WASTE INJECTION INTO THEHAWAIIAN GHYBEN-HERZBERG AQUIFER:

A LABORATORY STUDY USINGA SAND-PACKED HYDRAULIC MODEL

Stephen W. WheatcraftFrank L. Peterson

Duane L. Heutmaker

Technical Report No. 96

February 1976

Project Completion Reportfor

SUBSURFACE WASTE INJECTION IN HAWAII

OWRT Project No. B-038-HIGrant Agreement Nos.: 14-31-0001-5011

14-31-0001-5068Principal Investigator: Frank L. Peterson

Project Period: 1 July 1974 to 30 September 1975

The programs and activities described herein were supported in part by fundsprovided by the United States Department of the Interior as authorized underthe Water Resources Act of 1964, Public Law 88-379.

WATER RESOURCES RESEARCH CENTERUniversity of Hawaii

July 1976

ERRATA SHEET

Please note the following corrections to our Technical Report No.96 entitled, Waste Injection into the H(JJ;)aiian Ghyben-HerzbergAquifer: A Laboratory Study Using a Sand-Packed Hydraulic Model(Wheatcraft, Peterson, and Heutmaker 1976).

Page Line . Error Correction

32 4 -17°C ( 2°p). ±l. 1°C

60 15 V VP P

60 16 V average pore velocity Vp P

60 25 Vf

of 28.2 V of 28.2003 3 3

PO. 333

62 6 h ::: 9.02 h = 9.02 t

iii

ABSTRACT

Injection of wastes into the Hawaiian subsurface environment presents

unique problems because the waste effZuents normally are injected into the

salt or brackish water underlying the fresh Ghyben-Herzberg lens. Because

the waste water commonly has approximately the same density as fresh water~

in addition to any ~wient groundwater flow effects~ a buoyant uplift is

produced which causes the injected waste to move upward and outward from the

injection point as a buoyant plume.

A laboratory sand-packed hydraulic model was used to study the mechanics

of buoyant plume movement~ and the entrainment of salt water by the plume.

Simulated waste effZuent was injected into a density-stratified aquifer sys­

tem under static groundwater conditions~ and the effects on plume mechanics

of varying several different injection parameters~ such as injection depth~

injection rate~ type of injection source~ density of receiving water~ etc.~

were observed.

The laboratory studies indicated that although several of the injection

parameters (most notably depth of the injection with respect to the salt­

fresh interface) have an effect on the details of the injection process and

the plume movement and configuration~ none of the injection parameters

exerts a truly significant control on the ultimate fate of the injected

plume. That is~ for the conditions stipulated in this study~ the injection

plumes always migrated well up into the freshwater lens~ regardless of

variations in any of the several injection parameters. Furthermore~ these

experiments showed little evidence of entrainment of the surrounding salt

water into the injected buoyant plumes~ which strongly suggests that the

principal means of plume movement is by mass displacement rather than by

mixing processes.

~'.

v

CONTENTS

THEORETICAL DESCRIPTION OF PLUME MOVEMENT .Pore Velocity of the Injected Effluent.Buoyant Plume Movement in the Freshwater Zone.

EXPERIMENTAL RESULTS .Summary of Experiments . . . . . .Effects of Injection Parameter VariationSalt Water Entrainment .

LABORATORY MODELING EXPERIMENTS .Selection of Model and Model ExperimentsDescription of Sand-Packed Hydraulic ModelModel Calibration and Experimental Methods.

7·

1

1

2

5

5

6

6

11

12

13

14

15

15

16

28

37

37

40

52

59

59

60

64

64

64

65

66

66

67

68

iii

on Plume Shape..Head Buildup .Relative Influence of Injection ParametersSalt Water Entrainment.Theoretical Conclusions.

ABSTRACT...

INTRODUCTI ON.Background of Study.Waste Injection Practices in Hawaii.Objectives . . .Conduct of Study

NATURE OF PROBLEM .Hawaiian Hydrogeology.Waste Injection under Hawaiian Hydrogeologic Conditions.Other Models of Waste Injection in Porous Media ..Buoyant Plume Models ...Entrainment of Salt Water..

CONCLUSIONS . . . . . . .

RECOMMENDATIONS .

ACKNOWLEDGMENTS

REFERENCES....

vi

APPENDICES.

FIGURES

1. Cross Section of Typical Volcanic Dome Showing Occurrenceand Recovery of Ground Water . . . . .. .

2. Mixing Zone Characteristics for Various Oahu Aquifers.3. Photographs of Sand-Packed Hydraulic Model4. Front, Top, and End Views of the Model ..5. Drawing of the End Chambers. . . . . .. .6. Drawing of Sample Ports and Manometer Taps7. Placement of Sample Ports .8. Details of the Salt Water Entrance Chambers.9. Drawing of the Perforated Well Casing ..

10. Drawing of the Injection Wells .11. Drawing of the Injection Well Mounting .12. Diagram of the Salt Water Emplacement Apparatus .13. Fluorescein-Corrected Calibration Curve of Electrical

Conductivity vs. NaCl .14. Defining Sketches for the Interface Angle. . .. .15. Height of Plume vs. Time for Static 12 .16. Comparison of Injection Depths: Height ys. Time for

Statics 4 and 8. . . . . . . . . . . . . . . . .17. Comparison of Injection Depths: Height ys. Time for

Statics 5, 9 and 10 .18. Comparison of Injection Depths: Height vs. Time for

Statics 13 and 14. . . . . . . . . ....19. Comparison of Injection Depths: Width ys. Time for

Statics 4 and 8. . ...•..20. Comparison of Injection Depths: Width ys. Time for

Statics 5, 9 and 10. . . . .. . .21. Comparison of Injection Rates: Width Ys. Log Time

for Statics 8 and 9 .22. Comparison of Injection Rates: Height ys. Log Time

for Statics 4 and 10 .

71

8

1018202122232527

29

30

34

36

39

42

43

44

45

46

47

49

50

23.

24.

Comparison of Injection Rates: Height ys. Log Timefor Statics 8 and 9 .Comparison of Lengths of Discharging Section: Heightys. Log Time for Statics 4 and 11 .

51

53

25.

26.

27.28.29.

30.

1.

Comparison of Lengths of Discharging Section: Heightvs. Log Time for Statics 3 and 10.

Width vs. Log Time for Static 10 .

Chloride Concentrations for Static 12.

Chloride Concentrations for Static 13.Chloride Concentrations for Static 14.

Comparison of Theoretical Curve (eq. 16) with ExperimentalCurves (Statics 12, 13, and 14) ...

TABLE

Summary of Experiments and Parameter Variations.

vii

54

55

5657

58

63

38

INTRODUCTI ON

Background of Study

Subsurface liquid waste disposal can be accomplished by two different

methods: the direct introduction of waste materials into the earth by in­

jection through wells, and percolation of wastes from surface and near­

surface spreading and leaching ponds, cesspools and septic tanks, sanitary

landfills, etc. The study described herein will deal primarily with sub­

surface disposal by injection, and only indirectly with surface percolation.

Subsurface disposal by injection wells is the emplacement of wastes

within the earth, usually below the water table and often beneath confining

strata which serve to isolate the wastes from potable water supplies or

other valuable or potentially valuable resources. Use of subsurface strata

for disposal of liquid wastes is not a new concept. The petroleum industry

pioneered the development of injecting liquids into the subsurface, origi­

nally to increase crude oil production by injecting fresh water into oil­

bearing strata, and later for disposal of salt brines brought to the surface

during oil and gas production. In recent years, the diminishing capability

of surface waters to receive liquid waste effluents has made the direct

emplacement of these wastes into the subsurface increasingly more attractive.

Furthermore, in many areas subsurface injection of liquid wastes is feasible

due to the enormous subsurface fluid storage capacity. Consequently, injec­

tion wells have come into more common use for underground storage and dis­

posal of various industrial and municipal wastes. Although currently a

minor practice compared to the reinjection of brine wastes by the petroleum

industry, the number of reported industrial and municipal injection wells in

the United States has increased from approximately 125 in 1968 to over 270

by 1972 (Ballentine, Reznek, and Hall 1972). Undoubtedly, there are thou­

sands of other small injection wells which dispose of waste materials to the

subsurface which have never been reported.

Until recently, little consideration has been given to the effects of

waste disposal practices on the subsurface environment. Furthermore, sub­

surface waste disposal often is practiced without adequate control. Only

about half of all the states have regulations concerning waste disposal

(Ballentine, Reznek, and Hall 1972). Waste injection into the saturated

zone below a water table or piezometric surface can be accommodated only by

2

compressing or displacing the existing fluids, or by compressing or deform­

ing the surrounding reservoir strata. Possible consequences of waste injec­

tion under pressure include displacement of formation waters quite distant

from the injection site, hydro-fracturing of the receiving formation, migra­

tion of wastes along existing or newly-created fractures, movement of wastes

upward along well casings, and even gross readjustment of subsurface strata,

such as at the Denver Arsenal injection well where liquid waste injection is

thought to have triggered a series of small earthquakes (Hollister and

Weimer 1968). The injection of liquid wastes into the subsurface presents

problems which are not confined only to hydrodynamics. Some injected wastes

most likely react with the formation waters and rocks in the injection hori­

zon to change the permeability and strength of the formation. Furthermore,

radioactive and chemically unstable wastes may produce heat and pressure

after they have been injected.

In general, although much of the technical knowledge and experience

necessary to carry out subsurface injection of liquid wastes is available,

further investigation is necessary to solve specific problems that remain as

barriers to the safe, efficient, and economic use of this method of waste

disposal. In particular, predictive relationships for groundwater velocity,

mixing, dispersion and stratification, as well as the geochemical reactions

between the injected fluid and the resident formation fluid and rock still

need refinement. Furthermore, adequate knowledge of the local hydrogeology,

hydromechanics, and geochemistry of many groundwater systems is presently

not available to confidently locate, design, and manage the operation of

waste injection systems.

Waste Injection Practices in Hawaii

Historically, the principal means of waste disposal in the Hawaiian

islands have always been the dumping of domestic sewage and other liquid

wastes via ocean outfalls into the Pacific Ocean, and this remains today as

the primary means of waste disposal in Hawaii. In addition, but to a lesser

extent, cesspools have served as a principal means of subsurface waste dis­

posal in many rural and outlying areas, especially those inland from the

ocean. As Hawaii has become increasingly more populated and urbanized, the

use of individual cesspools has gradually diminished and the use of central­

ized sewage collection systems with ocean outfalls has become by far the

3

most important means of waste disposal.

The practice of ocean waste disposal has served Hawaii remarkably well

in the past, primarily for two reasons: first, the Pacific Ocean provides a

tremendously vast sink for dilution of waste products, and secondly, much of

the population of the Hawaiian islands is located in close proximity to the

coast. Within the past several years, however, due both to a rapid increase

in population and to a growing concern about the quality of Hawaii's coastal

waters and the stringency of state water quality standards, alternative

methods of waste disposal have received increased consideration. The alter­

natives of greatest promise and increasing use in Hawaii at the present time

are disposal into the subsurface by wells and pits and recycling treated

waste effluents by irrigation (Peterson and Lau 1974).

Evaluation of artificial recharge practices in Hawaii by Hargis and

Peterson (1970) shows that artificial recharge to the fresh groundwater body

through injection wells is practiced on a very limited scale in Hawaii, and

nowhere is treated waste effluent being used to recharge the fresh ground­

water supply at the present time. Injection of storm runoff and other liquid

wastes through wells into the subsurface for the purpose of disposal is,

however, practiced on a limited scale at numerous locations throughout the

state of Hawaii. Hargis and Peterson (1970) and Peterson and Hargis (1971)

have described many instances of storm runoff injection on Maui and Hawaii.

Takasaki (1974) has indicated some 115 instances where subsurface dis­

posal of waste materials is practiced presently in Hawaii, and an additional

97 cases where subsurface disposal is pending. The bulk of these cases con­

sists of shallow wells and pits for the disposal of domestic sewage effluent

and, in a few cases, various industrial wastes and cooling waters. The in­

jection capacity of all of these small installations totals probably only

a few million gallons per day (mgd). However, Takasaki (1974) also lists

several much larger installations, primarily for the subsurface injection of

treated sewage effluent, which are either already completed, presently under

construction, or in the planning stage, which will have a total injection

capacity of many tens of mgd. Almost all waste disposal to the subsurface

in Hawaii occurs in shallow coastal aquifers, often within a few hundred

feet from the shoreline (Peterson and Lau 1974).

Disposal of liquid wastes into the Hawaiian subsurface environment des­

cribed above raises two potential areas of concern: possible contamination

4

of potable groundwater bodies, and contamination of shallow near-shore

coastal waters. Because fresh potable groundwater is restricted primarily

to lava flows, it usually is not present in developable quantities in the

immediate coastal areas where most Hawaiian waste injection is practiced.

Thus, with present waste disposal practices, in most areas contamination of

fresh groundwater supplies is not a major problem. However, because most

waste injection in Hawaii occurs in shallow coastal aquifers where the ulti­

mate fate of the injected waste is to discharge, often quite rapidly, into

shallow coastal waters, impending danger of contaminating and deteriorating

the quality of these waters may be considerable (Peterson and Lau 1974).

Because of the possible adverse effects of waste injection on the

groundwater and near-shore environments, the state of Hawaii has evolved

some regulatory laws to control contamination. In addition, the state regu­

latory program also serves to satisfy the Federal Water Pollution Control

Act Admendments of 1972, which require state regulation of waste injection

for qualification for Federal funding of waste-treatment management. The

power for regulation within the state of waste disposal of all types lies

with the Department of Health, and is granted specifically under Chapters

321-16 and 342, HaLJaii revised statutes. Regulations that pertain to sewage

effluent are contained in Chapters 37 (1974) and 38 (1973) of the Public

health regulations, Department of Health, State of Hawaii. The regulations

stipulate that waste injection is prohibited under all circumstances unless

a permit from the Director of Public Health is obtained.

To acquire a permit to operate an injection installation, an applicant

must be able to provide an "affirmative demonstration" that such waste in­

jection will not pollute or degrade potable groundwater reservoirs or

neighboring coastal waters. If such an "affirmative demonstration" cannot

be provided, additional treatment of the effluent is required. However, if

an "affirmative demonstration" can be made, only a minimum amount of treat­

ment, approximately equivalent to that given by a septic tank, is required.

The pertinent details and regulations regarding waste injection are set

forth in Sections 7 and 8 of Chapter 38 of the Public health regulations

(1973). Because of the environmental and economic benefits of producing an

"affirmative demonstration," it is of considerable importance to develop a

meaningful and standardized set of criteria to assess the possible environ­

mental consequences of proposed injection wells. To date, this has not been

5

done adequately in Hawaii, owing primarily to the lack of sufficient knowl­

edge to accurately describe the nature of movement and the ultimate fate of

injected effluent in the Hawaiian subsurface environment.

