UNLV Retrospective Theses & Dissertations

1-1-1995

Experimental study of heat transfer and fluid flow in unsaturated Experimental study of heat transfer and fluid flow in unsaturated

porous media porous media

Abdullah Abdullatif Izzeldin University of Nevada, Las Vegas

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EXPERIMENTAL STUDY OF HEAT TRANSFER AND FLUID FLOW IN UNSATURATED POROUS MEDIA

Abdullah Abdullatif Izzeldin

A thesis submitted in partial fulfillment

of requirements for the degree of

Master of Science

m

Mechanical Engineering

Department of Mechanical Engineering

University of Nevada, Las Vegas

December 1994

UMI Number: 1374885

DMI Microform 1374885 Copyright 1995, by DMI Company. All rights reserved.

This microform edition is protected against unauthorized copying under Title 17, United States Code.

UMI300 North Zeeb Road Ann Arbor, MI 48103

The thesis of Mr. Abdullah A bdullatif Izzeldin tor the degree of Master of Science in Mechanical Engineering is approved.

Chairperson, Robert F. Boehm, Ph.D

W . i“

Examining Committee, Darrell Pepper, Ph.D

Examining Committee, M ohamed B. E. Trabia, Ph.D

■ M/ -• ./ 'I [j .'I'

G raduate Faculty Representative, W illiam Culbreth, Ph.D

G raduate Dean, Ronald W. Smith, Ph.D

University of N evada, Las Vegas December 1994

11

Abstract

A laboratory experim ent was conducted to investigate therm al and

flu id flow behavior in an unsaturated porous m edium . The experim ent

consisted of a bed of homogeneous glass beads packed uniform ly in a Lexan

rectangular box. A cylindrical heat source was located horizontally in the

m iddle region of the bed and the bed was heated to steady state conditions.

W ater was then introduced uniformly through square nozzles located over

the fill material for short periods of time. The box w as fitted with a screen at

the bottom to keep the porous material intact w hile allow ing the w ater to

flow out. Below the box, an outflow system was located w hich consisted of a

partitioned catch cham ber for m easuring the special variation of the w ater

flow ing out. M easurem ents in the bed were obtained using two types of

devices that are p laced in selected locations. These devices include

capacitance elem ents for inferring moisture presence and therm ocouples for

m easuring tem peratures.

The experim ental results confirmed that the dom inan t m ass and heat

transfer m echanism s w ere vaporization, condensation , conduction , and

convection. The sim ulated m edium was observed to develop a d ry zone, a

tw o-phase zone, and liquid zone. Moreover placem ent of a heat source in an

u n sa tu ra ted porous m edium causes a shifting of w ater around the heat

source.

ill

ACKNOWLEDGMENTS

The au thor w ishes to express his profound g ra titu d e and sincere

appreciation to Dr. Robert F. Boehm for his inspiration and indispensable

guidance throughout the course of this study. I rem ain specially indebted to

him for all his suggestions, guidance, encouragem ent, constructive criticism,

and financial support of this project.

Special thanks are extended to Dr. Yi-Tung Chen for his valuable

suggestion, encouragem ent, and constructive criticism of this project. Much

thanks goes to Dr. W oosoon Yim for all of his help. Also, thanks to Dr.

Darrell Pepper and Dr. M ohamed Trabia of the D epartm ent of Mechanical

E ngineering and Dr. W illiam C ulbreth of the D epartm ent of Civil and

Environm ental Engineering for offering me invaluable advice regarding this

project. F inally, 1 w ould like to extend m y thanks to D epartm ent of

M echanical Engineering for the financial support and other items during the

course of m y study.

I V

TABLE OF CONTENTS

Abstract........................................................................................................................... iii

LIST OF FIGURES....................................................................................................... v iii

ACKNOWLEDGEMENTS............................................................................................ iv

CHAPTER 1................................................................................................... 11.1 IN T R O D U C T IO N .................................................................................. 11.2 PROBLEM DESCRIPTION.......................................................... 7

CHAPTER 2 LITERATURE SURVEY................................................ 8

CHAPTERS EXPERIMENTAL STU D Y ............................................ 163.1 General Outline of the Experim ent......................................................... 163.2 Experimental A pparatus.............................................................................. 173.2.1 Quartz Beads-Filled Test C ell.................................................................. 193.2.2 Inflow System ............................................................................................ 193.2.3 Outflow System ......................................................................................... 203.3 Instrum entation............................................................................................. 213.4 Assembly of the Experimental A p p a ra tu s ................................. 23

CHAPTER 4 OPERATION OF THE EXPERIMENT....................... 284.1 Preliminary P rocedure................................................................................. 284.2 Operational Procedure................................................................................. 29

CHAPTER 5 EXPERIMENTAL RESULTS AND ANALYSIS ..... 315.1 Temperature Profiles.................................................................................. 315.2 Moisture Migration Profiles...................................................................... 41

CHAPTER 6 SU M M ARY A N D C O N C L U SIO N ................................. 45

CHAPTER 7 BIBLIOGRAPHY.............................................................. 48

A PPE N D IX I: Capacitance Element Calibrations....................................... 52

APPENDIX II: Labview Data Acquisition................................................... 59

A PPE N D IX III: Coefficient of Permeability Falling-Head M eth o d 65

V I

LIST OF FIGURES

1. Diagram of how ground water might be diverted by a "hot repository."... 3

2. A sketch of the experimental apparatus sy s tem ............................................... 5

3. Schematic of the developm ent of heat pipe in porous m edium .............. 11

4. A sketch of the modified experimental apparatus system .......................... 22

5. Location of thermocouples distribution in the b e d ....................................... 25

6. Design of the capacitance e lem ents.................................................................... 26

7. Location of capacitance elements distribution in the b e d ............................ 27

8. Tem perature profile vs time for thermocouples 6, 8, and 9 ......................... 36

9. Tem perature profile vs time for thermocouples 1, 4, 7, 10 and 11 ............. 37

10. Tem perature profile vs time for thermocouples 2, 3, and 5 ........................ 38

11. Schematic of condition achieved during the experim ent r u n .................. 39

12. The distribution of water collected in the p a rtitio n s .................................... 40

13. M oisture content in the bed for sensor 1, 2, and 3 .......................................... 43

14. M oisture content in the bed for sensor 4, 5, and 6 .......................................... 44

15. Schematic diagram of capacitance-to-voltage converter c irc u it ................ 53

16a. Plots of the capacitance element sensors 1 calib ra tion ................................ 56

16b. Plots of the capacitance element sensors 2 calib ration ................................ 56

16c. Plots of the capacitance element sensors 3 calib ration ................................. 57

16d. Plots of the capacitance element sensors 4 ca lib ra tion ................................ 57

16e. Plots of the capacitance element sensors 5 calib ra tion ................................ 58

16f. Plots of the capacitance element sensors 6 calib ra tion ................................. 58

vii

17a. Front panel for thermocouple virtual instrum ent program ..................... 61

17b. Block diagram for thermocouple virtual instrum ent p ro g ra m ............... 62

18a. Front panel for voltage virtual instrum ent p ro g ra m ................................. 63

18b. Block diagram for voltage virtual instrum ent p ro g ra m ............................ 64

19a. Sketch details of falling-head ap p ara tu s ........................................................... 67

19b. Sketch details of test m o ld ................................................................................... 68

Vlll

CHAPTER 1

1. 1 Introduction

H eat and mass transfer in porous m edia are im portant contributors to

processes governing many of the environm ental questions. Everything from

trying to figure out w here groundw ater contam ination will go to where it

came from and how to deal w ith it depends on these processes. This work

deals w ith issues that have bearing on the prevention of w ater contamination

from nuclear waste that will be buried underground . The effects of w ater

flow and heat transfer around a buried nuclear waste canister are examined in

detail.

Com bined heat and mass transfer w ith phase change in an unsaturated

porous m edia has been a topic of much research over the past decade because

of its applications in geothermal energy, underground disposal of nuclear and

chem ical w astes, therm ally enhanced oil recovery , w ater table and

g ro u n d w a te r p o llu ta n t flow , d ry in g of g ra in s, th erm al in su la tio n

1

perform ance and solar pond design. An analysis of these processes is

complicated by the possible presence of two phases (liquid and vapor) and the

varieties of the structure of the porous matrix. Energy transfer in such a

m edium occurs by conduction, in all of the phases, as well as by convection,

evaporation, and condensation. M oisture transport occurs w ithin the voids

of the porous m edium as a resu lt of vapor pressure gradients, pressure

gradients, and thermal gradients. These studies led to a current concept called

the "hot repository" design which is a concept for the design of the proposed

high level radioactive waste repository. This concept has been analyzed by

researchers at Lawrence Berkeley N ational Laboratory (e.g. [Pruess and

Duoghty, 1988]), Lawrence Livermore N ational Laboratory (e.g. [Buscheck and

N itao, 1993]), and others. In this design, the high level radioactive nuclear

w aste package is emplaced in the repository such that heat generated by the

waste results in tem peratures in the su rrounding form ations that are above

the boiling point of water. These high tem peratures can persist for thousands

of years. As tem peratures around the repository increase to the saturation

tem p era tu re , evaporation of any w ater flow ing vertically tow ard the

repository increases and vapor pressure becomes appreciable. Essentially, the

vapor will flow radially away from the heated source. In the cooler region,

the w ater will condense and again flows vertically. In this w ay w ater should

be d iverted around the repository area. The conditions surrounding a heat

source are shown schematically in Figure 1. This general phenom ena have

also been denoted as the "heat-pipe" effect, w hich im plies essentially

evaporation/condensation phenom ena transporting m oisture. Problems of

this sort have been analyzed theoretically and analytically through the use of

num erical m ethods.

