preliminary development of carbonate rock core ...

PRELIMINARY DEVELOPMENT OF CARBONATE ROCK CORE TESTING APPARATUS TO EVALUATE TURBULENT FLOW REGIMES 1

SZEWS E., 1REDA D., 1SHAHBAZIAN O., 1KELSAY D.,1BROWN C.*, 1HUDYMA N. and 2MIRECKI J. 1

University of North Florida, School of Engineering, Civil Engineering, [email protected], [email protected], [email protected], [email protected], *[email protected], Jacksonville, FL USA 2 U.S. Army Corps of Engineers, Jacksonville, FL USA, [email protected] Keywords: Vuggy Limestone, Hydraulic Conductivity, X-ray computed tomography Abstract Determining the hydraulic conductivity of vuggy carbonate rock cores subjected to turbulent flow regimes is difficult to accomplish using typical laboratory methods. This study outlines the preliminary development of a core testing device designed to operate within the turbulent zone. The testing apparatus is based upon the assumption that rock core conduits can be modelled as a system of equivalent pipes. Several vuggy limestone samples bored from the Biscayne Aquifer in South Florida, USA were collected for further testing. One of these cores was tested to evaluate “proof of concept” of the testing apparatus and to develop a corresponding data processing methodology to determine typical rock properties such as effective porosity and the apparent hydraulic conductivity. The core to be used for testing was selected by its overall condition and porosity. The test core that was selected was then processed. Data processing included use of Xray computed tomography (CT) image data, which permitted the estimation of the total volume of voids, hydraulic radius of pore conduits, conduit area, and total volume. The headloss through the test core was determined using the testing device with a superposition approach in which specimens were tested with and without cores in place. A second limestone test core consisting of fossiliferous limestone, collected in northern Florida, USA, was also tested for comparison. Further development of the overall testing methodology is underway but this paper demonstrates the general feasibility of the approach.

1.

Introduction

Hydraulic conductivity within aquifers can vary by up to 13 orders of magnitude between fractured competent rocks to karst limestone (Sukop et al. 2013). Defining the hydrologic characteristics of vuggy, macro-porous limestone found in Florida, USA, particularly those that include the Biscayne Aquifer of South Florida (see Figure 1 for the general study area), was the motive for this research study. It is believed that as fluid flows through these materials in regions of higher hydraulic gradient (e.g. near pumping wells or canals), head loss results in a component of turbulent flow characterized by Reynolds numbers in excess of 1 (DiFrenna et al. 2007; Chin et al. 2009). Simulation of turbulent flow in rock cores obtained from porous carbonate rocks such as those that comprise the Biscayne Aquifer is difficult. Traditional laboratory techniques such as constant head tests or falling head tests are valid for laminar flow conditions. Hydraulic conductivity and intrinsic permeability is determined using traditional laboratory techniques usually resultin in inaccurate interpretation due in part to short-circuiting due to interconnected vugs within the karstic limestone specimens. The phenomenon of turbulent flow within aquifer has been the focus of many computer simulation and physical testing research studies. Sukop et al. (2013) developed a numerical model that could be used as an alternative to these traditional, inaccurate laboratory techniques. Essentially,

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Figure 1. General Study Area in South Florida, USA. the numerical model was developed as a “virtual permeameter” capable of simulating fluid flow in both the laminar and turbulent zones. X-ray CT scan data was obtained and the Lattice Boltzmann method was applied to simulate flow as a particle distribution function (Sukop et al., 2013). However, development of a testing apparatus that could physically replicate the results of such studies would be useful (DiFrenna et al., 2007). Typically, estimation of hydraulic conductivity and aquifer transmissivity within any aquifer requires larger field tests. The interpretation of such tests assumes laminar flow within the aquifer, and homogeneous permeability. In extensive karst-conduit systems, laminar flow may not accurately represent the flow regime. Several recent studies in the Biscayne Aquifer in south Florida, USA illustrate such problems. Shapiro et al. (2008) conducted a regional tracer study to evaluate potential contaminant transport to a large, municipal well field west of Miami, FL USA. Tracer tests in the Biscayne Aquifer show that in spite of the aquifer’s highly transmissive nature, concentration results of sulphur hexafluoride show an elongated tail, with less than half of the test contents recovered 160 hours after injection (Shapiro et al., 2008).The researchers reasoned that the morphology of touching-vug pores may induce turbulent flow (such as exchange with eddies) that could be responsible for the chemical retention observed during this test. More research on the relationship of turbulent flow and chemical transport is required. Brown and Motz, (2007) characterized the transmissivity, leakance, skin friction, and storativity of the upper portion of the Biscayne Aquifer using a project-scale canal drawdown test. Canal L-31N, which is incised into the Biscayne Aquifer, was chosen for the pumping test. Canal