The failure of available technology to adequately predict the details

of the injection process as it occurs in Hawaii, together with the growing

demand to install injection systems has created the need for more basic re­

search into the process of liquid waste injection into the Hawaiian hydro­

geological systems. It is this critical demand for more knowledge of this

subject that led directly to the work described in this report and other

reports on the same subject which will be forthcoming from the University of

Hawaii Water Resources Research Center.

Objectives

The overall objective of the studies on subsurface waste disposal by

injection is to provide a comprehensive understanding of the subsurface waste

injection proc~ss in the Hawaiian environment. To achieve this objective,

an investigation over a 2-yr period on the hydrodynamics and fluid flow, and

geochemistry and water quality aspects of subsurface waste injection is cur­

rently underway. During the first year of investigation, the hydrodynamics

of waste injection into an Hawaiian density-stratified groundwater environ­

ment were studied in the laboratory by means of physical modeling techniques,

and some of the results are described in this report. During the second and

final year of the project, investigation will consist of laboratory studies·

of geochemical and water quality aspects, and numerical analysis and theo­

retical studies of the hydrodynamics of waste injection. In addition, if

opportunity and time allows, it is anticipated that the results of the above­

described investigations will be applied to the hydrogeology, hydrodynamics

and geochemistry of actual field injection operations in Hawaii.

Conduct of Study

Initial investigation of subsurface waste disposal by injection in

Hawaii was begun in the fall of 1973 with support from the University of

Hawaii Environmental Center. Investigation was continued during the 1974

to 1975 academic year with support from the U.S. Department of the Interior,

Ii.".~.

~~

6

Office of Water Research and Technology, together with matching support from

the State of Hawaii, Maui County, and Conoco Oil Company. This project con­

sisted of investigation of the hydrodynamics of waste injection into a

density-stratified groundwater system by laboratory physical modeling, using

both a sandbox model and a vertical Hele-Shaw model.

The sandbox modeling experiments have consisted of systematically vary­

ing important injection parameters such as rate of injection, depth and

method of injection, and injection and resident fluid characteristics, and

of evaluating the resultant effects on the injection process. The above

experiments were conducted for two different sets of conditions: (1) where

fluid potentials are maintained such that resident aquifer fluid is static

prior to injection (static experiments), and (2) where fluid potentials are

maintained such that an ambient flow field exists (dynamic experiments).

The vertical Hele-Shaw modeling experiments were used to study the dy­

namics of the Ghyben-Herzberg salt-fresh interface under injection conditions

for two-dimensional cases. Two well injection problems are under considera­

tion: injection of liquid wastes into a confined aquifer, and injection into

an unconfined aquifer.

The Phase 1 investigation described in this report consists of the sand­

box modeling of so-called "static" experiments. Subsequent technical reports

for Phase 2 of this project will describe the sandbox "dynamic" modeling

experiments and the Hele-Shaw modeling experiments.

NATURE OF PROBLEM

Hawaiian Hydrogeology

The basic approach to subsurface waste injection in the Hawaiian islands

varies considerably from that commonly practiced in continental areas of the

world, primarily owing to major hydrogeological differences. A knowledge of

Hawaiian hydrogeology, thus, is essential in order to more fully understand

the waste injection process in the Hawaiian environment.

All the major islands in the Hawaiian chain consist essentially of one

or more shield volcanoes which are comprised of thin basaltic lava flows,

which are among the most permeable rocks on earth. According to Peterson

(1972) :

7

The high permeability of Hawaiian lavas results primarily frommajor flow structures, the most important of which include clinkerzones in aa, lava tubes and gas vesicles in pahoehoe, vertical con­traction joints formed by the cooling of the lavas, and irregularopenings associated with the surface between flows.

Associated with most of these basalt lava flows (mainly the aa flows) are

dense, relatively impermeable cores that are caused by slow cooling in the

center portion of the flows. These dense cores retard water movement in the

direction normal to the plane of flow and hence Hawaiian basalt aquifers are

highly anisotropic. The irregular nature of basalt flow structures also

causes Hawaiian basalt aquifers to be nonhomogeneous. Interbedded with the

lava flows are occasional ash beds which are relatively impermeable and

which tend to retard the downward flow of groundwater, often acting as perch­

ing members. Calderas and rift zones of volcanoes also contain many steeply

dipping dikes which cut through the more gently dipping lava flows. The

dikes are dense and have low permeabilities and, thus, also may act as bar­

riers to groundwater movement. In addition, Peterson (1972) stated that:

On most Hawaiian islands, especially the older ones like Kauai andOahu, the margins of the volcanic domes are overlapped by coastalplain sediments of alluvial and marine origin.

These alluvial and marine sediments, collectively referred to as the oaprook,

are relatively impermeable compared to the Hawaiian basalts and, therefore,

act to retard seaward movement of groundwater from the underlying lavas.

In the above-described Hawaiian geologic environment, fresh groundwater

may accumulate in three principal types of bodies (Peterson 1972):

(1) High-level bodies perched on ash beds or soils interbeddedwith flows, on unconformities, or on other relatively imperviouslava flows, such as the dense cores of aa flows; (2) high-levelbodies impounded within compartments formed by impermeable dikesthat have intruded the lava flows; and (3) basal water bodiesfloating on and displacing salt water.

The occurrence and development of these groundwater bodies are illustrated

in Figure 1.

Compared to the total volume of basal groundwater, the amount of perched

and dike-confined groundwater is very small, and is of importance primarily

because of its high elevation. In any event, because current waste injection

practices in the Hawaiian islands are limited primarily to low-elevation

coastal regions, high-level perched and dike-confined groundwater bodies are

of little significance in this regard.

00

I. UNERODED STATE ~I. ERODED

SOURCE: After Peterson (1972).

FRESH WATER PERCHEDON ASH BED

A ARTESIAN WELL PRODUCING SALT WATER

B ARTESIAN WELL PRODUCING BRACKISH WATER

C ARTESIAN WELL PRODUCING FRESH WATER

D SKI t·1M ING TUNNE LS

E DIKE SPRING

F DIKE TUNNEL

G PERCHED WATER TUNNEL

CAPROCK

FIGURE 1. CROSS SECTION OF TYPICAL VOLCANIC DOME SHOWING OCCURRENCE AND RECOVERY OF GROUNDWATER

------------...'-

9

The principal source of fresh groundwater in the Hawaiian islandsis the roughly lens-shaped basal water body floating on and dis­placing denser sea water. Recharge of the basal water body resultsdirectly from percolating rain water or by underground leakage fromperched-water bodies and bodies impounded by dikes. Where the per­meable lava flows containing basal water extend to the coast with­out a cover of sediments, the head above sea level, which generallyincreases at an approximate rate of one foot of head per mile ofdistance from the coast, is small. Along some dry leeward coaststhe head gradient may be even less. Where the basaltic aquifer isdirectly overlain by the less permeable sedimentary caprock alongsome of the coastal margins, artesian heads of a few feet to over20 feet above sea level may occur. No lower limits to the zone ofpermeable lava flows within a range of several thousand feet belowsea level are known or suspected for most of the basal aquifers(Peterson 1972).

When steady-state conditions exist, the Ghyben-Herzberg principle

applies and the head of fresh water above sea level should be balanced by a

thickness about 40 times as great of fresh water below sea level. The actual

ratio depends on the relative densities of the two liquids, and is given by

the following equation:

6z =Ps

(1)

where 6z = thickness of the freshwater lens below sea level

Pf = density of fresh water

Ps = density of sea water

6h = freshwater head above sea level.

According to equation (1), the salt and fresh water zones are separated

by a sharp interface. In most natural situations, however, a transition, or

mixing zone which results from the miscibility of fresh and salt water, oc­

curs. The shape of the salt concentration curve in the mixing zone is gener­

ally sYmmetrically or aSYmmetrically sigmoidal, and both the shape of the

curve and the thickness of the mixing zone are governed by numerous factors,

such as tidal effects, seasonal fluctuations in recharge and discharge, and

discharge caused by pumping. In Hawaii, the depth to the bottom of fresh

water is normally a few tens to many hundreds of feet and the thickness of

the transition zone varies from only a few tens of feet in relatively undis­

turbed areas to as great as 1,000 ft in parts of southern Oahu where exten­

sive development of the basal lens has occurred. Figure 2 illustrates the

mixing zone curve shapes and thicknesses for various Oahu aquifers. The very

thick mixing zones at Pearl Harbor, Kaimuki, and Beretania, reflect the

O. I

~

o

2

-lLLJ>LLJ-l

<x:LLJ(/')

:3o-lLLJ!Xl

l-LL.

o 10LLJ0::oz::::>:z: 12

14

16

Beretania Area 1

Punaluu

Pearl HarborT-67

18· I I I I I I I I I I

o 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

CHLORIDE CONCENTRATION, ppmSOURCE: After Lau 1967.

FIGURE 2. MIXING lONE CHARACTERISTICS FOR VARIOUS OAHU AQUIFERS

11

effects of tidal action, nonuniform recharge, pumping stresses and seasonal

head fluctuations (Lau 1967). The very thin transition zone indicated in

the Punaluu aquifer can be interpreted as being due to the relatively pris­

tine condition of the Punaluu aquifer at the time of sampling.

Waste Injection under Hawaiian Hydrogeologic Conditions

Most liquid waste injected into the subsurface in the Hawaiian islands

is treated sewage effluent, and has a density approximately the same as that

of fresh water. Furthermore, as described previously, most waste injection

occurs in coastal regions where the groundwater lens is either quite thin or

consists of brackish rather than fresh water. Consequently, the wastes are

normally injected into brackish or salt water rather than into the fresh

basal lens. The Hawaiian waste injection situation, then, is at variance

with typical waste injection practices in most of the rest of the United

States and other parts of the world, where both the waste effluents and the

ambient groundwaters have approximately the same densities.

Waste effluent injected into an aquifer saturated with denser ambient

brackish or salt water experiences a buoyant lift. In response, the efflu­

ent then moves upward in a plume-like body, which is given the name buoyant

plume. The strength of the buoyant effect depends upon two things: (1) the

initial density difference that exists between the effluent and the ambient

liquid, and (2) the amount of mixing or entrainment of ambient water that

occurs during the interaction of the effluent with the ambient water.

The degree to which salt or brackish water is entrained into the buoyant

plume is a critical factor in determining the ultimate fate of the effluent.

Peterson and Lau (1974) have postulated that entrainment probably is signifi­

cant in the immediate vicinity of the well, and initial mixing and dilution

of the injected liquid by the ambient liquid will occur. This would result

in a buoyant plume pssessing a density intermediate between that of salt

water and fresh water, which would then be transported upward and outward

from the well by the combined action of injection, buoyant force and region­

al flux. For very low injection rates, the injected effluent mixes with the

ambient salt water and loses its unique identity within a short distance

from the well. For high injection rates, the effluent would entrain a sig­

nificant quantity of salt water and would move upward under the continuous

buoyant effect. During ascent, the diluted effluent would continue to en-

12

train ambient liquid and would ultimately level off after acquiring a density

equal to that of the ambient salt or brackish water. This leveling off would

probably occur someplace within the transition zone. This hypothetical

process is, of course, very desirable because it limits the upward migration

of the effluent and keeps the effluent beneath the freshwater lens.

If, however, very little salt water entrainment occurs during the injec­

tion process, the buoyant plume would retain its initial density, and would

ascend through the salt water and the brackish water of the transition zone

and on up into the fresh basal lens. Thus, the potential for pollution of

potable groundwater supplies is much greater if the entrainment factor is

relatively small or insignificant.

Other Models of Waste Injection in Porous Media

The simplest model of an injection well is that of a pumping well, but

with the mathematical sign of the injection rate, Q, taken to be negative,

or opposite to the sign of the pumping rate. In this way, any of the well

equations that have been developed for pumping wells can also be used to

describe injection processes.

Bear and Jacobs (1964) produced solutions for the case where an ambient

flow exists in the vicinity of the injection well for both steady and non­

steady cases. These solutions assume that the injection well fully pene­

trates a confined aquifer and that the injected liquid and the ambient liquid

are immiscible and have the same density. These assumptions are, however, at

variance with the conditions that exist in Hawaiian aquifers and, therefore,

the solutions seem to be of limited use in evaluating most Hawaiian waste

injection.

While Bear and Jacobs (1964) dealt with the two-phase flow of immisci­

ble liquids, other workers have taken into account the effects of dispersion.

Hoopes et al. (1973) developed relationships for the longitudinal and lateral

dispersion coefficients in terms of the flow and the properties of the media.

However, this study was carried out with a dilute salt water tracer, and the

density difference between ambient and tracer liquids was not a parameter of

variation. Mercado (1967) investigated the nature of the "breakthrough

curve" associated with an injected water body into a permeable stratified

medium. This work also assumed that the density difference between injected

and host liquids was negligible and considered only salinity differences.

13

Another aspect of waste injection that has received considerable atten­

tion is injection head buildup at the well face (Van Everdingen 1972; Wither­

spoon and Neuman 1972). Because of the extremely high permeability of Hawai­

ian basaltic aquifers, and assuming that clogging of the aquifer and well

face by waste effluent is not an appreciable factor, injection head buildup

owing to resistance to flow of the effluent through the aquifer should not

be a significant problem. However, injection head buildup resulting from

buoyancy effects may be significant. As Mink (Sunn, Low, Tom and Hara 1973)

describes, "an injection well cased throughout the freshwater zone and open

only in salt water would require an initial gravity head to overcome buoyancy

effects before effluent would move away from the well." If the standard

Ghyben-Herzberg equation (eq. [1] in this report) is modified slightly,

he = Ps - Pf zPs c (2)

where he is the head of waste effluent column above sea level, Zc is the

depth below sea level to the bottom of the well casing, and Ps and rr are

the densities of salt and fresh water. Thus, the extra head, hi' required

for injection is

h. = (h - r:,hJ + h (3)-z., e 'Owwhere hw is the well hydraulic head (theoretically equal in magnitude but

opposite in sign to well pumping losses), and r:,h is the freshwater head

above sea level. Mink (Sunn, Low, Tom and Hara 1973) gives the following

example to illustrate the buoyancy effect on injection head buildup:

If an injection well penetrating a basal lens with a head of 10feet were cased to its bottom in salt water at a depth 600 feetbelow sea level, the required gravity effluent head for injectionwould be 15 feet, or an excess of 5 feet over the natural regionalhead. Actually, for total injection head, the gravity effluenthead would have to be added to the well hydraulic head. For in­stance, in the above example, if the specific capacity of a wellwere 30 gpm/ft, the total injection head needed to force 0.75 mgd(521 gpm) into the formation would be 32.4 feet. This relation­ship is especially important in locations where surface elevationdoes not greatly exceed the free water table surface; obviouslyfor an artesian condition it would be impractical to attempt in­jection by gravity.

