eogenetic karst from the perspective of an equivalent...

EOGENETIC KARST FROM THE PERSPECTIVE OF AN EQUIVALENT POROUS MEDIUM

lH.L. Vacher and 2John E. Mylroie'Department of Geology, University of South Florida, Tampa FL 33620

"Department of Geosciences, Mississippi State University, Mississippi State. MS 39762

ABSTRACT: The porosityofyoung limestonesexperiencingmeteoricdiagenesisin the vicinityof theirdeposition(eagenetic karst) ismainlya doubleporosityconsistingoftouching-vug channelsandpreferredpassagewayslacingthrougha matrixof interparticleporosity. Incontrast,theporosityoflimestonesexperiencingsubaerialerosionfollowingburialdiagenesisandupliftitelogenetic karst) ismainlyadoubleporosityconsistingofconduits withina network offractures. The stark contrast between these two kinds of karst is illustratedby their position on a graphshowingthehydraulic characteristics ofanequivalentporousmediumconsistingofstraight,cylindricaltubes(II-Dspace,wheren isporosity,D isthediameterofthe tubes,and log n is plotted against logD).

Studiesofthe hydrologyof small carbonateislandsshow that large-scale,horizontalhydraulicconductivity(K) increasesby ordersof magnitudeduringtheevolutionofeogenetickarst. Earlierpetrologicstudieshaveshownthereis littleifanychangeinthetotalporosityofthe limestoneduringeogeneticdiagenesis. The limestoneofeogenetickarst, therefore, trackshorizontallyinn-D space. Incontrast,the path from initialsedimentarymaterial to telogenetickarst comprises a descenton the graph with reductionof /l during burial diagenesis,then a sideways shift with increasingD due toopeningoffractures during upliftandexposure,and finallyan increaseinD and n duringdevelopmentofthe conduitsalongthefractures.

Eogeneticcavesare mainly limited to boundariesbetweengeologic unitsand hydrologiczones: streamcaves at the contact betweencarbonatesand underlying impermeablerocks(andcollapse-origin cavesderivedtherefrom); verticalcavesalongplatform-margin fractures;epikarst;phreaticpockets(bananaholes)alongthewatertable;andflankmargincaves thatformasmixingchambersat thecoastalfreshwater-saltwater"interface".Incontrast,thecavernsoftelogenetic karstarepartofa systemofinterconnected conduitsthatdrain anentireregion. The eogeneticcavesofsmallcarbonate islandsare, for the most part,not significantlyinvolved in thedrainageofthe island.

INTRODUCTION

The limestone of karst in such places as Bermuda, theBahamas, south Florida, and Pacific atolls is conceptuallydifferent from the limestone of classic monographs on karst.These young limestones, which are exposed in the generalareas of their deposition, are still undergoing early meteoricdiagenesis. Secondary porosity giving rise to large hydraulicconductivities occurs within a rock retaining large primaryporosity. This double porosity is unlike the double porosity of

karst developed in older limestones that have been deeplyburied.

The purpose of this paper is to provide a perspective on thehydraulic conductivity of young limestones still experiencingmeteoric diagenesis. The data necessary to draw a distinctionbetween this type of karst and the more-familiar karst ofolderlimestones are already in the literature in a different context.Our discussion will center on one of the classic conceptualdiagrams in the literature of karst (Fig. I).

~Zwoa::wa.

;:u;oa::oa.

0.1-+---'-....c...

0001 0.1 1

PORE SIZE (MM)

10 100

Figure 1. Location of limestone in n-D space in an equivalent porous medium with porosity n consisting of straight tubesofdiameter D. Slanting lines in background are contours ofhydraulic conductivity (K, m/day). Oval fields delineated bysolid lines indicate primary porosity, and oval fields delineated by dashed lines indicate the fractured counterparts.Recalculated and redrawn from Smith et al. (1976), Ford (1980), and Brahana et al. (1988).

Carbonates and Evaporites. v. 17,no. 2, 2002, p. 182-196.

VACHER AND MYLROIE

Table I. Disparate subdivisions of karst: geographic setting (rows) vs. time-porosity stage (columns).

Eogenetic karst Telogenetic karstisland karst Bermuda and Bahamas Gotland [Sweden] (Tell 1976).

(Mylroie et al, 1995a). Kephallenia IGreecel (Bonacci 1987)continental karst Biscayne aquifer (Fish Kentucky (White & White 1989)

and Stewart 1991) England (Waltham 1974)

EOGENETIC KARST

The Glossary of Geology (Jackson 1997, p. 345) defineskarst as "a type of topography that is formed on limestone,gypsum and other rocks, primarily by dissolution, and that ischaracterized by sinkholes, caves, and underground drainage."Among definitions in textbooks, that of Ford and Wiliams(1989, p. 2) is representative: "terrain typically characterizedby sinking streams, caves, enclosed depressions, fluted rockoutcrops, and large springs." The mention of undergrounddrainage, springs, and the like acknowledges that the word"karst" includes the plumbing as well as the landscape.

Choquette and Pray (1970) subdivided the postdepositionalevolution of carbonate porosity into three time-porositystages conforming to the rock cycle. They defined "the timeof early burial as eogenetic, the time of deeper burial asmesogenetic, and the late stage associated with erosion oflong-buried carbonates as telogenetic" (Choquette and Pray1970, p. 215). The eogenetic and telogenetic stages involvesurface processes. The eogenetic setting is the general area ofcarbonate deposition. The telogenetic setting is a decidedlyerosional environment, unrelated to the site of carbonatedeposition. The terms were intended to apply to "the porositycreated during the three stages, to processes acting during thestages, or to the respective burial zones" (Choquette and Pray1970, p. 215).

The circulation of meteoric water through recently deposited,newly exposed carbonate sediments leads to a diagenesis thatincludes stabilization of the depositional mineralogy,cementation of unconsolidated sediment, development ofsecondary porosity, and alteration of the landscape (Friedman1964; Land et al. 1967; Gavish and Friedman 1969; James andChoquette 1984). Although the particular sites of suchmeteoric diagenesis are erosional, they indisputably lie withina general environment of carbonate deposition. Suchmeteoric diagenesis ofyoung sediments and rocks is certainlyeogenetic in the sense of Choquette and Pray (1970).Accordingly, we use the term eogenetic karst for the landsurface evolving on, and the pore system developing in, rocksundergoing eogenetic, meteoric diagenesis. In contrast,telogenetic karst is the karst developed on and within ancientrocks that are exposed after the porosity reduction of burialdiagenesis.

As will be discussed in some detail below, the location ofeogenetic karst in Figure I is roughly the same as the field

labeled "Recent coral limestone". The label, "Recent corallimestone", however, is entirely inappropriate for the rock wehave in mind. The young limestone exposed in the shallowsubsurface ofplaces such as Bermuda, the Bahamas, and southFlorida - commonly called "coral limestone" by nonspecialists - is preponderantly bioclastic and/or oolitic. It isbioclastic grainstone in Bermuda, mostly bioclastic andoolitic grainstones and packstones in the Bahamas, and nearlyentirely bioclastic and oolitic limestone in the Biscayneaquifer of South Florida. (The "oolite" of Figure I isundoubtedly ancient - on the order of 108 years - muchdifferent than the 104 to 106 year age of the oolite of eogenetickarst discussed in this paper).

Small carbonate islands (Vacher 1997) are typically the sitesof meteoric diagenesis and eogenetic karst, and telogenetickarst typically occurs in continental settings; however, it doesnot follow that eogenetic karst is synonomous with islandkarst and telogenetic karst with continental karst. The point ismade by Table I. The eogenetic karst ofsouthernmost Florida,consisting of the Miami Limestone and associated rocks,characterizes both the islands of the lower Florida Keys andthe Biscayne aquifer of "mainland" Florida. To place theseoccurrences in different categories misses the point of thedistinction between the karst of places such as Bermuda, theBahamas, and southern Florida, on the one hand, and that ofKentucky and England on the other. The fundamentaldifference is relative age - the fact that the karst of onecategory is still experiencing eogenetic diagenesis, and thekarst of the other category is developing on "mature"limestone.

One of the characteristics of the depositional environment ofshallow-water carbonates is the occurrence of emergentshoals and more-permanent islands resulting from changes inrelative sea level from a variety of causes, and meteoricdiagenesis occurs in these small and very small islands. Muchof the hydrology of the process is related to the proximity ofthe site to the sea. For example, the position ofthe water table,the thickness of the freshwater, the flushing rate through thefreshwater zone and the freshwater-saltwater mixing zone areall related to the dynamics of the shoreline because of itseffect on island size (Vacher 1988; Vacher et al. 1990).

