3.3 Multiple Porosity and Permeability Structure
Heterogeneities within an aquifer affect the timing, velocity, direction, and amount of groundwater transmitted through an aquifer. Therefore, one of the most important concepts in karst hydrogeology is the recognition of the spectrum of heterogeneity created by the existence of multiple, or more precisely triple, porosity and permeability components and their influence on the hydraulics and hydrologic behavior of the aquifer. The porosity and permeability structure of a karst aquifer include 1) matrix (intergranular), 2) fracture, and 3) solutional (conduit) components. For some karst aquifers, solutional components include macro-porosity features from biologic activity at the time of formation. This triple porosity structure is sometimes described as “nested hydraulic discontinuities”, with each component contributing its own range of hydraulic conductivities, groundwater flow velocities, storage, and residence times to a portion of the aquifer. This nested structure is, in large part, the source of the “scaling effect” observed in hydraulic conductivity measurements (Halihan et al., 1999; 2000). The scaling effect is that different magnitudes of hydraulic conductivity are obtained when different volumes of the aquifer are sampled. Smaller samples of the aquifer generally include only matrix material. These samples have lower magnitude and a wider range of hydraulic conductivity values than larger samples that include fractures and conduits. The larger samples tend to have higher magnitude and a narrower range of hydraulic conductivity values (Figure 12).
Figure 12 – a) Graph showing typical range in hydraulic conductivities measured in matrix, fracture, or conduit porosity components in various karst aquifers; and b) photographs depicting typical karst matrix, fracture and conduit permeability components to illustrate scale effect created by these “nested” hydraulic discontinuities. Photographs by Taylor (2021b).
Exercise 3 invites the reader to look up the definition of porosity, permeability, and hydraulic conductivity and describe how hydraulic conductivity is related to permeability and porosity.
The occurrence of turbulent flow is one of the identifying characteristics of a karst aquifer. The Reynolds number is used to indicate whether flow is laminar, turbulent or in the transition zone between the two regimes. Critical Reynolds numbers for turbulence can occur within fractures or conduit openings on the scale of millimeters given the normal range of flow velocities common in karstic bedrocks (White, 1988). Sections 4.1 and 4.2 of this book describe the Reynolds number and how this applies to karst aquifers.
Conduit permeability contributes to the highest equivalent hydraulic conductivities, fastest flow velocities, and shortest residence times, but conduits typically occupy a relatively small volume of the karst aquifer and contribute relatively little to the storage of groundwater (Worthington et al., 2000). Section 4 of this book discusses fluid mechanics providing a foundation for better understanding of the hydraulics of large flow features in karst.
Fractures might occupy a greater aquifer volume than conduits, but their contribution to aquifer hydraulic properties depends on their apertures, frequency, distribution, and especially their interconnection with each other, with sources of recharge, and with water stored in the matrix. Fractures that are not well interconnected hydraulically may store and yield groundwater to nearby conduits, but are not influential in transmission of groundwater throughout the aquifer. Poorly interconnected fractures may function as either low velocity or hydraulic “dead” zones with long groundwater residence times.
While intergranular matrix porosity and permeability constitutes the largest volumetric proportion of water in the aquifer, their hydraulic influence on aquifer properties is variable. Carbonate rocks undergo changes in porosity over time and under different conditions. Choquette and Pray (1970) subdivided temporal porosity changes of karst into three stages:
- eogenetic changes occurring at deposition and early exposure to the surface;
- mesogenetic changes that occur during deep burial; and,
- telogenetic changes occurring after the rock has been re-exposed and eroded.
Most karst aquifers occur near the land surface because near-surface processes create karst. Thus, typically karst aquifers are subdivided into eogenetic (generally composed of younger near surface carbonates) and telogenetic karst aquifers (generally composed of uplifted older carbonate rocks). Figure 13 diagrams eogenetic, telogenetic, and mesogenetic time-porosity zones.