Buoyant Plume Models

Buoyant plume models have been developed in the study of ocean outfalls

for an open water environment (nonporous medium). Brooks (1973) summarizes

14

the results of a 5-yr laboratory study of the nature of buoyant plumes. Ex­

periments were conducted to evaluate the effects of a linear ambient density

stratification, as well as a constant ambient density, on a buoyant plume.

Similar studies were conducted by Anderson et al. (1973) in which an ambient

flow (cross flow) was added. Another study of open water buoyant plumes was

conducted by Waldrop and Farmer (1974). They developed a three-dimensional

flow field model of the interaction of a stream discharging into a much

larger body of water where the density differences are caused by both salin­

ity and temperature.

Because the three above-mentioned models are all designed for open

water, their results are strongly influenced by the effects of turbulence

and other consequences peculiar to the mechanics of open water fluid flow.

For these reasons, their results cannot be applied directly to the problem

of buoyant plume behavior in porous media. However, one method of reducing

turbulence in fluid flow is by using liquids of high viscosity, thus giving

relatively low Reynolds numbers. This is the type of approach used in

modeling salt domes, which are also a type of buoyant plume.

The most recent laboratory model of salt dome mechanics is the study by

Whitehead and Luther (1975) which investigates the dynamics of two immisci­

ble liquids of relatively high (but different) viscosities and densities.

The initial condition in this study is that the two liquids are horizontal

and layered, with the less dense layer beneath the denser layer. The study

then concentrates on the development of instabilities which lead to rising

buoyant plumes. Since this condition is quite dissimilar to the case of a

well acting as the source for one of the liquids, Whitehead and Luther's

study is not directly applicable to the present problem.

Entrainment of Salt Water

Brooks (1973) defines the entrainment relation for a round buoyant jet

plume as follows:

~~ = 27rabU (4)

where Q is the volume flux across the jet cross section, a is a coefficient

of entrainment for a round buoyant jet, b is a characteristic length defined

by a Gaussian (normal) velocity profile, s is the axis of the jet plume, and

U is the characteristic velocity along the s-axis. This can be interpreted

15

as meaning that the amount of entrainment is related linearly to the dis­

tance traveled by the plume and its velocity. The. coefficient of entrain­

ment is assumed to be a constant.

However, List and Imberger (1973) have shown theoretically that the

coefficient of entrainment, a, is a variable dependent upon the Froude num­

ber. The Froude number, F, is defined as:

F ="[CPo - P) Jt

P gD

(5)

where Va is the initial jet plume velocity, g is the acceleration of gravity,

Po is the ambient density, P is the plume density and D is the diameter of

the plume at the source.

These entrainment relationships were developed for cases where the

buoyant plume flow is fully turbulent, that is, Reynolds numbers greater

than about 2,000. Furthermore, experiments by Brooks (1973) and Anderson

et al. (1973) were carried out with Froude numbers that were at least on the

order of 10 to 100. For buoyant plumes in porous media, the Reynolds numbers

are always expected to be much less than one. Since liquids in porous media

do not acquire the characteristics of turbulent behavior until the Reynolds

numbers are greater than one, the relationships developed for these turbu­

lent buoyant plumes are not directly applicable to the porous medium case.

LABORATORY MODELING EXPERIMENTS

Selection of Model and Model Experiments

Ad described previously, one of the principal objectives of this inves­

tigation is the laboratory study of the mechanics of waste injection into a

density-stratified groundwater body by means of physical modeling techniques.

Specifically, the mechanics of buoyant plume movement and of salt water

entrainment are of critical importance in understanding the details of the

waste injection process under Hawaiian groundwater conditions. Several

basic questions need to be answered, for example, what is the vertical and

horizontal distribution of the buoyant plume at any time and how high will

it rise into the freshwater lens? How much entrainment of salt water occurs

within the plume during and after initial mixing, and will this entrainment

create an upper limit to the vertical rise of the plume? And finally, what

16

parameters have an important influence on the injection process and in what

way do they exert that influence with regard to flow mechanics?

In order to gain insight into these basic questions, a sand-packed hy­

draulic model was used to simulate injection into a homogeneous, isotrophic

aquifer saturated with density-stratified liquid. The study described in

this report was limited to consideration of injection into a system in which

the ambient groundwater body was "static" prior to the start of injection,

and in which the only movement was due to the injection process itself.

Additional experiments, the results of which will be described in a subse­

quent report, will be conducted under so-called "dynamic" conditions in which

the ambient freshwater lens is flowing. In addition to answering questions

about the mechanics of buoyant plume movement and salt water entrainment in

general, study of injection under so-called "static" conditions will be help­

ful in solving problems which relate to injection into Hawaiian leeward

coastal groundwater environments which have very small or negligible ground­

water gradients.

A study of waste injection through use of a sand-packed hydraulic model

can be conducted on two levels: (1) the effects of waste injection on water

quality, and (2) the fluid mechanics of liquid waste injection. Certain

parameters take on entirely different levels of importance depending upon

whether aspects of water quality or fluid mechanics are being studied. For

instance, in a study of water quality, the amount of salt water that is

entrained in a buoyant plume is important, no matter how small. Only a few

mg/~ of chloride entrained in a buoyant plume could significantly degrade an

overlying potable freshwater zone. However, in a study of the fluidmechan­

ics of buoyant plumes, one parameter of interest is the density difference

between ambient salt or brackish water and the injected effluent. A rising

buoyant plume could entrain up to 600 ppm of chloride before its density was

increased above 1.000 g/cm3 • Therefore, small amounts of salt water entrain­

ment, i.e., less than 600 ppm, are negligible in the study of the fluid

mechanics of porous media. The present study was conducted entirely from the

standpoint of fluid mechanics; chloride concentrations below 600 ppm were

considered as representing fresh water.

Description of Sand-Packed Hydraulic Model

A sand-packed hydraulic model is a reduced scale representation of

17

natural porous media and is a true model in the sense that both model and

prototype involve flow through porous media. The sand-packed hydraulic

model used in this study was originally constructed to serve as a hydraulic

scale model of the Kalauao Spring region above Pearl Harbor, Oahu (Lau 1962),

but has been modified extensively to fit present needs. Basically it con­

sists of a Plexiglas and plywood watertight box filled with sand and satu­

rated with water, a water supply system, an injection well assembly, and

measuring devices for head, discharge, and sample collection (Fig. 3).

During the original process of packing the model with sand, the sand was

saturated with fresh water. Later, a layer of salt water (dyed with green

flourescein dye for purposes of visual distinction) was emplaced beneath the

fresh water by means of the salt water entrance chambers (described in detail

later in this chapter) to create a salt water zone, a transition zone, and a

freshwater zone that simulates a static Ghyben-Herzberg lens system.

A model injection well consisting of small diameter perforated brass

tubing has been built into the sandbox next to the front Plexiglas face

which allows simulated effluent (tap water dyed with a blue tracer) to be

injected into the model at varying depth and injection rates. The brass

tubing also was designed to allow injection through varying lengths of the

well face, thus simulating both point and line recharge.

Several methods of measurement of hydraulic and chemical parameters

were employed. Manometers were used to measure head changes and to monitor

the position of the water table. Sample ports constructed in the front

Plexiglas face provided a means of collecting water samples from the model,

for analysis of chloride concentration and blue tracer dye concentration.

End chambers (on the right and left sides of the aquifer portion of the

model) fitted with funnels attached to point gages provided accurate control

of the water level in the model.

CONSTRUCTION DETAILS OF THE BASIC MODEL. The model has an overall

length of 1.83 m (6 ft), a width of 0.914 m (3 ft), and a height of 1.22 m

(4 ft). The two ends and the bottom of the sandbox are made of 3/4-in. ply­

wood, and the front and back faces are made of l/2-in. clear Plexiglas

plate. A l-cm2 grid pattern is etched on the Plexiglas plate to facilitate

data recordation. All of the sides and the bottom are bolted together with

3/4 x 3/4 x 1/8-in. brass angle screws and l~ x l~ in. brass machine screws.

The wood is sealed with fiberglass epoxy resin and all of the inside edges

. ',

(a) Model with Salt-Zone Plume

FIGURE 3. PHOTOGRAPHS OF SAND-PACKEDHYDRAUL IC MODEL

(b) Close-up of Salt-Zone Plume

(c) Close-up of Transition-Zone Plume

~;

.....00

19

and corners are sealed with Dow-Corning silicone rubber sealant No. 581.

To eliminate excessive stresses exerted by sand and water pressure on the

Plexiglas faces, 10 tie bars, constructed out of 1/4-in. diameter threaded

rod, are fastened to the outside of the front and back Plexiglas faces with

2-in. diameter fender washers and hex nuts. The threaded rods are coated

with varathane to retard rust, and the holes where they are fastened to the

Plexiglas plates are sealed with silicone rubber. Figure 4 shows front, top

and end views of the model.

END CHAMBERS AND WATER LEVEL REGULATION. Although the model is 1.83-m

(6-ft) long, only the central 1.52 m (5 ft) are filled with sand; the remain­

ing 15.24 cm (6 in.) on each side are used for the end chambers which serve

to regulate water levels in the model. The end chambers are separated from

the sand aquifer by a sheet of fiberglass cloth and monel window screen, both

of which are held together by a grid network of brass plates and angles

(Figs. 4 and 5). The water level, or head, in the end chambers was regulated

and maintained constant by means of a hook gage attached to a funnel to con­

trol overflow (Fig. 5).

DESIGN AND PLACEMENT OF SAMPLE PORTS AND MANOMETER TAPS. During the

initial phases of the study the sample ports consisted of the hypodermic

needles shown in Figure 6. However, the hypodermic needles proved unsatis­

factory because they tended to clog very quickly with sand. Consequently,

as they clogged, the hypodermic needles were replaced with ports similar to

those used for the manometer taps. The new sample ports were fitted with

removable plugs, as shown in Figure 6.

The manometer taps (the details of which are shown in Figure 6) were

placed in both end chambers, and at 10-cm intervals along a line across the

face of the model 70 cm above the bottom of the injection well. Thus, the

manometer taps could measure freshwater head without being affected by the

salt water, which was considerably below the line of manometer taps in the

sandbox.

Placement of the sample ports was changed several times during the

course of early experiments until a suitable arrangement was found. This

final array is shown in Figure 7. Sample measurements that were taken

before the final array of sample ports was installed have been relabelled to

conform with the labelling system of the final array. In photographs of the

sandbox, other sample ports may appear, however, these are sample ports used

TOP VIEWI/Z" LUC ITE PLATE N

o

3/4"--q"6" I 60" I 6"-j 1--3/4"1,; 131/2" 1

I IIIII

!.-'TIE lARS ........ IIIII

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WEll IMOUNTINC IPLATFORM I

.-J II II m II II : i Ii

END VIEW38 3 4"

\l:~W'HOOW scun ANO .L

"FIBERelASS cion IIp

1/2" ANCLE FRAMEWORK W'1H 6", 6"IIII

C~IOS SEE END CUMm DETAIL !!

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LlL II- IIk'tV -1r

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7'==- •I" 8

I •II,' •III aIii' !!I:: "" 9 3/4"" ""

·nII 8

" II

3i4" 3/4"

T6"

a

INJECTIONWEll CASINe

a

\4" TIE UIS1

3/4" PLYWOOD FASTENED103/4"' PL'WODD USE

3/4" PlYWODO

a

a

FRONT VIEW INJECTION1"r-WEll ASSEMIlY

3/4", 3/4 ", I/S" IRASS ANCm FASTENEO TOLaCITE PLATE BY 114" ,1"114" MACH'NESCREWS AT 6" CUTER

a

SEAWATER ENTRANCECUMBERS -. 3~ DIAMETER

II

I

IIIIII

a I a

1/2" ANCLE FUMEWORKWITH 6",6"ClIDS

3/4" PL 'WOOO

IIAIOMETERPLATForM

SOURCE:

FIGURE 4. FRONT, TOP, AND END VIEWS OF THE MODEL

\1/4" MACHINE SCREWS6" APAIT

'"

14" PLYWOOD

3/4" PLYWOODI. 1'·0" .I'3/4"

liZ" LUCIlE PUTE1111 II I • I "\.

2"13" WOODBRACING

III" LUCIlE PUTE

~48"I

2"16" WOODBRACING

'~IIII II II r~3/4 "16"16"PLYWOOD BLOCKSATTACHED TOBRASSFRAMEWORK

III" 1 3/4' 1 3/4"BRASS ANGLE

HOOK GAGE ATTACHED TOFUNNEL TO CONTROLOVERFLOW ....

SOURCE: After Lau

FIGURE 5. DRAWING OF THE END CHAMBERS N.....

"""'"',-~~~'lih~~m:~M"_~m~a;-a~!;:-;l== ...I!::..=-------

plexiglas face of model

SAMPLE PORT; FIRST TYPE

(used to withdraw samples)

hypodermic needle

--------...-~~ ~Syringe

plastic stopper

22

plexiglas tubing

Tygon tubing

lass rod stopper

SAMPLE PORT; SECOND TYPE

plexiglas tubing

Tygon tubing (leads to manometer)

MANm.1ETER TAPSSCALE: I in. = I in.

FIGURE 6. DRAWING OF SAMPLE PORTS AND MANOMETER TAPS

-

> • • • • • • •

> • • • • • • • • • • • • •-•••••

-- • • • • • • • • • • • • • • •- 0 c E .::£ :..c 4- Q) .c~....., .- en "'C u rc

- • • • • • • •-

- • • • • • • .. • • • •r f\ f "\"-ll \.. J

VII­a:o0-

UJ....J0­~<t:VI

I.L.oI­zUJ~UJu<t:....J0-

23

'.

24

only during previous experiments conducted with this model by Lau (1962) and

are not presently in use.

The manometers were made of 1 em 00 glass tubing inclined on a 1 to

9.95 slope. Because of the inclination, a I-unit head change in the model

produced a 9.95-unit response in the manometers. A group of 10 manometers

was mounted on a stand and placed at one end of the model. Unfortunately,

the manometers proved to be of minimal use, as explained later in this report.

SALT WATER ENTRANCE CHAMBERS. A system of salt water entrance chambers

was used to emplace a layer of salt water below the fresh water without

causing extensive mixing. This assembly consists of two 3-in. diameter

Plexiglas tubes which have been perforated with 1/8-in. holes and then

covered with fiberglass cloth in order to keep sand grains out of the inner

portions of the salt water entrance chambers. Figure 4 shows the placement

of the salt water entrance chambers in the model, and Figure 8 shows the

construction details of the chambers. Entry and egress of salt water to and

from the chambers are provided by 1/4-in. holes drilled through the rear

Plexiglas face of the model. Each hole was placed so that it coincided with

the center of each horizontal well tub~, and 1/4-in. 00, 4-in. long Plexiglas

tubes were glued into the holes (Fig. 8). During the running of experiments

these 1/4-in. tubes were normally clamped shut, but were also used to pump

salt water into or out of the model between experiments. These procedures

are described in detail in a later section of this chapter.