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Figure 1: Diagram of how ground water might be diverted by a " hot repository." In this case the repository heat would cause vaporization of the water, forcing

the vapor to flow in an approximately radial direction.

An experim ent was conducted to evaluate some aspects of the "heat

pipe" effect. The approach was to model the concept in tw o-dim ensions. To

apply this, a hom ogeneous, granular m edium in a box was used. For these

studies glass beads were chosen to represent the matrix form ation, and these

w ere uniform ly packed in a rectangular Lexan box. At 10.2 cm (4 in) from the

bottom of the box an electrical im m ersion heater was located horizontally to

sim ulate the heat source. At the top of the Lexan box the inflow system was

located w here the w ater was sprayed uniform ly through an array of square

nozzles. The Lexan box was fitted w ith screen at the bottom to keep the

porous m aterial intact while allowing the water to flow out. Below the Lexan

box, the outflow system was located which contained th irteen partitioned

catch cham bers for m easuring w ater flowing out of the test section. The

experimental apparatus is shown schematically in Figure 2.

M easurem ents were obtained using two types of devices that are placed

in carefully selected locations. These devices include capacitance elements

for in ferring m oistu re location and chrom el alum el therm ocoup les for

m easuring tem peratures. Locations for placing the various devices in the bed

w ere determ ined approxim ately to predict the heat transfer and flu id flow.

The fie ld near to the hea t source w as heavily in s tru m e n te d w ith

therm ocouples bu t had only a lim ited num ber of resistance elements.

(5.0 gallon capacity)

Head Tank

7'

Inflow System

Control Valves

Flow Distributor ( square nozzles )

Main Experimental Tank

Outflow System

Ball valve

Porous Media,InstrumentI ' OD Firerod heater

(lOOOW 120V )

Dram Va

Screen

CollectionPartitions

Figure 2: A sketch of the experimental apparatus system

6

The w ork p resen ted in this thesis investigates experim entally two

phase (liquid and vapor) fluid flow and energy transport in an enclosed

unsaturated porous m edium .

The m otivation for this study was to predict the heat transfer and fluid

flow m echanisms present w ithin the unsaturated, porous geologic setting like

the p ro p o sed high-level rad ioactive nuclear w aste reposito ry . The

em placem ent of heat generating waste in an unsaturated perm eable m edium

is expected to give rise to the developm ent of a heat pipe effect (Pruess et al.

1990). The heat pipe effect can be im portant in predicting the corrosion of

waste canisters and transport of radionuclides through the geologic setting.

The purpose of the experiment described here is designed to provide a

m odel that dem onstrates the processes controlling the transport of w ater and

energy in unsaturated porous media. Further it is desired to apply the model

to a hypothetical repository in order to predict the basic effects a high level

rad ioactive nuclear w aste repository w ould have on the m ovem ent of

ground w ater and energy in unsaturated porous media.

1.2 Problem Description

The thermal behavior of the near field of the em placed electrical heater

w as s tu d ie d experim entally u s in g v arious m easu rem en t techniques.

M onitoring the change in the m oisture distribution was accom plished using

capacitance elements for inferring m oisture migration, and these were located

at m any places throughout the m edium . The tem peratures were m easured at

several points of the porous m edium using chromel alum el thermocouples.

The m oisture and tem peratures changes gave evidence of the different heat

tran sfe r m odes in the m edium (conduction , convection). H ow ever,

m onitoring the tem peratures and the m oisture m igration helped locate the

phase change zones and the dry ing areas. This facilitated following the

form ation of a progression of d ifferent zones such as the saturated liquid

zone, the sa tu ra ted vapor zone, and the tw o-phase zone. By careful

m onito ring these zones, one could identify various phenom ena in the

phase-change region. This allowed detailed analysis of its effects.

CHAPTER 2

LITERATURE SURVEY

H eat transfer and fluid flow in unsaturated porous m edia are topics of

practical im portance and current research interest. Researchers have studied

m any aspects of these topics using numerical and sim ulated analyses.

M ultiphase flow in porous m edia w ith heat transfer involving phase

change is one topic that m any researchers have stud ied theoretically and

experim entally . Studies of therm al b ehav io r of a m ultiflu id -sa tu ra ted

form ation were conducted by Gomaa et al. [1974] showing the effect of vapor

sa tu ra tio n and apparen t therm al conductiv ity in a porous m edium . A

conceptual m odel was derived that represented both a theoretical derivation

and experim ent confirmation of the heat pipe concept in porous media. It

w as found that the dom inant m ode of hea t transfer in porous m edia

sa tu ra ted w ith two phase fluid flow under certain tem perature conditions

8

9

was a com bination of phase change and convection. This has been called the

"heat-pipe” effect. The study also shows that the heat pipe effect increases

w ith increasing perm eability and porosity of the m edium , latent heat of

vaporization of the saturating liquid, and vapor pressure.

A heat pipe is an effective tool in transferring heat at high rates by

evaporating the liquid at the warm parts and condensing the vapor at the

cooler p a rts of a cham ber. The porous heat p ipe effects have been

investigated extensively by many researchers. H ow ever an early investigation

was done by Ogniewcz and Tien [1979]. In this study, the governing equations

for fluid and heat flow for a one dim ensional heat pipe configuration were

developed neglecting the effect of fractures bu t including gravity effects. The

g o v e rn in g eq u a tio n s w ere solved for one d im en sio n a l h ea t p ipe

configuration. The results show the effects of various flu id and porous

m edium properties on the heat pipe performance. In a sim ilar study Su and

Som erton [1979] p roposed a one dim ensional theoretical derivation and

experim ental confirm ation for the heat pipe phenom ena in porous media.

The theoretical derivation described the functional dependence of the heat

pipe effect on liquid saturation gradient, capillary pressure, perm eability, heat

flux and gravity. The results of their study show ed that the length of the two

phase region is inversely proportional to the heat flux and tem perature

difference through the system. The presence of the heat pipe effect in a

partia lly sa tu ra ted porous media can cause large changes in the apparent

therm al conductivity.

1 0

Several investigators have developed num erical and m athem atical

m odels for two phase heat transfer and flu id flow in unsatu ra ted porous

m edia that accounts for processes controlling the transport of w ater and

energy. In particular, attention was focused on the analysis of heat pipe effects

in unsaturated or partially saturated porous m edia that m ight occur near a

high-level radioactive nuclear waste disposal.

The heat pipe behavior in porous m edia was presented by Doughty and

Pruess [1987,1989] in a semi-analytical study. Figure 3 shows the schematic

representation of heat transfer regimes and developm ent of the heat pipe

region in porous m edium due to the em placem ent of a high level nuclear

w aste package. H eat penetrates into the fo rm ation as soon as the waste

package is buried in the partially saturated perm eable m edium . This causes

tem peratures to rise in the surroundings w hich will vaporize the liquid water

present in the formation. The vapor generated in the porous m atrix flows

radially aw ay from the heat source, then at som e time later it condenses on

the cooler region of the formation. U nder the capillary pressure and gravity,

the condensed liquid migrates vertically dow n the saturated region towards

the w aste package. As time progresses the sa tu ra tion grad ien t causes a

backflow of the majority of the condensated liquid vertically tow ard the heat

source. The liquid is then revaporized as it flow s tow ard the waste package

and repeats the cycle. The vaporization and condensation cycle is repeated to

develop a heat pipe region.

From the Doughty and Pruess study, it w as found that, under steady

11

Inner Conduction Zone

Heat Pipe Region

Outer Conduction Zone

Figure 3: Schematic of the developm ent of heat pipe in porous medium. [Doughty and Pruess, 1988]

1 2

state conditions, three regions with different heat transfer m echanism s exist

in the porous m edium around the heat source. At the ou ter boundary a

liqu id conduction zone dom inates w here in the inner reg ion there is a

conduction dom inated single phase vapor zone. The m iddle dom ain is a

two-phase heat pipe region where heat flow is primarily convective. Also the

study shows that the extent of the heat pipe region is influenced strongly by

relative perm eability and capillary pressure. A porous m edium w ith larger

p e rm eab ility w ill p ro v id e m ore favorable conditions for h ea t p ipe

developm ent.

