heat changes .298800E+04 .870120E+05 .180000E+06 .268812E+06 .352800E+06

>> TEMPERATURE >>> ELEMENT: B9__2 >>>> ANNOTATION: T1 >>>> COLUMNS: 1 3 >>>> PICK : 10 >>>> DATA in DAYS on FILE: temp.dat >>>> DEVIATION: 1.0 degree C <<<< >>> ELEMENT: B5__2 >>>> ANNOTATION: T2 >>>> COLUMNS: 1 4 >>>> PICK : 10 >>>> DATA in DAYS on FILE: temp.dat >>>> DEVIATION: 1.0 deg C <<<< >>> ELEMENT: B3__2 >>>> ANNOTATION: T3 >>>> COLUMNS: 1 5 >>>> PICK : 10 >>>> DATA in DAYS on FILE: temp.dat >>>> DEVIATION: 1.0 deg C <<<< >>> ELEMENT: AZ__2 >>>> ANNOTATION: T4 >>>> COLUMNS: 1 6 >>>> PICK : 10 >>>> DATA in DAYS on FILE: temp.dat >>>> DEVIATION: 1.0 deg C <<<< >>> ELEMENT: AV__2 >>>> ANNOTATION: T5 >>>> COLUMNS: 1 7 >>>> PICK : 10 >>>> DATA in DAYS on FILE: temp.dat >>>> DEVIATION: 1.0 deg C <<<< >>> ELEMENT: AT__2 >>>> ANNOTATION: T6 >>>> COLUMNS: 1 8 >>>> PICK : 10 >>>> DATA in DAYS on FILE: temp.dat >>>> DEVIATION: 1.0 deg C <<<< >>> ELEMENT: AQ__2 >>>> ANNOTATION: T7 >>>> COLUMNS: 1 9 >>>> PICK : 10 >>>> DATA in DAYS on FILE: temp.dat >>>> DEVIATION: 1.0 deg C <<<<

>>> ELEMENT: AM__2

115

>>>> ANNOTATION: T8 >>>> COLUMNS: 1 10 >>>> PICK : 10 >>>> DATA in DAYS on FILE: temp.dat >>>> DEVIATION: 1.0 deg C <<<< >>> ELEMENT: AH__2 >>>> ANNOTATION: T9 >>>> COLUMNS: 1 11 >>>> PICK : 10 >>>> DATA in DAYS on FILE: temp.dat >>>> DEVIATION: 1.0 deg C <<<< >>> ELEMENT: AB__2 >>>> ANNOTATION: T10 >>>> COLUMNS: 1 12 >>>> PICK : 10 >>>> DATA in DAYS on FILE: temp.dat >>>> DEVIATION: 1.0 deg C <<<< >>> ELEMENT: A4__2 >>>> ANNOTATION: T11 >>>> COLUMNS: 1 13 >>>> PICK : 10 >>>> DATA in DAYS on FILE: temp.dat >>>> DEVIATION: 1.0 deg C <<<< <<<

>> HEAT FLOW >>> CONNECTION: B3__2 B3__3 >>>> ANNOTATION: HF1 >>>> FACTOR: -1.910E-3 [W/m^2 - W] >>>> COLUMNS: 1 3 >>>> PICK : 10 >>>> DATA in HOURS on FILE: hflux.dat >>>> DEVIATION: 10.0 W/m^2 <<<< >>> CONNECTION: B5__2 B5__3 >>>> ANNOTATION: HF2 >>>> FACTOR: -1.910E-3 [W/m^2 - W] >>>> COLUMNS: 1 4 >>>> PICK : 10 >>>> DATA in HOURS on FILE: hflux.dat >>>> DEVIATION: 10.0 W/m^2 <<<< >>> CONNECTION: B3__2 B3__3 >>>> ANNOTATION: HF3 >>>> FACTOR: -1.910E-3 [W/m^2 - W] >>>> COLUMNS: 1 5 >>>> PICK : 10 >>>> DATA in HOURS on FILE: hflux.dat >>>> DEVIATION: 10.0 W/m^2 <<<< >>> CONNECTION: AZ__2 AZ__3 >>>> ANNOTATION: HF4 >>>> FACTOR: -1.910E-3 [W/m^2 - W] >>>> COLUMNS: 1 6 >>>> PICK : 10 >>>> DATA in HOURS on FILE: hflux.dat >>>> DEVIATION: 10.0 W/m^2

116

<<<< >>> CONNECTION: AV__2 AV__3 >>>> ANNOTATION: HF5 >>>> FACTOR: -1.910E-3 [W/m^2 - W] >>>> COLUMNS: 1 7 >>>> PICK : 10 >>>> DATA in HOURS on FILE: hflux.dat >>>> DEVIATION: 10.0 W/m^2 <<<< >>> CONNECTION: AT__2 AT__3 >>>> ANNOTATION: HF6 >>>> FACTOR: -1.910E-3 [W/m^2 - W] >>>> COLUMNS: 1 8 >>>> PICK : 10 >>>> DATA in HOURS on FILE: hflux.dat >>>> DEVIATION: 10.0 W/m^2 <<<< >>> CONNECTION: AQ__2 AQ__3 >>>> ANNOTATION: HF7 >>>> FACTOR: -1.910E-3 [W/m^2 - W] >>>> COLUMNS: 1 9 >>>> PICK : 10 >>>> DATA in HOURS on FILE: hflux.dat >>>> DEVIATION: 10.0 W/m^2 <<<< >>> CONNECTION: AM__2 AM__3 >>>> ANNOTATION: HF8 >>>> FACTOR: -1.910E-3 [W/m^2 - W] >>>> COLUMNS: 1 10 >>>> PICK : 10 >>>> DATA in HOURS on FILE: hflux.dat >>>> DEVIATION: 10.0 W/m^2 <<<< >>> CONNECTION: AH__2 AH__3 >>>> ANNOTATION: HF9 >>>> FACTOR: -1.910E-3 [W/m^2 - W] >>>> COLUMNS: 1 11 >>>> PICK : 10 >>>> DATA in HOURS on FILE: hflux.dat >>>> DEVIATION: 10.0 W/m^2 <<<< >>> CONNECTION: AB__2 AB__3 >>>> ANNOTATION: HF10 >>>> FACTOR: -1.910E-3 [W/m^2 - W] >>>> COLUMNS: 1 12 >>>> PICK : 10 >>>> DATA in HOURS on FILE: hflux.dat >>>> DEVIATION: 10.0 W/m^2 <<<< >>> CONNECTION: A4__2 A4__3 >>>> ANNOTATION: HF11 >>>> FACTOR: -1.910E-3 [W/m^2 - W] >>>> COLUMNS: 1 13 >>>> PICK : 10 >>>> DATA in HOURS on FILE: hflux.dat >>>> DEVIATION: 10.0 W/m^2 <<<< <<< <<

117

> COMPUTATION >> STOPPING criteria >>> IGNORE WARNINGS >>> max. no. of ITERATIONS: 50 >>> IQIT=3: 50 >>> CONSECUTIVE: 100 >>> LEVENBERG: 0.01 >>> STEP : 0.5 <<< >> JACOBIAN >>> FORWARD: 9 >>> PERTURB: 0.01 <<< >> OUTPUT >>> PLOTFILE: COLUMNS >>> DAYS >>> generate file with CHARACTERISTIC curves <<< <<<

118

A.2 Linear model calibration input files

A.2.1 TOUGH2 input file.