INJECTION WELL ASSEMBLY. There were several criteria involved in de­

signing the injection well; most important of these were:

1. Well diameter. Even though there are no characteristic ratios of model

to prototype length (for explanation see "Model Scale Ratios," Appendix

B, a rough estimate of these length ratios shows that the model well

diameter should be on the order of a small hypodermic needle. For exam­

ple, if the prototype-model length ratio was 300:1 (a reasonable esti­

mate), then a .16 cm (1/16-in.) diameter well in the model would corres­

pond to a 48 em (18.75-in.) diameter well in the prototype. Therefore,

it is clear that for scaling considerations the model well should be

kept as small as possible.

2. Variabil ity of length of discharging section. A point source and a line

source were to be used as injection sources in the various experiments;

therefore, it was necessary to construct a well hich could perform both

RONT PLEXIGLASFACE

REAR PLEXIGLAS FACELEFT END CHAMBER

BACK VIEW)

SALT WATER'l"fl . II. ENTRANCE

CHAMBERS

angle and windowscreen framework

sa 1t waterinlet tubes(1/4 11 00 X 411

)

chamber supports

SECTION A-A REAR PLEXIGLAS(from Fig. 4) FACE

l/~' holes on l/~'centers (typical)

salt water entrancechambers(1/411 wall ><- 311 diameter)

----------_ ...... -_ ..... -----~!:!!~~~~~2~~~!~i!:!!~~--------_ ......... -- ---------

FIGURE 8. DETAILS OF THE SALT WATER ENTRANCE CHAMBERSN(J'I

26

functions, or to build two separate wells: one, a point source well,

and the other, a line source well.

3. Variability of injection depth. One of the major parameters of varia­

tion in the experiments was to be depth of injection. The ideal design

was a well that could inject over a wide and continuously variable range

of depths.

4. Shape of the well. The sandbox model is designed to exploit the plane

of symmetry which cuts through the center of the injection well. There­

fore, the injection well should be only a half-circle, or half-well,

attached directly to the inner face of the Plexiglas front wall.

Clearly, the difficulty of adhering strictly to all of the above design

considerations is nearly insurmountable and therefore, some compromise proved

desirable. After much study, it was found that points (1) through (3) above

could be included fairly easily by sacrificing the half-well symmetry in the

well design. Therefore, rather than using a half-well cemented to the inside

Plexiglas face, a fully round well was constructed and placed as close as

possible 0.32 em (1/8 in.) to the inside Plexiglas face. In this way, the

plane in which the experiments were viewed was a total of 0.48 em (3/16 in.)

in front of the true plane of symmetry. As long as measurements were taken

more than I or 2 em away from the well, it was assumed that the error that

this design caused was no more than the accuracy of the measurements that

were taken.

The injection well assembly consists of 5 parts: a constant head

source, a Gilmont No. 12 flow meter, Nupro series "M" precision brass needle

valve, perforated well casing, and an injection well. The use of a constant

head source attached to a Gilmont flow meter, and regulated by a precision

needle valve, allowed for consistently accurate and reproducible flow rates

through the injection well assembly.

The perforated well casing consisted of three 30.48-cm (12-in.) lengths

of 0.497-cm (S/32-in.) OD brass tubing. These 3 lengths were coupled to­

gether with two 7.62-cm (3-in.) lengths of 0.48-cm (3/l6-in.) brass tubing

which were slipped over the ends like connecting sleeves and soldered into

place. The entire 0.9l-m (3-ft) section was then perforated with O.lO-cm

(0.04-in.) holes (No. 60 drill bit size). After the perforations were com­

pleted, the inside of the well casing was reamed out to eliminate metal

burrs and to insure that there would be a smooth inner surface into which

the injection well could slide. Figure 9 shows the placement of the con-

27

TO NEEDLE VALVE

t3/16" BRASS TUBING

(NONPERFORATED)

.--, ------r--, ,, ,.O~I HOLES ON 1/~'~-

CENTERS (TYPICAL) ooooo

o

•oo

•

12"

12"

oo

3/16" 00 X 3" LONGBRASS SLEEVING

(TYPICAL)

5/3211 00 BRASS TUB ING(PERFORATED)

FIGURE 9. DRAWING OF THE PERFORATED WELL CASING

28

necting sleeves and the spacing of the perforations.

The construction details and dimensions of the injection wells are

shown in Figure 10. Both injection wells were constructed with 0.32-cm

(1/8-in.) 00 brass tubing designed to slide with a snug fit into the well

casing. The discharging sections of the point source well and the line

source well were 0.79 em (1/32 in.) smaller in diameter than the rest of the

well (Fig. 10), allowing the effluent to flow out of the perforations of the

injection well and into the space between the injection well and the well

casing. The tight fit of the injection well insured that the effluent flowed

directly out of the well casing and did not leak up or down the well casing.

Figure 11 shows how the well casing is mounted to the front Plexiglas face of

the model.

By nature of construction, the point source well was actually an extreme­

ly short line source. The difference between this short line source and a

true point source was considered minimal and, in any case, the short line

source is closer to simulated field conditions than a true point source. The

short line source will be referred to as a point source for the sake of sim­

plicity.

Model Calibration and Experimental Methods

PREPARATION OF SAND. The sand used in the model was "sand blast beach

sand," a variety of pre-sieved Molokai beach sand purchased from Hawaiian

Construction and Dredging Company. A sieve size analysis was performed and

the coefficient of uniformity was determined to be 1.2, a value which indi­

cated that the sand was fairly uniform in size and did not need further

sieving. To remove fines and any salinity that might have adhered to the

sand, it was washed thoroughly in a cement mixer and then placed in the model.

Packing the sand under a layer of water assured minimum air entrapment, and

constant agitation during the packing process minimized the development of

stratification.

POROSITY DETERMINATION. The porosity of the sand in the model was deter­

mined by two different methods. In the first method, a small representative

sample of sand with a known volume was weighed while saturated with water,

and then placed in an oven and dried. After drying, the sample of sand was

weighed again. From the difference in weight after drying, the volume of

water that was in the void spaces of the saturated sand could be calculated.

29

TO NEEDLEVALVE

10 3/411

12'1

,--II I

3/3211 00 brasstubing

typical coupling211 long

TO NEEDLEVALVE

t

oI 1

LJ

1211

1211

r-'I I --------1...­I I'-I

.0411 00 hal eson 1/811 centers

(typical)

3 7/811 5 7/8"0

L0

01/8" 00 brass0

0 tubing 1/4"I f1

III 1"1" III.,I

LINE SOURCE POINT SOURCE

FI GURE 10. DRAWING OF THE INJECTION WELLS

30

o

";

SIDE VIEW

PLEXIGLAS FACEOF MODEL

WELL MOUNTI NG

TO NEEDLE VALVE

WOODENPLATFORM

1/8" SPACER(TYGON TUB ING)

INJECTION WELL

INJECTION WELL------~

1/8" SPACER(TYGON TUBING)

SCALE: I" = 1/2"

PLEXIGLAS FACEOF MODEL

TOP VIEW

WELL MOUNTING

FIGURE 11. DRAWING OF THE INJECTION WELL MOUNTING

31

The volume of water occupying the void spaces of the sand divided by the

total volume of the original saturated sample gave the porosity, which was

calculated to be 35%.

A second method used to determine porosity employed the relationship

between specific discharge, average pore velocity, and porosity. This rela­

ship is given as

n = q/V = Q/AV (6)

where n is the porosity, q is specific discharge (flow rate per unit area),

Q is the flow rate of aquifer fluid, A is the cross-sectional area of the

sandbox model aquifer in a plane normal to the direction of flow, and V is

the average pore velocity. By injecting a slug of dye into the model and

recording its displacement with respect to time, the average pore velocity

could be measured. By using this method several times, an average of 39%

was calculated for the porosity. This value was used in all calculations

involving porosity.

HYDRAULIC CONDUCTIVITY. The model aquifer's hydraulic conductivity was

determined by use of the Dupuit equation (Todd 1959, p. 80), in which the

hydraulic conductivity, K is given as

(7)2LQK =

(h I2 - h2

2 )W

where L is the length of the aquifer (in the direction of flow), Q is the

discharge rate, hi is the height of the water table in the entry end chamber,

h2 is the height of water in the exit end chamber, and W is the width of the

model aquifer. Both hi and h2 are measured from the bottom of the model

aquifer to the free surface. Using this equation, K was determined for

several different gradients, and was calculated to be 5.1 ±0.08 cm/min or,

in Meinzer units, 1800 ±28 gpd/ft 2 .

EQUIPMENT CALIBRATION. Prior to running the actual experiments, it was

necessary to calibrate several parts of the model. Before the sand was em­

placed in the model, the entire box was placed on concrete blocks and preci­

sion leveled from right to left, in the direction of flow. There was no need

to precision level the model from front to back because no measurements were

taken from the back face; however, the model was rough-leveled anyway from

front to back.

The Gilmont flow meter was checked for accuracy and found to give

readings accurate to ±0.05-m2/min for a flow-rate range from 0.5 m~/min up

32

to at least 30 mi/min. as long as the temperature of the water flowing

through the meter remained constant at 22°C (72°F). A thermograph was placed

in the laboratory near the sandbox and the temperature was found nearly

always to remain constant to within -17°C (±2°F). This temperature variation

was small enough so that no measureable difference in flow rates was found.

Each manometer tube was individually calibrated with its own scale be­

cause of slight variations in individual tube diameters. However. the mano­

meters proved to be of minimal value for several reasons. Capillary rise in

the sand introduced a large amount of "noise" in the manometer tubes. This

was compounded by the fact that the model was unconfined and. initially.

there was a significant amount of evaporation taking place within the model.

The evaporation problem was reduced by covering the top of the sand with

several layers of flexible plastic sheets. However. even with this modifica­

tion. the buildup of head in the vicinity of the injection well was so small

as to be immeasurable with these manometers. This was a significant and

desirable effect. however. as most natural Hawaiian aquifers experience very

small head buildup during injection. If the measurement of injection head

buildup is desired. then it would be necessary to use a confined aquifer

model and. preferably. a sand with a relatively low permeability. in order

to exaggerate the head buildup.

Point gages equipped with funnels to draw off excess water were attached

as shown in Figures 4 and 5 and were calibrated so that their readings cor­

responded with each other. In this way. the water levels in both end cham­

bers could be kept constant with respect to each other and with respect to

time.

EMPLACEMENT OF SALT WATER LAYER. About 320 R, of salt water were needed

to create the basal salt water and transition zone layers.· The salt water

was prepared a day or two before it was empiaced in the model by mixing tap

water with a saturated solution of sodium chloride (NaCl) rock salt until

the desired density was achieved. Normally. a density of 1.036 g/cm3 (0.04

lb/in. 3) was used. although a density of 1.025 was used also during one ex­

periment. Densities of the salt solutions were measured with a precision

hydrometer which was accurate to ±O.OOOS. Several methods of pumping the

salt water into the horizontal well tubes were tried until a procedure was

found that worked most conveniently and also prevented the intruding salt

water from mixing too much with the fresh water. The salt water was pumped

33

from a battery of four 80-t plastic barrels with a peristaltic tubing pump

equipped with a variable speed motor. The pump was normally set to pump

about 7.6 t/hr (2 gph). After the salt water passed through the pump, it

moved into a pressurized carboy. The carboy was connected to the two salt

water entrance chambers with Tygon tubing. When the pressure built up suffi­

ciently inside the carboy, the salt water flowed into the salt water entrance

chambers and through the model. The carboy had the effect of damping the

rough, peristaltic motions of the pump so that salt water flowed smoothly and

continuously into the model. As the salt water moved into the model, it dis­

placed the fresh water to the right and upward. The funnel in the right end

chamber was set to take the overflow of fresh water, and the funnel on the

left end chamber was clamped shut, thus allowing a natural head buildup to

take place so that the salt water could move towards the right side of the

model. Figure 12 is a diagram of the salt water emplacement configuration.

Normally, it took l~ to 2 days for complete salt water emplacement and,

occasionally, emplacement took considerably longer, particularly when salt

water with a lower density (1.025 instead of 1.035) was used.

REMOVAL OF DYED FRESH WATER. At the conclusion of each experiment,

there was a significant amount of dyed water, or simulated effluent, in the

model which had to be removed prior to the start of a new experiment. By

using the injection well as a pumping well, virtually all of the dyed water

could be removed. Since density stratification of the ambient fluids was

present, pumping liquid out of the well withdrew only water at the same level

from which the well was pumping. In this way, the transition zone was not

disturbed significantly.

MODEL FLUSHING AND EMPLACEMENT OF FRESH WATER. Although pumping the

dyed fresh water out through the injection well worked satisfactorily, after

about three experiments, the transition zone was dispersed unevenly to the

extent that the model needed to be flushed completely. Flushing the model

and emplacing new salt water assured greater consistency of experimental

results. To flush the model, the salt water entrance chamber at the left

side of the model was allowed to drain freely while an equivalent amount of

fresh tap water was introduced into the right end chamber. This flow was

maintained until the model was free of residual salinity (below 100 ppm).

CHLORIDE DETERMINATIONS. Several problems were encountered with the

COLLECTING FUNNEL(for displaced fresh water)

(,.l~

n

/"-

~ONNECTING TUBING

, -0- '-,\0/cI ,

SALT WATER

FRESH WATER

.....:::,::..~' ,...: .

.:: . ....

~

SALT WATERRESERVOIR

PERISTALTICPUMP

PRESSURI ZEDCARBOY

(flow integrator)

SAND BOX MODEL

FIGURE 12. DIAGRAM OF THE SALT WATER EMPLACEMENT APPARATUS

35

analysis of chloride distribution and content in the model aquifer. Ini­

tially, the mercuric nitrate method, as outlined in Standard Methods (APHA,

AWWA, and WPCF 1971), was used for chloride determination. This method had

three drawbacks. First, it is a colorimetric titration and, therefore, dyed

samples often obscured the end point. Secondly, this method is not designed

to accurately measure chloride concentrations over the wide range that was

present in the model. The chloride concentrations ranged from under 100 ppm

to well over 25,000 ppm. Lastly, tremendous dilutions were necessary because

only small samples could be pulled out of the model without disturbing the

experiment. The greatest amount of aquifer water that could be pulled out

was about 6 m~, and the mercuric nitrate chloride determination required a

minimum of 50 m~.