Extensive theoretical and experim ental studies of the hom ogeneous

porous heat pipe have been reported by Udell [1983,1985]. First, he conducted

an experim ental study on heat transfer in a porous m ed ium heated from

above exhib iting the effects of capillary, evaporation, and condensation.

From these experim ents, it was found that at steady state conditions, three

distinct regions existed: a liquid, conduction dom inated region at the bottom,

a tw o-phase convection dom inated transition zone, an d a conduction

dom inated vapor region at the top. Later he conducted a one-dim ensional

steady state experim ental analysis of the heat and mass transfer in a porous

m edia satu ra ted w ith the liquid and vapor phases. The resu lt of this analysis

shows tha t convection heat transfer dom inates in the tw o phase zone. In

addition, it w as found that the driving forces for convection in the heat pipe

region are capillary and vapor pressure gradients. The results also predicted

the critical d ry-ou t heat flux, the m inimum heat flux at w hich a vapor zone

will form for the bottom -heated case. For the horizontally-heated system, it

was found that the product of the heat flux and tw o-phase zone length is

1 3

constant for fixed fluid and media properties. Finally, the analysis show ed

that the effective therm al conductivity of the two-phase zone increased w ith

increasing perm eability.

Analytical and semi-analytical solutions in sim ultaneous flow of fluid

and heat associated w ith high-level radioactive nuclear waste disposal in a

porous m edium w ere carried out by Pollock [1986] and Pruess et al. [1985].

Pollock developed a m athem atical model analyzing one dim ensional vertical

transport in an unsa tu ra ted porous m edium accounting for the coupled

transport of heat, two-phase fluid (liquid and vapor), and air. The results he

presented illustrated the basic effects of high-level radioactive nuclear w aste

disposal on the m ovem ent of w ater and heat in an u nsa tu ra ted porous

medium. Em placem ent of waste w ith the high heat generation of spent fuel

resulted in a one dim ensional tem perature rise, vapor pressure, and liquid

and vapor fluxes. Thus he anticipated a convective circulation pattern in the

vapor phase in two dimensions. Also the analysis showed that the increases

in tem perature produce evaporation of the w ater, forcing the vapor to flow

away from the heat source. This led to developm ent of an initial dry zone in

the vicinity of the repository, and increased liquid saturation away from the

heat source due to condensation. The same result was reached by Pruess et al.

[1985]. They sim ulated the sim ultaneous heat transfer and fluid flow effects

on the waste package buried in partially saturated porous formations.

An extensive analysis on the subject of high-level radioactive nuclear

waste repository heat driven flow in partially saturated porous m edia was

1 4

perform ed by Buscheck et al. [1993,1994]. These analyses examined the impact

of the repository therm al condition on the hydrological perform ance of the

u n sa tu ra ted and partia lly sa tu ra ted porous form ation using "Tough"

(transport of unsaturated groundw ater and heat) com puter codes. In general,

these m odels predict a drying out of the repository form ation by boiling of

liquid w ater in the near field of the heat generation fuel and flow of the water

vapor to the cooler region. Further, these studies indicate that thermal and

fluid flow perform ance of the unsaturated form ation will be dom inated by

conduction heat transfer. The studies also show that the vapor-phase

convection and condensate backflow are influenced sharp ly by the bulk

perm eability of the formation. The vapor-phase convection will be increased

by increasing bulk permeability. Therefore, the convection heat transfer will

be dom inated in the vapor zone. Finally, it was found that the region of large

contrasting bulk permeability increases the vapor pressure differentials which

can drive w ater vapor into a high permeability region where it condenses and

backflows tow ard the repository.

A n experim ental s tudy on the heat transfer in a porous m edia

saturated by a liquid was also carried out by Cioulachtjian et al. [1989] using

bronze beads to sim ulate the porous media. Three different configurations

were studied: thermal transfer with a flowing liquid, therm al transfer w ith a

flowing liquid w ith vaporization, and drying of the porous m edium initially

saturated w ith liquid. W hen the heat source delivered sufficient heat flux,

the experim en tal results show the appearance of three zones in the

hom ogeneous porous media. This reaffirm ed U dell's experim ental finding

and Pruess's num erical results m entioned previously. The developm ent of

1 5

the two phase zone begins near the heat source and the vapor transport away

from the heat source leads to developm ent of a dry out zone.

Finally , an experim ental in v estig a tio n of the behavior of non-

isotherm al flow in two-dimensional saturated and partially saturated porous

m edia was performed by Ho et al. [1994]. In this paper, physical experiments

w ere conducted using three different saturation levels: fully saturated, half­

saturated, and residually saturated porous m edia to identify non-isotherm al

flow fields and temperature distributions in a bottom heating and top cooling

bed. The experimental results show that vapor convection took place in the

unsatu ra ted zone of the half-saturated case. Further, in all three cases two

counter-rotating convection cells were observed to develop in the saturated

region.

M ost of these studies, either num erical analysis or experim ental

analysis, w ere done in an initially fu lly sa tu ra ted porous m edium or a

partia lly satu ra ted porous m edium. H eat transfer studies in unsatu ra ted

porous m edia infiltrated by a liquid has had little attention in the literature.

For this reason, the objective of the present w ork will be developm ent of an

experim ental study of unsaturated porous m edia infiltrated by a liquid.

CHAPTER 3

EXPERIMENTAL STUDY

3.1 General Outline of Experiment

C oupled therm al and fluid flow processes in an u nsa tu ra ted porous

m edium are im portant in the performance evaluation of some aspect of high

level radioactive waste repository. The high tem perature fields resulting from

the h ea t p ro d u c tio n w ith in a radioactive w aste reposito ry in a deep

u n d erg ro u n d form ation can mobilize the liquid and vapor phases either

away from or into the heated region surrounding of the repository. Therefore

u n d e rs tan d in g the behavior of therm ally-induced flow s is of particu lar

im portance because of the possibility of radionuclide release, which could

con tam inate the mobile ground w ater if it comes in contact w ith the

radioactive waste.

1 6

1 7

For this work the m edium of interest is granular and initially dry, and

the geom etry of the whole assembly is such that essentially two dim ensional

flows of adm itted w ater are able to be examined. A horizontally m ounted

1000 W electrical cartridge heater was located 10.2 cm (4 inch) from the bottom

of the m edium spanning the tank. W hen the bed was dry, the heater was

tu rned on and came to a steady state tem perature typically around 270°C.

W ater was then in troduced from the top of the m edium in a spatia lly

uniform m anner.

Thermocouples (chromel alumel), located within the packed bed, w ere

m onitored as a function of time as the w ater flows through the system to

determ ine the tem perature field. In addition, catch-chambers at the bottom of

the apparatus collected the w ater flowing from the bed. These chambers serve

as a m onitoring device to see w hat shifting of the w ater occurs from the

region directly in a vertical line w ith the heater. This was done to exam ine

the possible shielding effect of the heated area.

32. EXPERIMENTAL APPARATUS

A medium -scale experim ent was designed to study the heat transfer

and m oisture m igration through the glass beads. In this regard the following

w ork was done;

1 8

1. Designed and fabricated the experim ental apparatus which includes an

inflow system, an outflow system, and a tank to hold the glass beads

and water.

2. Drawings of the apparatus setup and individual part components were

m ade using Macintosh CAD draw ing software.

A schematic of the experim ental apparatus is shown in Figure 2. This

consisted of :

a. Plastic box filled with quartz beads : The m ain part of the

experimental setup is 15.24 cm x 43.18 cm x 30.48 cm (6 x 17 x

12 in) in dimensions and considered to be the test section.

b. Inflow system ; The top part of the setup constitutes the

inflow system which is designed to give a spatially

uniform distribution of the w ater to the quartz beads-filled box.

c. Outflow system: The bottom part of the setup constitutes

the outflow system and is used to m easure the spatial

distribution of the w ater exiting the test section.