Figure 13 – Time-porosity terms and zones of creation and modification of porosity in sedimentary carbonates. a) Interrelation of major time-porosity terms. Primary porosity either originates at time of deposition (depositional porosity) or was present in particles before their final deposition (predepositional porosity). Secondary or postdepositional porosity originates after final deposition and is subdivided into eogenetic, mesogenetic, or telogenetic porosity depending on stage or burial zone in which it develops as shown in (b). The bar at the base of (a) depicts our concept of “typical” relative durations of stages. b) Schematic representation of major surface and burial zones in which porosity is created or modified. Two major surface realms are those of net deposition and net erosion. Upper cross section and enlarged diagrams A, B, and C depict three major postdepositional zones. The eogenetic zone extends from surface of newly deposited carbonate to depths where processes genetically related to surface become ineffective. The telogenetic zone extends from erosion surface to depths at which major surface-related erosional processes become ineffective. Below a subaerial erosion surface, the practical lower limit of telogenesis is at or near water table. The mesogenetic zone lies below major influences of processes operating at surface. The three terms also apply to time, processes, or features developed in respective zones. From Choquette and Pray (1970).
From field data collected over decades, karst hydrologists have begun to distinguish significant differences in the hydraulic characteristics of eogenetic and telogenetic karst aquifers because matrix porosity and permeability is reduced in the latter relative to the former due to increased diagenetic alteration usually associated with increased age and depth of burial (Florea and Vacher, 2006). For example, in the United States, the geologically younger and less diagenetically altered Floridan aquifer in the coastal southeastern states of Florida and Georgia, and the Edwards Aquifer in Texas, exhibit greater overall matrix porosity and permeability compared to the older Paleozoic Mississippian karst aquifers in the mid-continental states of Kentucky and Tennessee. The range of matrix hydraulic conductivities, spanning several orders of magnitude, as shown in Figure 12, reflects the differences in hydraulic conductivity between eogenetic and teleogenetic karst. The Tampa, Florida, and some of the Edwards Aquifer, Texas samples represent eogenetic karst while the Mammoth Cave, Kentucky and Smithville, Ontario, Canada samples represent telogenetic karst. In contrast, the range of hydraulic conductivity values depicted for fractures is greater than for conduits, but conduits have a far greater hydraulic conductivity overall than matrix or fracture porosity. Vacher and Mylorie (2002) developed a schematic diagram indicating the evolution of porosity and equivalent pore diameter for eogenetic to telogenetic karst; as porosity and pore diameters increase, hydraulic conductivity increases (Figure 14).
Figure 14 – Schematic diagram showing the evolution of porosity and pore diameter with progression from eogenetic to telogenetic karst. As karst is buried, both porosity and pore size decrease. After uplift, fracturing and exposure to geochemically aggressive water, dissolution may create caverns within the telogenetic karst, increasing hydraulic conductivity, K. Modified from Vacher and Mylroie (2002).
In practical terms, eogenetic karst aquifers are generally capable of supporting larger and more reliable withdrawals of groundwater than telogenetic karst aquifers because of their greater accessible storage and interaction between matrix and conduits (Florea and Vacher, 2006). In contrast, the low matrix permeability of most telogenetic karst aquifers render the largest volume of the aquifer body essentially impermeable, with little to no groundwater held in storage in the matrix, and little to no hydraulic interaction between the matrix and fractures and conduits.
Aquifer heterogeneities and preferential flow can be extreme in telogenetic karst, whereas groundwater flow in eogenetic karst aquifers can approach that of granular aquifers although preferential flow paths and turbulent flow may exist in localized zones where conduits and solution-enhanced intergranular permeability are more pronounced. Groundwater occurrence within telogenetic karst is dominated almost entirely by flow through highly localized and preferential flow paths created by the integrated network of fracture and conduit components. Consequently, development of higher-yielding and reliable water supply wells will depend significantly on the ability to locate and successfully drill into interconnected, transmissive fractures and/or water-bearing conduits.
Some studies of karst aquifers include digital borehole images acquired by lowering a camera into a well (Figure 15) to create a video of either the borehole wall (side-looking camera) or a downhole view. Figure 16 shows porosity types from eogenetic karst aquifers in Florida and Figure 17 shows borehole images from a telogenetic karst aquifer.
Figure 15 – Photograph of borehole tool lowered from a tripod into the well taken near Miami, Florida, USA (photograph by Johnson (2008)). The technician sets the borehole tool, such that the depth of the information is set at zero for land surface and the depth below land surface is known from the amount of cable lowered down the well from a winch system that is either a dedicated device directly connected to a data logger and computer or part of a suite of borehole tools connected to a controller box that can support different communications cables and wench systems. The controller box connects different data loggers and computers to different borehole tools that employ different communication systems. The schematic shows possible configuration of equipment that might be in a borehole logging truck. Note it is critical to keep these cables from kinking as this can damage the signal. Additionally, a logging truck may have multiple wench systems as different borehole tools require different communications cables and data loggers. Geophysicists and their technicians generally have some good electronics repair skills along with computer technology skills for repairing cables and connections and electronic communications between devices in the field. For simple borehole video and less depth, plumbing inspection cameras work great and often are simple dedicated devices that record length of cable with the video and encode that length date and time on the video.
