Three-Dimensional Geomodeling to Identify Spatial Relations Between

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THREE-DIMENSIONAL GEOMODELING TO IDENTIFY SPATIAL

RELATIONS BETWEEN LITHOSTRATIGRAPHY AND POROSITY IN THE

KARST CARBONATE BISCAYNE AQUIFER, SOUTHEASTERN FLORIDA

Richard Westcott

A Thesis Submitted to the Faculty of

The Charles E. Schmidt College of Science

in Partial Fulfillment of the Requirements of for the Degree of

Master of Science

Florida Atlantic University

Boca Raton, Florida

December 2014

ACKNOWLEDGEMENTS

The author wishes to express his sincere thanks and love to his wife, children, and parents for their support, patience and encouragement throughout the writing of this manuscript. The author is grateful to the staff of the Department of the Geosciences of

Florida Atlantic University and the United States Geological Survey for providing help, use of their facilities, computer resources and equipment while conducting the study.

ABSTRACT

Author: Richard L. Westcott

Title: Three-dimensional geomodeling to identify spatial relations between lithostratigraphy and porosity in the karst carbonate Biscayne aquifer, Southeastern Florida Institution: Florida Atlantic University

Thesis Advisor: Dr. Tara Root

Degree: Master of Science

Year: 2014

In southeastern Florida, the majority of drinking water comes from the Biscayne aquifer. This aquifer is comprised of heterogeneous limestones, sandstones, sand, shell and clayey sand with zones of very high permeability. Visualizing the spatial variations in lithology, porosity and permeability of heterogeneous aquifers, like the Biscayne, can be difficult using traditional methods of investigation.

Using the Roxar IRAP RMS software multi-layered 3D conceptual geomodels of the lithology, cyclostratigraphy and porosity were created in a portion of the Biscayne aquifer. The models were built using published data from borehole geophysical measurements, core samples, and thin sections. Spatial relations between lithology, cyclostratigraphy, porosity, and preferential flow zones were compared and contrasted to better understand how these geologic features were inter-related. The models show local

areas of differing porosity within and cross-cutting different cycles and lithologies.

Porosity in the Biscayne aquifer study area follows a hierarchy attributed to lithofacies with a pattern of increasing porosity for the high frequency cycles. This modeling improves understanding of the distribution and interconnectedness of preferential flow zones, and is thus an invaluable tool for future studies of groundwater flow and groundwater contamination in the Biscayne aquifer.

THREE-DIMENSIONAL GEOMODELING TO IDENTIFY SPATIAL

RELATIONS BETWEEN LITHOSTRATIGRAPHY AND POROSITY IN THE

CARBONATE BISCAYNE AQUIFER, SOUTHEASTERN FLORIDA

FIGURES ...... x

1. INTRODUCTION ...... 1

PROBLEM STATEMENT ...... 1

BACKGROUND ...... 5 BISCAYNE AQUIFER ...... 5

SCOPE OF STUDY ...... 10

OVERVIEW OF THESIS ...... 11

2. PREVIOUS STUDIES...... 12

BISCAYNE AQUIFER ...... 12

OVERVIEW OF GEOMODELING ...... 18 GEOMODELING STRATIGRAPHY ...... 18

GEOMODELING FACIES ...... 21

PORE TYPE GEOMODELING ...... 22

GEOMODELING POROSITY ...... 24

APPROPRIATE GEOMODELING FOR THE LAKE BELT STUDY AREA ...... 25

vii

3. METHODS ...... 26

SOFTWARE ...... 26

INPUT DATA SOURCES ...... 29 GEOLOGIC DATA ...... 29

LITHOFACIES AND CYCLOSTRATIGRAPHY ...... 29

POROSITY ...... 31

LAND SURFACE DATA ...... 33

BUILDING THE MODELS ...... 33 CREATING THE LAND SURFACE ...... 33

CREATING THE CYCLE TOP SURFACES ...... 35

STRUCTURE & ZONE MODELING ...... 37

CREATING THE GRIDDED MODELS ...... 38

RAYMER HUNT POROSITY MODELING ...... 41

FACIES MODELING ...... 43

INTERPRETATION & ANALYSIS ...... 44

4. RESULTS ...... 45

RELATIONSHIP BETWEEN SPATIAL VARIATIONS IN CYCLE STRATIGRAPHY, LITHOFACIES AND POROSITY ...... 45 QUALITATIVE SIDE BY SIDE COMPARISONS ...... 45

QUANTITATIVE ANALYSIS OF POROSITY TRENDS ...... 48

REYMER HUNT POROSITY ...... 57

viii

5. DISCUSSIONS OF APPLICATIONS OF THE MODELS ...... 58

INFERENCES ABOUT GROUNDWATER FLOW...... 58 ASSISTING IN THE DEVELOPMENT OF GROUNDWATER FLOW MODELS ...... 60

6. CONCLUSION ...... 62

BIBLIOGRAPHY ...... 64

FIGURES

Figure 1 – Lake Belt Study Area ...... 4

Figure 2 - Cross Section of Relation between geologic and hydrogeologic units ...... 6

Figure 3 - Map of the Biscayne aquifer and study area ...... 7

Figure 4 - Map of south Florida and the base of the Biscayne aquifer...... 8

Figure 5 - Facies geomodel created for the Lake Belt study area ...... 11

Figure 6 - Ophiomorpha from burrowing callianassid shrimp ...... 13

Figure 7 - Porosity table indicates how major pore types are related to lithofacies and porosity ...... 14

Figure 8 - Lithofacies and pore classes ...... 15

Figure 9 - Correlation of ages, formations, stratigraphy, and hydrogeologic units ...... 16

Figure 10 - Depositional environments, pore classes and lithofacies ...... 17

Figure 11 - Three-dimensional view of the facies association model ...... 20

Figure 12 – Facies geomodel of a carbonate shoal reservoir ...... 22

Figure 13 - 3-D hydrogeologic model with pore classes ...... 23

Figure 14 – Flow property modeling based on object-models ...... 24

Figure 15 - Flow chart for Geomodeling of the Lake Belt area...... 28

Figure 16 – Scaled facies table ...... 30

Figure 17 – Sonic logs side by side comparisons of optical bore hole images and logs ...... 32