1 9

3.2.1 Quartz Beads-Filled Plastic Test Cell:

The m iddle part of the experimental setup is a box 15.24 cm by 43.18 cm

in plan view and 30.48 cm high (6 x 17 x 12 in) and is fabricated from a 1.27

cm (1 /2 inch) thick Lexan sheet. Each side of the box was joined together

using acrylic solvent cement. The box was then fastened in each side by five

10-32 screws to secure and strengthen it. At 10.18 cm (4 in) from the bottom

and 15.24 cm (6 in) from the side a 3.84 cm (1.5 in) hole was drilled, in the

front and the back sides of the box, for m ounting an electrical heater. A 2.54

cm (1 in) diam eter and 15.24 cm (6 in) long 1000 W electrical im m ersion

cartridge heater spanning the box horizontally was m ounted in the 3.84 cm

(1.5 inch) hole using a 1.27 cm (1/2 in) diam eter Teflon plug. Locations were

established for m ounting therm ocouples and the capacitance elem ents for

m easuring the tem perature and the m oisture m igration, respectively, inside

the box. The box was fitted with a screen arrangem ent at the bottom to keep

the quartz beads from flow ing out w ith the exiting w ater. The box was

uniform ly packed with 0.094 cm (0.037 in) diam eter quartz beads.

3.2.2 Inflow System:

The inflow system was d esigned to give a spa tia lly uniform

distribution of w ater to the beads contained in the plastic box. The system

consisted of a 5 gallon head tank m ounted 2.13 m (7ft) above the top of the

m ain test cell, 0.19 cm (3 /4 in) PVC pipes, control valves, and a set of square

2 0

patterned spray nozzles. The square nozzles were m ounted on a 12.7 cm by

43.18 cm (5x17 in) plastic plate which was fitted on top of the m ain test cell.

Each nozzle was m ounted at 13.34 cm (5 1 /4 in) apart, and was attached to a

control valve w hich was placed above the nozzles in-flow line to allow

control of the am ount of w ater as well as to balance the flows betw een the

lines leading to the three spray nozzles. The nozzles were connected to the

head tank by a 183 cm long PVC pipe as shown in Figure 2.

The system was m odified to connect the in-flow line to the city w ater

line in order to control the pressure drop which might affect the uniform ity

of the flow. The m odification was as follows: A 3.05 m (10 ft) hose was

connected to the city w ater line by a control valve. A ball valve and pressure

gage were attached to the hose and the in-flow line, then the line w as split

into two lines by a tee joint. The two lines distributed the flow to the three

nozzles as show n in figure 3. Since the flow in the middle nozzle will have

twice the flow of the end nozzles, a gate valve was connected to the m iddle

nozzle to control the flow and insure a uniform flow from the three nozzles.

3.2.3 O utflow System:

The out-flow system consisted of a 15.24 cm by 43.18 cm in p lan and

15.24 cm high (6 x 17 x 6 in) plastic box fabricated from a 1.27 cm (1 /2 in)

Acrylic sheet. Twelve grooves were machined in the front and the back sides

for placing a partition plate. Then the box sides were joined together using

2 1

acrylic solvent cement and fastened by three 10-32 screws. Twelve partition

plastic plates spaced approxim ately 2.54 cm (1 in) apart were placed in the

groves and sealed by silicon sealant to create thirteen partitions of dimensions

15.24 cm by 2.54 cm by 15.24 cm ( 6 x 1 x 6 in). Partitions work as catch

chambers. With the partitions to catch the exiting water, it is possible to infer

the one-dim ensional spatial d istribu tion of w ater flowing out of the test

section. A 15.24 cm by 43.18 cm (6x17 in) Acrylic plate w ith thirteen drain

valves was attached to the bottom of the box.

3.3 Instrumentation

Instrum entation w ithin the m edium consisted of two types of devices

that are placed in various locations on small positioning wires. The devices

in c lu d e capacitance elem ents for in fe rrin g m o istu re p resence, and

thermocouples for m easuring bed tem peratures.

E leven sm all-d iam eter 30 gauge (0.012") w ire chrom el-alum el

therm ocouples are located in specific places around the heater element, as

show n in Figure 5.

Capacitance elem ents are being developed in our laboratory for

m apping m oisture presence throughout the apparatus [Hansen, 1993]. Since

point m easurem ents are desired then capacitance elements are desirable

2 2

Inflow System

Main Experimental Tank

Outflow System

To city water

Ball Valve

Flow Distributor ( spray nozzles)

Instrument RakePorous mediaWAW

1" OD looow Firerod Heater •VA'Teflon

Ceramic

CollectionPartitions

DrainValves

Figure 4: Sketch of the m odified experimental apparatus system .( not to scale)

23

d ev ices that will differentiate betw een porous m edia conditions that are

unsa tu ra ted and saturated with liquid water. The idea for this sensor is to

d e tec t the presence of w ater through a change in capacitance of the

ex p erim en t m edia. The elem ents are m ade from sim ple duplex solid

conducto r w ire, small diam eter 24 gauge (0.056 in), w ith tips on one end

s trip p ed of insulation and the two wires epoxied on each side of a small

dielectric spacer as show n in Figure 6. The conductor for this w ire was a

copper conductor. The gap between the probe was reduced to less than .094

cm (.037 in) which is the size of the glass beads. A probe gap smaller than the

beads should minimize any interference from the porous m edium itself. Six

of these capacitance elem ent probes were built. The d istribu tion of these

devices is show n in Figure 7.

3.4 A ssem bly of the Experimental Apparatus

A platform to support the apparatus 53.34 cm (21 in) off the floor was

fabricated from wood. On top of the platform thirteen holes were drilled to

p o rt the outflow system drainage lines. The outflow system box was then

placed on the platform with the screen frame m ounted on top. N ext the test

cell box w as placed and sealed on the screen fram e by silicon. The

therm ocouple probes and capacitance elements w ere positioned on small

w ire on a U -shaped screen and placed inside the test cell box. An electrical

cartridge heater was then m ounted in the box. W ith all instrum entation

installed , the bed was packed w ith 0.094 cm (0.037 in) quartz beads. The

packing m ethod consisted of shaking and tapping the box w hile filling to

2 4

insure consistent bed porosity. Finally the square nozzles were m ounted on a

12.70 cm by 43.2 cm (5 x 17 in) plastic plate which was fitted on top of the

main test cell. The nozzles were then attached to the head tank by a set of

control valves, ball valve , and 1.91 cm (3 /4 in) PVC pipe. The test section

was insulated completely by 7.62 cm (3 in) thick polyurethane foam.

The system was connected to a Labview data acquisition program . This

program includes libraries of functions and developm ent tools designed

specifically for data acquisition and instrum ent control. More details of this

program are given in A ppendix II. This system also allows the ability to view

the data while it is being collected, as well as to save it for further processing.

25

r

jjWMSS B5?5jSSSH?5BSiftS

4"mmmmm

^SSSSSSmSSSS^mSSSi

Porous m edia •<

[4] f

Teflon

sjssssssmssss ssssssms ^

6"

2"

17"

Figure 5: Location of thermocouple placements inthe center plane of the bed via a front view of the apparatus.

2 6

DetailShownBelow

Not to scale

ga WireÉ M | m i i ] i i i l i i i ? i i i t ) i it i i i h i i h i i i ï ï i î iIM M IIIU IIM IIM IIM iM M IIM III IN M III

Glass Spacer

Side View

GlassSpacer

Epoxy

End View

Figure 6. Design of the capacitance elem ents used for determining moisture content.

2 7

1" OD lOOOW Firerod Heater Porous media

î Teflon

Figure 7: Location of capacitance elem ent placementsin the center plane of the bed via a front view of the apparatus.

CHAPTER 4

OPERATION OF THE EXPERIMENT

4.1 Preliminary Procedure

The different instrum ents used in the experim ent w ere adjusted and

calibrated before the actual experim ental run. First, the inflow system was

ad justed and calibrated to insure a uniform flow in each nozzle. The

procedure involved an iterative process of adjusting the control valve until a

desirable flow was reached in each nozzle. Next the capacitance elem ents

w ithin glass beads were calibrated in both dry and fully saturated conditions

w ith liqu id w ater. The resu lts of these calibrations are show n in the

28

2 9

appendices. However, in order to calibrate these elements a circuit was built

to convert a capacitance reading into a voltage reading which was easier to

use w ith the data acquisition program . Finally, the relative perm eability of

the beads, which is a constant of p roportionality relating to the ease with

w hich a flu id passes th ro u g h a p o ro u s m ed ium , w as m easu red

experim entally. This was done using the falling head m ethod (a detailed

description is given in A ppendix III) by passing w ater through the m edium

and m easuring the associated head drop. The permeability was determ ined to

be 1.35 X 10'^^ m^ with 40% porosity.

Prior to packing the beads, the thermocouples and capacitance elements

w hich w ere to be located w ithin the bed w ere fixed in position and their

locations recorded. The therm ocouples and the sensors were placed in

approxim ately 5.08 cm (2 in) increm ents from the heater.

The complete experiment was run for several times w ithout the heater

on in order to see the distribution of the w ater exiting the test section. The

w ater collected in each partition w as m easured and recorded. The test cell

was unloaded and the wet quartz beads were dried. Then the bed was packed

w ith dry beads using the same packing m ethod as before to insure consistent

bed loading. The system was then ready for operation.