We know from informal conversations that many geologistspicture Jamaica and Puerto Rico when they hear the term"island karst". Cockpits and mogotes, respectevely, are notwhat we have in mind. Rather, Jamaica (Day 1976) and Puerto

183


Rico (Monroe 1976) are examples of karst on islands, asopposed to island karst, in that the limestones there are ofappreciable age and diagenetic maturity, and most are isolatedfrom Quaternary sea-level change and freshwater-saltwatermixing.

Island aspects of the evolution of eogenetic karst aresummarized by an integrative conceptual model beingdeveloped by Mylroie and colleagues. The model firstappeared in Mylroie and Carew (1997), where the effects ofautogenic versus allogenic recharge, sea-level change, andfreshwater-saltwater mixing were combined to explain howisland karst differs from the traditional karst of continentalinteriors. Mylroie and Vacher (1999) further explored thedevelopmental history of karst flow paths in the young rocksthat make up Quaternary. carbonate islands. The evolvingmodel was named the "Carbonate Island Karst Model"(CIKM) by Mylroie et al. (1999, 2001) in the context of islandkarst development on Guam, the most complex island to dateto which these ideas have been applied.

The term "eogenetic karst" reminds us of "syngenetic karst",a term used by Jennings (1968) for some rather uniquelandforms and caverns developed in Quaternary eolianiteperched on graniteat Kangaroo Island,Australia. As describedby Jennings (1968), these caves are the result of syngeneticdevelopment of calcrete, incipient cementation of theeolianite, the funneling of water downward through solutionpipes and, then, the development of vadose streams along thecontact between eolianite and underlying granite. Theconduits of the vadose streams enlarge rapidly, facilitated bymechanical erosion of the poorly consolidated eolianite.Jennings considered the subsequent collapse in these conduitsa major component of cave formation in these rocks. Fromour perspective, the syngenetic karst of Jennings (1968) is aspecial case of eogenetic karst - formed in the very younglimestones as a consequence of their mode of deposition (ascoastal dunes, hence immediately in the vadose zone) anddepositional setting (a noncarbonate coastline). Theeogenetic porosity development we discuss in this paper islargely a phreatic phenonmenon.

n-D SPACE

The framework of Figure 1 follows the tradition of usingconceptualized models of the pore space to deducerelationships between physical properties ofa porous medium(see Bear 1972, Sections 4.5.1 and 5.10 for detaileddiscussion). Well-known models include a pore spaceconsisting of parallel capillary tubes and one consisting ofparallel planar cracks. Such models become equivalentporous media when the relevant physical properties (e.g.,frequency, diameter, and tortuosity of tubes for capillary-tubemodels; frequency and aperture width for parallel-fracturemodels) are combined so that discharge (Q) per unit hydraulicgradient (dh/dl) is equivalent to that produced by Darcy's Law(specifically KA, the hydraulic conductivity times cross-

sectional area). Because of the simple geometry of thehypothetical pore space, other physical parameters, such asporosity and surface area, can be easily calculated and, then,related to the hydraulic conductivity. The Kozeny-Carmenequation for intergranular porosity is derived from such amodel for capillary tubes (Bear 1972, Section 5.10.3;Scheidegger 1974, Section 6.3). The cubic-law equation forfracture permeability is derived from such a model for planarcracks (Snow 1968).

Figure I shows the location of various types oflimestones onthe graph of porosity (n), pore size (D), and hydraulicconductivity (K) for the classic equivalent porous mediumconsisting of straight parallel tubes (Fig. 2). In its firstpublication (Smith et al. 1976,Fig. 6.3), the diagram showedthe location of the fields of primary porosity (solid-line ovals)and secondary porosity (dashed-line ovals) together with n. D,and K, and some numerical values ofK determined from fieldstudies. Ford (1980, Fig. 3) added the line labeled "karstfeatures" as "a boundary line to distinguish those conditionsthat appear to favor development of enterable cave systems,intermediate and large surface forms, from those that do not...The principle [the line] indicates [is] that where there iscomparatively high primary porosity, solutional attack iswidely diffused, producing a 'diffuse-flow aquifer' rather thanconduit flow" (Ford 1980,p. 354-355). Dreybodt (1988, Fig.8.4) and Ford and Williams (1989, Fig. 5.5) republished thefigure in their books on karst. Brahana et al. (1988, Fig. 1)

Figure 2. Diagram showing the equivalent porous mediumconsidered in this paper. In order to represent eogenetickarst with such uniform, circular tubes, they must numberon the order ofI rY per em' (see Fig. 3) and occupy some 40%of the block. The tube density shown in this diagram,therefore, is sparser than in the model corresponding toeogenetic karst.

184

VACHERAND MYLROIE

added the small field indicating the location ofcaverns in theirsummary paper on the hydrology of carbonate rocks. (4)

(5)

The main point of the original diagram is the horizontaldisplacement from the solid-line oval fields to the dashed lineoval fields. This displacement illustrates the effect of fissures(joints and bedding plane partings). The effect is substantialnote that n, D, and K are all shown on a log scale. Quoting Fordand Williams (1989, p. 135), "In the case of a massivelimestone with typically very low primary porosity, secondaryenlargement ofthe fissure network can lead to as much as a 106

increase in hydraulic conductivity (Smith et al. 1976)."

where As is the surface area of the particles, and Vb is bulkvolume.

It is useful also to define hydraulic radius (R) as the ratio ofthevolume of pores in a unit volume to the surface area of thepores in the unit volume. Thus:

nR=

M

The focus of our paper is the vicinity of the small field labeled"Recent coral limestone" by Smith et al. (1976), Ford (1980),Dreybodt (1988), and Ford and Williams (1989). Brahana etal. (1988) labeled the field "Holocene coral limestone".

With equation (5), equation (I) becomes

(6)

where rand D are the radius and diameter, respectively, of thecapillaries. Thus for the model of the porous medium as abundle of small capillaries,

It is important to realize that the values ofD for the limestonesin Figure I are interpreted from values of n and K and pertainto the equivalent porous medium (Fig. 2), not the actuallimestone. D, therefore, is a hydraulically equivalent porediameter - specifically, the diameter of the tubes in ahydraulically equivalent bundle of capillaries.

For tubes with a circular cross-section, co=0.5, and

R=r/2=D/4 (7)

With the values of density and viscosity for fresh water at20°C, and g = 981 ern/sec', equation (9) becomes

for K in em/sec and Din ern. ForK in m/day and D in mm (thetradition for Fig. I), the relation is

With ex =1 (for straight tubes), equation II produces thecontours ofK as a function ofporosity and equivalent pore size(tube diameter) shown in Figure I.

(9)

(8)

(11)

(10)

nD2

k=32a 2

Combining equations (2) and (8) produces

npgD2

K=--3211a2

All the authors using a version of Figure I mention theassumptions, but they do not give or cite a derivation of thequantitative relationships underlying the graph. Following is ashort derivation which we include because it leads easily toanother parameter of the equivalent porous medium - thenumber of tubes per unit area - that is useful to conceptualizethe evolution of hydraulic conductivity in eogenetic karst(historically, so-called "Recent coral limestone").

The derivation follows from the Kozeny-Carman equation(Bear 1972; Scheidegger 1974; Halek and Svek 1979), whichrelates porosity and permeability in a porous medium. Oneversion of the equation is (Halek and Svek 1979, eq. 1.3.21)

3

k=~ (1)a 2M 2

where k is permeability, Co is Kozeny's constant, n is porosity,ex is tortuosity, and M is specific surface. Hydraulicconductivity is related to permeability by:

where Il and yare the dynamic viscosity and specific weight(pg), respectively, of the fluid. Tortuosity is defined by

(12)L

a=......!..L

(2)

(3)

Now, consider a transverse cross section perpendicular to thetubes. If N is the number of tubes intersected by the crosssection, and At is the cross-sectional area of anyone of thetubes, and A is the total area of the cross-section (analogous tobulk volume), then the porosity is

NAtn=-

A

where L, is the (traveled) curvilinear distance along a micropathway, and L is the corresponding rectilinear distance.Specific surface is defined by

From equation (12), the tube density (number of tubes per unitarea of cross section perpendicular to the length of the tubes)IS

185


(14)

(13)

Tubes per ern' can be calculated directly from values of nandKin m/day by

N 3,350,OOOn2

K 2'.. Idaya

from Equations II and 13. An order-of-magnitude increase inD at constant n produces an increase in K of two orders ofmagnitude and a decrease in N/A by two orders of magnitude(Fig. 3).

As shown in Figure 3, if any two of the four parameters, n, D,K, or N/A isknown or assumed, the other two can be calculatedin this simple bundle-of-tubes model.