Figure 18 - Comparison of LiDAR DEM files with the Roxar derived files ...... 34

Figure 19 - Cycle top surfaces created in Roxar ...... 36

Figure 20 - Cycle top surfaces ...... 37

Figure 21 – Structure model of zones representing each high frequency cycle ...... 38

Figure 22 - Gridded zones for high frequency cycles ...... 40

Figure 23 - Porosity models ...... 42

Figure 24 - Facies geomodel of the Lake Belt study area for the Biscayne aquifer...... 44

Figure 25- North end fences of facies and porosity models...... 46

Figure 26 - Cross sections of porosity for each facies...... 47

Figure 27 - Breakdown of facies for the high frequency cycle 2b ...... 50

Figure 28 - Histogram for High frequency cycle 2b for Floatstone rudstone pore class I ...... 51

Figure 29- Lithology and porosity comparison chart for each cycle...... 53

Figure 30 - Average porosities for each high-frequency cycle ...... 55

Figure 31 - Histograms indicating porosity distribution for each lithofacies ...... 56

Figure 32 - Porosity of 60% or greater filtered out of porosity model ...... 59

1. INTRODUCTION

PROBLEM STATEMENT

Carbonate aquifers are highly heterogeneous and are important reservoirs for much of the world’s drinking water. Saltwater intrusion, pollution and over usage of groundwater are problems being experienced by populations all over the world. Accurately describing the lithology, cyclostratigraphy, porosity, and preferential flow paths, if any, in an aquifer is essential for determining water availability for water resources planning. However, capturing the framework and stratigraphy for large scale aquifers of areas greater than 50 square miles that are highly heterogeneous is a very difficult task.

In southeastern Florida, the Biscayne aquifer holds much of the drinking water for the population of the region. Properly characterizing the spatial variability in lithology and porosity is necessary for delineating groundwater flow, planning for water supply, and protecting water resources from potential future problems with groundwater contamination from pumping, mining, fracking, and saltwater intrusion as sea level is affected by climate change. Traditional methods such as borehole descriptions and 2D cross sections for aquifer characterization may provide a less accurate spatial representation than geomodels, when examining attributes such as porosity, lithology and cyclostratigraphy in highly heterogeneous aquifers like the Biscayne. Geomodels have been used extensively by the petroleum industry as a tool for visualizing and analyzing subsurface variability over large volumes, but to date no extensive geomodeling of areas

greater than 32 square miles have been done to characterize the Biscayne aquifer.

Cycl0stratigraphy is often unobservable within the reflectors in seismic data and scarcity of well data usually inhibits the ability to produce accurate facies and porosity models in

3D. Thus, stochastic geomodels inherently contain varying amounts of inaccuracies.

Limiting these inaccuracies is an important aspect of geomodeling. Although the

Biscayne aquifer is highly heterogeneous, the density of 79 wells within 89 square miles of the Lake Belt study area allows for a more deterministic approach to building the aquifer architecture than is normally possible in developing geomodels.

The purpose of this research is to improve the understanding of the porosity distribution and better understand relations between lithology, cyclostratigraphy and porosity in the

Biscayne aquifer. In order to accomplish this goal 3D conceptual geomodels of porosity, lithology and cyclostratigraphy within the Lake Belt area of the Biscayne aquifer were developed using Roxar IRAP RMS software. These 3D conceptualizations were then used to address the following questions.

1. Are spatial variations in porosity constrained by lithology and/or

cyclostratigraphy within the highly heterogeneous karst Biscayne aquifer?

2. Do porosities of each lithology remain constant throughout the Biscayne

aquifer or do they vary depending upon the cycle and or depth in which they

reside from influences such as depostional environment, burrowing, and

dissolution?

3. Will geomodels produced for the Lake Belt area of the Biscayne aquifer

support the hierarchy of porosity and pore class for lithologies as previously

determined by Cunningham et al, 2006.

The data integrated to create the geomodels came from a mixture of well logs, core samples, thin sections, optical borehole images and previously published data from the

Lake Belt study area (Figure 1).

Figure 1 – Lake Belt Study Area with wells used in geomodeling.

BACKGROUND

BISCAYNE AQUIFER

The Biscayne aquifer is comprised of highly heterogeneous limestones, sandstones, sand, shell and clayey sand (Fish & Stewart, 1991). In the study area, the upper part of the

Biscayne aquifer is comprised of Holocene peat and marl generally between 0 to three feet thick above the Pleistocene Miami Limestone and Fort Thompson Formation

(Cunningham, 2004) (Figure 2). Upper parts of the Pliocene Tamiami Formation are also locally included in the lower part of the Biscayne aquifer.

Figure 2 - Cross Section of relation between geologic and hydrogeologic units of the surficial aquifer system across central Miami-Dade County (modified from Reese and Cunningham, 2000)

In north Miami-Dade County, Broward County and south Palm Beach County the aquifer consists mainly of limestone and minor quartz sand. In the south and western part of

Miami-Dade County the aquifer is mainly comprised of the Miami Limestone and Fort

Thompson Formation (Figure 3).

Figure 3 - Map of the Biscayne aquifer and study area (Figure from Cunningham & Florea, 2009).

In Miami-Dade County the limestone is thickest along the coast. The semi-confining part of the Tamiami Formation is below the Biscayne aquifer. The highest part of the aquifer is along the Atlantic Coastal Ridge with a maximum elevation of 24 feet above sea level

(Hoffmeister et al., 1966). A maximum thickness of more than 260 feet is observed in northeastern Miami-Dade County as well as Broward County (Fish and Stewart, 1991).

The aquifer thickness decreases and feathers out westward forming a wedge shape

(Figure 4).