Because of these drawbacks, the mercuric nitrate method was abandoned

and it was decided to try electrical conductivity as a means of measuring

chloride concentrations. Standard solutions of NaCl were prepared and a

calibration curve of conductivity vs. concentration of NaCl was constructed

using an Industrial Instruments model RC-16b2 conductivity bridge. However,

the conductivity method seemed to give anomolously high readings of NaCl con­

centration. It was felt that the presence of the flourescein in the salt

water was probably the cause of these high readings, therefore, new standard

solutions of NaCl were prepared with the proper percentage of flourescein

added to each one. A calibration curve with the flourescein-corrected stand­

ard solutions proved to give better results. This calibration curve is shown

as Figure 13.

DISPERSION MEASUREMENTS AND BLUE TRACER DYE CONCENTRATION. One of the

objectives of this study was to measure the dispersion and dilution of the

simulated effluent. A blue tracer dye ("Pylam Brilliant Blue," from Pylam

Products Co., Inc., Queens Village, New York) was added to the effluent

before injection (at a concentration of 200 ppm) both for photographic pur­

poses and to enable colorimetric determination of blue tracer dye concentra­

tions. By preparing a series of known standard solutions of blue dye, a

spectrophotometer could be used to construct a calibration curve of blue dye

concentrations vs. percent absorbance of a given wavelength of light. Using

a Bausch and Lomb Spectronic 20 spectrophotometer, a calibration curve was

constructed for a wavelength of 760 nm. This wavelength was chosen because

it afforded the widest needle deflection on the instrument scale for the

111

10 5 ,- ---------- ---> •

(/l

o 104..c:~

........:>:::

>­~

:::>

~u::lClZ 10 3ou

1021 I I I LI I I I I I I I I I I I I I I I I I I I I I I I

10 2 3 456 810 2 2 3 4 56 810 3 2 3 456 810 4 2 3 4 5 6 810 5

CONCENTRATION (NaCl), mg/~

FIGURE 13. FLUORESCEIN-CORRECTED CALIBRATION CURVE OF ELECTRICALCONDUCTIVITY V5. NaCl

Vl0'

37

range of blue dye conoentrations that were encountered (0 to 200 ppm) without

the needle going off the scale.

However, samples obtained from the model during the course of an expe­

ment contained small amounts of fluorescein, which interfered severely with

the calibration curve. The instrument was so sensitive to the presence of

fluorescein that as little as I ppm would yield significantly different

readings of percent absorbance. Because of this problem, no quantitative

measurements of dispersion were possible.

EXPERIMENTAL RESULTS

Summary of Experiments

A total of 14 experiments were performed in order to systematically vary

all of the parameters of interest. The experiments were numbered from Stat­

ics 1 to 14, in the order in which they were performed. Each experiment was

also labeled "static" to facilitate discussion and to distinguish the present

set of experiments from future "dynamic" experiments. The data from Statics

1 and 2 were discarded because of a leak in the injection well. This leak

was repaired satisfactorily and no further leakage problems were encountered.

Each experiment required a considerable amount of time to perform (3 ex­

periments lasted over 190 hr), and as explained previously, the turnaround

time between experiments was often as long as one week. Thus, the experi­

ments performed were limited to a relatively small number. In this way, the

effects of varying several different parameters were studied. This method

was considered more desirable than extensively studying the effects of

varying a single parameter, such as injection rate.

The parameters selected for variation and study included: length and

depth of the discharging section of the injection well, injection rate, and

density of the salt water layer. As described earlier, different lengths of

the injection well discharge section were used, one to represent a point

source, and the other a line source. Two different injection rates also were

used: 5 milmin and 20 mi/min. The choice of these two injection is dis­

cussed later in the Appendix B section on "Model Scale Ratios." Two differ­

ent depths of injection were chosen: one in the salt water zone at the 100%

isochlor, and the other in the center (50% isochlor) of the transition zone.

In addition, one experiment was carried out with injection taking place at "~!I

38

the 75% isochlor level. Table I gives a summary of all the experiments and

parameter variations.

TABLE 1. SUMMARY OF EXPERIMENTS AND PARAMETER VARIATIONSTYPE OF INJECTION INJECTION

EXPERIMENT DISCHARGE SECTION RATE DEPTH(Static) (Source) (mR./rnin) (Zone)

3 Line 20 Salt

4 Point 5 Salt

5 Point 20 Transition(75% i so-chlor)

6 Line 20 Transition(50% iso-chlor)

7 Line 5 Transition(50% iso-ch 1or)

8 Point 5 Transition(50% i so-chlor)

9 Point 20 Transition(50% iso-ch 1or)

10 Point 20 Salt

11 Line 5 Salt

12 Line 5 Salt (lowdensity)

13 Point 5 Salt (lowdensity)

14 Point 5 Transition(SO% i 50-

chlor)

The experimental results are reported in several ways. Appendix A,

which consists of two-dimensional graphs of the visual front of the injected

effluent plumes at various times throughout the course of the experiments,

provides an accurate and complete record of each experiment. In addition, a

graph of chloride concentration vs. depth as measured prior to each experi­

ment is provided adjacent to the graph ·of the plume, and on the same vertical

scale, so that direct comparison of chloride concentration vs. outward expan-

39

sion of the plume is possible. For transition zone experiments, the dis­

charging section was positioned so that its center coincided with the center

of the transiticm zone. For salt zone' experiments ,the: lower end of the dis­

charging section coincides with the origin of axes in the Appendix A figures.

The samples were taken mainly in sample row III (Fig. 7). During some of the

later experiments chloride samples were taken from the interior of the efflu­

ent plume, and these data are discussed in the later section on salt water

entrainment.

In discussing and comparing the variation of injection parameters, many

cumbersome terms and phrases must be used repeatedly; therefore, several

shortened terms are defined. Salt-zone experiment and salt-zone plume refer

to experiments and developing plumes in which injection took place in the

salt water zone (Statics 3, 4, 10, 11, 12, and 13). Similarly, the terms

transition-zone experiment and transition-zone plume refer to experiments and

developing plumes where injection took place in the transition zone (Statics

5, 6, 7, 8, 9, and 14). The term effluent is used to indicate the simulated

effluent consisting of blue-dyed tap water that serves as the injected liquid.

The word plume refers to the entire body of injected effluent whereas column

refers only to that portion of the plume which resides in the salt water

zone. The term interface angle refers to the angle defined by the interface

between the outer margin of the column (in salt zone plumes) or plume base

(in transition zone plumes) and the ambient salt or brackish water. Figure

14 illustrates the concept of interface angle.y-axis y-axis

"..'~f-- -""" x-ax i s

Interface angle forsalt zone plumes

Interface angle fortransition zone plumes

x-axis

v,

FIGURE 14. DEFINING SKETCHES 'FOR THE INTERFACE ANGLE

40

Effects of Injection Parameter Variation

VARIATION OF INJECTION DEPTH. The first parameter investigated for its

effect on the shape of the injection plume was the depth of injection in re­

lation to the position of the transition zone. In a typical salt ,zone expe­

riment, the effluent initially took the shape of a rising, roughly hemicylin­

drical column, the dialneter of which was dependent upon the injection rate

and density difference between the ambient salt water and the injected liquid.

The column continued to rise until it reached the transition zone, where the

rapidly decreasing buoyant force caused a correspondingly rapid decrease in

upward velocity. In order for the plume to maintain continuity (law of mass

conservation) the decrease in upward velocity caused a corresponding increase

in the longitudinal cross-sectional area of the plume. Statics 3, 4, 10, 11,

12, and 13 are characteristic of the above (App. A). As the plume estab­

lished itself in the freshwater zone, it began to expand outward and upward

in a hemispherical fashion with a center of curvature at approximately the

level of the 50% isochlor. This spherical expansion of the plume was carried

to an extreme in Statics 12, 13, and 14 where after 200 hr 9£ continuous

injection, the plumes had developed vertically through approximately 80% of

the freshwater layer, and were still moving upward, but at a decreasing rate

(Fig. 15). Additional discussion is present in later sections on both the

topics of the upper limit of plume rise, and on the spherical expansion of a

plume in the fresh water.

In contrast to salt zone plumes, transition zone plumes developed in a

markedly different fashion, and are characterized by the experiments in

Statics 5, 6, 7, 8, 9, and 14 (App. A). The typical transition zone plume,

unlike salt zone plumes, developed no vertically rising column, but rather

the effluent immediately began to move outward, as well as upward, from the

point of injection. This was expected, because as the effluent moved upward,

it was subjected to a continuously decreasing buoyant force from the time

that the injection began. In comparison, it was necessary for the effluent

of a salt zone plume to move upward through the salt water zone before expe­

riencing any significant change in buoyant force caused by the transition

zone.

Because of the vertical feeder columns associated with salt zone plumes

(which are not developed by transition zone plumes), the configuration of

the salt and transition zone plumes vary significantly from each other if

41

the entire plumes are considered. However, if the salt zone feeder columns

are ignored, the remaining umbrella-shaped portion of both the salt and

transition zone plumes are quite similar in appearance and movement. To

illustrate this, Figures 16 and 17 are graphs of plume heights as a function

of time for both salt and transition zone plumes. Figure 16 shows plots for

salt zone injection (Static 4) and transition zone injection (Static 8), at

an injection rate of 5 mtjminusing a point source. Figure 17 shows similar

plots of salt zone injection (Static 10), injection at the 75% salt isochlor

(Static 5) and injection at the 50% salt isochlor (Static 9), also using a

point source, but at a higher injection rate of 20 mt/min. In both Figures

16 and 17, the height is measured from the zero datum on the model (see

drawings in App. A) so the salt zone injection always starts at zero height,

and the transition zone injection starts at the height of the appropriate

isochlor, usually between +25 and +35 cm.

The significant aspect of the plots in Figures 16 and 17 is that, first,

the overall shapes of all the curves are quite similar to each other, indi­

cating that the plumes, regardless of whether they initiate in the salt zone or

somewhere in the transition zone, all develop in a similar fashion at roughly

similar rates. Of even greater significance is the fact that although ini­

tially the heights of the salt zone plumes begin well below those of the

transition zone plumes (because of the different injection points), as the

experiments progress, the heights of the salt zone plumes begin to catch up

with and approach those of the transition zone plumes. This is especially

evident in Figure 18, which is a plot of plume height as a function of time

for Statics 13 and 14, both of which ran for approximately 200 hr.

Plots of plume width vs. time for salt and transition zone experiments

also show a similar correspondence. Figures 19 and 20 show plots of plume

width vs. time for salt and transition zone injection from point sources at

injection rates of 5 and 20 mt/min, respectively. The curves in both of

these figures show roughly similar rates of plume width development for salt

and transition zone injection.

VARIATION OF INJECTION RATE. The second parameter investigated was the

variation of injection rate. In salt-zone plumes, the interface angle of

the rising column of injected effluent was greatly affected by the injection

rate. For low injection rates, the interface angle was very nearly 90°,

resulting in a small-diameter column with a very nearly vertical interface

w::> 'lH~13H 3Wnld

42

oLI'\

o~

oM

oN

o

00N

)~.

;~

000

.~

'ii

0 r..0

N

U

0 I-~ c::(

I-l/l

ec.0l.L.

0 WN l.. ~

- .c -I-

w~ lfl- >I-

0 0w~Ow ::>

-l/l ~

Cl.. Cl..c::(~ l.L.W 0

I-0 :I:00 t.:l

w:I:

LI'\

0..0 w

ec.::>t.:l

l.L.

0~

oN

o

60

4-I::U00·-.- ............... ttI1::.- ~~l/lV'l

~I::X C'll ~Wl..Cj~ I::

oN

10

I::o~-::l"

l/l U1::.-ttl .....l.. ttl..........

V'l\I-o ~,

~~ I::I:: 0~ N~

XLIJ

9875 6

ELAPSED TI ME, hr

43

5 mt/min, point source, transition zoneinjection (50% salt isochlor)

5 mt/min, point source, salt zone injection

2

<:>--0 STATIC 4:

~--8. STAT IC 8:

~ -A--- "--..-"-- ----~-----------_...-..­

/~,t;1/

jf//

o

50

EU

~

~0

::: 400II)

...J

...JLIJ:3

~ 300II)

«I-:x::l!l

~ 20:x::LIJ~::>...JQ..

10

FIGURE 16. COMPARISON OF INJECTION DEPTHS: HEIGHT vs. TIME FOR STATIC 4 AND 8

+:­V'l

<';:;{t~;~ :C2c,*,i:S;; ",' T,,'"'C' ~.' ,~.~------

70~

~

• • STATIC 10: 20 mQ,/min, point source, salt zone injection

&----& STATIC 5: 20 mQ,/min, point source, 75% salt isochlor injection

Eu • • STATIC 9: 20 mQ,/min, point source, 50% salt isochlor injection __ -.--- -- -___ .. -- -- ..a.. ----- . -----.-------------------- - & -------------------.-- -- - - ----

~.-- ---------~ ~ /' ... --------. .o r _-- -I- 40 .' _ ---I- r ... -- •o __

cc "-~ .. ~/ ...oa:I.L.

I­~Cl

UJ~

UJ 20~:::>....Ja...

I.L.o

....J

....JUJ:3

I I I I , I I

o . 2 3 4 5 6

ELAPSED TIME, hr

FIGURE 17. COMPARISON OF INJECTION DEPTHS: HEIGHT vs. TIME FOR STATIC 5, 9 AND 10

75

70

65

60Eu

~55o........g 50

UJ>g 40«....~ 35UJ~

~ 30::>...J0...

25

20

15

......

_-----------A. -----------~

.-------------------- -_-a

• • STATIC 13: 5 m£/min, point source, salt zone injection

A----A STATIC 14: 5 m Imin, point source, transition zoneinjection (50% salt isoch1or)

:_~, .

I I I I I I I' I I I I

o 25 50 75 100 125 150 175 200 225 250ELAPSED TI ME, hI'

FIGURE 18. COMPARISON OF INJECTION DEPTHS: HEIGHT vs. TIME FOR STATICS 13 AND 14

~~T~'~~.tlo~*

.j:>.U1

70

60

50

• • STATIC 4: 5 m Imin, point source, salt zone injection

A----A STATIC 8: 5 m Imin, point source, transition zone injection(50% salt isochlor)

.j::.(J\

Eu

4~ 0:::J:I­o3

~ 30::>-ICL.