HYDRAULIC CONDUCTIVITY OF EOGENETICKARST

that is familiar in early meteoric diagenesis (Friedman 1964,1975; Gavish and Friedman 1969; Land et al. 1967; Bathurst1975)occur while the porosity averaged over large volumesremains about the same. For example, Halley and Evans(1983) found the that bulk porosity of oolite of the LatePleistocene Miami Limestone (-45%) is like the averagevalue for the" IOOO-year-old oolite" (Halley and Harris 1979)of Joulters Cay, Bahamas, and newly deposited ooid sand(Enos and Sawatsky 1981)(see Scholle and Halley 1985, Fig.1). Porosity values from downhole gravity measurements which average over large bodies of rock - start at about thesame value (-42%) at the surface in south Florida and decreaseexponentially with depth (Schmoker and Halley 1982; Halleyand Schmoker 1983). The conclusion drawn from thesestudies (Scholle and Halley 1985; Halley 1987) is that burialdiagenesis is responsible for the reduction of formation-scaleporosity to values typical of unkarsted ancient limestone. Interms of time-porosity stages (Choquette and Pray 1970),reduction of formation porosity is a mesogenetic, not aneogenetic, phenomenon.

Redistribution of Porosity

Halley and associates (Halley and Beach 1979; Schmoker andHalley 1982; Halley and Evans 1983; Scholle and Halley1985) have established that the lithification and cementation

Preservation of large-scale porosity during the cementationofearly diagenesis means that porosity is largely redistributedduring the process. As noted by Halley and Beach (1979, p.460), "Secondary porosity development during early

100

~

\ ~"$

....I

\ ~II

$I

I

~-0cJ'

x. \,' \,' \....\,'

\ ~II

~"tI

I

\,'

0.01 0.1 1 10EQUIVALENT PORE DIAMETER (MM)

~ n,

\ ,f \ ,f~"t $

II

Kin m/day

NIA in em-2

I I

\\/~ '~ I

-0 ,,» ~oo~ o~"\,' \,' \ "I

II

0.1 ~--'_'--"--~~--'-'-'--'~_'--"--""'-~--"'-'-"-rC---1 4-~+-

0.001

-.....z~ 10a:wQ.-~eno 1a:oQ.

100 -+-___r.....,.-~-or---..,.-........-..r--__r_.........--,.-___r---~-.,..... .....

Figure 3. Relation of tube density (N/A, in tubes per em], dashed lines) and hydraulic conductivity (K, m/day, solid lines)in the equivalent porous medium consisting ofstraight tubes ofdiameter D (Fig. 2), calculated from Equations 14 and II,respectively. Axes as in Figure 1. Oval field is the so-called "Recent Coral Limestone" ofFigure 1.

186

VACHER AND MYLROIE

Progressive Increase in Hydraulic Conductivity

Thus the redistribution of porosity in eogenetic karst found byHalley and Evans (1983) from the difference in porosityvalues between l-inch vs. 4-inch cores of the MiamiLimestone produces an increase in K as the rock develops asecondary porosity and becomes partially cemented. Thecementation reduces the K of the "matrix" between thetouching vugs. For the oolite of Robinson's (1967) study, forexample, K is 10-133 mlday (geometric mean of 14 samples)for the subset of l-inch cores in which the aragonite contentis less than 50%. For comparison, the initial condition(unconsolidated Bahamian ooid sand) is 450 times larger: Ko= 10132 m/day (geometric mean, 21 samples, Enos andSawatsky 1981).

The size, shape, and dynamics ofthe freshwater lenses ofverysmall islands are like aquifer tests in that they provideinformation on the value of large-scale K. This informationinvariably shows that large-scale K of eogenetic karstincreases with age of the rock (Vacher 1997).

In general, one must be careful in inferring K vs. age bycomparing rocks ofdifferent islands, because K can vary withisland climate (Whitaker and Smart 1997 a,b). But there aremany islands where the upper saturated zone occupied by thefreshwater lens is composed of two time-stratigraphic units.In such cases, the time-stratigraphic units are alsohydrostratigraphic units. That is, the units have different Ks.Consistently, the older unit of the two is the more permeable.

The shape of the lens reflects the disparity ofKs in these "K 1K2 islands" (Vacher 1988). For example, if the uppersaturated zone consists of two units of different K lyingalongside each other, the lens is relatively thick in the lesspermeable unit and relatively thin in the more-permeable unit(Fig. 4A). If the upper saturated zone consists of twosuperposed units, with the lower one more permeable than theupper one, the lens tends to be truncated at the contact betweenthe two units (Fig. 4B). Modeling the lenses of these KI-K2islands provides a measure ofKlK

1ratios and, with estimates

of recharge, produces an estimate of the Ks. Following aresome published examples; in each case, the KI unit is theyounger of the two units, and K

2>K!.(A note on notation:

hydrostratigraphic units, KI and K2, are unsubscripted, andtheir hydraulic conductivies, K , and K

2, respectively, are

subscripted. )

At Great Exuma Island, Bahamas, the KI unit is bioclastic sandof a Holocene strandplain (K] '" Ko' the initial value)accumulated in a cuspate reentrant in the Pleistocene bedrockofthe island (K2 unit). A separate lens is developed in each ofthe two units. The lens in the K I sand isjust as thick as the lensin K2limestone, although the sand body covers a much smallerarea. Dupuit-Ghyben Herzberg (DGH) modeling (Fetter1962; Vacher 1988) gives a fit of the sizes with K]=101 andK

2=Wmlday (Wallis et al. 1991).

187

cementation preserves overall porosity". From a study of theHolocene oolites of the Schooner Cays, Bahamas, Budd(1984, p. 283) concluded the following from the reduction ofporosity found in thin section: "These are still very porousrocks! The significance of the porosity changes is therelocation of the porosity. That is, the porosity network isbeing shifted from primary interparticle pores to secondaryoomoldic pores" (see also Budd 1988, Fig. J3).

The significance of the secondary porosity is shown by thestudy by Halley and Evans (1983) on 4-inch cores of oolitesof the Miami Limestone. Half of the porosity values fromtheir 14 samples are in the 40-50% range, the modal class oftheir sample distribution. Halley and Evans (1983) contrastedthese results with the 27 porosity values in a study by Robinson(1967) on Holocene and Pleistocene oolites of the Bahamasand south Florida. The earlier values were "on those sampleswhich were sufficiently consolidated to allow the cutting of3/4 or J in cylindrical plugs" (Robinson 1967, p. 358,emphasis added). Half these values are in the 30-40 percentrange, the modal class of the sample distribution. Accordingto Halley and Evans (1983), their larger values reflect thepresence of vuggy porosity captured in their larger cores.

The presence ofpervasive vuggy porosity in the phreatic zoneis familiar to people who have drilled wells in the younglimestones ofBermuda, Bahamas, and south Florida and hopedto obtain good samples: below the water table, the rock breaksup into small, cemented pieces. As noted in the summaryreport on the surficial aquifer system of south Florida (Fishand Stewart 1991, p. 30), "The marine limestones of [one ofthe units in the Biscayne aquifer] are generally riddled withsecondary solution cavities.... The cavities generally are 2 in.or less across but are so abundant that the limestone resemblesa sponge, making collection of representative samplesdifficult. "

Good photographs of the secondary porosity in the MiamiLimestone of the Biscayne aquifer are in Fish and Stewart(1991, Fig. 10) and Lucia (1995, Fig. J8.1). The latter figurewas included as an example of what Lucia (1995) calledtouching-vug pore systems. "Touching-vug pore systems aredefined as pore space that is (1) significantly larger than theparticle size, and (2) forms an interconnected pore system ofsignificant extent" (Lucia 1995, p. 1290). The interconnectedsystem oftouching-vug pores produces large values ofK. ThusFish and Stewart (1991), who mapped the distribution ofhorizontal hydraulic conductivity in the Miami area by in situfield tests, defined the Biscayne aquifer as the part of thesurficial aquifer system where at least lOft of section consistsof contiguous beds with values of horizontal K of 1000 ftJday(102 5 mlday) or higher. (K-values are cited in exponentialnotation in this paper because they range over several ordersof magnitude, and because K commonly is lognormallydistributed.) K-values in the Biscayne aquifer commonlyexceed 1035 m/day (Fish and Stewart 1991).


A 1 1 1 1 (1 1 1 1 1e01.0 ------- ------~ 0.6 ----...c

-0.

eoN.... O.N

i

0.0i

0.6

x/L

I

1.0

1

bo/zcm=O.5

-------

--------K2/K1=150 ---..=::::::::....