Figure 4 - Map of south Florida and the base of the Biscayne aquifer. Contours of base of the Biscayne aquifer from Fish & Stewart, 1991.

This aquifer is unique because of its high permeability and high porosity. The Biscayne aquifer has zones of very high permeability with hydraulic conductivities exceeding

10,000 feet per day and transmissivities that may exceed 2,000,000 feet squared per day as reported in Fish and Stewart (1991). This is a higher conductivity than the range of

.28 feet per day to 5669 feet per day Duffield (2014) indicated for karst and reef limestone. DiFrena et al. (2007) conducted research on the Key Largo Limestone that indicated that where effective porosity values are less than 33% Darcian flow is present, but when effective porosity is greater than 33% non-Darcian flow occurs within the Key

Largo Limestone and methods of quantifying aquifer properties and flow need to be adapted to adequately account for the non-Darcian conditions in those cases. The highly heterogeneous nature of the Biscayne’s karst features makes it difficult to characterize the distribution of the differing pore types and the extent and connectivity of high porosity zones. Due to this uniqueness and heterogeneity information such as depositional environment, pore type, lithology and cyclostratigraphy can be helpful when trying to create an accurate representation of the spatial variability of aquifer properties in the 8

Biscayne. A 32 square mile section in the snapper creek area of the Biscayne aquifer was studied by Wacker et al. (2014). Evaluations of lithostratigraphy, lithofacies, paleontology, ichnology, depositional environments and cyclostratigraphy from 11 test coreholes were geophysically interpreted. From the resulting data, geologic and hydrogeologic frameworks were constructed. Cross sections and a porosity geomodel were developed.

The average monthly rainfall for the Miami area ranges from 1.88 inches in January to

8.63 inches in August. The four summer months of June, July, August and September account for approximately 54% of the 59 inches of average annual rainfall

(Rss.Weather.com). The large amounts of rainfall during the summer months play a role in the high dissolution and karsting in the vadose zone of the Biscayne aquifer.

SCOPE OF STUDY

The area of study approximates the boundaries of an area known as the Lake Belt region located in north central Miami-Dade County bordered by Everglades wetlands to the west and the Snapper Creek extension to the east (Figure 3). While some of the area is populated, much of the area contains rock mines and protected wetlands. It is an area of approximately 89 square miles. The geomodels created for this thesis (Figure 5) extend vertically from approximately 10 feet above sea level to 80 feet below sea level. The geomodels were built by extrapolating from data collected at wells. As with all models, these geomodels cannot be assumed to be spatially precise when creating horizon surfaces for cycle tops or populating the gridded cells with attributes such as lithologies or porosity. The geomodels presented here are unique in that they provide a three- dimensional conceptualization of a large volume of the highly heterogeneous Biscayne aquifer.

Figure 5 - Facies geomodel created for the Lake Belt study area within the Biscayne aquifer. Topography was developed from DEM files produced by the South Florida Water Management District.

OVERVIEW OF THESIS

Chapter 2 of this thesis puts the study area into context with other studies of the Biscayne aquifer as well as with other applications of geomodeling. Chapter 3 describes the detailed methods used in creating geomodels for the Lake Belt area as well as how other geomodels have been built and used for hydrogeologic applications. Chapter 4 describes the interpretation and analysis of the geomodels and data derived from geomodels.

Chapter 5 demonstrates how this thesis and the geomodels can be applied in future studies and understanding of the Biscayne aquifer. Finally, conclusions based on the findings of this study are presented in Chapter 6.

2. PREVIOUS STUDIES

BISCAYNE AQUIFER

The Biscayne aquifer has been intensively studied due to its importance as the main source of drinking water to the south Florida population (miamidade.gov) . Rain, canals and the Everglades wetlands make up the majority of the recharge for Biscayne aquifer

(Jenkins, 2009). In spite of this, there remains uncertainty about the location, extent, and interconnectedness of preferential flow zones and the distribution of matrix porosity and macro porosity. In parts of the Biscayne aquifer, the macro-porosity is related to burrowing, especially by callianassid shrimp, during and shortly after deposition, but pre- lithification. Callianassids can create the burrow trace fossil Ophiomorpha. Other parts of the aquifer have been subject to solution pipes, bedding-plane vugs and cavernous vugs creating additional pore types and flow zones (Cunningham et al., 2006) (Figure 6).

Figure 6 - Ophiomorpha from burrowing callianassid shrimp can enhance porosity within the Biscayne aquifer where hand samples have been found to range from 15 to 50%. (Figure from Cunningham et al. (2012))

The preferential flow zones related to the ichnofabrics were suggested by Cunningham et al. (2009) to have permeabilities greater than Jurassic “super-K” zones attributed to burrowing by thallasinidean shrimp (Pemberton and Gingras, 2005) within the giant carbonate Ghawar oil field in Saudi Arabia. Mount et al. (2014) found that using GPR in conjunction with whole core samples was a reliable way to identify, quantify, and map the vuggy porosity in the Biscayne aquifer within parts of Miami-Dade County. Manda and Gross (2005) applied geospatial analysis to digital borehole images that were classified using remote sensing software to determine flow “conduits” within the

Biscayne aquifer.

Cunningham (2004) found porosities of whole-core samples from the Lake Belt area of the Biscayne aquifer ranging from about 15 to 50%. Cunningham et al. (2006) broke

down the differing pore types into three different classes (Figure 7): (1) touching vug porosity of fossil-moldic burrowing, root-moldic, inter-root-cast, irregular vugs and conduit porosity from bedding plane vugs and cavernous vugs, (2) matrix porosity including interparticle porosity and separate vugs and (3) separate vugs including moldic porosity and thin vertical solution pipes.

Figure 7 - Porosity table indicates how major pore types are related to lithofacies and porosity. Modified from Cunningham et al. (2006).