20

10

,_A---

-- -- - _... - - - - - - - ----- - -... - -- - ----

.. I , I I I

o 2 3 4 5ELAPSED TIME, hr

FIGURE 19. COMPARISON OF INJECTION DEPTHS: WIDTH vs. TIME FOR STATICS 4 AND 8

_____A

-- -A_---------------A-------------- .__.-._---.-----_.­_....-

70I • • STATIC 10: 20 ml/min, point source, salt zone injection

60~ A----A STATI C 5: 20 m£/min, point source, 75% salt isochlor injection

.---11 STATIC 9: 20 m£/min, point source, 50% salt isochlor injection

I50

s::U

3

~ 40l­e

LLI

5 30...J~

oI I I r . I I I

2 3 4 5 6

ELAPSED TIME, hr

FIGURE 20. COMPARISON OF INJECTION DEPTHS: WIDTH vs. TIME FOR STATICS 5, 9 AND 10

+:­'-l

~.mtliih¥{\.~ ~.rt.'Iz"Z';;"",.

48

u~ to the level of the bottom of the transition zone (Statics 4, 11, and 12,

App. A). However, for high injection rates, the interface angle wasconsid­

erably smaller (Statics 3 and 10, App. A), causing the column to be more

cone-like and of a much larger diameter than observed in columns of low in­

jection rates.

The effects of injection rate variation for transition-zone plumes were

similar to the effects on salt-zone plumes. A high injection rate produced

a low interface angle (Statics 5, 6, and 9, App. A), and low injection rate

resulted in a relatively high interface angle (Statics 7 and 8, App. A).:.,',

However, for transition-zone plumes, even a low injection rate did not pro-

duce a column, or a nearly vertical interface like those of the low injection

rate salt-zone plumes. The theoretical aspects of interface mechanics are

discussed in more detail in the "Theoretical Description of Plume Movement"

section of this report.

A second effect produced by the variation of injection rate is shown by

comparing the graphs of plume width (or height) ve~sus log time for various

experiments. Figure 21 is a graphical comparison of the graphs of a low in­

jection rate plume and a high injection plume for transition-zone experiments

in which all other parameters were equal; Figure 22 shows similar plots for

salt-zone experiments. In both cases, the effect of increasing the injection

rate is to shift the graphs of width vs. log time upward with very little

change in slope. In addition, the graph of plume height vs. log time (Fig.

23) is shifted upward with little change in slope in the same way as the

width vs. log time graphs. This trend generally holds true for other high­

low comparisons of injection rate. Consequently, it appears as though the

injection rate simply changes the relative size of the resulting injection

plume and does not greatly affect either the rate of movement of the plume

or the plume shape.

VARIATION OF LENGTH OF DISCHARGING SECTION. The parameter whi~h proved

to be of least importance in affecting the shape of the plumes was the length

of the discharging section. In many cases, it made little difference whether

the point source or the line source was used, all other parameters being

equal. In those experiments where differences were observed, the evidence

tended to be conflicting, inconclusive, or some other interpretation could be

given to the observations.

The single observation that proved to be consistent was that for the

low injection rate, little or no difference was observed in the graphs of

e----e STATIC 8: 5 m~/min, point source,transition zone injection

20 m~/min, point source,transition zone injection

STATIC 9:.. &

"It,,"

",'"",'"

,,'",,'"

",,",."",,"",,""

",,-4.........",,"......, .........

,,"" .......".........--_ .....",

--------------~--------------------~--------

so

40

Eu~

~ 30:;:)...JQ..

Ll-e::c~ 20:3...J«l-eI-

10

;01 .02 .03 .04 .06 .08 .10 .2 .3.4.5.6.8 1.0ELAPSED TIME, hr

2 3 4 5 6 8 10

FIGURE 21. COMPARISON OF INJECTION RATES: WIDTH V5. LOG TIMEFOR STATICS 8 AND 9

~I.Q

~:"........."~,-",~""

•

lJ1o

/,/'/'

,,'.,/',

."/"/,,,

",,,'"/'."j¥',"r.',,'

".-------_.'......-....----------------

20 m£/min, point source,injection in salt water zone

5 m£/min, point source,injection in salt water zone

- - STATIC 10:

• ---. STAT IC 4:

--- ....-------

50

10

eu

40

-I<I­oI-

~

LI.J~

:3 300......o::r:I­o3 20

'.01 .02 .03 .04 .06 .08 .10 .2 .3.4.5.6.8 1.0ELAPSED TIME, hr

FIGURE 22 .. COMPARISON OF INJECTION RATES: WIDTH vs. LOG TIMEFOR STATICS 4 AND 10

<,:';;.;r~,bi;~;f'.£~~~!l.~,:.:- ....,r

t::.---t::. STATIC 9: 20 m£/min, point source, transition zone injection

50

Eu 40~

-I-II.LI3:u.o

~ 30ol-I-oco~o0:::

U. 20I-:I:~

I.LI:I:

I.LI

5 10-Ia..

• • STATIC 3: 5 m1/min,point so~rce, transition zone injection

~--

oo

No.o

C"'\...:r Ln-.D coo 0 0 0 0. . .. . .o 0 0 0 0 0

N

oC"'\ ...:r·Ln-.D coo.o 0 0 0 0

oN

oC"'\

o 0'0 0,0. .. . ....:r L.f\ -.D co 0

ELAPSED TJt~E, hr

FIGURE 23. COMPARISON OF INJECTION RATES: HEIGHT vs.LOG TIME FOR STATICS 8 AND 9

~~·;;a;:t~~~~--·'''''"'''~

U1.....

52

~eight (or width) versus time between a point source experiment and a line

source experiment (all other parameters being equal). Figure 24 provides an

example of this trend.

For high injection rates, the evidence is conflicting. Comparison of

Statics 10 and 3 in Figure 25 tends to indicate that a point source (for a

high injection rate) causes a "depression" or "blip" (in Static 10) in the

rise of the plume just after the plume reaches the freshwater layer (at about

38 em, between 2 and 5 hr after the experiment began). However, the "blip"

should have caused a corresponding increase in the time rate of horizontal

expansion of the plume of Static 10 in order to accommodate the upwelling

mass of fluid. On the contrary, however, rather than an increase in horizon­

tal expansion at the same point in time, a decrease occurred that was quite

similar to the "blip" for Static 10 (Fig. 26). This decrease in both the

vertical and horizontal time-rate of expansion of Static 10 indicates that

the effect was most likely caused by some other factor, perhaps experimental

error as the "blips" were not observed in other experiments.

Salt Water Entrainment

As explained earlier in this report, the relative importance of salt

water entrainment is dependent upon whether water quality or fluid mechanics

is being studied. From the standpoint of fluid mechanics, only chloride con­

centrations in the plume above 600 ppm (0.60 g/t) are important, because

water contai~ing 600 ppm or less of chloride still has a density of 1.00

g/cm3 , the density of fresh water. The present study is being conducted from

the standpoint of fluid mechanics and therefore chloride concentrations below

600 ppm will be considered identical to fresh water.

No upper limit to the rise of the effluent plume was observed in any of

the 14 experiments, and in each experiment, the plume rose through the tran­

sition zone and into the freshwater layer.. These two facts suggest that

there was not enough salt water entrainment within the effluent plume to

establish an upper limit to the rise of the plume. This was further con­

firmed by chloride data taken from Statics 12, 13, and 14, all run for ap­

proximately 200 or more hr. Figures 27, 28, and 29 show chloride concentra­

tions taken from the plume interiors. All of the concentrations in the cen­

ter portion of the plume were well below the value of 600 ppm, indicating

that the effluent plume rises essentially intact through the salt-water zone.

8 10

•,,'"'"",6.

'"'";";!.

45632

,;/'

",'"

",'"",'"

".'"

'"",e'"e","''''.;/

".'/

".'"".'"",.

"."

",'"".

.2 ·3.4.5.6.8 1.0ELAPSED TIME, hr

Line source, 5 m~/min,

salt zone experiment

/"",'"

""",,,,,""i

--------'---

STATIC 11:

.06 .08 1.0

• ---. STATIC 4: Point source, 5 mUmin,

T~4- 1:.-o 0 ~

.- co~ ~ ~

I: .- VlaJ l/1~ I:X ttl ..

LJJ L. aJ~ I:

-lr8

.03 .04.02

~4- 0ON-::r

~ I: UI: 0·­aJ .- ~

~ ~ ttlX .- ~

LJJ l/1 VlI:r

-----------------.01

50

40

Eu.LJJ~

:3 30c..

u..0

~:J:c..:l-~ 20...Jc::r::~0~

10

FIGURE 24. COMPARISON OF LENGTHS OF DISCHARGING SECTION: HEIGHT vs.LOG TIME FOR STATICS 4 AND 11

U1V-l

..~~~~~4,.~~~~~~.iY~~~i.\iirl-ri~X

(,n~

8 104 5 632.81. 0.2 .3.4 .6ELAPSED TIME, hr

Point source, 20 m~/min,

salt water zone injection

Line source, 20 m~/min,

salt water zone injection

STATIC 10:------

.06 .08. 10

.---. STATIC 3:

..<I)c:

~ooON~

... c: uc: 0 ._<I)'; ~~._ ttlX Vl ...wc:V'

ttlI.......

.03 .04.02

Tc:o.- C""\....- uVl'-c: ...ttl ttlI.. ...

..... V'

~o ..<I)

... c:c: 0<l)N~

X

~

/'~/

,,'"","

,,'".",,'",,",," A.-- .. -

" ....."

,,",,",,'"."/'

,/,/'.'///

,/

"""".",.",,"

.,..,.,,. ........._...------_..---

------------_-e-----

.01

40

:=U

10

50

;.....

~ 20..J~.....o.....

UJ:::c:3 300-

1.1...o.....:I:CJ

FIGURE 25. COMPARISON OF LENGTHS OF DISCHARGING SECTION:HEIGHT vs. LOG TIME FOR STATICS 3 AND 10

50

40 STATIC 10: Point source, 20 m£/min, salt water zone injection

•/

//,

......"Eu

UJ~

:: 30ll..

.....o:J:I­oi 20..Jc:x:I­oI-

10......

----_.",_----- - - _--..e-- - ----

..... ",

.'",,,,/"".,/

.....".....",/.....

,/

~/.... '.",,.e/

", ....... "'"... '"

.... ",,,,","

,,"

.01 . 02 . 03 .04 . 06 . 08 .10 .2 .3 .4 .6

ELAPSED TI ME, hr

.8 1.0 2 3 4 5 6 8 10

FIGURE 26. WIDTH vs. LOG TIME FOR STATIC 10

~;~-r~~~jt~~~~4i~;,;;El},~fik~Q¢.~o:rt:'~;t"~h •.-' ·_~t~<;{#&-

U1U1

Eo

70

60

E 50u

.c 40...c.(1)

~ 30(1)

"C

~ 20

10

o

-10

I I 'II I II I I

-

-l-

e--

I- ~

-• - -It"

I---I--r--

-~,

-

~.-

I

....- -.....

-....-..............

i""o...

I

I- .... ......._~r--

rt.... -I-

\ I1

f--t----r--

I ••I-

,,•

I I J

r-

I I I I: I I f, I ILII I I

- I I IVINJECTION WELL

-.-

/ '"~-

- / • 190 '"/ • 180,

-• 180

• 170- I 170 150 790 1330

• • • • • • 190 \730

"- • 150 ~~- ..... -- ....... .160./,- 160 •

380 •- 360 ".18,800.

I-

... II I I I I I

tJ1C]\

o 10 20 30Chloride Concentration, g/£

BEFORE EXPERIMENT

------- DURING EXPERIMENT

(at elapsed time of 142 hr)

40Chloride Concentration of Plume Interior, mg/£

FIGURE 27. CHLORIDE CONCENTRATIONS FOR STATIC 12 (TAKEN AFTER 142 hr OF CONTINUOUS INJECTION)

80

70

60

E 50u~

-t; 40CoQ)o_ 30Q)

"0

~ 20

10

o

-10

I "II I I I

Ir

II I IJ J I

I 1 I

-

~ I JI Ir"'-

""1\r

\1p

-.-

1 ·f I 1 _.--11...1.1...1. J...I. 1..L..JUl 1..L ..L

I I I

f- 1/ INJECTION WELL

f-

.".--- • 1~3

"f- / • 133

II' • 140

~f- / 273 2~3

• •I- ( • 150

f- " ,/~........