K2

R

1 1 111 1 1 1 1

e()

~ 0.5N

1.0

Be() 1.0.s::c 0.5

--0

6 1~O

Figure 4. Calculated position of the water table and freshwater-saltwater interface for freshwater lenses in infinite-strip,KI-K2 islands using Dupuit-Ghyben-Herzberg analysis (Vacher 1988) for a range ofKjK, values. Abbreviations: h, hem,z, zcm, x, L are elevation ofthe water table in the island, elevation ofthe water table in the same island consisting only ofKl, depth of the interface below sea level, depth of the interface in the same island consisting only ofKl, distance fromthe shoreline, and width of the island, respectively. In A, the Kl and K2 units lie side-by-side, and their vertical contactruns along the midline of the island (Vacher 1988, Fig. 12). In B, the island is horizontally stratified. and the base ofKllies at the halfway depth of the lens that would be present if the island consisted only ofKl (Vacher 1988, Fig. 16).

188

VACHERAND MYLROIE

Using values of nm

= 0.35 (Robinson 1967) and nb

= 0.45(Halley and Evans 1983),Equation] 5 produces n,= 0.15. Thisresult implies that 15% ofthe rock consists oflarge, touchingvug pores lacing through material with an interparticleporosity of 35%.

Although the hydraulics of the double-porosity system ofeogenetic karst have not been studied explicitly, it is possibleto get some insight of its general character from someelementary calculations using data in Halley and Evans (1983)and Robinson (1967) and various simplifying assumptions:

2. Let the hydraulic conductivity of the 85% of the rock withporosity n

mbe K

m• Let the large-scale, horizontal hydraulic

conductivity of the rock as measured in the in situ tests ofFishand Stewart (1991) be K

h, and let the contribution to it of the

touching-vug porosity be K,. Then,

K,=Kh-(l-n,)K", (16)

With '', = 0.15 from (1), Km

= 0.05 rnJday (10-133) from

Robinson (1967), and Kh

= 300 rnJdayas the lower limit fortheBiscayne aquifer (Fish and Stewart 1991), Equation 16produces K, = 299.96 rnJday, or 99.986% of K

h• In other

words, for horizontal flow in the Miami Limestone, only some0.01% of the discharge is conducted through the intergranularpore system, according to these assumptions.

(15)nb -n..n =-"-_:::"

, I-n..

1. Let the interparticle porosity recovered in the l-inch coresof Robinson (1967) be n

m(for matrix porosity in the

terminology of Barenblatt et al. 1960; White 1999;Worthington 1999). Let the bulk porosity of the 4-inch coresofHalley and Evans (1983) be n

b• Assume that the disparity of

these values (nb>nn) is due to touching-vug porosity notcaptured in the cores of Robinson (1967). Call this porositydue to larger pores n, (for tube porosity representing thetouching of vugs of Lucia, 1995, or channels in theterminology of Choquette and Pray 1970; Worthington]999). Then:

pores forming "an interconnected pore system independent ofthe interparticle system" is essentially the languagedescribing a double- (or dual-) porosity system. In doubleporosity systems, two continuous networks of pores areassumed to pervade the entire porous medium. Modeling offlow and solute transport in such media assumes that the twoporosity systems are superposed over the same volume(Gerke and Genuchten 1993). The two pore systems havedistinctly different hydraulic and solute-transport properties.The two pore systems interact by the exchange of water andsolutes in response to gradients in fluid pressure and soluteconcentration.

In northem Big Pine Key, the K1unit overlies the K2 unit. TheK I unit is the upper Pleistocene Miami Oolite, and the K2 unitis reefal limestone (Key Largo) of earlier interglacials (Keyswide, the Key Largo Limestone spans multiple interglacialsand is the upper Pleistocene unit in the Keys north of Big PineKey). The MiamilKey Largo contact on Big Pine Key sharplylimits the downward extension of the lens and marks thebeginning of the transition zone (Vacher et al. 1991). DGHmodeling fits the truncation with K, = 102 and K2=103 andshows that the lens had been thinned 20 percent by thepresence of the more permeable K2 unit at depth (Langvin eta1. 1998).

DOUBLE POROSITY OF EOGENETIC KARST

In Bermuda, the Kl unit consists oflate Pleistocene eolianitecomplexes that lie against middle Pleistocene eolianitecomplexes (K2). In the main part of the island, the freshwaterlens extends from one shoreline (Kl) to the other shoreline(K2). In the K1 unit, the lens is relatively inflated, and in theK2 unit, it is relatively thinned. DGH modeling gives a fit ofthe size and shape with Ki=IOL9 and K

2= 103 1 (Vacher 1978),

and these values are consistent with those calculated from thedampening of the tidal signal from the respective shorelines.

All these KI-K2 islands show order-of-magnitude jumps in Kin crossing major time-stratigraphic boundaries: betweenHolocene and Pleistocene units (Exuma and Pacific atolls)and between late and middle Pleistocene units (Bermuda, BigPine Key). Collectively, they show that large-scale Kincreases by orders of magnitude during meteoric diagenesis.By implication, the vugs and channels that form duringeogenetic diagenesis become larger and more interconnected.

The premier case of KI-K2 layering lies outside Bermuda,Bahamas and the Keys and is well known to carbonate-islandhydrogeologists as the "dual-aquifer model" (Buddemeier andHalladay (977). This is the model that applies to atoll islands;

the K1 unit is the Holocene island sands (K1 '" Ko)' and the K2unit is the underlying Pleistocene limestone. The chieffeatures are that freshwater lenses (if present) are truncated bythe K2 unit, the tidal signal passes largely undampened throughthe K2 unit, and the tidal fluctuation measured in boreholesincreases with depth through the K1 unit. K/K; is typically 10to 100, with K

1at 100 to JOl rnJday and K

2at 102 to 103 rnJday

(Vacher 1997). The widespread applicability of the dualaquifer model is illustrated by recent summaries of Enewetak(Buddemeier and Oberdorfer 1997), other Micronesian atolls(Peterson 1997; Anthony 1997), Tarawa (Falkland andWoodroffe 1997), and Diego Garcia (Hunt 1997). Big PineKey is an older-rock variant on the classical dual-aquifermodel of atoll islands.

Hydraulic Features

The characterization by Lucia (1995, p. 1275)oftouching-vug

3. Assume that the touching-vug pore system that results insuch large values of horizontal K consists of straight,

189


With Km

= 0.5 m/day and n, = 0.15, Equation 18 produces K"= 0.06 m/day for this simplified model of the porositystructure.

where K" is the vertical hydraulic conductivity, K,I' is thehydraulic conductivity for flow across the horizontal tube, andK

m.v

is the hydraulic conductivitiy for vertical flow in the

matrix. Because K",= 00 (no resistance) and Km l, = Km

(matrixassumed to be isotropic), Equation (17) reduces to

horizontal tubes. Assume that the tubes are lined up in such away that one tube overlies another, and that vertically flowingground water (if present), would pass across open tubes andbetween the tubes in travel-distance segments proportional ton, and I-n" respectively. Then, the equivalent hydraulicconductivity for travel sequentially across several tubes andbits of inter-tube matrix would be the harmonic mean of thetwo hydraulic conductivities weighted by n and I-n,:

4. The anisotrophy ratio, K/Kv

' implied by (3) is 5000. This isa large value given that the material starts out as a mass ofooliteand thus is reasonably isotropic (KIKI' = 1). For comparison,Segol and Pinder (1976), who modeled the position of thefreshwater/saltwater interface in the Biscayne aquifer nearMiami, settled on values ofK

h= 390 m/day and K, = 0.8 m/day

to calibrate the observed distribution of chloride concentration. Using their Ks, the anisotropy ratio is 500, which isanother large value.

Comparison to Other Double-Porosity Systems

Eogenetic karst is more like the double porosity resultingfrom the myriad, small-scale heterogeneities in agriculturalsoils (Gerke and Genuchten 1993; Ray et al. 1997; Jarvis1998) than like the double-porosity systems of sandstonereservoirs and conventional telogenetic karst. According toGerke and Genuchten (1993, Fig. 1), a macroprous soilconsists of porous soil aggregates within an irregular networkof pinching-and-swelling macropores among which fluid andsolutes move in a variety of ways: through the macropores;within the aggregates; between aggregates and macropores;between aggregates where they touch; and between continuousand stagnant pore space. Double-porosity models of this

In contrast, the double porosity of eogenetic karst consists ofmany small stringers, channels, tubes, and diverse irregularpassageways within a sea of interparticle porosity. Theinterparticle porosity provides the storage. The smallpreferred passageways conduct the fluids. Fractures andcaves, although locally present, are not a large part of the story(see next section).