The pore classes, and lithofacies are related to the six major depositional environments represented in the Biscayne aquifer (Figure 8) (1) middle ramp, (2) platform margin-to- outer platform, (3) open-marine platform interior, (4) restricted platform interior, (5) brackish platform interior, and (6)freshwater terrestrial environments (Wolffert-

Lohmannet al., 2007).

Figure 8 - Lithofacies and pore classes are associated with depositional environments. (Figure from Cunningham et al., 2006)

High frequency cycles containing stacked patterns of lithofacies make up the framework for the Biscayne aquifer. Vertical stacking of lithofacies can be seen on carbonate platforms (Kerans and Tinker, 1997) due to changes in sea level. Cunningham et al.,

(2004b, 2004c and 2006) (Figure 9) delineated the cyclostratigraphy and the high-

frequency cycles bounded by the surfaces created by these changes in sea level for the

Biscayne aquifer. The cycles are based on various ranges of ages that were proposed by

Multer et al. (2002) and Hickey (2004) for the five unconformity –bounded Quaternary marine units or Q units defined by Perkins (1977). The three types of high-frequency cycles within the Biscayne aquifer are upward-shallowing subtidal cycles, upward- shallowing paralic cycles and aggradational subtidal cycles (Wolffert-Lohmann et al.,

2007).

Figure 9 - Correlation of ages, formations, stratigraphy, and hydrogeologic units of the Miami Limestone, Fort Thompson Formation, and Tamiami Formation. (Figure from Cunningham et al., 2006)

Cunningham et al. (2006) correlated depositional environment, pore class, lithology and cyclostratigraphy for the Lake Belt area (Figure 10) which was integral in the creation of

22 different lithofacies.

Figure 10 - Chart shows depositional environments, pore classes, lithofacies and corresponding cyclostratigraphy from the Holocene back to the HFC2a for the Biscayne aquifer. Two cycle sets were present in the study area depending on the formation. (Figure from Cunningham et al, 2006)

OVERVIEW OF GEOMODELING

The purpose of 3D geologic modeling, also known as geomodeling is to model and visualize: (1) geometry of rock- and time-stratigraphic units, (2) spatial and temporal relations between geo-objects, (3) variation in internal composition of geo-objects (4) displacements or distortions by tectonic forces, erosion and dissolution, and (5) fluid flow through rock units (Kelk, 1991 – quoted in Turner, 2005).

Input into geomodels is both spatial data and properties data which are interpolated to create a geometric representation of subsurface geologic features. This geometric framework is then discretized (divided into a mesh) that serves as the control on the spatial distribution of rock properties. The discretization facilitates the use of equations to, for example, calculate volumes or interpolate porosity or facies between wells.

Computer graphics enable generation of 3d visualization of geomodels. These visualization products are useful tools for management and decision making for communicating information about the subsurface.

As previously noted, most geomodels have been developed and used by the petroleum industry but their potential application is broad including hydrogeology, engineering geology and mining. Numerous previous studies use several different approaches to build the geometric framework, discretize and analyze geomodels for different purposes.

The following sections summarize a select few examples from the literature.

GEOMODELING STRATIGRAPHY

Amour et al. (2013) proposed a scale-dependent geologic modeling approach based on stratigraphic hierarchy when modeling an oolitic carbonate ramp reservoir. Their study

area was a small scale location, 1 km wide and 100 m thick in the High Atlas mountain range of Morocco. They modeled the stacking pattern of high-frequency depositional sequences and lithofacies using a truncated Gaussian simulation. Their stratigraphic succession contained three large scale sequences and five medium scale sequences with four small scale sequence boundaries for a total of 19 stratigraphic sections (Figure 11).

These boundaries were delineated by abrupt water depth changes from inner-ramp lithofacies to distal middle-ramp lithofacies with modest paleotopographic relief and a base that was characterized by an open marine setting. They found that the use of one single simulation technique is unlikely to produce the natural patterns and variability of carbonates. Using a scale-dependent approach they were more able to capture the heterogeneities within the reservoir.

Figure 11 - Three-dimensional view of the facies association model vertically exaggerated 3x. (Figure from Amour et al., 2013)

GEOMODELING FACIES

The carbonate shoal reservoir of an epicontinental basin in southwest Germany was geomodeled by Palermo et al. (2010). Working with several laterally extensive outcrops, shallow cores, logs, several hundred hand samples and 451 thin sections they were able to create a 3-D geomodel of the Triassic geology of the area. The lateral facies changes for their study area were very subtle in the gently inclined carbonate ramp over an area of 25 by 36 km. Fourteen lithofacies were defined and used in the study. The vertical zones were correlated by cycle surfaces. A deterministic modeling approach was used as defined by Kerans and Tinker (1997) with well spacing typically less than dip width when working in a carbonate setting. They found that using a truncated sequential

Gaussian simulation algorithm confined by lateral and vertical trends worked best, but even then, the model did not always match the data. Thus, a manual correction for each layer was conducted. Without vertical exaggeration the facies changes were barely discernable, however with 200x vertical exaggeration facies changes were visible in the

3-D model (Figure 12).

Figure 12 – Facies geomodel of a carbonate shoal reservoir of an epicontinental basin in southwest Germany. (Figure from Palermo et al. (2010))

PORE TYPE GEOMODELING

Using a layer cake approach Cunningham et al. (2006) developed a three-dimensional conceptual model of the hydrogeology of the Biscayne aquifer by defining the 3 types of pore classes. Two dimensional views of the hydrogeologic framework for the Biscayne aquifer within the Lake Belt were translated into a simplified three-dimensional interpretation. Contained and represented in the model were an upper layer of peat, muck marl and/or fill with seven layers beneath it containing pore classes I, II, and III

(Figure 13). Conceptualized within this model were 3 relatively high permeability layers with a pore class of 1 (layers 2, 5, and 8), two relatively moderate permeability layers

with a pore class of 2 (layers 4 and 7) and two relatively low permeable layers with a pore class of 3 (layers 3 and 6).

Figure 13 - 3-D hydrogeologic model with pore classes delineated by cyclostratigraphy (Figure from Cunningham et al. (2006).)