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L-31N was held at a constant discharge level of 1.19×106 m3/d while the pumping test was conducted. The test ran one day during the dry season. Observations were made at monitoring wells adjacent to the canal. Using the information from observation well MW-2, located 640 meters west from the canal, a match point process was used to determine aquifer transmissivity (2.31×105 m2/day) and storativity (0.20). Since the wells were unconfined and had no vertical leakance, the vertical leakance was not relevant. The skin friction was calculated by dividing the hydraulic conductivity by the leakage coefficient for the sediment deposits resulting in a value of 156.8 m. The observation wells that were closer to the canal than MW-2 showed greater effects of canal pumping. During this study, other well transects were also reviewed to estimate aquifer parameters, but some resulted in abnormally low estimates of the key parameters possibly due to underflow of the canal system. Another explanation is that portions of the Biscayne Aquifer were flowing in the turbulent zone resulting in low estimates of hydraulic conductivity. Past research has shown that in the turbulent flow regime usually denoted by Reynolds number larger than about 10 (Sukop et al. 2013) and possibly up to 2,000 (Ghasemizadeh et al. 2012), Darcy flow deviates from a linear relationship. Sukop et al. (2013) demonstrated that as flow gradients increase, the estimates (using numerical modeling) of “apparent hydraulic conductivity” actually decrease.

Figure 2. Generalized Piezometric Heads in the Biscayne Aquifer Makuch et al. (1999) evaluated the scale dependence of hydraulic conductivity in heterogeneous media. The main focus was the relationship between hydraulic conductivity and how the scale measurement is affected by the flow type and heterogeneity of the medium. The team collected data from different aquifers and formations then characterized the dataset using three different

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criteria: flow type, type of lithology, and scale of measurement. Through their analyses, they observed bedrock formations containing solution conduits and fractures that have a larger scaling exponent than sandy formations controlled by pore flow alone. Their conclusion was hydraulic conductivity is dependent upon scale and that this scale measurement was a function of the degree of heterogeneity of the medium and the type of flow through the medium. In south Florida, the Biscayne Aquifer is included in marginal marine limestones of the Fort Thompson Formation and Miami Limestone. These limestones were deposited in shallow tropical marine environments during successive Pleistocene high sea stands. During episodes of low sea level (estimated at approximately 100 m lower than today), the regional hydraulic gradient was steeper. Infiltration and recharge of undersaturated water resulted in limestone dissolution and the formation of karst. The conceptual hydrogeologic model for the Biscayne Aquifer in the area of Canal L-31N was developed by Cunningham et al. (2006). The Biscayne Aquifer is conceptualized as a sequence of eight layers whose lithologies are characterized by three different pore classes. Thus, limestone lithologies are related to permeability. Limestones showing the “touching vug” pore class show the highest permeability, and serve as preferential flow zones in the aquifer. Micritic fresh water carbonates represent another, less permeable pore class, which serves as a leaky confining unit in the aquifer. The conceptual hydrogeologic model of Cunningham et al. (2006) presents a systematic framework for the aquifer that relates lithology, cyclostratigraphy, and hydrologic characteristics. The limestone generally has high hydraulic conductivity which when combined with the relatively flat topography results in widely spaced piezometric water levels in the aquifer except near man-made canals where the gradient steepens considerably. Figure 2 shows generalized historical water levels in the Biscayne Aquifer in the study area along with relevant water control structures and piezometer/observation well locations. A large portion of Everglades National Park in Florida, USA is underlain by the Biscayne Aquifer. 2.