The term "double porosity" was coined by Barenblatt et al.(1960) in a paper quantifying flow behavior in a block-andfracture reservoir. The term originated in the context that min their scheme, was the porosity attributable to fractures, andm

2was the interparticle porosity of the blocks. The fractures

dominate the flow. The porous blocks (the matrix porosity)dominate the storage. Hamm and Bidaux (1996) havedeveloped a fractal model to treat flow to a well in such asystem. Moench (1984) added the concept of a fracture skin,a thin skin oflow-permeability material deposited on the sidesofthe fracture that impedes fluid exchange between blocks andfractures. This type of double porosity is probably moreapplicable to sandstone reservoirs than to most carbonates(Fig. 5).

A double porosity consisting of conduits among fractures isimplied in discussions of the early development of karst(Dreybodt 1988; Groves and Howard 1994; Howard andGroves 1995; Dreybodt 1996; Siemers and Dreybodt 1998).The typical discussion of karst through time "begins with amass of fractured carbonate rock and then focuses on theevolution from a fracture aquifer to a fully developed conduitaquifer" (White 1999, p. II). A network of interconnectedsmall fissures along joints and bedding-plane partings servesas an initial condition of pore-space evolution. CO,containing ground water widens certain favorable fissure~and, because of the inherent positive feedback in the system:conduits develop along favorable pathways. The boundarybetween large fractures and small conduits is based on thepresence ofturbulent flow and has been placed at about 10mm(Palmer 1991; White 1999). The conceptualization of thepore space in these models is that labeled "telogenetic karst"in Figure 5. By this view, fractures would seem to provide thestorage in the limestone, and the conduits convey the fluids.

(18)

(17)K =---v n, 1-n,

-+-K Kt» 1111 "

K = Km

v 1-n,

In summary, a simplified conceptual model for the doubleporosity of eogenetic karst is as follows. A system ofsecondary touching-vug pores forms horizontal preferredpassageways through a limestone with somewhat reducedprimary porosity. The preferred passageways make up some10-20% of the rock and a third or so of the pore space. Due~o the horizontal alignment of the preferred passageways, K

h

Increases by orders of magnitude. Meanwhile K decreaseswith the cementation of the matrix. The rock:' therefore,becomes highly anisotropic.

Although some touching-vug pore channels in the MiamiLimestone are pencil-sized and larger (Fish and Stewart 1991,Fig. 10; Lucia 1995, Fig. 18J), they need not be this large tocreate high values of K typical of eogenetic karst. Forexample, with n=O.15 and ex =1, Equations 11 and 14 andK=300 m/day imply a tube diameter ofonly some 0.3 mm anda tube density of some 250 tubes per em- cross section. Fora more extreme case, n=O.15, ex =2, and K=105 m/day (notunheard of in the Biscayne aquifer), the equations produceD=I em, N/A=0.19 ern? (one tube cross section in a square 2.3ern on aside).

190

VACHERANDMYLROIE

Hydraulic "tubes"(channel porosity and/or conduits)

Matrix(interparticle porosity)

Figure 5. Concept triangle showing varieties of double-porosity systems. The triangle is intended to show conceptualmixtures. It is not intended to position mixtures quantitatively as in the scaled compositional triangles of sedimentarypetrology, for example. Whether cast in terms ofporosity or hydraulic conductivity, the order-of-magnitude disparity inthe percentages of the different types of porosity in the mixtures makes plotting on a scaled triangle impracticable.

EOGENETIC CAVES

importance ofmatrix permeability." Thus it is noteworthy thatHalihan et al. (2000) found that matrix permeability in theEdwards aquifer near San Antonio, Texas is 10·30±L5 m/day (±1o , lognormal) in a "fractured karst aquifer" where well yieldsare dominated by flow in fractures and some wells dischargeblind catfish (indicating conduits). According to the study byWorthington et al. (2000), the Km of the karst in centralKentucky near Mammoth Cave is 10-5 8 m/day and accounts forless than \0-7 of the permeability. Worthington et al. (2000),however, also calculated that the matrix porosity (2.4%) in thespring catchment they studied provides more than 95% of thestorage, whereas fracture and channel (conduit) porosityprovides only 0.2-2.0% and 2.4%, respectively.

In addition to the touching-vug, preferred passageways thataccount for the increase ofregional K vs. time, there are largerdissolution features, including some impressive caves, inlimestones experiencing eogenetic diagenesis (Mylroie andCarew 1995;Mylroie et al. 2001). There appear to be at leastsix different kinds. At least the first four of them tend to beassociated, one way or another, with boundaries or contacts.

I. Secondary porosity of leached intervals associated withsubaerial erosion surfaces (epikarsts). The action of meteoricwater with the subaerial land surface results in a system ofdisarticulated blocks, small tubes and crevices, and etchedoutcrop surfaces, commonly mantled in a residual soil. Thishighly porous and permeable layer is called the epikarst (Fordand Williams 1989) and represents a site of significant waterstorage. If meteoric water becomes concentrated as a resultof high recharge events, vadose fast flow routes called pitcaves may develop (Mylroie and Carew 1995). These large

191

challenging type of porous medium have made progress intreating preferential flow and solute transport resulting fromthe surface application of agricultural chemicals such aspesticides (Jarvis 1994; Jarvis et a1. 1994; Larsson and Jarvis1999). Adapting these models for lateral flow in a fullysaturated medium may prove equally valuable in modelingsite-specific details of transport in eogenetic karst.

The concept of triple-porosity systems is becomingprominent in the karst literature (White 1999; Worthington1999; Worthington et al. 2000; Halihan et al. 1999,2000) andpromises to clarify the picture of flow, storage, and reactivetransport in karst aquifers. Worthington (1999) distinguishedbetween (I) one-dimensional linear elements ("channels",following Choquette and Pray 1970), (2) two-dimensionalfractures including bedding planes, joints, and faults, and (3)the three-dimensional matrix. In his scheme, channels includeconduits, where flow is commonly turbulent, and caves if theyare accessible by people. As described by White (1999), thethree types ofporosity are matrix, fractures and conduits. Thematrix permeability is measurable at the laboratory scale.Fracture permeability integrates over hundreds of meters.Conduits act like storm drains and operate on the scale ofentire drainage basins of km2 and tens of km'. According toWhite (1999, p. 13), "The matrix permeability of manyPaleozoic limestones and dolomites is very low and can oftenbe ignored. Young limestones such as those ofFlorida and theCaribbean islands may have very high matrix penneabilities".Accordingly, we have put the labels for "eogenetic karst" and"telogenetic karst" on two opposite sides of the concepttriangle on Figure 5.

White (1999, p. 13)continued: "There is indeed a continuum,and actual measurements are needed to determine the


shafts may be tens ofmeters deep and allow rapid movementof vadose water to depth in the carbonate land mass.

2. Secondary porosity of leached intervals associated withactive and fossil water tables. The top ofthe water table, wherevadose and phreatic waters mix, is a zone of porositydevelopment. Dissolution may form isolated voids withdiameters to tens of meters as well as dissolutional porosityat the vug scale. In islands with low relief such as the low (asopposed to the eolianite) islands ofthe Bahamas the epikarstand water-table porosity can be physcially close to each other.In some cases water-table caves in the young rocks presentlyexposed in the Bahamas have collapsed and can be entered.These features are called banana holes (Mylroie and Carew1995). In the subsurface, the leached intervals are several tensof meters thick and are "characterized by vugs, channels, andsmall caverns" (Beach 1995, p. 16).

3. Flank margin caves (Mylroie et al. 1995), which form at theperiphery of the islands. At this location, there is bothfreshwater-saltwater mixing at the interface and mixing ofwaters of different PC02 at the water table. These caves formhuge voids (104 m' in the Bahamas). Typically they are ratherequidimensional in plan (up to 70 m across) and limited inheight (5-6 m). They line up alongside each other parallel tothe coast. They can form quickly; for example, 104 m' flankmargin caves formed in the Bahamas at elevations of -1 to +5m in the -10 ky-period of time that sea level was at that levelduring Oxygen Isotope Substage 5e (-130 to -120 ka).

4. Vadose "stream caves" along the contact separating thelimestones from underlying less-permeable rocks. As notedin our discussion of sygenetic karst, modem examples occurin Kangaroo Island (Jennings 1968). At some places the zoneof stream caves passes down dip into a freshwater phreaticwedge (e.g., Barbados, see Humphrey 1997; Guam, see Minkand Vacher 1997). Recent work in Guam shows that the streamcaves, upon reaching the top of the freshwater lens, lead tobroad, phreatic chambers, which, with changes in sea level,may produce stacked chambers and thick collapse breccias(Mylroie et al. 2001). The Walsingham caves of Bermuda area variant (Mylroie et al. 1995): the modem caves are collapsefeatures formed as the voids created at the contact with therealtively shallow volcanic rocks of the Walsingham districthave stoped their way toward the land surface.