Figure 16 – Illustration of porosity and permeability components in an eogenetic karst aquifer: a) digital borehole image from Biscayne Aquifer in southern Florida, USA showing multiple porosity types; b) sample of rock also from the Biscayne Aquifer showing macro porosity created by burrowing shrimp before the carbonate sediment solidified; and c) a scuba diver within a conduit in the Floridan aquifer that transmits water to Wakulla Springs near Tallahassee, Florida, USA. Photographs a and b by Cunningham (2008). Photograph c obtained from Suwanee River Water Management District (2008) and used with permission.
Figure 17 – Borehole camera photographs illustrating permeability features typical of a telogenetic karst aquifer. a) Intergranular matrix porosity is essentially nonexistent in this Paleozoic limestone, and porosity and permeability are provided by solutional-enhanced vugs (downhole view); b) and c) solution modified fractures and brecciated zones (b) side view and (c) downhole view); and d) conduit like voids (side view). Borehole diameter is approximately 8 inches (20.3 cm). Photographs by Taylor (2021c).
A complicating form of porosity is the macro porosity created by biological activity. Martin and Screaton (2001) define three types of karst porosity: 1) intergranular matrix porosity, 2) fracture porosity, and 3) cavernous porosity (conduit porosity), but they define a two-component flow system because they include the smaller fracture porosity with intergranular porosity and larger fractures with cavernous porosity. However, the larger biogenic interconnected macro porosity units are considered a fourth form of porosity by Vacher and Mylroie (2002) and by Cunningham and others (2006), thus creating a triple porosity flow system.
The Edwards Aquifer and Biscayne Aquifer in south Florida have formations with macro porosity layers formed by burrowing animals along with larger conduit features (Figure 16). The Floridan aquifer occurs in rocks of Tertiary Period (approximately 66 to 2.6 million years ago) and are older than the Biscayne Aquifer that occurs in rocks of the Quaternary Period (2.6 million years ago to the present). Some of the large horizontal voids and higher-permeability, relatively-horizontal planar features in the Floridan aquifer may have been burrowed units in pure limestone. In the younger Biscayne limestone, interconnected shrimp burrows have not had time to dissolve into large horizontal openings although, as revealed in Figure 16, larger openings are beginning to form in some of these layers (Cunningham and Aviantara, 2001). The Edwards Aquifer (in rocks of the lower Cretaceous 145 to 100 million years ago) in Texas contains mudstone units that do not dissolve readily so the small, interconnected, biologically-formed, macro porosity remains intact and this zone was named the burrowed unit by Rose (1972). These burrowed units of macro pores can be found in older and younger rocks because the burrows form at the time of deposition. Depending on the amount of clay, sand, and dolomite, these burrowed units may retain their void shape regardless of exposure (telogenetic or eogenetic karst). These units have large water transmitting properties and are considered preferential flow layers because typically they are laterally extensive layers within the carbonate rock strata. Additionally, in buried burrowed units of pure limestone, the voids left by biological activity may be infilled with clastic materials that become cemented and do not dissolve, while the surrounding limestone disappears over time. These casts remain, also creating a layer of macro porosity.
Figure 16 and Figure 17 reveal a huge range in water transmitting properties of the relatively horizontal layers shown in the borehole images of the carbonate aquifers. It is not uncommon for hydraulic conductivity to range over 5 orders of magnitude in karst systems.
Exercise 4 invites the reader to download materials showing borehole images and compare the character of the disolution features.
Exercise 5 illustrates how hydraulic conductivity contrasts between layers effects flow parallel to (that is, horizontal flow if layers are relatively flat) or perpendicular to (that is, vertical flow in relatively flat layers) layers of contrasting hydraulic conductivity, thus has a significant influence on the magnitude of flow in horizontal and vertical direction.
Exercise 6 invites the reader to explore how the scale of heterogeneity effects advective transport in aquifers.
Exercise 7 invites the reader to consider the difference between hydraulic conductivity (K) and intrinsic permeability (k).