GEOMODELING POROSITY

Eisinger and Jensen (2009) created geomodels to represent the Nisku petroleum reservoir that formed in a large open marine environment that is now located within Alberta,

Canada. They found that, due to the lack of nearby wells a deterministic approach was not suitable. A more probabilistic method, such as Sequential Gaussian Simulation

(SGS), did a better job but still did not fully capture the heterogeneity of the reservoir.

Using objects in a Boolean-modeling method produced a more realistic representation

(Figure 14). This method required an understanding of the porosity distribution, plausible three-dimensional facies geometries and permeability zones within the reservoir.

Figure 14 – Flow property modeling based on object-models. Porosity (left) scaled 0 to 15% and permeability (right) scaled 1 to 1000 mD. (Figure from Eisinger and Jensen, (2009))

APPROPRIATE GEOMODELING FOR THE LAKE BELT STUDY AREA

A deterministic approach was found to be the most suitable for the Lake Belt study area with the closely located 79 wells within the 89 square miles of the project. Each cycle unit was manually corrected so only facies that were present at the wells or between wells would form the geobodies representing those lithologies. A continuous petrophyscial geomodeling algorithm within Roxar RMS software worked best when modeling the porosity.

3. METHODS

SOFTWARE

The IRAP RMS software, which is widely used in the petroleum industry for reservoir geomodeling (Burns et al., 2010) allows geologists to integrate a wide range of data from different sources to create 3D geomodels. The RMS program comes with the unique ability for object modeling. Object modeling allows the program create and manipulate shapes with a realistic geological appearance, and unlike pixel based methods, the connectivity within objects is preserved, which can be critical when mapping flow zones.

Facies modeling using RMS not only can correlate between wells it can also be used to create a 3D conceptualization of the distribution of lithologies. Volumes of porosity and fluids can be produced within a variety of constraints as the algorithm the software uses is very flexible. Roxar’s Facies Composite software is capable of handling complex geological environments such as the heterogeneous nature of the Biscayne aquifer by using a variety of geostatistical methods including the Metropolis-Hastings algorithm with simulated annealing, a multi-Gaussian distribution object-based modeling technique, and a truncated Gaussian method for modeling transitional environmental facies.

Determining the appropriate algorithm for the model to run the physical properties is important as attributes such as porosity may vary at a much smaller scale than well spacing. The porosity models for this study were produced using the Roxar petrophysical modeling method which interpolates continuous trend differences between wells. The

RMS software has the capability of small scale modeling for porosity and 26

permeability using interpolation, krigging, stochastic simulation and a water saturation calculator (www.emerson.com, 25/5/2010). The software includes geostatistics for integrating and spatially correlating the cyclostratigraphy, lithofacies and porosity which were used in creating the 3D geomodels. The modeling workflow for this thesis is shown in Figure 15 below.

Figure 15 - Flow chart for Geomodeling of the Lake Belt are

INPUT DATA SOURCES

GEOLOGIC DATA

The geomodels produced included the unconsolidated peat and marl, the Miami

Limestone, the Fort Thompson Formation and sections of the Tamiami Formation. Field work conducted by the USGS from 2000 to 2004 produced much of the data used in this study. This initial time consuming work collected vital information for the subsurface modeling process including cores, hand samples, logs, and approximately 240 thin sections from 79 drilled wells of varying depths from 20 to 120 ft. (Cunningham et al.,

2004, 2006). These data were used to identify both the top elevation of high frequency cycles and the distribution of different lithofacies throughout the study area.

LITHOFACIES AND CYCLOSTRATIGRAPHY

Cunningham et al. (2004, 2006) had previously defined twenty two-different lithofacies within the Lake Belt area by a combination of allochem types, fabric, sedimentary structure, bedding type, and diagenetic features using a combination of classifications and terminology from Dunham (1962), Embry and Klovan (1971), and Lucia (1999). The geomodels presented in this thesis build upon and enhance this previous research. To reduce the complexity of building the models and shorten the model run times,

Cunningham et al.’s (2004, 2006) twenty-two lithofacies were reduced to nine by grouping lithofacies with similar lithologies and porosities (Figure 16).

Figure 16 – Scaled facies table indicates how lithofacies from Cunningham et al. (2004, 2006) were upscaled to create the geomodels for the Lake Belt study area.

Cyclostratigraphy relates relative sea level changes to the vertical facies successions of sedimentary bodies interpreted from the depositional settings. The elevations of the top of fourteen high frequency cycles (HFC) surfaces were identified from both well data and from cross sections that had been previously delineated by Cunningham et al. (2004,

2006). The well data included borehole images, hand samples, thin sections, induction

logs, sonic logs and flow meter logs. The criteria for delineating the cycle boundaries were based on previous work by Cunningham et al. (2004, 2006).

POROSITY

Sonic data were previously collected from fifty wells using full-waveform sonic (FWS) logging, which were previously processed by WellCad and Log Cruncher to compute the

Raymer-Hunt porosity. Wacker & Cunningham (2003) determined porosities derived from the Raymer-Hunt equation (Raymer, Hunt, and Gardner, 1980) and the Stoneley inversion process. The Raymer-Hunt equation produced porosity values which more closely resembled whole core sample porosities than the Stoneley inversion process

(Figure 17). Therefore, the Raymer-Hunt porosities were used to create the porosity geomodels.

Figure 17 – Sonic logs side by side comparisons of optical borehole images and logs from two wells within the Lake Belt study area. The red disks indicate whole core porosity values. The sonic porosity log using the Raymer-Hunt equation is in red and the Stoneley amplitude log is in black. (Figure from Wacker and Cunningham, 2003)

LAND SURFACE DATA

The pre-existing data used to produce the land surface for the geomodels include Digital

Elevation Model (DEM) files from 2003 LiDAR data sources (CSOP-USACOE, IHRC-

FIU, and Woolpert-ETSD). The DEM files contained 25 ft. horizontal tiles of bare earth with a fundamental vertical accuracy (FVA) of .6 ft. at the 95% confidence level and a

3.8 ft. horizontal accuracy at the 95% confidence level.