5. Extensive cavern systems associated with bank-marginfractures as along the edge of the Bahamian platforms. In anexample described by Whitaker and Smart (l997c), waterfilled voids on the edge of Andros Island are 2-5 m wide andmore than 80 m deep along fracture systems marked on thesurface by a chain of blue holes. At depth, and because offreshwater-saltwater mixing and bacterial oxidation oforganic matter, the fracture-guided caverns may open outhorizontally to 200 m on either side of the vertical fracture.The steepness of the Bahama platform margins promotesbank-margin failure, but once the cracks are formed, they

directly affect the lens flow systems in a manner that createsa positive feedback system for further enlargement.

6. Linear cave systems that may be phreatic conduits exploredby cave divers at 15-20 m depths in the interior of GreatBahama Bank (e.g., Conch Blue Hole on Andros I.,Palmer andWilliams 1984), Little Bahama Bank (e.g., Lucayan Cavernson Grand Bahama I., Palmer and Williams 1984) and theBermuda Platform (e.g., Green Cave, Illife 1987).

With the exception of the last category, none of these featurescan be construed to fit the model of connected conduitsystems that one associated with groundwater flow in thetelogenetic karst of continental settings. The systems alongbank-margin fractures, for example, run more or less alongisland margins, normal to the flow from the island interiors.The flank margin caves, however huge and phreatic, are notconduits, but rather mixing chambers.

The conduit-like systems of the sixth category are clearlyrelict features, unrelated to the present groundwater system.When these caves were occupied by fresh water, sea levelnecessarily was low enough that the large platforms werewholly emergent; the sites were no longer very small islands.We suspect that there may be a critical areal dimension abovewhich discharge (Q) due to autogenic recharge is large enoughand shorelines are distant enough from the interior thatconduits successfully out-compete the diffuse flow throughthe interconnected voids and channels typical of small-islandeogenetic karst.

These larger solution features, it should be noted, are not likelyto contribute much to the KI-to-K2 disparities so typical ofthe shallowest part of the saturated zone, where the disparity isbetween Holocene and late Pleistocene or late and middlePleistocene units. The occurrence of KI-to-K2 contrasts inlaterallyjuxtaposed units (Great Exurna, Bermuda) argues thatthe disparity involves pervasive, hydraulically connectedsecondary pores forming a system extending across the entirefreshwater lens. The contact- and boundary-related cavefeatures noted in this section are more local.

With depth, however, the larger pores are likely moreimportant contributors to the regional-scale permeability for a couple of reasons. First, there is the effect of repeatedexposures of the deeper rocks due to the greater number ofsea-level oscillations and, therefore, there is a potentiallylarger number of leached intervals from fossil water tables.Second, there is the effect of larger island-size during lowersea levels and, therefore, the possibility of reaching thethreshold where conduits may be more competitive. In theBahamas, the freshwater lenses are truncated at the base of thePleistocene unit (K1) in islands that are large enough andrecharged enough that the lenses extend down to prePleistocene limestones (K2) (Cant and Weech 1986).Although the lenses have not been modeled with KI-K2layering, there is abundant evidence of high regional-scale K

192

VACHER AND MYLROIE

,.- ';V

,- ,c 10 ,Q) , .'

~• r"t"::J\

Q) •. ' . (j'f..0-~ 'f.\e\~

~i.e\O~e; .•

ii5 /'" . '0 . a"o....

1 .. \00\>\\\\ !,,\(\90-

~ . ~'~!"ac\U .: ~. (j.\ "-. . II

" $

0.1

0.001 0.01 0.1 1 10 100

Equivalent Pore Diameter (mm)

Figure 6. Paths of the evolution of limestone hydraulic conductivity in the n-D space of the equivalent porous mediumconsisting of straight tubes of diameter D.

in the pre-Pleistocene rocks (Kl) (Beach 1995; Whitaker andSmart 1997a). Beach (1995) and Whitaker and Smart (1997a)also found a downsection increase of K in the K I unit. Thesevariations ofK with age (depth) could well reflect a differentcause than the ones we discuss for the uppermost part of thesaturated zone of very small islands.

CONCLUDING REMARKS: EVOLUTION OFHYDRAULIC CONDUCTIVITY IN n-D SPACE

Judging from hydrogeologic studies of Holocene sands inExuma and atoll islands, newly exposed grainstonesstart witha K on the order of 101 m/day, which, with n=O.4, places thesand in n-D space at the "initial condition" shown in Figure 6.The equivalent, bundle-of-tubes medium for such a sandconsists of some 50,000 tubes with a diameter of 0.03 mm.The groundwater in these environments is propelled by alargely horizontal gradient. The groundwater finds inevitablepermeability heterogeneities - e.g., small grain-sizevariations due to bedding, cross-bedding, and burrowing;cementation variations developed on exposure surfaces; vugsfrom dissolved aragonitic fossils and fragments that happen tooccur next to each other - and flow concentrates there. Withsolution focussed at these sites, the rock develops stringersand channels of touching vugs, and horizontal hydraulicconductivity of the rock increases by orders of magnitude.Meanwhile, the rock between the channels becomescemented and its porosity and permeability diminishes.Overall, the bulk porosity of the rock remains of the same

order, and so, the equivalent porous medium ofthe developingeogenetic karst tracks horizontally in n-D space (Fig. 6). AtK=102 m/day typical of the Late Pleistocene of Bermuda, theequivalent porous medium consists of some 5,000 tubes withdiameter of 0.1 mm. At K=103 m/day typical of the MiddlePleistocene of Bermuda and "tighter" parts of the Biscayneaquifer of south Florida, the equivalent porous mediumcontains fewer tubes (500) with still larger diameters (0.3mm).

The horizontal track of eogenetic karst in n-D space is vastlydifferent than the route to conventional telogenetic karst (1)burial with loss of porosity (Scholle and Halley 1985); (2)uplift and opening of fractures (Saskowski and White 1994);and (3) formation ofconduits along favorable sites in fractures(Dreybodt 1988). The classic diagram of n-D spaceoriginated by Smith et al. (1976) makes this conceptualdifference clear.

Eogenetic karst is widespread along the shorelines ofcarbonate depositional areas today. It may be overrepresentedbecause we are sampling a time of glacioeustatic fluctuationsand aragonitic seas. In the absence of subaerial exposure,eogenetic karst does not develop and so, although alllimestones pass through eogenetic diagenesis (Choquette andPray 1970), not all limestones have been affected byeogenetic karst.

193


ACKNOWLEDGMENTS

With two authors and a summary paper giving a perspectivefrom many years ofstudy in places with eogenetic karst, spacedoes not allow acknowledgment of all the people who havebenefited us with constructive discussions and argument aboutthe subject. Nevertheless HLV wants particularly to thank BobHaIley, Phil Choquette, and Mark Sewart. JEM thanks JimCarew and John Jenson. We both thank David Budd, FionaWhitaker, and Pete Smart.

We gratefuIIy acknowledge Gerry Friedman for years ofencouragement ofall ofus who have worked on the carbonategeology of young limestone islands. Likewise, we have bothbenefited from years of encouragement from Art Palmer,whom we thank for an especially helpful review of this paper.

REFERENCES

ANTHONY, S.S., 1997, Hydrogeology of selected islands of theFederated States of Micronesia, in Vacher, H.L. and Quinn,T.M., eds., Geology and Hydrogeology of Carbonate Islands.Elsevier, Amsterdam, p. 693-706.

BARENBLATT, G.I., ZHELTOV, LP., and KOCHINA, LN., 1960,Basic concepts in the theory ofseepage ofhomogeneous liquidsin fissured rocks: Journal of Applied Mathematics andMechanics,v.24,no.5,p.1286-1303.

BATHHURST, R.G.e., 1975, Carbonate sediments and theirdiagenesis. Elsevier, Amsterdam, 658 p.

BEACH, D.K., 1995, Controls and effects of subaerial exposure oncementation and development of secondary porosity in thesubsurface ofGreat Bahama Bank, in Budd, D.A, Saller, A.H.,and Harris, P.M., eds., Unconformities in carbonate strata - theirrecognition and the significanceofassociated porosity. AmericanAssociation ofPetroleum Geologists Memoir63, p. 1-33.

BEAR, L, 1972, Dynamics of fluids in porous media. Elsevier, NewYork, 764p.