ROCKS----1----*----2----*----3----*----4----*----5----*----6----*----7----*----8BEREA 2 2163. 0.210 0.0E-20 0.0E-20 7.800E-13 4.989858.240.0000E+000.0000E+000.2163E+010.1000E+01 1 0.300 0.100 0.800 0.800 1 1.0E05 0.000 1.000HEATE 0 2200. 0.010 0.0E-15 0.0E-15 0.0E-15 2.885246.6HEATB 0 240. 0.010 0.0E-15 0.0E-15 0.0E-15 0.1631046.6EPOXY 0 1200. 0.010 0.0E-15 0.0E-15 0.0E-15 0.5771046.6INSUL 0 192. 0.010 0.0E-15 0.0E-15 0.0E-15 0.115104.7BOUND 0 2163. 0.990 0.0E-15 0.0E-15 0.0E-15 0.642-1611.0AMBIE 1.293 0.990 0.0E-20 0.0E-20 1.0E-10 0.055-1611.0

START----1----*----2----*----3----*----4----*----5----*----6----*----7----*----8PARAM 123456789012345678901234 -31500 1500100000100101000400001000 2.130E-05 1.0 6.1020E5 1.00E+03 9.8100 1.E-5 1.0065E5 24. 0.0MESHMAKER1----*----2----*----3----*----4----*----5----*----6----*----7----*----8RZ2DRADII 5 0 0.0254 0.0304 0.0812 5.0812LAYER----1----*----2----*----3----*----4----*----5----*----6----*----7----*----8 51 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.01000.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.01000.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.01000.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.01000.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.01000.0100 0.0100 0.0100 0.0100 0.0100 0.0050 0.0100 0.01000.0100 0.0100 0.0100 5.0000

ELEME --- 4 5 0 0 0.00000 5.132BOU 1 BOUND .2027E+540.2027E-02 0.1270E-01 -.5000E-02A2 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.1500E-01

119

A3 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.2500E-01A4 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.3500E-01A5 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.4500E-01A6 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.5500E-01A7 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.6500E-01A8 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.7500E-01A9 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.8500E-01AA 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.9500E-01AB 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.1050E+00AC 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.1150E+00AD 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.1250E+00AE 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.1350E+00AF 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.1450E+00AG 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.1550E+00AH 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.1650E+00AI 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.1750E+00AJ 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.1850E+00AK 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.1950E+00AL 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.2050E+00AM 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.2150E+00AN 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.2250E+00AO 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.2350E+00AP 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.2450E+00AQ 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.2550E+00AR 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.2650E+00AS 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.2750E+00AT 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.2850E+00AU 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.2950E+00AV 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.3050E+00AW 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.3150E+00

120

AX 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.3250E+00AY 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.3350E+00AZ 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.3450E+00B1 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.3550E+00B2 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.3650E+00B3 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.3750E+00B4 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.3850E+00B5 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.3950E+00B6 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.4050E+00B7 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.4150E+00B8 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.4250E+00B9 1 BEREA .2027E-040.0000E+00 0.1270E-01 -.4350E+00BA1 1 HEATE2.0260E-060.0000E+00 0.1270E-01 -.4425E+00BA2 1 HEATE2.0260E-060.0000E+00 0.1270E-01 -.4425E+00BA3 1 HEATE2.0260E-060.0000E+00 0.1270E-01 -.4425E+00BA4 1 HEATE2.0260E-060.0000E+00 0.1270E-01 -.4425E+00BA5 1 HEATE2.0260E-060.0000E+00 0.1270E-01 -.4425E+00BB 1 HEATB .2027E-040.0000E+00 0.1270E-01 -.4500E+00BC 1 HEATB .2027E-040.0000E+00 0.1270E-01 -.4600E+00BD 1 HEATB .2027E-040.0000E+00 0.1270E-01 -.4700E+00BE 1 HEATB .2027E-040.0000E+00 0.1270E-01 -.4800E+00BF 1 HEATB .2027E-040.0000E+00 0.1270E-01 -.4900E+00AMB 1 AMBIE .1013E+540.2027E-02 0.1270E-01 -.2995E+01A2 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.1500E-01A3 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.2500E-01A4 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.3500E-01A5 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.4500E-01A6 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.5500E-01A7 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.6500E-01A8 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.7500E-01

121

A9 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.8500E-01AA 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.9500E-01AB 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.1050E+00AC 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.1150E+00AD 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.1250E+00AE 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.1350E+00AF 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.1450E+00AG 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.1550E+00AH 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.1650E+00AI 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.1750E+00AJ 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.1850E+00AK 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.1950E+00AL 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.2050E+00AM 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.2150E+00AN 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.2250E+00AO 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.2350E+00AP 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.2450E+00AQ 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.2550E+00AR 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.2650E+00AS 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.2750E+00AT 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.2850E+00AU 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.2950E+00AV 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.3050E+00AW 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.3150E+00AX 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.3250E+00AY 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.3350E+00AZ 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.3450E+00B1 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.3550E+00B2 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.3650E+00B3 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.3750E+00

122

B4 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.3850E+00B5 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.3950E+00B6 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.4050E+00B7 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.4150E+00B8 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.4250E+00B9 2 EPOXY .8765E-050.0000E+00 0.2790E-01 -.4350E+00BA 2 EPOXY .4383E-050.0000E+00 0.2790E-01 -.4425E+00BB 2 HEATB .8765E-050.0000E+00 0.2790E-01 -.4500E+00BC 2 HEATB .8765E-050.0000E+00 0.2790E-01 -.4600E+00BD 2 HEATB .8765E-050.0000E+00 0.2790E-01 -.4700E+00BE 2 HEATB .8765E-050.0000E+00 0.2790E-01 -.4800E+00BF 2 HEATB .8765E-050.0000E+00 0.2790E-01 -.4900E+00A2 3 INSUL .1781E-000.0000E+00 0.5580E-01 -.1500E-01A3 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.2500E-01A4 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.3500E-01A5 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.4500E-01A6 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.5500E-01A7 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.6500E-01A8 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.7500E-01A9 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.8500E-01AA 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.9500E-01AB 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.1050E+00AC 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.1150E+00AD 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.1250E+00AE 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.1350E+00AF 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.1450E+00AG 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.1550E+00AH 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.1650E+00AI 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.1750E+00AJ 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.1850E+00