Materials

2.1

Testing Apparatus

The testing apparatus (Figure 3) consisted of three main components, housing for specimens, a frame, and pumping mechanism. The housing for the specimens was constructed primarily of Plexiglas. The base of the housing was a 61×61 cm sheet of Plexiglas with 15.24 cm walls surrounding the perimeter (overflow tank). The primary housing for the samples, a 48 cm tall cylinder with a 30.5 cm diameter, was epoxied to the base of the housing. A 5.08 cm hole was then drilled in the center of the base for the placement of a coupler. The coupler was comprised of two 15.24 cm square steel plates with a threaded double female connector epoxied to the top plate. The female connector was 1.27 cm in diameter. Silicone was used to seal the attached coupler to the housing. The frame supporting the housing was made out of wood. The frame is 1.4 m tall with four legs in a square configuration spaced approximately 0.5 m apart. Top, middle and bottom support brackets were constructed around the legs for stability. A timber was then attached to the center support bracket to support the pump located beneath the coupler extending through the housing. The pumping mechanism consisted of 1.27 cm outer diameter tubing, a pump, two pressure gauges, a ball valve, a flow gauge, and 2.54 cm diameter hose. The main pressure gauge was placed directly beneath the housing. This gauge was attached to 18.42 cm of tubing, which then attached to the ball valve. Another 18.42 cm of tubing connected the ball valve to the secondary pressure gauge which then attached to the pump. The pump was attached to the 2.54 cm hose which led back to the top of the housing where a flow gauge recorded the total volume of water pumped during testing. A CAD model of the entire assembly is shown below in Figure 1, along with annotation regarding the various components installed in the system. The testing apparatus was designed to transmit water through a vuggy limestone core at a variable rate with constant head. This was achieved with the constant head tank which holds both the lime-

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stone core, as well as the test fluid (water). The limestone cores were fitted with a pipe adaptor that permitted the cores to be directly connected to the pump and piping system. Pressure was recorded using gauges at two locations; beneath the core and just prior to the pump. A ball valve was located within the testing system, between the two pressure gauges, to allow variability in the fluid flow through the core. A totalizing flow meter recorded the flow rate through the limestone sample. Tubing which was large enough to minimize head loss while fitting to various pressure gauges was selected to connect all the necessary components and return the water to the system. The result was a closed loop system that provided a constant head above the core and a steady flow through the core that could be accurately monitored. The design of the testing apparatus allowed the rapid sampling of vuggy limestone cores with simple data collection. During testing, the system pressure drop was recorded at a particular flow rate without the core in place. Then the same setup was used with the core installed, constituting another head loss in the system. Using the simple concept of superposition, the difference in head loss between the two test runs represents the head loss in the core alone. Flow rates with the cores in place had to be slightly adjusted so that flow through the system was the same for both trials.

Figure 3. Core Test Device. 2.2

Sample Selection and Preparation

Core samples (standard PQ core barrel size) for this study were collected by the US Army Corps of Engineers (USACE) from 1974 to 2006. The two specimens used in this initial study were a vuggy limestone from the preferential flow zones of the Biscayne Aquifer (Fort Thompson Formation), and a fossiliferous limestone from the Surficial Aquifer System (Anastasia Formation). The testing objective was to determine the “apparent hydraulic conductivity” of the rock cores, and to characterize the flow regime using pipe flow approach to calculate the Reynolds

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number for each test run. Once the samples were selected from the USACE provided core boxes they were cut to a standard length of 2 specimen diameters (typical length was approximately 15.25 cm) using a wet diamond saw. A 1.27 cm diameter by 10.16 cm long hole was then drilled in the center of the base of each core. Specimens were then X-ray CT scanned at a local hospital. The scans were used to determine the degree of interconnectivity of the vugs and various volumetric vug parameters such as volume, perimeter, and hydraulic radius. After X-ray CT scanning, epoxy was used to seal the bottom and top of the specimens to obtain predominately horizontal flow into the specimen. The threaded double female connector was then epoxied into the specimen and epoxied to the top plate. Table 1 provides details of the specimens used in this study. Table 2. Rock Core Information. Specimen ID