BONACCI, 0.,1987, Karst hydrology. Springer-Verlag, New York,184p.

BRAHANA, r.v., THRAILKILL, J., FREEMAN, T., and WARD,W.e., !988, Carbonate rocks, in Back, W., Rosenshein, J.s., andSeaber, P.R., eds., Hydrogeology. Geological Society ofAmerica, The Geology ofNorth America, Boulder, Colorado, v.0-2, p. 333-352.

BUDD, D.A., 1984, Freshwater diagenesis of Holocene ooid sands,Schooner Cays, Bahamas (PhD dissertation). The University ofTexas at Austin, TX,491 p.

BUDD, D.A., 1988, Peterographic products offreshwater diagenesisin Holocene ooid sands, Schooner Cays, Bahamas: Carbonatesand Evaporites, v. 3, p. 143-163.

BUDDEMEIER,R.W.and HOLLADAY,G.L., I977, Atoll hydrology:Island groundwater characteristics and their relationship todiagenesis: Proceedings of the Third Coral ReefSymposium(Miami),v. 2, p. 167-174.

BUDDEMEIR, R.W. and OBERDORFER, lA, 1997, Hydrogeologyof Enewetak Atoll, in Vacher, H.L. and Quinn, T.M., eds.,Geology and Hydrology of Carbonate Islands. Elsevier,Amsterdam, p. 667-692.

CANT,R.V. and WEECH, P.S., 1986, A review ofthe factors affectingthe development ofGhyben-Hertzberg lenses in the Bahamas:Journal ofHydrogeology, v. 84, p. 333-343.

CHOQUETTE, P.W. and PRAY, i.c, 1970, Geologic nomenclatureand classification of porosity in sedimentary carbonates:American Association ofPetroleum Geologists Bulletin, v. 54,p.207-250.

DAY, M., 1976,The morphologyand hydrology ofsome Jamaican karstdepressions: Earth Surface Processes and Landforms, v. I, p.111-129.

DREYBODT, W., 1988, Processes in karst systems: physics,chernsitry, and geology. Springer-Verlag, New York, 288 p.

DREYBODT, W., 1996, Principles of early development of karstconduits under natural and man-made conditions revealed bymathematical analysis of numerical models: Water ResourcesResearch, v. 32, p. 2923-2935.

ENOS, P. and SAWATSKY, L.H., 1981, Pore networks in Holocenecarbonate sediments: Journal 0.(Sedimentary Petrology, v. 51,p.961-985.

FALKLAND, x.c and WOODROFFE, c.n, 1997, Geology andhydrogeology of Tarawa and Christmas Island, Kiribati, inVacher, H.L. and Quinn, T.M., eds., Geology and hydrogeologyofcarbonate islands. Elsevier, Amsterdam, p. 577-610.

FETTER, e.W., 1972, Position of the saline water interface beneathoceanic islands: WaterResourcesResearch. v.8,p.1307-1315.

FISH, J. and STEWART, M.T., 1991, Hydrogeology of the surficialaquifer system, Dade County Florida. U.S. Geological SurveyWater-Resources Investigations Report 90-41 08,50 p.

FORD, D.e., 1980,Thresholds and limiteffects inkarst geomorphology,in Coates, D.R. and Vitek, J.D., eds., Thresholds ingeomorphology. Allen and Unwin, Boston, p. 345-362.

FORD, D.e. and WILLIAMS, P.W., 1989, Karst geomorphology andhydrology. Unwin and Hyman, London, 601 p.

FRIEDMAN,G.M., 1964,Early diagenesis and lithification incarbonatesediments: Journal ofSedimentary Petrology, v. 34, p. 777813.

FRIEDMAN, G.M., 1975, The making and unmaking oflimestones orthe ups and downs of porosity: Journal of SedimentaryPetrology, v. 45, p. 379-398.

GAVISH, E. and FRIEDMAN,G.M., 1969, Progressive diagenesis inQuaternary to late Tertiary carbonate sediments: Sequence andtime scale: Journal ofSedimentary Petrology, v. 39, p. 9801006.

GERKE, H.H. and GENUCHTEN, M.T., 1993, a dual-porosity modelfor simulating the preferential movement ofwater and solutes instructured porous media: Water Resources Research, v. 29, p.305-319.

GROVES, e.G. and HOWARD, A.D., 1994, Early development ofkarst systems, I. Preferential flow path enlargement underlaminar flow: Water Resources Research, v. 30, p. 2837-2846.

HALEK, V. and SVEK, J., 1979, Groundwater hydraulics. Elsevier,Amsterdam, 620 p.

HALLEY, R.B., 1987, Burial diagenesis ofcarbonate rocks: ColoradoSchool ofMines Quarterly, v. 82, p. 1-15.

HALLEY, R.B. and EVANS, c.c, 1983, The Miami Limestones: Aguide to selected outcrops and their interpretation. MiamiGeological Survey, 67 p.

HALLEY, R.B. and BEACH, D.K., 1979, Porosity preservation andearly freshwater diagenesis of marine carbonate sands(abstract): American Association of Petroleum GeologistsBulletin,v.63,p.460.

HALLEY, R.B. and HARRIS, P.M., 1979, Fresh-watercementation ofa I,OOO-year-old oolite: Journal ofSedimentary Petrology, v.49,p.969-988.

HALLEY, R.B. and SCHMOKER, lW., 1983, High-porosityCenozoic carbonate rocks ofsouth Florida: Progressive loss of

194

VACHERANDMYLROIE

porosity with depth: American Association of PetroleumGeologists Bulletin, v. 67, p. 191-200.

HALIHAN, T., SHARP, 1.M, JR, and MACE, R.E., 1999, Interpretingflow using permeability at multiple scales, in Palmer, A.N.,Palmer, M.V., and Sasowsky, I.D., eds., Karst modeling. KarstWaters Institute Special Publication, Charles Town, WestVirginia, no. 5, p. 82-96.

HALIHAN, T., SHARP,J.M., JR, and MACE, R.E., 2000, Flow in theSan Antonio segment ofthe Edwards aquifer: matrix, fractures,or conduits? In Sasowsky, I.D. and Wicks, CM, eds.,Groundwater flow and contaminant transport in carbonateaquifers. Balkema, Rotterdam, p. 129-146.

HAMM,S.-Y.andBIDAUX,P.,1996,DuaI-porosityfractalmodeisfortransient flow analysis in fissured rocks: Water ResourcesResearch, v. 32, p. 2733-2745.

HUMPHREY,1.D., 1997, Geology and hydrogeology ofBarbados, inVacher, H.L. and Quinn, T.M., eds., Geology and hydrology ofcarbonate islands. Elsevier, Amsterdam, p. 381-406.

HUNT, C.D., 1997, Hydrogeology ofDiego Garcia, in Vacher, H.L.and Quinn, T.M., eds., Geology and hydrogeology ofcarbonateislands. Elsevier, Amsterdam, p. 909-931.

ILIFEE, T.M., 1987, Observations on the biology and geology ofanchialine caves, in Curran, H.A., ed., Proceedings, ThirdSymposium on the geology of the Bahamas: Ft. Lauderdale,Florida, CCFL Bahamian Field Station, p. 73-80.

JAMES, N.P. and CHOQUETTE, P.W., 1984, Diagenesis 9.Limestones - the meteoric environment: Geoscience Canada,v. II,p. 161-194.

JARVIS, N.J., 1994, Modeling the impact ofpreferential flow on nonpoint source pollution, in Selig, H.M. and Ma, L., eds., Physicalnonequalibrium insoils: modeling and application. Chelsea Press,Ann Arbor, Michigan, p. 195-216.

JARVIS, N.J., STAHLI, M., BERGSTROM, L.F., and JOHNSON,H., 1994,Simulation ofdichlorprop and bentazon leaching insoilsof contrasting texture using the MACRO model: Journal ofEnvironmental Science and Health, v. A29, p. 1255-1277.

JENNINGS,J.N., 1968, Syngenetic karst in Australia: Contributions tothe study ofkarst, Department ofGeography Publication no. G/5, Australian National University, p.4I-IIO.

LAND, L.S., MACKENZIE, F.T., and GOULD, S.J., 1967,Pleistocene history ofBermuda: Geological Society ofAmen'caBulletin, v. 78, p. 993-1006.

LANGEVIN, c.n, STEWART, M.T., and BEAUDOIN, e.M., 1998,Effects of sea water canals on fresh water resources: Anexample from Big Pine Key, Florida: Ground Water, v. 36, p.503-513.

LARSON,M.H.andJARVIS,N.J.,1999,Evaluationofadual-porositymodel to predict field-scale solute transport ina macroporous soil:Journal ofHydrology, v. 215, p. 153-171.