'\ I..-

f-

If- .193

f- \ I)f-

rI I I II I I

o 10 20 30Chloride Concentration, gft

40Chloride Concentration of Plume, mgft

~~~~

FIGURE 28. CHLORIDE CONCENTRATIONS FOR STATIC 13 (TAKEN AFTER 192 hr OF CONTINUOUS INJECTION)

til-...J

l-

I-

l-

I-

~ ""'-

" "l-

I- 1\I- \-

.,I I I I I I I I

80

70

60

E 50u~

-5 400-<UCl

~ 30<U

"'0

~ 20

10

0

-10

o 10 20 30Chloride Concentration, gft

40

I I I- / INJECTION WELL

-.- ..--- 93· ---.

/", ..........-

"/ e 93 • 120 \-e,oo e 113

"e 140 • 117 )-e440

• 103

.............. e 140 /- I'--.. """'--- e 173

,.... '"~l-

I-

.....

I- 1 1 1 I I I I I I ·1 I I

Chloride Concentra~ion of Plume, mgft

(Jl00

FIGURE 29. CHLORIDE CONCENTRATIONS FOR STATIC 14 (TAKEN AFTER 238 hr OF CONTINUOUS INJECTION)

59

. Chloride concentrations shown in the outer portions o'f the p'lume :(1, 700 ppm,

1,500 ppm, etc.) indicate that'a degree of mixing takes place between the

effluent and the brackish water of the transition zone. However, it is evi­

dent from the behavior of the plume and the chloride concentrations for the

freshwater zone shown in Figures, 27, 28, and 29, that the mixing that took

place in the transition zone did not substantially inhibit the rise of the

effluent into the freshwater zone.

The initial concentration of chloride in the effluent was the same as

that of regular tap water, apout 50 ppm. The chloride values obtained from

the center of the plume ranged from 150 ppm to 380 ppm. 'This suggests that

although entrainment was not significant from a fluid mechanics standpoint,

it may have been enough to significantly increase chloride concentrations in

the the freshwater zone. If this was the case, even if'the injected liquid

was tertiary-treated sewage effluent, there would still be a danger of con­

tamination of the freshwater zone from entrained chloride.

However, it should be emphasized that the only conclusion that can be

drawn here is that entrainment of salt water is not significant enough to

inhibit upward growth of the plume, and that detailed studies of dispersion

and mixing will be required in order to draw any conclusions with respect to

the effects of injection on water quality. Ongoing Phase 2 experiments of

this project are presently being conducted which will produce breakthrough

curves for chloride concentration and total concentration of the effluent.

THEORETICAL DESCRIPTION OF PLUME MOVEMENT

Pore Velocity of the Injected Effluent

In the previous chapter, it was noted that in general, the interface

angle was relatiVely large for low injection rates and'relatively'small for

high injection rates. There are two primary driving forces that contribute

to 'the movement of the injected effluent: (1) buoyancy from the density

difference between the injected effluent and the ambient aquifer liquid, and

(2) injection head, the head at which injection takes place in order to

drive the effluent out of the well and into the porous medium. Both driving

forces are vector'quantities and produce corresponding vector velocities.

The velocity due to buoyant force is always directed upward, and the velocity

due to injection head is, for the most part, directed horizontally outward

60

frDm the well. The vector addition of the two velocities is reflected in

the interface angle. Dominant buoyant forces result in large interface

angles, and dominant injection head forces result in small interface angles.

Interface angles of approximately 45° result when the velocity component con­

tributed by buoyancy is about equal to the velocity component contributed by

the injection head.

For the low injection rate salt-zone plumes, the nearly vertical inter­

face angle indicated that the injection head velocity component was very

small compared to that of the buoyant force. Therefore, the injection head

velocity component can be neglected, and it can be assumed that there is only

one velocity component (due to buoyancy) which is tangent to the interface

between the injected effluent and the ambient salt water. Making this assump­

tion, it is possible to use the boundary condition first developed by Hubbert

(1940) :

v = kg(L\P)sineP llfn

where: Vp = average pore velocity

k = intrinsic permeability

g = acceleration of gravity

L\P = Ps - Pf = saltwater density minus freshwater density

llf = viscosity of freshwater at laboratory temperature

e = interface angle

(8)

n = porosity

Substituting the following values from the sand-packed model into the above

equation: k = 8.66 x 10-7 cm2 , L\P = 0.036, llf = 0.01 poise, a = 90°, and

n = 0.39, yields a value for the average upward pore velocity, ~, of 28;2

cm/hr. The observed pore velocities from the two experiments, Statics 4 and

11, that satisfy the boundary conditions required for equation (8) above,

were 26.9 and 26.3 cm/hr, respectively, in the salt-water portion of the

model. The close agreement between the calculated velocity and actual ob­

served velocities suggests that this approach is satisfactory for predicting

upward velocities for low injection rate plumes, as long as the interface

angle approaches 90°

Buoyant Plume Movement in the Freshwqter Zone

Experimental observation has shown that the plumes seem to expand out-

61

ward and upward in the freshwater zone in a hemispherical fashion. Because

of the symmetry of the sandbox model, the expansion is actually one-half of

a hemisphere, or a quadrisphere. However, in a prototype injection well

situation, the expansion would be hemispherical. In both the model and the

prototype, the lower boundary of the expanding plume is the center of the

transition zone. The hemisphere can be imagined to be expanding horizontally

outward from a point located at the center of the injection well, and expand­

ing upward from a point at the center of the transition zone. This point of

expansion will be called the imaginary point source.

The volume, V, of an expanding quadrisp)lere of injected liquid in a

porous medium is:

(9)

and

dV/dP = 11"n1'2

where n =porosity, and l' =radius of the quadrisphere.

tion rate, Q, is defined by:

(10)The constant injec-

Q =dV/dt (11)

Noting that:

dV/dt = (dV/dP) (dP/dtL (12)

equa~ions (10) and (11) can be substituted into equation (12), resulting

in:

It should be emphasized here that although the initial conditions l' = 0 and

Q = 11"nr2 dP/dt (13)

If it is assumed that·the initial boundary conditions, l' = Owhent = 0

exist~ equation (13) can readily be integrated. In reality; the plume begins

to expand spherically into the freshwater zone at some time greater th~n

t = 0, and at some radius greater than l' = O. However,the expanding spher­

ical model is not designed to predict the movement of the plume in the salt.­

water or the transition zones, but rather it is designed only to predict the

plume expansion in the freshwater zone.

Integrating equation (13) using the initial conditions that l' = 0 when

t = 0 yields:

(14)

(15)

11"n 3t =-1'3Q

or,

62

t. = 0 were used in developing equation (15), the plume would not be expected

to behave according to equation (15) until it had penetrated into the fresh­

water zone.

Letting r = h, the height of the plume above the imaginary point source;

n = 0.39, the model porosity; and Q = 5 cm3/min, equation (15) becomes:

h = 9.02°·333 (16)

In order to compare the experimental results with the theoretical

equation (16) derived above, a plot of experimental data of plume height

(measured from the imaginary point source) vs. log time for Statics 12, 13,

and 14, together with the graph of equation (16), have been plotted in

Figure 30. Here, only the data from the time that the plume penetrated into

the freshwater zone have been plotted, as shorter time data would not be

expected to fit into this model. The curves in Figure 30 representing the

experimental data was plotted by using the least squares method to fit the

power curve:

h=a~ (17)

to the actual data. By doing this, the coefficient, a, was assigned values

of 8.24, 7.12, and 8.59, respectively, for Statics 12, 13, and 14, and the

exponent, b, values of 0.318, 0.367, and 0.297, respectively. Comparison of

the coefficients a and b above with those in equation (16), and also the

plots of these equations in Figure 30, shows that fairly good agreement is

achieved with this simple, first approximation to a theoretical solution.

A review of the assumptions and limitations of equation (15) is appro­

priate here.· The first assumption (not mentioned previously) that was made

in deriving equation (15) was that the freshwater zone of the aquifer extends

upwards infinitely and is of infinite horizontal extent. In reality, the

upward movement of the plume would be limited by the presence of the water

table and the horizontal movement would be limited by the presence of an

impermeable boundary. In addition, initial conditions were used that were

based on the concept of an imaginary point source. Since this imaginary

point source does not exist, it would be incorrect to use equation (15) to

predict the movement of the plume in the salt-water zone and in the transi­

tion zone. Only the longer time data of plume growth in the freshwater zone

can be predicted.

./.,,/,/

.,,/ //

/ ,/

.,,/ //

,/ //

,/ ",//

/ ,//

/. ,/,/

/0,/ .....-/..../. ",..",..--:...

/. ",.. ---: ...-"". ,..,.,."""""" ..

"~o~- ...... ....? ...

-~: .

Static 12

Static 13

Static 14

Theoretical equation 16E 50u.

I.LJUex:::::::>0III

I- 40z-0c...

>-ex::«z-~ 30«~-I.LJ>0a::l«I.LJ

20~:::::>....Jc...lL.0

I- 10::J:~-I.LJ::J:

300200150o I I I I I I I I I I I

10 20 30" 40 50 60 80 100

ELAPSED TIME, hr

FIGURE 30. COMPARISON OF THEORETICAL CURVE (eq. 16) WITHEXPERIMENTAL CURVES (STATICS 12, 13, AND 14)

(]\v.l

_~ilIa';O~~~"" c ••tI£I

64

CONCLUSIONS

The two most significant conclusions to be obtained from these experi­

ments are: (1) although several of the injection parameters have an effect

on the details of the injection process and the plume movement and configu­

ration, none of the injection parameters exerts a truly significant control

on the general overall movement pattern of the injected plume, that is, for

the conditions given in these experiments the injection plumes always mi­

grated well up into the freshwater lens, regardless of variations in any of

the several injection parameters, and (2) in general, these experiments show

little evidence of entrainment of the surrounding salt water into the in­

jected effluent plumes, which suggests that the principal means of plume

movement is by mass displacement rather than by mixing processes. Details

of these conclusions and other conclusions from this study are discussed

more fully below.

Head Buildup

There was no measurable head buildup observed in any of the experiments.

This result was desirable because the same effect is observed for injection

into most Hawaiian aquifers.

Relative Influence of Injection Parameterson Plume Shape

Although none of these parameters exerted a truly controlling effect,

the parameter which had the greatest influence on the shape of the plume was

the depth of injection. Injection into the salt-water zone produced a rising

column of effluent that eventually assumed the shape of a hemispherically

expanding plume front. Injection into the transition zone produced a simi­

larly-shaped effluent plume, but without the feeder column. Instead, the

effluent plume immediately began to move outward and upward from the point

of injection. A secondary effect of variation of injection depth was that

65

tafter a certain amount of time) a given salt-zone plume was always larger

than an equivalent transition-zone plume when all other parameters remained

constant. This effect was attributed to the increased dispersion experienced

by the salt-zone plume owing to higher velocities of the salt-zone plume rela­

tive to the.transition-zone plume.

The parameter which had the next greatest ~ffect on the shape of the

plume was variation of injection rate. The principal consequence of varia­

tion of injection rate was that a high injection rate produced a smaller

interface angle than a low injection rate.

Variation of the length of the discharging section of the well had the

least effect on the shape of the plume. For low injection rates, very little

difference in the rate of development of plume height (or width) was observed

between a point source and a line source. This was true for both low injec­

tion rate salt-zone plumes and low injection rate transition-zone plumes.

For high injection rates, the evidence was conflicting and no consistent

conclusions could be drawn.

SALT WATER ENTRAINMENT

No upper limit to the rise of the effluent plume was detected in any

experiment. Three experiments (Statics 12, 13, and 14) were conducted long

enough so that the plumes rose through approximately 80% of the freshwater

zone. The graphs of plume height vs. time for the other experiments all

suggested that the plumes in these expe~iments also would have continued to

rise through the.. freshwater zone similar to the plumes in Statics 12, 13,

and 14. Chloride samples taken from the plume interiors during the course

of Statics 12, 13, and 14 show that the rising plumes have the same density

as fresh water. This evidence indicates that the degree ,of salt-water

entrainment into the plume is not sufficient to cause an upper limit to the

rise of the plume. In fact, in the salt-zone experiments, it appeared that

once the column of effluent had displaced the ambient salt or brackish water,

it served as a direct conduit for the upward migration of all the remaining

injection effluent, which is thus shielded very effectively from any addi­

tional mixing except on the outermost perimeters of the column. Ongoing in­

vestigations in Phase 2 of this project support this conclusion by showing,

for other cases, that chloride concentrations in the plume interiors are

66

also well below 600 ppm.

Theoretical Conclusions

The expanding spherical model was shown to be fairly accurate as a first

approximation for effluent movement in the freshwater zone. Furthermore,

through use of interface mechanics, the upward velocities in a salt-zone

column can be estimated theoretically as long as the injection head velocity

component is small relative to the buoyancy velocity component. The injec­

tion head velocity component is relatively small when the interface angle is

approximately 90 0•

RECOMMENDATIONS

This study provides a considerable amount of information about the be­

havior of buoyant plumes in a static environment. However, to properly eval­

uate and more fully understand the nature of waste injection in Hawaii, it

is also necessary to study the behavior of buoyant plumes in an environment

in which the freshwater zone is dynamic. A study of this type should include

more sophisticated and complete methods for data collection that will enable

a quantitative analysis of the dispersion and mixing processes.

Statics 12, 13, and 14 indicated that relatively small (from the stand­

point of fluid mechanics) amounts of chloride were entrained in the upward

moving plume. From a standpoint of water quality, however, this amount could

be quite significant. Therefore, it is suggested that breakthrough curves

for chloride concentration in the effluent plume be taken (as well as break­

through curves for the dye in the effluent) in the freshwater-zone dynamic

experiments that are being conducted currently.

If the results of the study of buoyant plumes in a dynamic freshwater

zone are consistent with the results of the present study (that is, minimal

control of plume movement by the injection parameters, and little to no salt

water entrainment), then investigations should be made into ways in which

entrainment of salt water within the effluent plume could be induced artifi­

cially.

67

ACKNOWLEDGMENTS

The authors wish to express their grateful appreciation to the following

persons and organizations: L. Stephen Lau, for his continued assistance and

encouragement throughout the project; John A. Williams, for his many helpful

suggestions; the University of Hawaii Environmental Center, for providing

financial assistance to initiate the project; and Maui County and Conoco Oil

Company for financial assistance.

68

REFERENCES

American Public Health Association, American Water Works Association, andWater Pollution Control Federation. 1971. Standapd methods fop theexamination of watep and wastewatep. 13th ed.

Anderson, J.L.; Parker, F.L.; and Benedict, B.A. 1973. Negatively buoyantjets in a oposs flow. Tech. S~r. Rep. EPA-660/2-73-0l2, U.S. Environ­mental Protection Agency.

Ballentine, R.K.; Reznek, S.R.; and Hall, C.W. 1972. Subsupfaoe pollutionppoblems in the United States. Tech. Studies Rep. TS-00-72-02, U.S.Environmental Protection Agency.

Bear, J., and Jacobs, M. 1964. On the movement of water bodies injectedinto aquifers. JoUP. Hydrol. 3:37-57.

Brooks, N.H. 1973. Dispepsion in hydrologio and ooastal enviponments.Ecological Res. Ser. Rep. EPA-660/3-73-0l0, U.S. Environmental ProtectionAgency.

Hargis, D.R., and Peterson, F.L. 1970. Aptifioial peohapge ppaotioes inHawaii. Tech. Rep. No. 43, Water Resources Research Center, Universityof Hawaii.

Hollister, J., and Weimer, R.J., eds. 1968. Geophysical and geologicalstudies of the relationships between the Denver earthquakes and the RockyMountain arsenal well, Part A. Colopado Sohool of Mines Quarteply 63(1):25l.

Hoopes, J.A.; Monkmeyer, P.L.; and Fattah, Q.N. 1973. Dispepsion of sub­stanoes fpom well peohaPge opepations in an anisotpopio~ homogeneousoontinued aquifep. Tech. Rep. 73-11; University of Wise. Water Resources.

Hubbert, M.K. 1940. The theory of ground-water motion. JoUP. Geology 48:785-944.

Lau, L.S. 1962. Watep deveZopment of Kalauao basal sppings hydraulio modelstudies. University of Hawaii and Honolulu Board of Water ~upply, Hono­lulu, Hawaii.

1967. Seawater encroachment in Hawaiian Ghyben-Herzberg systems.In Ppoo. Amep. Watep Resoupoes Assoo.~ Natiqnal Symposium on Ground WaterHydrology, pp. 259-71.

List, E.J., and Imberger, J. 1973. Turbulent entrainment in buoyant jetsand plumes. JoUP. Hydraul. Div. ~ Prooo. Amep. Soo. Civil Engp. 99 (HY 9):1461-74.

Mercado, A. 1967. The spreading pattern of injected water in a permeabil­ity stratified aquifer. In Symposium of Haifa~ IntI. Assn. ScientificHydrology, Pub. No. 72, pp. 23-37.

Palmer, H.S. 1946. The geology of the Honolulu gpound watep supply.Honolulu Board of Water Supply, Honolulu, Hawaii.

Peterson, F.L. 1972. Water development on tropic volcanic islands-typeexample: Hawaii. Gpoundwatep 10(5):18-23.

69

Peterson, F.L., and Hargis, D.R. 1971. Effect of storm runoff disposal andother artificial recharge to Hawaiian Ghyben-Herzberg aquifers. Tech.Rep. No. 54, Water Resources Research Center, University of Hawaii.

, and Lau, L.S. 1974. Subsurface waste disposal by injection in Hawaii:----,--

A conceptual formulation and physical modeling plan. Tech. Memo Rep.No. 41, Water Resources Research Center, University of Hawaii

, and Takasaki, K.J. Effect of subsurface waste disposal practice on--g-r-ound water resources in the Hawaiian Islands. In Proc. 1974 Circum­

Pacific Energy and Mineral Resources Conference~, Honolulu, Hawaii, inpress.

State of Hawaii. 1975. Hawaii revised statutes. Vol. 4 and 1975 Supple­ment, chaps. 341 and 342.

State of Hawaii, Department of Health. Public health regulations. Honolulu,Hawaii. .1974. Water pollution control, chap. 371973. Sewage treatment and disposal systems, chap. 38.

Soroos, R.L. 1973. "Determination of hydraulic conductivity of some Oahuaquifers with step-drawdown test data." M.S. thesis, University of Hawaii.

Sunn, Low, Tom, and Hara, Inc. 1973. Kauai water quality management plan.Honolulu, Hawaii.

Takasaki, J.J. 1974. Hydrologic conditions related to subsurface and sur­face disposal of wastes in Hawaii. U.S. Geol. Surv. Open File Report.

Todd, D.K. 1959. GroundWater hydrology. New York: Wiley.

van Everdingen, A.F. 1968. Fluid mechanics of deep-well disposals. InSubsurface disposal in geologic basins--A study of reservoir strata~ Amer.Assoc. of Petroleum Geologists--Memoir 10, pp. 32-42.

Waldrop, W.R., and Farmer, R.C. 1974. Three-dimensional computation ofbuoyant plumes. Jour. Geophys. Res. 79:1269-76.

Whitehead, J.A., and Luther, D.S. 1975. Dynamics of laboratory diapir ahdplume models. Jour. Geophys. Res. 80:705-17.

Witherspoon, P.A., and Neuman, S.P. 1972. Hydrodynamics of fluid injection.In Underground waste management and environmental implications~ Proc.Symposium~ Dec. 6-9~ 1971~ Amer. Assn. of Petroleum Geologists--Memoir 18,pp. 258-72.

71

APPENDICESCONTENTS

APPENDIX A. VISUAL FRONT POSITIONS OF THE EXPERIMENTS ANDCORRESPONDING CHLORIDE CONCENTRATION PROFILES.

FIGURES

73

A.1

A.2A.3A.4A.5A.6A.7

A.8A.9A. 10A.11

A.12

Static 3:Stati c 4:Static 5:Static 6:Static 7:Static 8:Static 9:Static 10:Stati c 11:Static 12:Static 13:Stati c 14:

Line Source, 20 m~/min .Point Source, 5 m~/min .Point Source, 20 m~/min.

Line Source, 20 m~/min

Line Source, 5 m~/min..Point Source, 5 mi/min ..Poi nt Source, 20 m~/mi n.Point Source, 20 mi/min .Line Source, 5 mQ;/min ..Line Source, 5 m~/min .5 mi/min, Salt Zone Point Source. . ...5 mi/min, Transition Zone, Point Source.

73747576

77

7879

80

81

82

83

84

APPENDIX B. MODEL SCALE RATIOS .

TABLE

85

B. I Summary of Scale Ratios from Selected Sandbox Model Experiments. 88

l-

I-

T

IfI,

........~....~-- -....-.

~...

- 1\,-

- •I- , , I , I ,

" I

80

70

60

E 50u~

~ 400-(j)

0

30(j)

'"00~ 20

10

0

-10

o 10 20 30Chloride Concentration, gft

I I I

l- LlNJECTION WELL

l-

I-

l-

I-.

I-

/ ~~t::"I- ~~v.:::~K'\Yf -/

"K~~IYl-

I- (/~~I- lG~l-

I- ,I I I I I I , I , , I

40 -50 -40 -30 . .,.20 -10 0 10 20 30 40 50Position of the Visual Front of the Plume at Equal Times, cm

1. 0.017 hr2. 0.100 hr3. 0.283 hr

LEGEND

4. 0.567 hr5. 0.850.hr6. 1.683 hr

7. 2.783 hr8. 4.500 hr9. 6.200 hr

FIGURE A.l. STATIC 3: LINE SOURCE, 20 mtfmin