123

AK 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.1950E+00AL 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.2050E+00AM 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.2150E+00AN 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.2250E+00AO 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.2350E+00AP 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.2450E+00AQ 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.2550E+00AR 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.2650E+00AS 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.2750E+00AT 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.2850E+00AU 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.2950E+00AV 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.3050E+00AW 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.3150E+00AX 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.3250E+00AY 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.3350E+00AZ 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.3450E+00B1 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.3550E+00B2 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.3650E+00B3 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.3750E+00B4 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.3850E+00B5 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.3950E+00B6 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.4050E+00B7 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.4150E+00B8 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.4250E+00B9 3 INSUL .1781E-030.0000E+00 0.5580E-01 -.4350E+00BA 3 INSUL .8905E-040.0000E+00 0.5580E-01 -.4425E+00BB 3 HEATB .1781E-030.0000E+00 0.5580E-01 -.4500E+00BC 3 HEATB .1781E-030.0000E+00 0.5580E-01 -.4600E+00BD 3 HEATB .1781E-030.0000E+00 0.5580E-01 -.4700E+00BE 3 HEATB .1781E-030.0000E+00 0.5580E-01 -.4800E+00

124

BF 3 HEATB .1781E-030.0000E+00 0.5580E-01 -.4900E+00

CONNEA2 1A2 2 10.1270E-010.2500E-020.1596E-02A3 1A3 2 10.1270E-010.2500E-020.1596E-02A4 1A4 2 10.1270E-010.2500E-020.1596E-02A5 1A5 2 10.1270E-010.2500E-020.1596E-02A6 1A6 2 10.1270E-010.2500E-020.1596E-02A7 1A7 2 10.1270E-010.2500E-020.1596E-02A8 1A8 2 10.1270E-010.2500E-020.1596E-02A9 1A9 2 10.1270E-010.2500E-020.1596E-02AA 1AA 2 10.1270E-010.2500E-020.1596E-02AB 1AB 2 10.1270E-010.2500E-020.1596E-02AC 1AC 2 10.1270E-010.2500E-020.1596E-02AD 1AD 2 10.1270E-010.2500E-020.1596E-02AE 1AE 2 10.1270E-010.2500E-020.1596E-02AF 1AF 2 10.1270E-010.2500E-020.1596E-02AG 1AG 2 10.1270E-010.2500E-020.1596E-02AH 1AH 2 10.1270E-010.2500E-020.1596E-02AI 1AI 2 10.1270E-010.2500E-020.1596E-02AJ 1AJ 2 10.1270E-010.2500E-020.1596E-02AK 1AK 2 10.1270E-010.2500E-020.1596E-02AL 1AL 2 10.1270E-010.2500E-020.1596E-02AM 1AM 2 10.1270E-010.2500E-020.1596E-02AN 1AN 2 10.1270E-010.2500E-020.1596E-02AO 1AO 2 10.1270E-010.2500E-020.1596E-02AP 1AP 2 10.1270E-010.2500E-020.1596E-02AQ 1AQ 2 10.1270E-010.2500E-020.1596E-02AR 1AR 2 10.1270E-010.2500E-020.1596E-02AS 1AS 2 10.1270E-010.2500E-020.1596E-02AT 1AT 2 10.1270E-010.2500E-020.1596E-02AU 1AU 2 10.1270E-010.2500E-020.1596E-02AV 1AV 2 10.1270E-010.2500E-020.1596E-02AW 1AW 2 10.1270E-010.2500E-020.1596E-02AX 1AX 2 10.1270E-010.2500E-020.1596E-02AY 1AY 2 10.1270E-010.2500E-020.1596E-02AZ 1AZ 2 10.1270E-010.2500E-020.1596E-02B1 1B1 2 10.1270E-010.2500E-020.1596E-02B2 1B2 2 10.1270E-010.2500E-020.1596E-02B3 1B3 2 10.1270E-010.2500E-020.1596E-02B4 1B4 2 10.1270E-010.2500E-020.1596E-02B5 1B5 2 10.1270E-010.2500E-020.1596E-02B6 1B6 2 10.1270E-010.2500E-020.1596E-02B7 1B7 2 10.1270E-010.2500E-020.1596E-02B8 1B8 2 10.1270E-010.2500E-020.1596E-02B9 1B9 2 10.1270E-010.2500E-020.1596E-02BA1 1BA 2 10.1270E-010.2500E-021.5960E-04BA2 1BA 2 10.1270E-010.2500E-021.5960E-04BA3 1BA 2 10.1270E-010.2500E-021.5960E-04BA4 1BA 2 10.1270E-010.2500E-021.5960E-04BA5 1BA 2 10.1270E-010.2500E-021.5960E-04BB 1BB 2 10.1270E-010.2500E-020.1596E-02BC 1BC 2 10.1270E-010.2500E-020.1596E-02BD 1BD 2 10.1270E-010.2500E-020.1596E-02BE 1BE 2 10.1270E-010.2500E-020.1596E-02BF 1BF 2 10.1270E-010.2500E-020.1596E-02A2 2A2 3 10.2500E-020.2540E-010.1910E-02A3 2A3 3 10.2500E-020.2540E-010.1910E-02A4 2A4 3 10.2500E-020.2540E-010.1910E-02A5 2A5 3 10.2500E-020.2540E-010.1910E-02