3 0

4.2 Operational Procedure

Once the test cell was loaded, the apparatus was ready for the next test.

The heater pow er was adjusted at the desired level to give the desired test

tem perature. The thermocouples and capacitance elem ents were connected

to the Labview data acquisition program and tu rned on. The program

recorded the tem peratures and m oisture sensor ou tpu ts at regu lar time

periods up to steady state. The system required 4-7 hours to reach steady state

conditions. Once steady state is established, the Labview program is changed

to record data every five seconds. Five m inutes later, the w ater is introduced

in a spatially-uniform , time varying m anner from a head tank above the

experim ent into the d ry bed. Then the system is allow ed to run to steady

state which took from 1-3 hours. After steady state is reached, the pow er was

turned off, the Labview program was stopped, and the data saved. The water

collected in the partitions of the outflow system was m easured and recorded.

It is w o rth no ting tha t the experim ental data was collected using the

apparatus in Figure 2 and the m odified apparatus show n in Figure 4. The

ap p ara tu s show n in Figure 2 was used to collect the tem peratu re field

inform ation w hile the apparatus in Figure 4 was used to determ ine the

m oisture content data. This way the results of the m oisture content can be

used to confirm the tem perature field results.

CHAPTER 5

EXPERIMENTAL RESULTS AND ANALYSIS

5.1 Temperature Profiles

The purpose of this experim ent w as to determ ine tem perature profiles

and m oisture migration as a function of time. Figures 8 through 10 show the

experim ental results for tem perature profiles obtained from the steady state

condition. A transient condition occurred for a certain period of tim e after

the w ater w as adm itted into the test section.

The tem perature of the 1000 W cylindrical cartridge heater was set to

app rox im ate ly 273 °C, w hich is the m axim um form ation tem perature

currently expected from nuclear w aste storage. The tem peratures w ithin the

3 1

3 2

bed exhibited the expected trends of linear tem perature profiles in the steady-

state condition. However, the heater pow er was controlled at 490 W to give

the steady state tem perature, which was recorded by thermocouple 7, of 274.0

°C, and 1.5 gal of water was adm itted into the bed during a 35 second time

period.

Figure 8 gives an example of the tem perature field obtained in the

vertical m edian plane of the heater w ith therm ocouples located as shown in

Figure 5. From the tem perature profiles obtained it appears that the heat

transfer is dom inated by conduction in the porous medium. Temperatures in

location 8 show a very small change which is an indication of that area being

a vapor region. At steady-state conditions the tem perature in location 9,

w hich is 10.16 cm (4 in) above the heater, is below the boiling point. As the

w ater reaches this location the tem perature takes a sharp drop and stays below

the boiling point. This indicates the effects of being saturated w ith liquid

w ater. Therefore the effects of boiling, vapor, and condensate flow are

apparen t in a line vertically through the heater area. Vapor is driven away

from the heater region (locations 6 and 8) to w here cooler tem peratures

(location 9) cause it to condense. This sets up a saturation profile. There is

essentially no tem perature variation in location 6 indicating there is no fluid

reaching this location.

The tem peratures on the horizontal line from the heater are shown in

F igure 9. Therm ocouple 7 w as at the top surface of the heater, and

thermocouples 4 and 10 were 5.08 cm (2 in) aw ay from the heater axis at each

33

side as show n in Figure 5. Thermocouples 10 and 11 were 10.16 cm (4 in)

aw ay from the heater. Thermocouples 7 and 10 show the steady state dry

tem peratures w ith apparently no water reaching this location. Accordingly, a

d ry-out region was developed closer to the heater due to the therm al shield

created by the high temperature field (274 °C). As the water flows toward the

heat source, boiling occurred, creating a v apor zone. C onsequently, the

tem perature at location 4 takes a slight dip bu t stayed above the boiling point

of w ater, which is an indication of presence of superheated vapor. However,

the straight line portions of the tem perature profiles in Figure 9 imply that

conduction is the dom inant heat transfer m echanism in these regions.

T em peratures in locations 1 and 11 show a sim ilar behavior w here the

tem perature takes a small increase sensing vapor before w ater reaches that

location. The high porosity of the m edium allow s the w ater vapor to travel

faster to this point than the liquid water. These tem peratures simply flatten

as sufficient time elapsed which is attributed to the condensate of the vapor

convecting heat away from the boiling zone.

Figure 10 shows the tem perature profiles in the plane away from the

heater. As the water reaches positions 3 and 5 these tem peratures take a sharp

d ro p , and after a short time the tem peratu re profiles fla tten out. This

represents the effects of these thermocouples being bathed in the high heat

capacity fluid. The tem peratures at these positions indicated that the phase

change has occurred in this region. This region, which can be identified as a

m ixing zone, is located between the vapor zone (location 4) and the liquid

zone (locations 1 and 2). Here water is evaporated at the intersection with the

vapor zone and the vapor is condensed w ithin the mixing zone. The return

3 4

flow of condensate back toward the boiling region establishes a heat transfer

m echanism called the "heat pipe" effect. In the heat pipe region, the heat

transfer mechanism is driven by the convection of latent heat. Therefore, the

flattening of the tem perature profile in Figure 10 is prim arily attributed to the

heat pipe effect. Thermocouple 2 is located in the liquid zone because the

tem perature there takes a small drop w hich indicates the effects of being

sa tu ra ted w ith liquid water. Since therm ocouple 2 is located in a cooler

region of the bed w ater vapor condenses and deposits its latent heat of

vaporization there. This is indicated by the jum p in the tem perature profile

at that point.

Figure 11 schematically sum m arizes the results recorded in the water's

infiltration period during the experim ental run. These conditions were

clearly visualized by looking through the transparen t front wall of the test

cell. Visual inform ation was attained by distinguish ing betw een the liquid

regions (darker contrast) and the dryer regions (lighter contrast). This visual

inform ation was supported by the experim ental results which show that the

heater is surrounded by a dry zone in w hich heat transfer was undoubtedly

dom inated by conduction. Accordingly, h igh rate heating was capable of

driving steam away from the heat source faster than the rate which liquid can

flow tow ard the heat source, thereby causing a dry-out zone to form. At some

distance away, a two-phase zone, the heat-pipe region, m ay be present, where

the vapor and liquid are mixed. In the heat-pipe region heat flow is primarily

convective. Beyond the two-phase zone a liquid region is present which is

dom inated by conductive heat transfer, w here tem peratures are too low for

evaporation or for the heat-pipe effect to occur.

35

The results of this study were in good agreem ent w ith the numerical

and semi-analytical results presented by Pruess et al.[1988]. In their study a

m odel of mass and energy transport was used to develop semi-analytical

solutions for tem perature, saturation fields, and pressure around the heat

source. The study results show three domains may exist around a cylindrical

heat source em placed in a partia lly satu ra ted form ation: a conduction

dom inated inner vapor zone, a tw o-phase zone, and a liqu id outer

conduction zone. A lso com parisons w ith the p rev io u sly repo rted

experim ental studies of Udell et al. [1985] and Cioulachtjian et al. [1989]

indicate an agreem ent betw een their results and experim ental results

reported here. Accordingly, these results confirm U dell's, Pruess's, and

Cioulachtjian's findings that under steady-state conditions, three distinct

regions may appear around the heat source in porous media.

Finally, the distribution of w ater collected in partitions on the bottom

of the experim ent's test cell is shown in Figure 12. The result in Figure 12

shows the ratio (heated case over unheated case) of the am ount of water

collected in each partitio n at the end of experim ental run . Several

characteristics are to be noted. It is apparent there is some water deficiency

under the heater location which is attributed to divergence of the w ater

around the heater. W ater is decreased by 70-77% in partitions 6, 7, and 8 and

56% in partition 9. In contrast, partitions 2, 3, 4, 5, and 11 show an increase of

47-53%. A nother item of significance is that the w ater collection is not

symmetrical which is attributed to chaimeling that occurs due to packing the

y

II

300

250-Steady-state heater temperature = 294.0 °C Water admitted into the bed = 1.5 gal Time required for water to exit the bed = 59 sec

200 -

Thermocouple position [8] Thermocouple position [6] Thermocouple position [9]

100

50- Water admission

30840 30885 30930 30975 31020 31065 31110 31155 31200 31245

Time, sec

31290

Figure 8: Temperature profile vs time for thermocouples 6, 8, and 9. wOn

300

250-Steady-state heater temperature = 294.0 °C Water admitted into the bed = 1.5 gal Time required for water to exit the bed = 59 sec

200 -

U Thermocouple position [1] Thermocouple position [4] Thermocouple position [7] Thermocouple position [10] Thermocouple position [11]

sSrH

150-

100-

50-Water admission

30840 30885 30930 30975 31065 3124531020 31110 31155 31200 31290

Time, sec

Figure 9: Temperature profile vs time for thermocouples 1,4, 7,10, and 11. w<1

uoCJ

ÎAIH

200

Steady-state heater temperature = 294.0 °C Water admitted into the bed = 1.5 gal Time required for water to exit the bed = 59 sec

150-o-o-o-o-o-o

100 -

Thermocouple position [5] Thermocouple position [3]Thermocouple position [2]

50-

Water admission

30840 30885 30930 30975 31020 31065 31110

Time, sec

31155 31200 31245

Figure 10: Temperature profile vs time for thermocouples 2,3, and 5.