Specimen Depth (m below ground surface)

Core Location

Aquifer Zone

B-7

South Florida location, 8.5 SMA, Boring # CP-02-85SMA-CB96

10

Fort Thompson Formation, Biscayne Aquifer

B-10

North Florida location, Upper St. Johns Levee 74, Boring # CB-L74N 72

0.56

Anastasia Formation, Surficial Aquifer System

3.

Methods

3.1

Volume Calculations

Several calculations were produced to provide a general indication of the total specimen volume and volume of voids of each specimen. Each core diameter was measured at the top middle and bottom, an average was taken of these diameters for nominal volume calculation. Four heights were recorded for each sample. These heights were taken at the end points of the measurements for the top and bottom diameters, and an average was calculated for use in nominal volume calculation. Equation 1, shown below, was used to calculate nominal volume. Where Vn is the nominal volume, Ha is the average height, Da is the average diameter. 2

Vn

§D · SH a ¨ a ¸ (1) © 2 ¹

The specimen effective porosity was then determined using volume displacement. Each specimen was submerged into a cylindrical contain of known volume and containing a known initial volume of water. The specimen was allowed to equilibrate for ten minutes to ensure the vugs were completely filled with water. After ten minutes, the change in volume was recorded and the specimen was removed. This change in volume was subtracted from the volume calculated using Equation 1 to determine the volume of vugs. Table 2 provides the nominal dimensions, volumes, and estimated effective porosity of each sample tested and discussed in this paper. Table 2. Rock Core Dimensions and Computed Porosity. Core ID

Nominal Dimensions (cm)

Nominal Volume (cm3)

Estimated Effective Porosity (%)

B-7

9.6 cm diameter by 17.6 cm high

1,274.30

11.5

B-10

9.85 cm diameter by 19.9 cm high

1,516.41

14.8

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3.2

Preliminary CT Scanning Results

Preliminary analysis of the X-ray CT scans was performed using a free image reader provided by the X-ray CT scanner manufacturer (Syngo by Siemens AG Medical Solutions, www.syngo.com). Using the image reader, preliminary measurements were made on interconnected vugs. These measurements include vug area and wetted perimeter. Figure 4 contains Xray CT scan slice images from specimen B-7. Note the drilled connector hole in the bottom of the test core.

Figure 4. Typical CT Scan Image Due to the limitations of the image reader software, further work is ongoing using other visualization software. In addition, custom MATLAB® programs have been written to automatically process the numerous X-ray CT scan images into a three dimensional image of the primary test core. The MATLAB® scripts will permit automated calculation of the bulk core porosity, conduit areas, and other key dimensions. At the time of development of this paper, these efforts were not yet complete. 3.3

Testing Procedure

Calibration of the testing apparatus was conducted using three configurations of the ball valve: completely open, three quarters open, and half open. Before testing cores, a preliminary test run was conducted on the assembly to record head loss and flow rate throughout the assembly. Each configuration was run for five minutes to calculate average flow rate and average head loss from the pressure gauges. After calibration, specimen B-7 was placed into the assembly and the three modes were run again. Once again each mode was allowed to run for five minutes in order to calculate an average flow rate and head loss. Once specimen B-7 was tested, specimen B-10 was tested. 3.4

Calculations

The data collected from the tests includes specimen pressure drop and flow rate. These data were then combined with the CT scan data to determine the head loss across the core in meters, the apparent hydraulic conductivity, and the Reynolds number in order to evaluate the flow regime. The temperature of the water used was 20 degrees C. Equations 2 and 3 provide the basic equations used along with the description of the relevant variables. Q K ¹ IANe (2)

Where K* is the apparent hydraulic conductivity of the core, I is the gradient across the core calculated from the recorded head loss divided by the mean flow length taken as half the nominal length of the core plus half of the nominal diameter, A is the flow area taken as the surface

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area of the core not including the bottom, and Ne is the effective porosity.