125

A6 2A6 3 10.2500E-020.2540E-010.1910E-02A7 2A7 3 10.2500E-020.2540E-010.1910E-02A8 2A8 3 10.2500E-020.2540E-010.1910E-02A9 2A9 3 10.2500E-020.2540E-010.1910E-02AA 2AA 3 10.2500E-020.2540E-010.1910E-02AB 2AB 3 10.2500E-020.2540E-010.1910E-02AC 2AC 3 10.2500E-020.2540E-010.1910E-02AD 2AD 3 10.2500E-020.2540E-010.1910E-02AE 2AE 3 10.2500E-020.2540E-010.1910E-02AF 2AF 3 10.2500E-020.2540E-010.1910E-02AG 2AG 3 10.2500E-020.2540E-010.1910E-02AH 2AH 3 10.2500E-020.2540E-010.1910E-02AI 2AI 3 10.2500E-020.2540E-010.1910E-02AJ 2AJ 3 10.2500E-020.2540E-010.1910E-02AK 2AK 3 10.2500E-020.2540E-010.1910E-02AL 2AL 3 10.2500E-020.2540E-010.1910E-02AM 2AM 3 10.2500E-020.2540E-010.1910E-02AN 2AN 3 10.2500E-020.2540E-010.1910E-02AO 2AO 3 10.2500E-020.2540E-010.1910E-02AP 2AP 3 10.2500E-020.2540E-010.1910E-02AQ 2AQ 3 10.2500E-020.2540E-010.1910E-02AR 2AR 3 10.2500E-020.2540E-010.1910E-02AS 2AS 3 10.2500E-020.2540E-010.1910E-02AT 2AT 3 10.2500E-020.2540E-010.1910E-02AU 2AU 3 10.2500E-020.2540E-010.1910E-02AV 2AV 3 10.2500E-020.2540E-010.1910E-02AW 2AW 3 10.2500E-020.2540E-010.1910E-02AX 2AX 3 10.2500E-020.2540E-010.1910E-02AY 2AY 3 10.2500E-020.2540E-010.1910E-02AZ 2AZ 3 10.2500E-020.2540E-010.1910E-02B1 2B1 3 10.2500E-020.2540E-010.1910E-02B2 2B2 3 10.2500E-020.2540E-010.1910E-02B3 2B3 3 10.2500E-020.2540E-010.1910E-02B4 2B4 3 10.2500E-020.2540E-010.1910E-02B5 2B5 3 10.2500E-020.2540E-010.1910E-02B6 2B6 3 10.2500E-020.2540E-010.1910E-02B7 2B7 3 10.2500E-020.2540E-010.1910E-02B8 2B8 3 10.2500E-020.2540E-010.1910E-02B9 2B9 3 10.2500E-020.2540E-010.1910E-02BA 2BA 3 10.2500E-020.2540E-010.9550E-03BB 2BB 3 10.2500E-020.2540E-010.1910E-02BC 2BC 3 10.2500E-020.2540E-010.1910E-02BD 2BD 3 10.2500E-020.2540E-010.1910E-02BE 2BE 3 10.2500E-020.2540E-010.1910E-02BF 2BF 3 10.2500E-020.2540E-010.1910E-02A2 3AMB 1 10.2540E-011.0000E-110.5102E-02A3 3AMB 1 10.2540E-011.0000E-110.5102E-02A4 3AMB 1 10.2540E-011.0000E-110.5102E-02A5 3AMB 1 10.2540E-011.0000E-110.5102E-02A6 3AMB 1 10.2540E-011.0000E-110.5102E-02A7 3AMB 1 10.2540E-011.0000E-110.5102E-02A8 3AMB 1 10.2540E-011.0000E-110.5102E-02A9 3AMB 1 10.2540E-011.0000E-110.5102E-02AA 3AMB 1 10.2540E-011.0000E-110.5102E-02AB 3AMB 1 10.2540E-011.0000E-110.5102E-02AC 3AMB 1 10.2540E-011.0000E-110.5102E-02AD 3AMB 1 10.2540E-011.0000E-110.5102E-02AE 3AMB 1 10.2540E-011.0000E-110.5102E-02AF 3AMB 1 10.2540E-011.0000E-110.5102E-02AG 3AMB 1 10.2540E-011.0000E-110.5102E-02AH 3AMB 1 10.2540E-011.0000E-110.5102E-02

126

AI 3AMB 1 10.2540E-011.0000E-110.5102E-02AJ 3AMB 1 10.2540E-011.0000E-110.5102E-02AK 3AMB 1 10.2540E-011.0000E-110.5102E-02AL 3AMB 1 10.2540E-011.0000E-110.5102E-02AM 3AMB 1 10.2540E-011.0000E-110.5102E-02AN 3AMB 1 10.2540E-011.0000E-110.5102E-02AO 3AMB 1 10.2540E-011.0000E-110.5102E-02AP 3AMB 1 10.2540E-011.0000E-110.5102E-02AQ 3AMB 1 10.2540E-011.0000E-110.5102E-02AR 3AMB 1 10.2540E-011.0000E-110.5102E-02AS 3AMB 1 10.2540E-011.0000E-110.5102E-02AT 3AMB 1 10.2540E-011.0000E-110.5102E-02AU 3AMB 1 10.2540E-011.0000E-110.5102E-02AV 3AMB 1 10.2540E-011.0000E-110.5102E-02AW 3AMB 1 10.2540E-011.0000E-110.5102E-02AX 3AMB 1 10.2540E-011.0000E-110.5102E-02AY 3AMB 1 10.2540E-011.0000E-110.5102E-02AZ 3AMB 1 10.2540E-011.0000E-110.5102E-02B1 3AMB 1 10.2540E-011.0000E-110.5102E-02B2 3AMB 1 10.2540E-011.0000E-110.5102E-02B3 3AMB 1 10.2540E-011.0000E-110.5102E-02B4 3AMB 1 10.2540E-011.0000E-110.5102E-02B5 3AMB 1 10.2540E-011.0000E-110.5102E-02B6 3AMB 1 10.2540E-011.0000E-110.5102E-02B7 3AMB 1 10.2540E-011.0000E-110.5102E-02B8 3AMB 1 10.2540E-011.0000E-110.5102E-02B9 3AMB 1 10.2540E-011.0000E-110.5102E-02BA 3AMB 1 10.2540E-011.0000E-110.2551E-02BB 3AMB 1 10.2540E-011.0000E-110.5102E-02BC 3AMB 1 10.2540E-011.0000E-110.5102E-02BD 3AMB 1 10.2540E-011.0000E-110.5102E-02BE 3AMB 1 10.2540E-011.0000E-110.5102E-02BF 3AMB 1 10.2540E-011.0000E-110.5102E-02BOU 1A2 1 31.0000E-100.5000E-020.2027E-021.A2 1A3 1 30.5000E-020.5000E-020.2027E-021.A3 1A4 1 30.5000E-020.5000E-020.2027E-021.A4 1A5 1 30.5000E-020.5000E-020.2027E-021.A5 1A6 1 30.5000E-020.5000E-020.2027E-021.A6 1A7 1 30.5000E-020.5000E-020.2027E-021.A7 1A8 1 30.5000E-020.5000E-020.2027E-021.A8 1A9 1 30.5000E-020.5000E-020.2027E-021.A9 1AA 1 30.5000E-020.5000E-020.2027E-021.AA 1AB 1 30.5000E-020.5000E-020.2027E-021.AB 1AC 1 30.5000E-020.5000E-020.2027E-021.AC 1AD 1 30.5000E-020.5000E-020.2027E-021.AD 1AE 1 30.5000E-020.5000E-020.2027E-021.AE 1AF 1 30.5000E-020.5000E-020.2027E-021.AF 1AG 1 30.5000E-020.5000E-020.2027E-021.AG 1AH 1 30.5000E-020.5000E-020.2027E-021.AH 1AI 1 30.5000E-020.5000E-020.2027E-021.AI 1AJ 1 30.5000E-020.5000E-020.2027E-021.AJ 1AK 1 30.5000E-020.5000E-020.2027E-021.AK 1AL 1 30.5000E-020.5000E-020.2027E-021.AL 1AM 1 30.5000E-020.5000E-020.2027E-021.AM 1AN 1 30.5000E-020.5000E-020.2027E-021.AN 1AO 1 30.5000E-020.5000E-020.2027E-021.AO 1AP 1 30.5000E-020.5000E-020.2027E-021.AP 1AQ 1 30.5000E-020.5000E-020.2027E-021.AQ 1AR 1 30.5000E-020.5000E-020.2027E-021.AR 1AS 1 30.5000E-020.5000E-020.2027E-021.AS 1AT 1 30.5000E-020.5000E-020.2027E-021.