31290

OJ00

3 9

C O '

m

I I

IIi l

1 1

Jn l iU

Heater Location

6 7 8

Horizontal Partition

Figure 12: The distribution of water collected in the partitions on the bottom of the experiment's tank. o

4 1

bed w ith instrum entation present. A final item of note is th a t differences

between cases are always seen. This is due to the repacking of the bed that

m ust occur each time. Note that repacking of the bed m ust occur both in the

heated and unheated cases if w ater is admitted.

5.2 Moisture Migration Profiles

M oisture m igration in the bed was m onitored using capacitance

elem ent sensors as a function of time. The results are depicted in Figure 13

through 14. Each figure consists of three plots that show the m oisture profile

in vertical and horizontal locations in the bed. The results show n here are

for the system w hen it reaches steady state conditions and the w ater was

sprayed on the bed. It is im portan t to notice that the m oisture content in

these figures represents the ratio of mass of w ater to mass of dry beads w here

zero is a dry condition and 0.174 is a fully saturated condition.

Figure 13 show s sam ple results for the sensors located in the vertical

m edian plane of the heater. These sensors were placed in approxim ately 5.08

cm (2 in) increm ents from the heater axis as shown in Figure 7. The sensor in

location 1 show s a m oisture content change from dry to fu lly sa tu ra ted

conditions w hen the w ater is adm itted to the bed. As tim e p rogress, the

m oisture profile takes small drop which is an indication of the w ater drain

ou t of the test cell. The saturation level stays high in this location which

confirms the tem perature profile result m entioned above as being in a liquid

4 2

region. W hen the sensor in location 2 indicates the liquid front has arrived,

it takes a slight jum p but stays in the low saturation region. This m ight be

attributed to be in the vapor region as shown in Figure 11. Finally the

location 3 m oisture profile is shown to be in a dryer region which is a good

indication of being in a dry-out zone as is confirmed by the tem perature

results.

The profiles of m oisture content indications in a horizontal line are

shown in Figure 14. The sensor in location 4 shows a quicker jum p and a

settling in the in term ediate saturation region. The m oisture profile in

location 4, w hich is located in the vapor zone, shows a series of cycling

patterns. Such a cycling pattern is attributed to cyclic evaporation phases

where the vapor flows away from the heat source and the condensate returns

back tow ard the heat source. Location 5 shows a small m oisture change

profile. This represents the possibility that the location is in a dry-out zone.

Finally location 6 shows the expected trend of a sharp increase to fully

saturated conditions since it is in a region far away from the heater. As time

progresses the m oisture profile takes a small dip which is due to drainage of

water into the partitions of the outflow system.

By exam ination of the behavior of sensors 2, 3, 4, and 5 an im portant

observation can be made. It can be seen that the distribution of m oisture was

not radially symmetric relative to the heater axis. This might be attributed to

uneven packing of the bed with instrumentation.

0.15-

W) Steady-state heater temperature = 294.0 °C Water admitted into the bed = 1.5 gal Time required for water to exit the bed = 59 sec

0.10-

Q Sensor ■ Sensor ♦ Sensor

0.05-

0.008 10 12-2 0 2 4 6

Time [ min]

Figure 13: Moisture migration in the bed for sensor 1 , 2, and 3.u>

Steady-state heater temperature = 294.0 °C Water admitted into the bed = 1.5 gal Time required for water to exit the bed = 59 sec

0.15-

0OD Sensor

I SensorSensor

0.1 0 -

0.05-

0.00-2 0 2 8 124 106

Time [mini

Figure 14: Moisture migration in the bed for sensor 4, S , and 6.

CHAPTER 6

SUMMARY AND CONCLUSION

This study exam ined the impact of therm al conditions on fluid flow in

an unsa tu ra ted porous m edium . Most of the attention in this w ork was

focused on the tem perature field and m oisture content profiles in the near

field of a horizontal cartridge heater. This illustrated the basic effects of the

heat source on the m ovem ent of w ater and energy in unsa tu ra ted porous

media. In general, the fluid flow is influenced the tem perature field through

the form ation of a heat p ipe and creation of a boiling zone. The heat

convective effects in the heat pipe region have a local, transient effect on the

tem perature d istribu tion and m oisture change. H ow ever, the increase in

tem perature induces evaporation and vapor transport aw ay from the heat

source region w hich results in the developm ent of a d ry zone surrounding

the heat source and increased liquid saturation levels aw ay from the heater ,

due to condensation.

4 5

4 6

The study show s that the porosity is an im portant com ponent for heat

and flu id flow that developed during the test. The pores of the porous

m edium served as flow paths for steam, served as condensation points w here

cool tem peratures exist, and served as drainage flow paths for condensate

form ing in the cooler zones.

The following rem arks will serve as sum m ary and conclusion.

1) The results presented in this study dem onstrate som e possible

effects of w ater interaction with a horizontal heat source

w hich m ay have implications for high level radioactive waste

disposal.

2) The experimental results show that 75% of the w ater is

diverted around the heater area.

3) U nder steady state conditions, the results show the

appearance of several zones in the hom ogeneous porous

m ed ium :

a. dry and vapor zones where conduction heat transfer is

dom inan t.

b. convection dom inated two-phase heat pipe zone .

c. far field liquid saturation region.

4 7

4) The results of this study resemble a degree of agreem ent w ith

the experimental results of Udell and Cioulachtjian et al.,

and the numerical results of Pruess et al. presented in the

literature survey.

Future w ork can be done to im prove the experim ent in several areas.

First, from the p rio r w ork in this general area, it is ap p a ren t that the

perm eability (and thus the porosity) of the m edium play an im portan t role in

the outcom e of the results. Therefore, experimental w ork needs to be done

using a range of porous m edia w ith different permeabilities (and porosities).

Also the experim ent can be run w ith a range of tem peratures instead of one

tem pera tu re to determ ine the effect of this im portant variable. Finally,

im provem ent of the inflow system should be done to in su re consistent

uniform ity of the input spray.

CHAPTER 7

BIBLIOGRAPHY

Buscheck, T. A., and Nitao, J. J., 1993, "THE ANALYSIS OF REPOSITORY- HEAT DRIVEN HYDROTHERMAL FLOW AT YUCCA MOUNTAIN," Proceedings of the Fourth Annual International High Level Radioactive Waste Managemeyit Conference, ANS/ASCE, pp. 847-867.

Buscheck, T. A., Wilder, D. G., and Nitao, J. J., 1993, "LARGE-SCALE IN SITU TESTS FOR HYDROTHERMAL CHARACTERIZATION AT YUCCA MOUNTAIN," Proceedings of The Fourth Annual International High Level Radioactive Waste Management Conference, ANSIASCE, pp. 1854-1872.

Buscheck, T. A., and Nitao, J. J., 1994, "THE IMPACT OE BUOYANT, GAS- PHASE FLOW AND HETEROGENEITY ON THERMO- HYDROLOGICAL BEHAVIOR AT YUCCA MOUNTAIN," Proceedings of The Fifth Annual International High Level Radioactive Waste Management Conference, ANS/ASCE, pp. 2450-2474.

4 8

4 9Cioulachtjian, S., Tadrist, L., Occelli, R., Santini, R., and Pantaloni, J., 1989,

"HEAT TRANSFER IN POROUS MEDIA CROSSED BY A FLOWING FLUID," Physicochemical Hydrodynamics, PCH, 11(5), pp. 671-679.

Doughty, Christine, and Pruess, K., 1988, "A SEMI ANALYTICAL SOLUTION EOR HEAT-PIPE EFEECTS NEAR HIGH-LEVEL NUCLEAR WASTE BURIED IN PARTIALLY SATURATED GEOLOGICAL MEDIA," International J. Heat and Mass Transfer, 31(1), pp. 79-90.

Doughty, Christine, and Pruess, K., 1990, "A SIMILARITY SOLUTION FOR TWO-PHASE FLUID AND HEAT FLOW NEAR HIGH-LEVEL NUCLEAR WASTE PACKAGES EMPLACED IN POROUS MEDIA," International J. Heat and Mass Transfer, 33(6), pp. 1205-1222.