BUILDING THE MODELS

CREATING THE LAND SURFACE

The DEM files were imported into ArcGis and converted to points. These points were then exported from ArcGis and imported into the Roxar software. Within Roxar, a local

B-spline algorithm was used to produce the land surface in NAVD88 with tile spacing of

82 by 82 ft (25 meters). Buildings were then removed from the surface Figure 18.

Figure 18 - Comparison of LiDAR DEM files with the Roxar derived files that where exported and interpolated from ArcGis point files. Ground truthing was then done at locations where well elevations that had been derived from topo maps did not closely match the modeled surface elevation. In all cases surveyed well elevations matched closely with the modeled LIDAR land surface and were not adjusted. It was not feasible to survey the elevations of all wells, and in those

cases where surveyed elevations were not available, well elevations were adjusted to match the modeled LIDAR land surface.

CREATING THE CYCLE TOP SURFACES

Cycle tops were interpolated between wells from well picks of the cycle tops. The Local

B-spline method was used for the interpolation with cell spacing of 82 x 82 feet (25 meters). Cycle surfaces (Figure 19) that intercepted lower surfaces and that were not present in wells were cut where the surfaces met so as not to cross the lower surface which would be representative of unconformities from erosion (Figure 20).

Figure 19 - Cycle top surfaces created in Roxar from well picks delineated from Cunningham et al. (2006). X and Y are UTM.

Figure 20 - Cycle top surfaces showing the 2a (silver cycle top surface) onlapping against an unconformity.

STRUCTURE & ZONE MODELING

A structure model with zones to fill in the space associated with each high frequency cycle between corresponding cycle tops was built using well pics and the cycle top surfaces described above. The individual zones were built with 25 meter horizontal cell spacing. The structure model contains the zones that would be used for creating the gridded models (Figure 21).

Figure 21 – Structure model of zones representing each high frequency cycle within the structure model.

CREATING THE GRIDDED MODELS

Model grid cells are required for input of parameters to detail a more complex geologic model. Increasing the number of grid cells increases time to run each simulation but provides greater spatial resolution allowing for small scale changes within the attributes being modeled. Understanding the significance of the geology and the scale to represent

the heterogeneities within the geology can be challenging when working within the computational and run time limits. In this study, individual gridded models were created from zones of each of the high frequency cycles, containing a cell thickness of ~3 feet.

Fluctuating z (elevation) corner nodes were necessary to produce cells that conformed to surface tops and bottoms forming the cycle unit. These cells are not exact squares and may have irregularly shaped trapezoidal or triangular shapes. In areas where a cycle unit may pinch out the cell thicknesses would become thinner until they became non-existent.

The x-y coordinates were spaced at a constant 100 feet north to south and east to west.

All of the gridded models for their corresponding zones (high frequency cycles) were cropped down to the shape of the Lake Belt study area (Figure 22).

Figure 22 - Gridded zones for high frequency cycles. Note the variation of size and shape of cells as zone thickness changes and/or pinches out.

The overall rectangular area of the geomodel is 36450 feet by 15675 feet with a thickness of approximately 90 feet. The cells ranged from zero to three feet thick. By using this scale for the model ~ 94% of the grouped facies in the well logs were able to be incorporated into the blocked wells to be used in the composite facies models.

RAYMER HUNT POROSITY MODELING

Roxar Petrophysical modeling was used to populate the gridded zones with the interpolated Reymer Hunt Porosity between the wells. Models were run both with the porosity constrained to follow high frequency cycle zones and again with the porosity not constrained to follow any zonation. Constrained porosity geomodels were interpolated between wells from only porosity values at well depths inside the cycle unit.

Unconstrained porosity geomodels allowed for interpolation of cells to be influenced by well porosity values from well depths from cycle units above and below. The models produced both ways were very similar to each other (Figure 23). Individual porosity geomodels for each cycle unit were used in the development of the visual and calculation comparisons.

Figure 23 - Porosity models run with Roxar’s petrophysical modeling with no zone constraints and the lower image shows the model run the same way except with the porosity constrained by the zones.

FACIES MODELING

When using the Roxar facies composite modeling, the length, width, and height of the geobodies of a particular facies have a multi-Gaussian distribution with user-defined constraints for orientation, shape, size and dip. Attempting to create a facies model for the entire volume of the study area with the number of wells involved was too complex, so individual facies models were created for each cycle to allow for a more deterministic approach (Figure 24). Most importantly, facies representative of the blocked wells were present around and between wells where the facies were present in the well logs.

The study area contains a relatively dense proportion of wells, but there are areas that are unoccupied by wells. Initially the software defaulted to populating cells which were not between and not close to wells with the most abundant facies of the cycle. In these areas, models were adjusted manually taking into account probable depositional environments and tectonics.

Figure 24 - Facies geomodel of the lake Belt study area for the Biscayne aquifer.

INTERPRETATION & ANALYSIS

The various models were displayed as overlays containing one or more data sets and as side-by-side visual comparisons. Additional statistical and spatial analysis of the geomodels were derived from analytical tools in the Roxar RMS software. The software comes with the ability to filter out a particular facies and populate that facies with it’s associated porosity. Histograms and rose diagrams can further investigate this filtered data. Statistical data of means, medians and standard deviation were used for comparison purposes. These visual comparisons of the 3D images, along with analysis of the frequency and distribution of different lithofacies and porosity zones, facilitated identification of possible preferential flow zones and determination of whether preferential flow zones tend to cut across cycle and lithologic boundaries.

4. RESULTS

RELATIONSHIP BETWEEN SPATIAL VARIATIONS IN CYCLE

STRATIGRAPHY, LITHOFACIES AND POROSITY

QUALITATIVE SIDE BY SIDE COMPARISONS

The geomodels developed for this thesis allow for visual comparisons of cross sections showing lithology and cycles with those showing porosity (Figure 25). Additionally, the porosity of different facies was compared by creating separate cross sections for each facies showing only porosity (Figure 26).