127

AT 1AU 1 30.5000E-020.5000E-020.2027E-021.AU 1AV 1 30.5000E-020.5000E-020.2027E-021.AV 1AW 1 30.5000E-020.5000E-020.2027E-021.AW 1AX 1 30.5000E-020.5000E-020.2027E-021.AX 1AY 1 30.5000E-020.5000E-020.2027E-021.AY 1AZ 1 30.5000E-020.5000E-020.2027E-021.AZ 1B1 1 30.5000E-020.5000E-020.2027E-021.B1 1B2 1 30.5000E-020.5000E-020.2027E-021.B2 1B3 1 30.5000E-020.5000E-020.2027E-021.B3 1B4 1 30.5000E-020.5000E-020.2027E-021.B4 1B5 1 30.5000E-020.5000E-020.2027E-021.B5 1B6 1 30.5000E-020.5000E-020.2027E-021.B6 1B7 1 30.5000E-020.5000E-020.2027E-021.B7 1B8 1 30.5000E-020.5000E-020.2027E-021.B8 1B9 1 30.5000E-020.5000E-020.2027E-021.B9 1BA1 1 30.5000E-020.5000E-030.2027E-021.BA1 1BA2 1 30.5000E-030.5000E-030.2027E-021.BA2 1BA3 1 30.5000E-030.5000E-030.2027E-021.BA3 1BA4 1 30.5000E-030.5000E-030.2027E-021.BA4 1BA5 1 30.5000E-030.5000E-030.2027E-021.BA5 1BB 1 30.5000E-030.5000E-020.2027E-021.BB 1BC 1 30.5000E-020.5000E-020.2027E-021.BC 1BD 1 30.5000E-020.5000E-020.2027E-021.BD 1BE 1 30.5000E-020.5000E-020.2027E-021.BE 1BF 1 30.5000E-020.5000E-020.2027E-021.BF 1AMB 1 30.5000E-021.0000E-110.2027E-021.BOU 1A2 2 31.0000E-100.5000E-020.8765E-031.A2 2A3 2 30.5000E-020.5000E-020.8765E-031.A3 2A4 2 30.5000E-020.5000E-020.8765E-031.A4 2A5 2 30.5000E-020.5000E-020.8765E-031.A5 2A6 2 30.5000E-020.5000E-020.8765E-031.A6 2A7 2 30.5000E-020.5000E-020.8765E-031.A7 2A8 2 30.5000E-020.5000E-020.8765E-031.A8 2A9 2 30.5000E-020.5000E-020.8765E-031.A9 2AA 2 30.5000E-020.5000E-020.8765E-031.AA 2AB 2 30.5000E-020.5000E-020.8765E-031.AB 2AC 2 30.5000E-020.5000E-020.8765E-031.AC 2AD 2 30.5000E-020.5000E-020.8765E-031.AD 2AE 2 30.5000E-020.5000E-020.8765E-031.AE 2AF 2 30.5000E-020.5000E-020.8765E-031.AF 2AG 2 30.5000E-020.5000E-020.8765E-031.AG 2AH 2 30.5000E-020.5000E-020.8765E-031.AH 2AI 2 30.5000E-020.5000E-020.8765E-031.AI 2AJ 2 30.5000E-020.5000E-020.8765E-031.AJ 2AK 2 30.5000E-020.5000E-020.8765E-031.AK 2AL 2 30.5000E-020.5000E-020.8765E-031.AL 2AM 2 30.5000E-020.5000E-020.8765E-031.AM 2AN 2 30.5000E-020.5000E-020.8765E-031.AN 2AO 2 30.5000E-020.5000E-020.8765E-031.AO 2AP 2 30.5000E-020.5000E-020.8765E-031.AP 2AQ 2 30.5000E-020.5000E-020.8765E-031.AQ 2AR 2 30.5000E-020.5000E-020.8765E-031.AR 2AS 2 30.5000E-020.5000E-020.8765E-031.AS 2AT 2 30.5000E-020.5000E-020.8765E-031.AT 2AU 2 30.5000E-020.5000E-020.8765E-031.AU 2AV 2 30.5000E-020.5000E-020.8765E-031.AV 2AW 2 30.5000E-020.5000E-020.8765E-031.AW 2AX 2 30.5000E-020.5000E-020.8765E-031.AX 2AY 2 30.5000E-020.5000E-020.8765E-031.AY 2AZ 2 30.5000E-020.5000E-020.8765E-031.AZ 2B1 2 30.5000E-020.5000E-020.8765E-031.