Gomaa, E. E. , and Somerton, W. H., 1974, "THERMAL BEHAVIOR OF MULTIFLUID-SATURATED FORMATIONS PART II: EFFECT OF VAPOR SATURATION HEAT PIPE CONCEPT AND APPARENT THERMAL CONDUCTIVITY," SPE Paper 4896-B, Proc. Society of Petroleum Engineers California Regional Meeting, San Francisco.

Hanson, Eric M., 1993, "SIMPLE MEASUREMENT OF SATURATED SOIL CONDITIONS," Senior Design Report, Department of M echanical Engineering, UNLV.

Ho, Clifford K., Marki, K. S., and Glass, R. J., 1994, "STUDIES OF NON- ISOTHERMAL FLOW IN SATURATED AND PARTIALLY SATURATED POROUS MEDIA," Proceedings of The Fifth Annual International High Level Radioactive Waste Management Conference, ANS/ASCE, pp. 2450-2474.

Izzeldin, A bdullah A., Hanson, E., and Boehm, R. E., 1994,"UNSATURATED ELOW EXPERIMENT WITH PHASE CHANGE THE HEAT PIPE EFFECT," Proceeding of The Fifth Annual

5 0

International High Level Radioactive Waste Management Conference, ANS/ASCE, pp. 2450-2474.

Izzeldin, Abdullah A., Chen, Yi-Tung, and Boehm, R. P., 1995, " HEAT TRANSEER WITH PHASE CHANGE IN UNSATURATED FLOWS,” Accepted for the Fourth ASME/JSME Thermal Engineering Joint Conference.

LabView for Windows, 1992, "User Manual," National Instrum ents, Austin, Texas.

Liu, C., and Evett, J., 1990, Soil Properties, Second Edition, Prentice Hall, Inc., N ew Jersey.

Ogniewicz, Y., and Tien, C. L., 1979, "ANALYSIS OF THE HEAT PIPE PHENOMENON ON POROUS MEDIA," AIAA 14th Thermophysics Conference.

Pollock, D. W., 1986, "SIMULATION OF FLUID FLOW AND ENERGY TRANSPORT PROCESSES ASSOCIATED WITH HIGH-LEVEL RADIOACTIVE WASTE DISPOSAL IN UNSATURATED ALLUVIUM," Water Resources Research, 22(5), pp. 765-775.

Pruess, K., Tsang, Y. W., and Wang, J. S. Y., 1985, "MODELING OE STRONGLY HEAT-DRIVEN ELOW IN PARTIALLY SATURATED FRACTURED POROUS MEDIA," Proceedings of The 17th International Congress on The Hydrogeology of Rocks of Low Permeability, lAH, pp. 486-497.

Su, Ho-Jeen, and Somerton, W. H., 1979, " THERMAL BEHAVIOR OE FLUID SATURATED POROUS MEDIA WITH PHASE CHANGES," Proceedings of the 16th hiter^iational Thermal Conductivity Conference, pp. 193-204.

5 1

Udell, Kent S., 1985, " HEAT TRANSFER IN POROUS MEDIACONSIDERING PHASE CHANGE AND CAPILLARY- THE HEAT PIPE EFFECT," International J. Heat and Mass Transfer, 28(2), pp. 485-495.

Udell, Kent S., 1983, "HEAT TRANSEER IN POROUS MEDIA HEATED FROM ABOVE WITH EVAPORATION, CONDENSATION, AND CAPILLARY EFFECTS," International J. Heat and Mass Transfer,105(3), pp. 485-492.

APPENDIX I

Capacitance Element Calibrations

The m oistu re sensors used in this experim ent are a so lid state

capacitive type w hich w ere built in our laboratory. These sensors w ork w ith

sensing th e changes of m o istu re by conductance, re su ltin g in linear

capacitance changes as a function of moisture content.

C apacitance elem ent sensors can easily be in terfaced to a data

acquisition system by converting the capacitance read ing in to a voltage

output. F igure 15 shows the schematic diagram of the capacitance to voltage

converter circuit. The circuit features the use of an op era tio n a l cmos

am plifier (ICL 7556) and precision instrum entation capacitors and resistors.

The circuit requires a 2.5 V DC input. This design will m aintain excellent DC

accuracy d o w n to m icro-volts. The circuit ou tpu t was connected to the

Labview data acquisition system for automatic monitoring.

52

+2.5 V +2.5 V+2.5 V+2.5 V.5V

lOOK65K:

Ul/A Ul/B0.1 }iF

DIS DISlÜK7556 755610 M CAPACITANCE

ELEMENTSSENSOR

TRG cm OUTTRG

eu euTHR THR

220 pF

10 K

:= 10 pF

Figure 15: Schematic diagram of capacitance-to-voltage converter circuit for the use w ith the capacitance element sensors.

LnOJ

5 4

The capacitance element sensors were calibrated using the capacitance-

to-voltage converter circuit. Since the purpose of using these sensors w as the

m onitoring of the m oisture m igration th rough the porous m edium bed, the

sensors w ere calibrated in d ry and fully w ater saturated fill material. The

calibration procedure was as following:

1. The sensors were connected the converter circuits, and the

circuits were connected to the Labview data acquisition

program. Then the system was turned on.

2. 579.6 grams of dry glass beads were m easured and placed in a

400 ml graduated cylinder. This represented a zero moisture

content (dry) condition.

3. The sensors were inserted into the dry glass beads and

m onitored until a constant reading was achieved.

4. The Labview program was stopped and the data collected

was saved.

5. 100 grams of w ater was added to the dry glass beads. This

represented a 100% m oisture content (fully saturated) condition.

6. The sensors were inserted into the fully saturated glass beads

and m onitored until a constant reading was achieved, then the

data collected was saved.

7. The data collected w ere plotted and curve fitted.

55

Figures 16a through 16f show the results of the sensor calibrations.

The ratio of the moisture content (mass of w ater over mass of glass beads) in

these figures was plotted versus the voltage reading and curve fitted using a

first order polynomial equation. The resulting equation was used in the data

collected from the experim ental run to generate the m oisture content plot.

5 6020

y= - 3.6330e-2 + 8.6500e-2x

0.15-

IaS

0 .1 0 -

a5.2os

0.05-

0.000 31 2

Sensor reading [veils]

Figure 16a : Calibration of capacitance element [sensor 1].

0.20

y= - 2.78710-2 + 8.3696e-2x

3t o 0.15 -

a

0.1 0 -II • II 0.05-

I0.00

0 321

Sensor reading [volts]

Figure 16b : Calibration of capacitance element [sensor 2].

5 70.20

y= -2.1217e-2 + 8.1604e-2x

M) 0.15 -

0.1 0 -

0.05-

0.000 321

Sensor reading [volts] Figure 16c : Calibration of capacitance element [sensor 3].

y = - 3.28910-2 + 8.5432e-2x

sA60 0.15 -

S60

0.10 -

III 0.05-

0.0030 21

Sensor reading [volts]

Figure 16d : Calibration of capacitance element [sensor 4].

5 8

y= - 2.9438e-2 + 8.4349e-2x

0 .1 0 -II ■3 0.05- «

I0.00

0 2 31

Sensor reading [volts] Fignrel6e : Calibration of capacitance element [sensor 5].

y= -1.99376-2 + 8.0390e-2x

CtO0 .1 0 -

(o 0.05 -

0.0030 21

Sensor reading [volts]

Figure 16f : Calibration of capacitance element [sensor 6].

APPENDIX II

Labview Data A cquisition

LabView is a program developm ent applications package which uses a

graphical program m ing language to create program s in block-diagram form

instead of text-based languages (that create lines of code). In addition LabView

is a general purpose program m ing system that includes libraries of functions

an d developm en t tools designed specifically for data acquisition and

in stru m en t control. LabView program s are called "virtual instrum ents"

because their appearance and operation im itate actual instrum ents. A virtual

instrum ent is a software construction that has the characteristics of an actual

in stru m en t. The program has two m ain functions that are com bined

together for the program to work. These functions are an interactive user

interface which is called a front panel and receiver instructions know n as a

block diagram . The front panel is a p rogram representing an assem bly of

electronic com ponents that perform the v irtual instrum ent functions, and a

5 9

6 0

calling interface for com m unication w ith other v irtual instrum ents. The

block diagram is the v irtu a l in stru m en t source code w hich contains

in p u t/o u tp u t, com p u ta tio n a l, and sub -v irtua l in stru m en t com ponents

interconnected by wires directing the flow of data.