~~~~~~~~~

--JVI

--J~

I I I

- /-1 NJ ECTION WELL

-

--

- / ~/' ~

- V/' ,.-/ '\",'"/~~~.~~..-2~I-

~~'i

v

~I- (\ ~

~ ~ JI-

~N~/

-- I I I I I I I I I I I I

Il-

I-

t-

I~

JfT

~I

''''''I-~

I

l-

I

-l-

I

-l-

II

~ I, ..L.II-

i I I-

10

E 50u

80

30

70

-10

o

60

Q)"'0o:L 20

~

-E 40a.Q)Cl

o 10 20 30Chloride Concentration, 9ft

40 -50 -40 -30 -20 -10 0 10 20 30 40 50Position of the Visual Front of the Plume at Equal Times, cm

LEGEND

1. 0.017 hr 5. 0.917 hr 8. 2.000 hr2. 0.100 hr 6. 1. 250 hr 9. 4.500 hr3. 0.317 hr 7. 1.500 hr 10. 9.50 hr4. 0.500 hr

FIGURE A.2. STATIC 4: P01NT SOURCE,S mtfmin

'y~

-

I-

1"

~

~ ........r---:---.I- --....

~..........

\I--

I--

l- II

I

1-, I I I I I I I

80

70

60

E 50u

.r:.~ 40....0..<Ll

C 30<Ll

"'C

~ 20

10

a

-10

a 10 20 30Chloride Concentration, 9ft

I I II-- /INJECTION WELL

~

I--

l-

I--

/1---...

I-

........--::t'l=~~~ """-I-- ~~~~~ 'Y~

I- ~K(c ))~~......... -'

l-

I-

l-

I--I I iI I I I I I I I

40 -50 -40 -30 -20 -10 a 10 20 30 40 50PosJtionofthe Visual Front of the Plume at Equal Times, cm

1. 0.017 hr2. 0.083 hr3.0.167hr

LEGEND

4. 0.750 hr5. 1.500 hr6. 2.500 hr

7. 4.000 hr8.6.167hr

FIGURE A.3. STATIC 5: POINT SOURCE, 20 m~fmin

-....IU1

.-

l-

I-

t

r-\.. r--.I-

~~ -..!..

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---l0\

LEGEND

1. 0.017 hr 4. 1.000 hr 7. 4.750 hr2. 0.083 hr 5. 1.750 hr 8. 5.611 hr3. 0.333 hr 6. 3.250 hr

FIGURE A.4. STATIC 6: LINE SOURCE, 20 mtfmin

80

70

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10

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40 - 50 - 40 - 30 - 20 -10 0 10 20 30 40 50Position of the Visual Front of the Plume at Equal Times, cm

~~~iG'#l'mt.:t'4iib'.-:i4¥;:-c;;g;;g;aa;i

LEGEND--1. 0.017 hr 5. 1.083 hr2. 0.083 hr 6. 2.000 hr3. 0.167 hr 7. 4.000 hr4. 0.667 hr 8. 6.000 hr

FIGURE A.5. STATIC 7: LINE SOURCE, 5 ml/min--.J--.J

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FIGURE A.6. STATIC 8: POINT SOURCE, 5 m~/min

80

70

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7. 4.533 hr8. 5.083 hr

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LEGEND

4. 1.000 hr5. 1.500 hr6. 3.500 hr

4030

1. 0.017 hr2. 0.050 hr3. 0.500 hr

2010o

FIGURE A.l STATIC 9: POINT SOURCE J 20 ml/min -...]

lD

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LEGEND

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1. 0.033 hr2. 0.100 hr3. 0.267 hr

10 20 30Chloride Concentration, 9ft

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LEGEND

1. 0.050 hr 4. 0.583 hr. 7. 2.083 hr2. 0.183 hr 5. ·1.000 hr 8. 3.500 hr3. 0.333 hr 6. 1.250 hr 9. 7.750 hr

FIGURE A.9. STATIC 11: LINE SOURCE, 5 m~/min

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LEGEND

00tv

1. 0.083·hr2. 0.500 hr

3.1.167hr4. 1. 750 hr

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11. 97.00 hr· 13. 202.5 hr12. 142.0 hr

FIGURE A.10. STATIC 12: LINE SOURCE,S ml/min

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40 -50 -40 -30 -20 -10 0 10 20 30 40 50Position of the Visual Front of the Plume at Equal Times,

cmLEGEND

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40 -50 -40 -30 -20 -10 0 10 20 30 40 50Position of the Visual Front of the Plume at Equal Times, cm

7. 192 hr8. 238 hr

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FIGURE A.12. STATIC 14:

LEGEND

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5 m£/min, TRANSITION ZONE, POINT SOURCE

85

APPENDIX B. MODEL SCALE RAnos

The sand~packed hydra~lit model used in the present study ~as not de­

signed to simulate a specific prototype but, rather'~' to model the effects of

various injection parameters in a general way. However, without some charac­

teristic model-prototype ratios, a direct correspondence between such param­

eters as model and prototype distances, times, ,and injection rates is not

possible. Consequently, in this appendix, equations for model-prototype

ratios are first developed for the general case of flow of two liquids in a

phreatic aquifer. Then these general equations are used to calculate appli­

cable mode1~'p~ototrPe"ratios for the various experiments run during the

course of the present study.

General Equations for Model-Prototype Ratios

The development of general equations for model-prototype ratios for flow

of two liquids in a phreatic aquifer follows the method used by Bear, Zas­

1avsky, and; I~may.1

Ratios of model magnitudes to the corresponding prototype magnitudes

are given as follows:

Xl' = dxm/dxp ; Yr = dym/dyp ; zr = zm/zp;

ky. = l<m/~; t = tm/tp ; Qr = ~/Qp; 4>1' = 4>m'l4>p;l'

Yr = Ym/Yp ; u =Urn/up; nr =nm/np ;l'

Kxr = ~/Kxp; K.yr = VKyp ; Kzr = ~/Kzp; (B.1)

where x, y, and z, are the principal directions, k is the permeability, t is

time, Qis discharge rate, 4> is potential, Y is specific weight of the liq­

uids, u is viscosity, n is porosity; ~, ~, and ~ are the principal values

of the anisotropic hydraulic conductivity, the subscript m denotes model

values, subscript p denotes prototype values, and subscript l' denotes the

ratio between ,the two.

Equations (B.2) through (B.6) given below are required to describe the

flow of two liquids in a phreatic aquifer. In these equations, the model is

assumed to be isotropic and the prototype, anisotropic. The subscript i de­

notes the 2-phase flow and is i = 1,2, where 1 is the fresh water, and 2 is

1J. Bear, and D. Zas1avsky, Physical principles of water percolation andseepage, ed. S. Irmay (Paris, France: UNESCO, 1968), pp. 357-59.

86

(B.2)a2 <t> •

+ k ~p = 0;zp az 2

p

the saline water for the experiments in this study. As defined previously,

the subscript p denotes parameters for the prototype, and the subscript m

denotes parameters for the model. The continuity equations for the proto­

type and model are given by:

a2 <t>. a2 <t>.'k~ a ~1 + k ~p-/:' YP ay.2xp p

The elementary discharge as giveny. a<t>.

dQ. = _7< .:..YiP...~ dy dz .x~p ·Xl-!. oX P p'

~p P

by Darcy's law is:

Yim a<t>imdQxim = -Jm~ ax-dYmdzm

~m m(B.3)

and similar equations for the y and z directions. The average velocity is

given by:

vxp

(B.4)

and similar equations for the y and z directions. At a phreatic surface,

pressure, p = 0, thus:

(B.S)"

Along an interface between liquids 1 and 2, PI = P2' therefore:

Y2p <P2p YIp<P Ip = (Y2p YIp)Zp;

(B.6)

In order to make the corresponding equations for the prototype and

model given above proportional, the following conditions must exist:

(B.2')

= Q )l'

(B.3')

(B.4')

(B. S')

Y <P = Y <P (Y Y)11' 11' 22" 21' = 2 - 1 Z1'2"

(B.6')

87

Equations (B.2, B.3, B.4, B.5, B.6) define 13 model parameters (xm, Ym' zm'

km, tm, Qm"<P 1m' <P2~' Ylm,'Y2m' u;lm' u2m' nm), and equat,~ons (B.2', B.3',B.4', B.5', B.6') stipulate 8 conditions. Consequently, this leaves 5 param­

eters to be chosen arbitrarily. Furthermore, in~ phreatic aquifer the con­

ditions [(1'2 - 1'1)/1'1]1' = 1, or (1'2/1'~)r = 1 must also occur.. If the param­

eters to be chosen arbitrarily are:' np' zp' kz1" I'll" and u11" then the

remaining model-prototype scale ratios are given by equation (B.7):

- .

t p = zpnr,u1.iI(Yz---· I' l)rkzp;·

1Y1) k / U 1 (k k )~

. l' zp l' xp yp (B.7)

Examples of Model-Prototype Ratios for Actual Experiments

If the parameters, n1' , zp' kzp , I'll" and ulp' are assigned the arbitrary

values given below (the values for the model are actual measured values and

those for the prototype are typical values for Hawaiian basaltic aquifers):

np = nmlnp = 0.39/0.25 = 1.56

zp = zmlzp = 3 ft/300 ft = 0.010

241 ft/day - 0 482500 ft/day - .

62.4 Ib/ft 3

I' 1r = I' 1m I' Ip = -62-.-4-1b--'-/-f-t3 = 1. 00

U 11' = uIm!u 1p = 1. 00

The model-prototype scale ratios are calculated by using the relationships

given by equation (B.7). For example:

x~ = Y~ = z (X IX )~ = 0.01(500/5000)~ = 0.00316.L' .L l' zp xp

<PIP = zp = 0.010

88

t ( )/(Y ) k 0.01 • 1.56 • 1.00 =1" = z!'n!'u1!' .. 2 - Y 1 1" Z!' = 1. 00 • 0.482

Q!, = z!'kZ!'(Y2 - Yl)!,kzp/Ul!,(kXpkyp)l

= 0.01 2• 0.482 • 1.00 • 500 = 4.82 x 10- 6

1.00 • (5000 • 5000)1

0,032

Values for length, head, time, and injection rate ratios are summarized in

Table B.1.

TABLE B.l. SUMMARY OF SCALE RATIOS FROMSELECTED SANDBOX MODEL EXPERIMENTS

PARAMETER

Length (horizontal) .....•...Head .Time ...........•.•......

Injection rate .

MODEL

1 ft1 ft1 da~5 cm /min

20 cm 3/min

PROTOTYPE

316 ft100 ft30.3 day0.395 mgd1.58 mgd