LUCIA, F.J., 1995, Rock-fabric/petrophysical classification ofcarbonate pore space for reservoir characterization: AmericanAssociation ofPetroleum Geologists Bulletin, v. 79, p. 12751300.

MINK, J.F. and VACHER, H.L., 1997, Hydrogeology ofnonhernGuam, in Vacher, H.L. and Quinn, T.M., eds., Geology andHydrology ofcarbonate islands. Elsevier, Amsterdam, p. 743761.

MOENCH, A.F., 1984, Double-porosity models for a fissuredgroundwater reservoir with fracture skin: Water ResourcesResearch, v. 20, p. 831-846.

MONROE, W.H., 1976, The karst landforms of Puerto Rico. U.S.Geological Survey Professional Paper 899.

MYLROIE, 1.E. and CAREW, 1.L., 1997, Land use and carbonate

island karst, in Beck, B.F. and Stephenson, 1.B., eds., Theengineering geology and hydrogeology ofkarst terranes. A.A.Balkema, Brookfield, p. 3-12.

MYLROIE, 1.E. and VACHER, H.L., 1999, A conceptual view ofcarbonate island karst, in Palmer, A.N., Palmer, M.V., andSasowsky, I.D., eds., Karst modeling. Karst Waters InstituteSpecial Publication, Charles Town, West Virginia, v. 5,p. 48-57.

MYLROIE, r.t., CAREW, i.t., and VACHER, H.L., 1995, Karstdevelopment in the Bahamas and Bermuda, in Curran, H.A. andWhite, B., eds., Terrestrial and shallow marine geology of theBahamas and Bermuda. Geological Society ofAmerica SpecialPaper, Boulder, Colorado, v. 300, p. 251-267.

MYLROIE, lE., JENSON, 1.W., JOCSON, J.M.U., and LANDER,MA, 1999,Karst geology and hydrology ofGuam: A preliminaryreport. Water and Environmental Research Institute of theWestern Pacific, University ofGuam, Technical Reportno.99,32p.

MYLROIE, J.E., JENSON,J.W., TABOROSI, D., JOCSON,J.M.U.,VANN,D.T.,andWEXEL, C.,2001, Karst features ofGuam interms of a general model of carbonate island karst: Journal ofCave and Karst Studies, v. 63, p. 9-22.

PALMER, A.N., 1991, Origin and morphology of limestone caves:Geological Society ofAmerica Bulletin, v. 103, p. 1-21.

PALMER, R. and WILLIAMS, D.W., 1984, Cave development underAndros Island, Bahamas: Cave Science, v. 13, p. 79-82.

PETERSON, F.L., 1997, Hydrogeology of the Marshall Islands, inVacher, H.L and Quinn, T.M., eds., Geology and hydrogeologyofcarbonate islands. Elsevier, Amsterdam, p. 611-636.

RAY, C., ELLSWORTH, T.R., VALOCCHI, AJ., and BOAST,e.W., 1997, An improved dual porosity model for chemicaltransport in macroporous soils: Journal cfHydrology, v. 193, p.270-292.

ROBINSON, R.B., 1967, Diagenesis and porosity development inRecent and Pleistocene oolites from southern Florida and theBahamas: Journal ofSedimentary Petrology, v. 37, p. 355-364.

SASOWSKY, LD. and WHITE, W.B., 1994, The role ofstress releasefracturing in the developmentofcavernous porosity in carbonateaquifers: Water Resources Research, v. 30, p. 3523-3530.

SCHEIDEGGER, A.E., 1974, The physics of flow through porousmedia, 3med. University ofToronto Press, 353 p.

SCHMOKER, 1.W. and HALLEY, R.B., 1982, Carbonate porosityversus depth: a predictable relation for south Florida: AmericanAssociation ofPetroleum Geologists Bulletin, v. 66, p. 25612570.

SCHOLLE, PA and HALLEY, R.B., 1985, Burial diagenesis: out ofsight, out ofmind! InSchneidermann, N. and Harris, P.M., OOs.,Carbonate cements. Society of Economic Paleontologists andMineralogists, Special Publication, no. 36, p. 309-334.

SEGOL, G. and PINDER, G.F., 1976,Transient simulation ofsaltwaterintrusion in southeastern Florida: Water Resources Research, v.12, p. 65-70.

SIEMERS, land DREYBODT, W., 1998, Early developmentofkarstaquifers on percolation networks offractures in limestone: WaterResources Research, v. 34, p. 409-419.

SMITH, D.1., ATKINSON, r.c, and DREW, D.P., 1976, Thehydrology oflimestone terrains, in Ford, T.D. and Cullingford,e.H.D., eds., The science ofspeleology. Academic Press, NewYork,p.179-212.

SNOW, D.T., 1968, Rock fracture spacings, openings, and porosities:Journal Soil Mechanics Foundation Division, ProceedingsAmerican Society ofCivil Engineers, v. 94, p. 73-91.

TELL, L., 1976, 50 typical Swedish caves: Archives of SwedishSpeleology, v. 14, 41 p.

195


VACHER,H.L., 1978,HydrogeologyofBennuda - Significanceofanacross-the-island variation in permeability: Journal 0/Hydrology, v. 39, p. 580-591.

VACHER, H.L., 1988, Dupuit-Ghyben-Herzberg analysis of stripislandlenses:Geological Society 0/America Bulletin, v. 100,p.223-232.

VACHER,H.L., 1997,Introduction:varietiesofcarbonateislandsanda historicalperspective, in Vacher, H.L. and Quinn, T.M., eds.,Geology and hydrogeology of carbonate islands. Elsevier,Amsterdam,p. 1-33.

VACHER, H.L., BENGTSSON, T.O., and PLUMMER, L.N., 1990,Hydrologyof meteoric diagenesis: residence time of meteoricground water in island fresh-water lenses with application toaragonite-calcite stabilization rate in Bermuda: GeologicalSociety 0/America Bulletin, v. 102,p. 223-232.

VACHER, H.L., WIGHTMAN, MJ., and STEWART, M.T., 1992,Hydrology of meteoric diagenesis: effect of Pleistocenestratigraphyon freshwater lenses of Big Pine Key, Florida, inFletcher,C.H., 1lIand Wehmiller, J.F., eds., Quaternary coastsof the United States: marine and lacustrinesystems. Society ofEconomic Paleontologists and Mineralogists Special Publications,v.48, p. 213-219.

WALLIS, T.N., VACHER, H.L., and STEWART, M.T., 1991,Hydrogeology of the freshwater lens beneath a Holocenestrandplain,Great Exuma, Bahamas:Journal ofHydrology, v.125,p.93-100.

WALTHAM,A.c., 1974,LimestoneandcavesofNorthwest England.David and Charles,Newton Abbot,Great Britian,477 p.

WHITAKER, F.F. and SMART, P.L., 1997a, Hydrogeology of theBahamian archipelago, in Vacher, H.L. and Quinn, T.M., eds.,Geology and hydrogeology of carbonate islands. Elsevier,Amsterdam,p.183-216.

WHITAKER, F.F. and SMART, P.L., I997b, Climatic control ofhydraulicconductivityofBahamian limestones:Ground Water,v. 35, p. 859-868.

WHITAKER,F.F.and SMART,P.L., I997c,Groundwatercirculationandgeochemistryofakarstifiedbank-marginalfracturesystem,South Andros Island, Bahamas:Journal ofHydrology, v. 197,p.293-315.

WHITE, W.B. and WHITE, E.L., 1989, Karst hydrology: conceptsfrom the Mammoth Cave area. Van Nostrand Reinhold, NewYork, NY, 346 p.

WHITE,W.B.,1999,Conceptualmodelsforkarsticaquifers,inPalmer,A.N.,Palmer, M.V., and Sasowsky,LD.,eds.,KarstModeling.KarstWaters InstituteSpecialPublication,CharlesTown,WestVirginia,no.5,p.II-16.

WORTHINGTON, S.R.H., 1999, A comprehensive strategy forunderstanding flow in carbonate aquifers, in Palmer, A.N.,Palmer, M.V., and Sasowsky,LD.,eds., Karst modeling.KarstWaters Institute Special Publication, Charles Town, WestVirginia,no.5, p.30-37.

WORTHINGTON, S.R.H., FORD, D.C., and DAVIES, GJ., 2000,Matrix,fracture,andchannelcomponentsof storageand flowinPaleozoiclimestoneaquifer,in Sasowsky,LD.andWicks,C.M.,eds.,Groundwater flowand contaminant transport incarbonateaquifers.Balkema,Rotterdam,p. 113-128.

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