128

B1 2B2 2 30.5000E-020.5000E-020.8765E-031.B2 2B3 2 30.5000E-020.5000E-020.8765E-031.B3 2B4 2 30.5000E-020.5000E-020.8765E-031.B4 2B5 2 30.5000E-020.5000E-020.8765E-031.B5 2B6 2 30.5000E-020.5000E-020.8765E-031.B6 2B7 2 30.5000E-020.5000E-020.8765E-031.B7 2B8 2 30.5000E-020.5000E-020.8765E-031.B8 2B9 2 30.5000E-020.5000E-020.8765E-031.B9 2BA 2 30.5000E-020.2500E-020.8765E-031.BA 2BB 2 30.2500E-020.5000E-020.8765E-031.BB 2BC 2 30.5000E-020.5000E-020.8765E-031.BC 2BD 2 30.5000E-020.5000E-020.8765E-031.BD 2BE 2 30.5000E-020.5000E-020.8765E-031.BE 2BF 2 30.5000E-020.5000E-020.8765E-031.BF 2AMB 1 30.5000E-021.0000E-110.8765E-031.BOU 1A2 3 31.0000E-100.5000E-020.1781E-011.A2 3A3 3 30.5000E-020.5000E-020.1781E-011.A3 3A4 3 30.5000E-020.5000E-020.1781E-011.A4 3A5 3 30.5000E-020.5000E-020.1781E-011.A5 3A6 3 30.5000E-020.5000E-020.1781E-011.A6 3A7 3 30.5000E-020.5000E-020.1781E-011.A7 3A8 3 30.5000E-020.5000E-020.1781E-011.A8 3A9 3 30.5000E-020.5000E-020.1781E-011.A9 3AA 3 30.5000E-020.5000E-020.1781E-011.AA 3AB 3 30.5000E-020.5000E-020.1781E-011.AB 3AC 3 30.5000E-020.5000E-020.1781E-011.AC 3AD 3 30.5000E-020.5000E-020.1781E-011.AD 3AE 3 30.5000E-020.5000E-020.1781E-011.AE 3AF 3 30.5000E-020.5000E-020.1781E-011.AF 3AG 3 30.5000E-020.5000E-020.1781E-011.AG 3AH 3 30.5000E-020.5000E-020.1781E-011.AH 3AI 3 30.5000E-020.5000E-020.1781E-011.AI 3AJ 3 30.5000E-020.5000E-020.1781E-011.AJ 3AK 3 30.5000E-020.5000E-020.1781E-011.AK 3AL 3 30.5000E-020.5000E-020.1781E-011.AL 3AM 3 30.5000E-020.5000E-020.1781E-011.AM 3AN 3 30.5000E-020.5000E-020.1781E-011.AN 3AO 3 30.5000E-020.5000E-020.1781E-011.AO 3AP 3 30.5000E-020.5000E-020.1781E-011.AP 3AQ 3 30.5000E-020.5000E-020.1781E-011.AQ 3AR 3 30.5000E-020.5000E-020.1781E-011.AR 3AS 3 30.5000E-020.5000E-020.1781E-011.AS 3AT 3 30.5000E-020.5000E-020.1781E-011.AT 3AU 3 30.5000E-020.5000E-020.1781E-011.AU 3AV 3 30.5000E-020.5000E-020.1781E-011.AV 3AW 3 30.5000E-020.5000E-020.1781E-011.AW 3AX 3 30.5000E-020.5000E-020.1781E-011.AX 3AY 3 30.5000E-020.5000E-020.1781E-011.AY 3AZ 3 30.5000E-020.5000E-020.1781E-011.AZ 3B1 3 30.5000E-020.5000E-020.1781E-011.B1 3B2 3 30.5000E-020.5000E-020.1781E-011.B2 3B3 3 30.5000E-020.5000E-020.1781E-011.B3 3B4 3 30.5000E-020.5000E-020.1781E-011.B4 3B5 3 30.5000E-020.5000E-020.1781E-011.B5 3B6 3 30.5000E-020.5000E-020.1781E-011.B6 3B7 3 30.5000E-020.5000E-020.1781E-011.B7 3B8 3 30.5000E-020.5000E-020.1781E-011.B8 3B9 3 30.5000E-020.5000E-020.1781E-011.B9 3BA 3 30.5000E-020.2500E-020.1781E-011.BA 3BB 3 30.2500E-020.5000E-020.1781E-011.BB 3BC 3 30.5000E-020.5000E-020.1781E-011.

129

BC 3BD 3 30.5000E-020.5000E-020.1781E-011.BD 3BE 3 30.5000E-020.5000E-020.1781E-011.BE 3BF 3 30.5000E-020.5000E-020.1781E-011.BF 3AMB 1 30.5000E-021.0000E-110.1781E-011.

TIMES----1----*----2----*----3----*----4----*----5----*----6----*----7----*----8 2 4.320E+05 6.048E+05INDOM----1----*----2----*----3----*----4----*----5----*----6----*----7----*----8BOUND 1.1861E5 24.AMBIE 1.0065E5 24.

GENER----1----*----2----*----3----*----4----*----5----*----6----*----7----*----8BA1 1HTR 1 9 HEAT 0.0000000E+00 0.2988000E+04 0.8701200E+05 0.1800000E+06 0.2688120E+06 0.3528000E+06 0.4403880E+06 0.5256600E+06 0.6102000E+06 0.1728000E-03 0.1903238E+00 0.4641463E+00 0.9936570E+00 0.1349678E+01 0.1679179E+01 0.1789800E+01 0.2083600E+01 0.2083600E+01

BA2 1HTR 2 9 HEAT 0.0000000E+00 0.2988000E+04 0.8701200E+05 0.1800000E+06 0.2688120E+06 0.3528000E+06 0.4403880E+06 0.5256600E+06 0.6102000E+06 0.1728000E-03 0.1903238E+00 0.4641463E+00 0.9936570E+00 0.1349678E+01 0.1679179E+01 0.1789800E+01 0.2083600E+01 0.2083600E+01

BA3 1HTR 3 9 HEAT 0.0000000E+00 0.2988000E+04 0.8701200E+05 0.1800000E+06 0.2688120E+06 0.3528000E+06 0.4403880E+06 0.5256600E+06 0.6102000E+06 0.1728000E-03 0.1903238E+00 0.4641463E+00 0.9936570E+00 0.1349678E+01 0.1679179E+01 0.1789800E+01 0.2083600E+01 0.2083600E+01BA4 1HTR 4 9 HEAT 0.0000000E+00 0.2988000E+04 0.8701200E+05 0.1800000E+06 0.2688120E+06 0.3528000E+06 0.4403880E+06 0.5256600E+06 0.6102000E+06 0.1728000E-03 0.1903238E+00 0.4641463E+00 0.9936570E+00 0.1349678E+01 0.1679179E+01 0.1789800E+01 0.2083600E+01 0.2083600E+01

BA5 1HTR 5 9 HEAT 0.0000000E+00 0.2988000E+04 0.8701200E+05 0.1800000E+06 0.2688120E+06 0.3528000E+06 0.4403880E+06 0.5256600E+06 0.6102000E+06 0.1728000E-03 0.1903238E+00 0.4641463E+00 0.9936570E+00 0.1349678E+01 0.1679179E+01 0.1789800E+01 0.2083600E+01 0.2083600E+01

ENDCY----1----*----2----*----3----*----4----*----5----*----6----*----7----*----8

130

A.2.2 ITOUGH2 input file.

> PARAMETERS >> ABSOLUTE permeability >>> MATERIAL: BEREA >>>> LOGARITHM >>>> INDEX: 3 >>>> DEVIATION: 0.2 <<<< <<< >> RELATIVE permeability function >>> MATERIAL: BEREA >>>> PARAMETER No.: 1 >>>> ANNOTATION : Slr >>>> standard DEVIATION : 0.05 >>>> max STEP : 0.05 >>>> PERTURB : -0.001 >>>> estimate VALUE >>>> RANGE : 0.00 0.50 <<<< >>> MATERIAL: BEREA >>>> PARAMETER No.: 2 >>>> ANNOTATION : Sgr >>>> standard DEVIATION : 0.05 >>>> max STEP : 0.05 >>>> PERTURB : -0.001 >>>> estimate VALUE >>>> RANGE : 0.00 0.50 <<<< >>> MATERIAL: BEREA >>>> PARAMETER No.: 3 >>>> ANNOTATION : Sls >>>> standard DEVIATION : 0.05 >>>> max STEP : 0.05 >>>> PERTURB : -0.001 >>>> estimate VALUE >>>> RANGE : 0.51 1.00 <<<< >>> MATERIAL: BEREA >>>> PARAMETER No.: 4 >>>> ANNOTATION : Sgs >>>> standard DEVIATION : 0.05 >>>> max STEP : 0.02 >>>> estimate VALUE >>>> RANGE : 0.51 1.00 >>>> PERTURB : -0.001 <<<< <<<