Figure 25- North end fences of facies and porosity models.

Figure 26 - Cross sections of porosity for each facies.

These comparisons indicate that the spatial patterns of porosity are similar to those of lithology. Both Figure 25 and the Figure 26 show a wide range of porosities within individual facies. However, Figure 25 shows changes in porosity tend to correlate with boundaries between facies. The short dashed lines are examples of places where lithologic boundaries align very closely with boundaries between zones of varying porosities. There are also several locations (indicated by the dot-dash line) where, although the boundaries between lithologic and porosity zones do not align exactly, the porosity distribution has a pattern very similar to that of the lithology. There are some areas in the cross sections where there is not an obvious relationship between porosity and lithology patterns (see the example indicated by the solid line). Undoubtedly, some of these areas are likely places where porosity remains constant across lithologic boundaries, and others are likely places where the model gridding, zonation, and interpolation did not capture the full spatial variability of the subsurface. Nonetheless, it is apparent from these side by side comparisons that there is a good relationship between the spatial distribution of porosity and lithology in the study area. Similar conclusions can be made about the relationship between cycle stratigraphy and porosity. Although there are areas where porosity varies within cycles and where porosity is constant across cycle boundaries, patterns of porosity tend to mirror cycle boundaries.

QUANTITATIVE ANALYSIS OF POROSITY TRENDS

A different approach to using the geomodels to analyze how porosity varies across lithofacies and cycles is to isolate each lithofacies within specific cycles as in Figure 27.

Once the lithofacies is isolated, Roxar is capable of tabulating basic statistical information about the porosity distribution and these can be compared across cycles. For

example, high frequency cycle 2b was examined and the floatstone rudstone pore class I facies (light blue) was extracted from the cycle model. The Raymer Hunt Porosity was populated into the facies and shown using a rainbow color spectrum (Figure 27). Finally, statistical information about the variability of the porosity within the facies was calculated (Figure 28). The Raymer Hunt Porosity in the 2b for the Floatstone rudstone

Pore Class I as seen below ranges from 32.7% to 69.5% with a mean of 50.6% within 1 standard deviation of 8.49% (Figure 28).

Figure 27 - Breakdown of facies for the high frequency cycle 2b. Lower section shows the same corresponding areas with the Raymer-Hunt porosity for floatstone rudstone pore class I.

Figure 28 - Histogram for High frequency cycle 2b for floatstone rudstone pore class I. Pore class/Porosity breakdown can be seen with bar charts for the relative frequency (%)

The statistics can be presented in a variety of ways such as histograms, scatterplots, and vertical proportion curves, to help identify patterns and trends in porosity within the cycles. Figure 29 compares histograms and statistics derived for the porosity of each facies shown by the hierarchy within each cycle with the highest porosity facies displayed at the top of each cycle and the lowest porosity facies displayed at the bottom.

There is some variation in the porosity of individual lithofacies across cycles. But, patterns do seem to exist indicating that the hierarchy of porosity for facies appears to be somewhat consistent for the varying cycles. For example, the mean porosity of the very porous floatstone rudstone pore class I ranges from 44% ± 8% in the 3a to 48% ± 9% in

the 2g3. The skeletal packstone grainstone facies ranges from 41% ± 7% in the 3a to 42%

± 11% in the 2g3. The less porous mudstone for the same cycles ranges from 37% ± 9% in the 3b to 40% ± 10% in the 2g3.

These data indicate that certain lithofacies tend to consistently be higher porosity than others. However, anomalies do also exist, such as in the 2f where the average porosity for mudstone, 45% ± 11%, is slightly higher than the average porosity of skeletal packstone grainstone 45% ± 10% and floatstone rudstone pore class II 44% ± 8%. In general consistencies in the hierarchy of porosity can be seen where floatstone rudstone I is present but in cycles not containing floatstone rudstone I, small anomalies can be present (Figure 29).

The porosity for each facies depends on the cycle in which they reside. Increasing or decreasing trends in porosity across cycle boundaries are consistent among all the facies common to adjacent cycles (except for the 2d2 where slight variations occur). For example, the mean porosity of all the facies common to both the 3a and the 2h is higher in the 3a than the 2h, and the mean porosity of all the facies common to both the 2h and the 2g is lower in the 2h than in the 2g.

Figure 29- Lithology and porosity comparison chart for each cycle.

Statistics were also produced from the Roxar software for the median, mean and standard deviation of the porosity for all the occurrences of each facies within the model as a whole. When comparing the porosity of different lithofacies for the entire depth of the

Biscayne aquifer in the study area (Figure 30) overlap of porosity for many of the lithofacies was seen. But, an overall trend for median Raymer-Hunt calculated porosities did exist (Figure 30) and follows previously set forth patterns for pore classes of I, II and

III by Cunningham et al. (2006) (Figure 7). For example, floatstone rudstone pore class I has a higher median Raymer-Hunt calculated median porosity than floatstone rudstone pore class II which has a higher calculated median porosity than floatstone rudstone pore class III. However as seen in Figure 17 above, the Raymer-Hunt calculated porosities tended to produce higher values than the hand sampled porosity values calculated for the pore classes determined by Cunningham et al. (2006).

Figure 30 - Average porosities for each high-frequency cycle were calculated. The figure above shows the minimum and maximum average Raymer-Hunt porosity for all cycles. Included in the figure is the median of all Raymer-Hunt porosities that were modeled. Note: Peloid packstone grainstone and peloid wackestone packstone were only modeled in one of the high-frequency cycles. Quartz sand / sandstone can be problematic due to washout during drilling causing erroneously high levels of porosity from sonic logs.