T herm ocoup le a n d v o ltag e v irtu a l in s tru m e n t p rog ram s are

developed to collect data from the experim ental apparatus. These program s

acquire data from an SCXI-1100 (Signal C ond ition ing ex tension for

Instrum entation), linearize it, and save it into a file. SCXI-1100 is a high

perform ance, signal cond ition ing and data acquisition system that can

accom m odate 32 differential channels. SCXI-1100 is a m odule for signal

conditioning of therm ocouples, volt, and millivolt sources. Figures 17 and 18

show schem atic d iag ram s for the therm ocouple p rogram and voltage

program , respectively.

device(l)

channels(sc11 mdl 10:15)

scl I mdl 10:10

offset channel (sol calgnd)

idl

scl I mdl I calgndcold junction channel (sc Imdl I mtemp)

scl I mdl I mtempnumber of samples to aveijage for each data point(IOO)

200

scan rate(100 scans/sec)

g |40.0

Input limits (+0.001V to -0.001V)

I D

thermocouple type (J)

K

Interchannel Delay in seconds (20 usees)

20.0E-6

String Written to file21:39:03 75.8406 75.845345 75.856743 75.866570 75.877975 75.883865 75.899200 75.908638 75.921608 75.931435 75.934975

[latest temperature data ] [STOP

I channel] gO

Iugh limitj liDw llmil0.010 i -0.010

75 8errorout

code source

ERROR -10846 1 [Analog Input Buffer Read |

Figure 17 a: Schematic front panei for thermocoupie virtual instrument program.ON

|device(lj)

| î ^channels(s|:

•Hinput limits[5ns]

interchanne Delay in

11 ij !J U U L ll! L i.U iJ .lli n i l I II n i l U-U !-! 1 ' 11 1 \ U 2 WU 1 ! previous error clusterjLJJ l±) mjblnary amplifier olrsei] '

I I I I I I I I ! I I I I I I ! I [ LI I I I I I I I I I I I I I I I I I I I I IEnter file name c \excel\lesf.dat

I ,*V ru^

oVcmI>lnterchannel Delay

— >scan rale>|<numberof ctians<

<error cluster<< laskID >

scan rate

fefring Written to filenumber of sam ples to

erroroutII

CLEflRMean

>error cluster>

thermocouple type (j||sTop|f-fr

g j |cold junction temp (ambient temp) [[ 1 1 I I 1 1 1 1 1 1 1 I I 1 1 I I 1 1 1 1 1 1 I I 1 1 1 1 1 ! 1 1 1 1 1 1 1 1 1 1 1 1 1 1 i i i i I I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 i i f [ 1 1 I I I I 1 1 1 ! I i I I 1 1 1 1 I I

Figure 17b: Schematic block diagram for thermocouple virtual Instrument program.ONK)

device(l)

channels (obO I scl I mdl I 0:3)

bbO ! scl I mdl 10:5

offse t channel(obO I scl I mdl I calgnd)

obO I scl I mdl I calgnd

Strip Chart

" S .

num ber of sam ples to average for eaCh data point

I200

scan rate

<1 0.04

4 0.02

RH3 Id

RH4 Id

RH5 d

1

11 0 0~ 1

) 14

la te s t vo ltage data S T O P

(200 scans/sec) RH6 |d 0.02 "T jchanneipo | L n a i3 2 0 .0 I

e rro rInput limits (no change) o u t

E high limit low limit

113.000 I r — IEcode source

Figure 18a: Front panel for voltage virtual instrument programOvU)

Input limit#

•ca n rat#(200 scan s/iec )

number of •am ple# to average tor each datapoin t (100)

B n a n n n n n p t n j B p g n o o n o o i g o h n in i h t h h b itttb n n a n n cm b gTTPPtrn n btth o o o

Madntoeh HD: lzzdr.dat

loreWou# error du»teH Iblnaty amplifier off#at from Ira m e q

continuous acq>buller sized a v lc e ( l )

>#can rate)— («number of chans ctasklD

[« iro rauste r< task D >

la tes t v o ltage data

B DV oltage Strip Chart

>error duster*

STOP

□ Ü B B Ü □ n il n a tjn □ P n □ □ □ □ B B B B B B B B BB'P B B B B B B B B ü ü b a n Ü D d ü B n a a ü n n ü d

Figure 18b: Schematic block diagram for voltage virtual instrument programG \4:

APPENDIX III

Coefficient of Permeability via the Falling-Head Method

Permeability generally relates to the propensity of a porous m edium to

allow w ater to move through its void spaces. According to Darcy's law, the

flow rate of water q th rough a porous m edia of cross-sectional area A is

directly proportional to the im posed gradient (slope) i, or q = kiA. The

constant k is known as the coefficient of perm eability which indicates the ease

w ith w hich a fluid passes th ro u g h a porous m edium . The falling head

m ethod is one of the general laboratory m ethods that is available for

determ ining the coefficient of perm eability of a porous m edia directly. The

coefficient of perm eability is necessary to determ ine the time for fluid to

travel between two points. This m ethod is accurate to w ithin about one order

of m agnitude.

6 5

6 6

A fa lling -head perm eability test w as ru n using the s tan d a rd

com paction m old permeameter. This perm eam eter contains a standpipe, top

cap w ith rubber gasket and inlet orifice, test m old, porous stone at the base,

and outlet drain hose. A drawing of the apparatus is show n in Figure 19. The

first step of the general test procedure was to saturate the glass beads with

w ater. W ater was then was allowed to move through the specimen under a

falling-head condition, while the time required for a certain quantity of water

to pass through the specimen was m easured and recorded. Using these data

one can determ ine the coefficient of perm eability. The actual step-by-step

procedure was as follows:

1. The permeameter mold w ith the base plate and gasket attached

was weighed. The inside diam eter of the perm eam eter mold

and its length were m easured and recorded.

2. A dry sample of glass beads was placed into the permeameter

m old and compacted to a desirable density. The permeameter

m old with base plate and gasket attached plus compacted beads

was weighed and the density of the sample was determined.

3. W ith the outlet tube open, the sam ple was saturated with

water. The specimen was assum ed to be saturated when water

in the inlet tube on top of the m old reached equilibrium with

w ater exiting the mold.

6 7

A

Ring stand

Cap and inlet , orifice P

Standpipe

Porous stone

Test mold

O utlet drain tube

Figure 19a : Sketch details of the falling-head test apparatus.

6 8

Cap

Inlet orifice

Gasket

Pan 7.10 cm

330 cm

Gasket

Base

Porous stoneOutlet drain

tube

Figure 19b: Sketch details of the test mold.

6 9

4. After the specimen was saturated the outlet tube was clamped.

The standpipe was then filled to a convenient h e ig h t, and the

hydraulic head across the sample was m easured.

5. The test was started by opening the outlet tube and

sim ultaneously the test was timed. The w ater was allowed to

flow through the sample until the standpipe was alm ost empty.

The outlet tube was clamped and the elapse time was recorded.

The hydraulic head was measured.

6. The standpipe was refilled to the same height as in step 4 and

step 5 and was repeated five times.

The coefficient of perm eability was calculated using the form ula [Liu

and Evett, 1990]

w here k-p = coefficient of permeability, m /s

a = cross-sectional area of standpipe, m^

1 = length of specimen, m

A = cross-sectional area of glass beads specimen, m^

7 0

h% = hydraulic head at beginning of test, m

h2 = hydraulic head at end of test, m

t = total time for water in standpipe to drop from h% to h2 , s

The com puted coefficient of perm eability was the value for w ater at 24

°C at the time w hen the test was conducted. It was necessary to correct this

. perm eability to that for 20 °C by m ultiplying the com puted value by the ratio

of the viscosity (a) of w ater at 24 °C to viscosity of water at 20 °C. The ratio of

the viscosity (a) of 24 °C w ater to that of 20 °C water was 0.9095 [Liu and Evett,

1990].

Falling Head Data Sheet

Sample Dimensions: D = 3.30 cm Area = 8.55 cm^

Mass beads + pan init. = 941.9 g H t = 7.10 cm

Mass beads + pan final = 1037.6 g

Mass of the sample = 95.7 g

Vol = 60.73 cm3

Density = 1.576 g /cm ^

Area standpipe = 0.40 cm^ Temperature = 24 °C

Test data

alk ^ = — In

0.4 X 7.1 39.5 cm‘ = 8 .5 5 x 28.3 '" Ï 6 7 =

k»., = a k ^ = 0.9095 x 0.00989 = 9.0x10

7 1

I t no. h | , cm h 2 , cm t , s

1 39.5 16.7 28.23

2 40.2 17.0 28.02

3 39.5 16.8 28.16

4 39.5 16.4 29.00

5 39.5 17.1 30.75

20 T ........................ sec

The following equation was used to determ ine the permeability:

K =^ 2 0 "

Ph 2o ®

7 2

where K = permeability, m^

k = coefficient of permeability at 20 °C, m /s

|i = viscosity of the water, N s /m ^

p = density of the water, K g/m ^

g = acceleration of gravity, m /s^

Then the perm eability is

— X1468xlO = 135x10 ^^m^1000x9.80