>> parameters of the CAPILLARY pressure function >>> MATERIAL: BEREA >>>> PARAMETER No.: 1 >>>> ANNOTATION : Pc max >>>> standard DEVIATION : 0.50 >>>> max STEP: 0.2 >>>> estimate LOGARITHM <<<< <<<

131

>> RATE >>> SOURCE: HTR1_ +4 >>>> ANNOTATION : H7 >>>> PARAMETER No.: 7 >>>> DEVIATION : 0.1 >>>> VALUE >>>> STEP : 0.1 <<<< >>> SOURCE: HTR1_ +4 >>>> ANNOTATION : H8 >>>> PARAMETER No.: 8 >>>> DEVIATION : 0.1 >>>> VALUE >>>> STEP : 0.1 <<<< <<< <<

> OBSERVATIONS >> TIMES: 50 EQUALLY spaced in [DAYS] between 0.140 7.000 >> TIMES: 8 in SECONDS at heat changes .298800E+04 .870120E+05 .180000E+06 .268812E+06 .352800E+06 .440388E+06 .525600E+06 .610200E+06

>> TEMPERATURE >>> ELEMENT: B3__2 >>>> ANNOTATION: T1 >>>> COLUMNS: 1 2 >>>> PICK : 10 >>>> DATA in DAYS on FILE: temp.dat >>>> DEVIATION: 1.0 deg C <<<< >>> ELEMENT: B5__2 >>>> ANNOTATION: T2 >>>> COLUMNS: 1 4 >>>> PICK : 10 >>>> DATA in DAYS on FILE: temp.dat >>>> DEVIATION: 1.0 deg C <<<< >>> ELEMENT: B3__2 >>>> ANNOTATION: T3 >>>> COLUMNS: 1 5 >>>> PICK : 10 >>>> DATA in DAYS on FILE: temp.dat >>>> DEVIATION: 1.0 deg C <<<< >>> ELEMENT: AZ__2 >>>> ANNOTATION: T4 >>>> COLUMNS: 1 6 >>>> PICK : 10 >>>> DATA in DAYS on FILE: temp.dat >>>> DEVIATION: 1.0 deg C <<<<

132

>>> ELEMENT: AV__2 >>>> ANNOTATION: T5 >>>> COLUMNS: 1 7 >>>> PICK : 10 >>>> DATA in DAYS on FILE: temp.dat >>>> DEVIATION: 1.0 deg C <<<< >>> ELEMENT: AT__2 >>>> ANNOTATION: T6 >>>> COLUMNS: 1 8 >>>> PICK : 10 >>>> DATA in DAYS on FILE: temp.dat >>>> DEVIATION: 1.0 deg C <<<< >>> ELEMENT: AQ__2 >>>> ANNOTATION: T7 >>>> COLUMNS: 1 9 >>>> PICK : 10 >>>> DATA in DAYS on FILE: temp.dat >>>> DEVIATION: 1.0 deg C <<<< >>> ELEMENT: AM__2 >>>> ANNOTATION: T8 >>>> COLUMNS: 1 10 >>>> PICK : 10 >>>> DATA in DAYS on FILE: temp.dat >>>> DEVIATION: 1.0 deg C <<<< >>> ELEMENT: AH__2 >>>> ANNOTATION: T9 >>>> COLUMNS: 1 11 >>>> PICK : 10 >>>> DATA in DAYS on FILE: temp.dat >>>> DEVIATION: 1.0 deg C <<<< >>> ELEMENT: AB__2 >>>> ANNOTATION: T10 >>>> COLUMNS: 1 12 >>>> PICK : 10 >>>> DATA in DAYS on FILE: temp.dat >>>> DEVIATION: 1.0 deg C <<<< >>> ELEMENT: A4__2 >>>> ANNOTATION: T11 >>>> COLUMNS: 1 13 >>>> PICK : 10 >>>> DATA in DAYS on FILE: temp.dat >>>> DEVIATION: 1.0 deg C <<<< <<<

>> PRESSURE >>> ELEMENT: B9__1 >>>> ANNOTATION: P1 >>>> SHIFT: 1.0065E5 >>>> COLUMNS: 1 2 >>>> PICK : 10 >>>> DATA in DAYS on FILE: pres.dat >>>> DEVIATION: 1000.0 Pa <<<<

133

>>> ELEMENT: B5__1 >>>> ANNOTATION: P2 >>>> SHIFT: 1.0065E5 >>>> COLUMNS: 1 3 >>>> PICK : 10 >>>> DATA in DAYS on FILE: pres.dat >>>> DEVIATION: 1000.0 Pa <<<< >>> ELEMENT: B3__1 >>>> ANNOTATION: P3 >>>> SHIFT: 1.0065E5 >>>> COLUMNS: 1 4 >>>> PICK : 10 >>>> DATA in DAYS on FILE: pres.dat >>>> DEVIATION: 1000.0 Pa <<<< >>> ELEMENT: AZ__1 >>>> ANNOTATION: P4 >>>> SHIFT: 1.0065E5 >>>> COLUMNS: 1 5 >>>> PICK : 10 >>>> DATA in DAYS on FILE: pres.dat >>>> DEVIATION: 1000.0 Pa <<<< >>> ELEMENT: AV__1 >>>> ANNOTATION: P5 >>>> SHIFT: 1.0065E5 >>>> COLUMNS: 1 6 >>>> PICK : 10 >>>> DATA in DAYS on FILE: pres.dat >>>> DEVIATION: 1000.0 Pa <<<< >>> ELEMENT: AT__1 >>>> ANNOTATION: P6 >>>> SHIFT: 1.0065E5 >>>> COLUMNS: 1 7 >>>> PICK : 10 >>>> DATA in DAYS on FILE: pres.dat >>>> DEVIATION: 1000.0 Pa <<<< >>> ELEMENT: AQ__1 >>>> ANNOTATION: P7 >>>> SHIFT: 1.0065E5 >>>> COLUMNS: 1 8 >>>> PICK : 10 >>>> DATA in DAYS on FILE: pres.dat >>>> DEVIATION: 1000.0 Pa <<<< >>> ELEMENT: AM__1 >>>> ANNOTATION: P8 >>>> SHIFT: 1.0065E5 >>>> COLUMNS: 1 9 >>>> PICK : 10 >>>> DATA in DAYS on FILE: pres.dat >>>> DEVIATION: 1000.0 Pa <<<< >>> ELEMENT: AH__1 >>>> ANNOTATION: P9 >>>> SHIFT: 1.0065E5 >>>> COLUMNS: 1 10 >>>> PICK : 10