With most of the lithofacies there is an upward trend of porosity as depth increases within the Fort Thompson formation. Scatter plots where made of five of the facies that were present in at least four cycles. Due to uncertainty of precise ages of the tops and bottoms of the high frequency cycles (Hickey et al., 2010) the mean porosities were plotted by the cycle rather than age. (Figure 31). All five facies showed a trend of increasing porosity in older cycles. A logical assumption may be derived from this that over time, facies of similar composition respond to a rate of dissolution or erosion or both with similar degradation causing the older similar facies to have a larger cumulative amount of dissolution and a higher porosity.

Figure 31 - Histograms indicate porosity distribution for each lithofacies with depth and high-frequency cycle.

REYMER HUNT POROSITY

The Reymer Hunt Porosity model produced a range of average porosity from 34% to

69% for the Lake Belt area (Figure 31). The upper 69% range of porosity produced from the geomodel was related to quartz sand/sandstone in the 2c2 high frequency cycle, which may erroneously have been influenced by borehole washout during drilling.

Skelital packstone grainstone porosity in the 2c2 may be more indicative of the maximum porosity within the Biscayne aquifer for the study area. This is assuming the voided volume contained water held in the modeled Lake Belt area. Pockets of high porosity were present in the study area, which often crossed cycle boundaries.

5. DISCUSSIONS OF APPLICATIONS OF THE MODELS

INFERENCES ABOUT GROUNDWATER FLOW

The side-by-side comparisons of cross-sections are useful for inferring possible preferential groundwater flow paths and distinguishing between areas where groundwater flow is likely to be more vertical versus more horizontal. For example, areas such as the midsection (Figure 32) of the western side of the Lake Belt area containing high porosity may indicate an area of faulting, profound burrowing, and/or dissolution with cavernous areas (Cunningham and Florea, 2009).

Figure 32 - Porosity of 60% or greater filtered out of porosity model and shown in lower image indicating volumes of high porosity.

Where these high porosity zones are sufficiently deep and thick, they might indicate good locations to target for water supply wells such as in the north region of the Lake Belt area. Where they are vertical and originate near the surface, such as the one seen on the right hand side of Figure 32, are likely to represent a vertical conduit for water from the surface to quickly enter the deeper parts of the aquifer. Identification of highly porous and permeable areas and characterization of their extent and depth can be useful for preventing contamination of the aquifer from surface water runoff, leaky underground storage tanks and waste injection wells. Contamination from surface water contaminants seeping into groundwater is likely to become more of an issue for the Biscayne aquifer if sea level rises and flooding becomes more frequent.

Although the geomodels are only approximations of the subsurface and these visualizations are not quantitative, they can be extremely useful tools for identifying areas to explore further with geophysics, boreholes and or modeling.

ASSISTING IN THE DEVELOPMENT OF GROUNDWATER FLOW MODELS

Better understanding of spatial trends in porosity and how porosity relates to lithostratigraphy and cyclostratigraphy helps groundwater modelers to develop a more realistic representation of the spatial variability of aquifer properties in their models, leading to more accurate models and improved water management.

“The main difficulty for karst aquifer characterization is to determine the location and geometry of highly permeable karst conduits” (Geyer, et al., 2013). In the past, water management has often relied on 2-d visualization from cross sections or 1-d data from

wells. Geomodels can provide a 3-d spatial representation to enhance knowledge of the subsurface.

Due to complexity of karst aquifers, modelers often use stochastics to develop a representation of the spatial distribution of subsurface characteristics (Pardo-Iguzauiza et al., 2012). Statistics from direction roses and histograms can help modelers more accurately represent the shape, size and spatial trends of aquifer properties within karst aquifers. Identifying trends in porosity can shed light on the understanding of depositional environments, diagenesis, and porosity formation and how they are interrelated. By implementing this knowledge into improving geomodels representation of the subsurface, more accurate calculations for groundwater storage and flow rates may be derived.

6. CONCLUSION

This thesis is aimed at improving the understanding of spatial variability of porosity and the relations between porosity, lithology and cyclotratigraphy in the Biscayne aquifer. In order to do this, 3D geomodels were used to facilitate the understanding of the subsurface within the Lake Belt study area. The work presented in this thesis shows how the spatial distribution of porosity in the study area within the cycles and lithologies are related and also offers examples of how geomodels can be used to improve management of highly heterogeneous aquifers such as the Biscayne aquifer.

While zones of similar porosity may or may not cross through lithologic and cycle boundaries in much of the study area, patterns in porosity generally mirror patterns in lithology and cycle stratigraphy. The geomodels proved useful for identifying high porosity conduits, such as the one in Figure 32. Statistical analysis from the geomodels was useful in identifying ranges in porosity within differing cycles and individual facies.

This statistical analysis allowed for investigation and identification of ranges in porosity and trends in porosity with depth and across lithologies and cycles. Hierarchy of porosity seems to follow a pattern with differing lithofacies, high frequency cycles and depth. Further investigation of porosity increase with depth, within a formation is warranted. It may be possible to ascertain a rate at which porosity increases within a formation over time.

However this would require greater certainty in the age of the tops and bottoms of the high frequency cycles than currently exists. For example, for some of the high frequency cycles, a literature review reveals age estimates that differ by as much as hundreds of thousands of years (Hickey, 2010). Future research that 1) reduces the uncertainty in age estimates and/or 2) develops ways of presenting rates of porosity change in a manner that acknowledges the uncertainty would be helpful. Accurately representing the porosity and flow is important to the public when facing possible groundwater contamination problems derived from septic tanks, deep well injection, salt water intrusion, contaminant transport, surface and groundwater interaction at well fields and well field protection.

These zones of flow may alternatively be helpful for pointing out areas to target for groundwater supply wells. Geomodels and porosity models in conjunction with traditional well data and cross sections can facilitate a more comprehensive understanding and representation of the subsurface. Over time as more well data and possibly seismic data are collected it will become possible to build on the geomodels created from this thesis in order to develop a deeper understanding of the dynamics within the Biscayne aquifer and how flow moves through pathways with wanted or unwanted consequences.

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