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>>>> DATA in DAYS on FILE: pres.dat >>>> DEVIATION: 1000.0 Pa <<<< >>> ELEMENT: AB__1 >>>> ANNOTATION: P10 >>>> SHIFT: 1.0065E5 >>>> COLUMNS: 1 11 >>>> PICK : 10 >>>> DATA in DAYS on FILE: pres.dat >>>> DEVIATION: 1000.0 Pa <<<< >>> ELEMENT: A4__1 >>>> ANNOTATION: P11 >>>> SHIFT: 1.0065E5 >>>> COLUMNS: 1 12 >>>> PICK : 10 >>>> DATA in DAYS on FILE: pres.dat >>>> DEVIATION: 1000.0 Pa <<<< <<<

>> VAPOR SATURATION >>> ELEMENT: B9__1 >>>> ANNOTATION: Sst1 >>>> SHIFT: -0.10 >>>> FACTOR: 1.1111 >>>> COLUMNS: 1 2 >>>> DATA in DAYS on FILE: sat.dat >>>> DEVIATION: 0.02 >>>> WINDOW: 5.00 8.00 [DAYS} <<<<

>>> ELEMENT: B7__1 >>>> ANNOTATION: Sst2 >>>> COLUMNS: 1 4 >>>> SHIFT: -0.075 >>>> FACTOR: 1.0811 >>>> DATA in DAYS on FILE: sat.dat >>>> DEVIATION: 0.01 >>>> WINDOW: 5.0 8.0 [DAYS} <<<< >>> ELEMENT: B6__1 >>>> ANNOTATION: Sst3 >>>> COLUMNS: 1 5 >>>> SHIFT: -0.065 >>>> FACTOR: 1.0695 >>>> DATA in DAYS on FILE: sat.dat >>>> DEVIATION: 0.01 >>>> WINDOW: 5.0 8.0 [DAYS} <<<< >>> ELEMENT: B5__1 >>>> ANNOTATION: Sst4 >>>> COLUMNS: 1 6 >>>> SHIFT: -0.07 >>>> FACTOR: 1.0753 >>>> DATA in DAYS on FILE: sat.dat >>>> DEVIATION: 0.01 >>>> WINDOW: 5.0 8.0 [DAYS} <<<< >>> ELEMENT: B4__1 >>>> ANNOTATION: Sst5

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>>>> COLUMNS: 1 7 >>>> SHIFT: -0.06 >>>> FACTOR: 1.0638 >>>> DATA in DAYS on FILE: sat.dat >>>> DEVIATION: 0.01 >>>> WINDOW: 5.0 8.0 [DAYS} <<<< >>> ELEMENT: B3__1 >>>> ANNOTATION: Sst6 >>>> COLUMNS: 1 8 >>>> SHIFT: -0.06 >>>> DATA in DAYS on FILE: sat.dat >>>> DEVIATION: 0.01 >>>> WINDOW: 5.0 8.0 [DAYS} <<<< <<<>> HEAT FLOW >>> CONNECTION: B5__2 B5__3 >>>> ANNOTATION: HF2 >>>> FACTOR: -1.910E-3 [W/m^2 - W] >>>> COLUMNS: 1 4 >>>> PICK : 10 >>>> DATA in HOURS on FILE: hflux.dat >>>> DEVIATION: 20.0 W/m^2 <<<< >>> CONNECTION: B3__2 B3__3 >>>> ANNOTATION: HF3 >>>> FACTOR: -1.910E-3 [W/m^2 - W] >>>> COLUMNS: 1 5 >>>> PICK : 10 >>>> DATA in HOURS on FILE: hflux.dat >>>> DEVIATION: 10.0 W/m^2 <<<< >>> CONNECTION: AZ__2 AZ__3 >>>> ANNOTATION: HF4 >>>> FACTOR: -1.910E-3 [W/m^2 - W] >>>> COLUMNS: 1 6 >>>> PICK : 10 >>>> DATA in HOURS on FILE: hflux.dat >>>> DEVIATION: 10.0 W/m^2 <<<< >>> CONNECTION: AV__2 AV__3 >>>> ANNOTATION: HF5 >>>> FACTOR: -1.910E-3 [W/m^2 - W] >>>> COLUMNS: 1 7 >>>> PICK : 10 >>>> DATA in HOURS on FILE: hflux.dat >>>> DEVIATION: 10.0 W/m^2 <<<< >>> CONNECTION: AT__2 AT__3 >>>> ANNOTATION: HF6 >>>> FACTOR: -1.910E-3 [W/m^2 - W] >>>> COLUMNS: 1 8 >>>> PICK : 10 >>>> DATA in HOURS on FILE: hflux.dat >>>> DEVIATION: 10.0 W/m^2 <<<< >>> CONNECTION: AQ__2 AQ__3 >>>> ANNOTATION: HF7 >>>> FACTOR: -1.910E-3 [W/m^2 - W] >>>> COLUMNS: 1 9

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>>>> PICK : 10 >>>> DATA in HOURS on FILE: hflux.dat >>>> DEVIATION: 10.0 W/m^2 <<<< >>> CONNECTION: AM__2 AM__3 >>>> ANNOTATION: HF8 >>>> FACTOR: -1.910E-3 [W/m^2 - W] >>>> COLUMNS: 1 10 >>>> PICK : 10 >>>> DATA in HOURS on FILE: hflux.dat >>>> DEVIATION: 10.0 W/m^2 <<<< >>> CONNECTION: AH__2 AH__3 >>>> ANNOTATION: HF9 >>>> FACTOR: -1.910E-3 [W/m^2 - W] >>>> COLUMNS: 1 11 >>>> PICK : 10 >>>> DATA in HOURS on FILE: hflux.dat >>>> DEVIATION: 10.0 W/m^2 <<<< >>> CONNECTION: AB__2 AB__3 >>>> ANNOTATION: HF10 >>>> FACTOR: -1.910E-3 [W/m^2 - W] >>>> COLUMNS: 1 12 >>>> PICK : 10 >>>> DATA in HOURS on FILE: hflux.dat >>>> DEVIATION: 10.0 W/m^2 <<<< >>> CONNECTION: A4__2 A4__3 >>>> ANNOTATION: HF11 >>>> FACTOR: -1.910E-3 [W/m^2 - W] >>>> COLUMNS: 1 13 >>>> PICK : 10 >>>> DATA in HOURS on FILE: hflux.dat >>>> DEVIATION: 10.0 W/m^2 <<<< <<< <<

> COMPUTATION >> STOPPING criteria >>> IGNORE WARNINGS >>> max. no. of ITERATIONS: 20 >>> IQIT=3: 50 >>> CONSECUTIVE: 100 >>> INCOMPLETE: 20 >>> LEVENBERG: 0.1 >>> STEP : 1.0 <<< >> JACOBIAN >>> FORWARD: 8 >>> PERTURB: 0.01 <<< >> OUTPUT >>> PLOTFILE: COLUMNS >>> DAYS >>> generate file with CHARACTERISTIC curves <<< <<<

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