Re#

v

D (3) Q

Re# is the Reynolds number, v is mean velocity through the core conduits, D is the mean diameter of the conduits, and Q is the kinematic viscosity of the water at the recorded temperature. For this study, D was replaced with 4 times the hydraulic radius to account for any conduits that were not perfectly circular in nature. As part of sample preparation, a 1.28 cm diameter hole was drilled in the bottom of the core to facilitate connection to the test apparatus. This means that the Reynolds number can usually be estimated using this diameter unless “wallowing” occurred with the drill bit due to the soft nature of the vuggy limestone.

4.

Results

Core B-7, selected for this analysis, was used as the “proof of concept” sample core. Core B-10 was used for comparison purposes. The results along with other pertinent core data are shown in Table 3. The apparent hydraulic conductivity value, K*, for specimen B-7 is 0.006 meters per second. The apparent hydraulic conductivity value, K*, for specimen B-10 is about one and one-half order of magnitude less than B-7 or about 0.0003 meters per second. The estimated Reynolds numbers were about 19,000 and 9,000 for specimens B-7 and B-10, respectively. These values are both well within the turbulent flow range, even if the transition to fully turbulent flow occurs at a value as high 2,000. Table3. Testing Results. Specimen

Valve Setting

Pressure Drop (kPa)

Delta Flow (m3/day)

Estimated (m/m)

K* (m/s)

B-7

Fully Open

6.89

15.78

5.18

0.006

B-10

Fully Open

49.93

7.96

34.27

0.000295

5.

Discussion

This paper presented results from the preliminary development and testing of a new rock core testing apparatus designed to simulate turbulent flow and measure apparent hydraulic conductivity. Two vuggy limestone specimens were tested successfully. The two specimens represent a range of expected carbonate rocks encountered in typical Florida surficial aquifers. Specimen B-7, collected in South Florida, was part of the highly permeable Fort Thompson Formation which is the lower portion of the larger Biscayne Aquifer. The measured apparent hydraulic conductivity of 0.006 m/s can be directly compared to regional estimates of the hydraulic conductivity of the same zone. Using a full canal pumping test, Genereux & Guardiario (1998) estimated the hydraulic conductivity of the Fort Thompson as 0.047 m/s. Zechner & Frielingsdorf estimated the same using a calibrated numerical model to be 0.06 m/s. Clearly, the estimated value from the specimen B-7 test is one order of magnitude lower. However, as pointed out by Sukop et al. (2013), estimates of hydraulic conductivity are generally made assuming laminar flow. Sukop et al. (2013) demonstrated that as the applied gradient and Reynolds number increase the estimate of hydraulic conductivity decreases. Therefore, the core test apparatus may provide a simple and cost effective means to estimate a minimum hydraulic conductivity value to use in model development or stochastic studies. Specimen B-10 revealed an even lower estimated apparent hydraulic conductivity value, consistent with its fossiliferous or coquina character which is dominated by much smaller vugs as compared to specimen B-7 from the Fort Thompson Formation. Therefore, a smaller estimated apparent hydraulic conductivity for this core is consistent with pre-test expectations. Further work with the other Biscayne Aquifer cores is underway. Also, further development of the data using CT Scans and numerical modelling is ongoing. The testing apparatus is also be-

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ing upgraded: a larger pump capable of variable speeds and flow rates is being considered. A variable speed pump would permit testing the apparatus assembly “without specimen” in place and “with specimen” in place but using the same flow rate. The current setup is more difficult to use for flow control since the control valve is operated manually. Therefore, in addition to a different pump, a motor operated valve would be a great addition to the testing apparatus. 6.

Acknowledgments

The research team would like to acknowledge the support of the Director of the School of Engineering for his financial support to build the testing device. Also, the team would like to thank the support of the U.S. Army Corps of Engineers who provided carbonate cores for testing and the Mayo Clinic which conducted the CT scans of 10 rock cores including the two discussed in this paper. The team also acknowledges the previous research by Sukop et al. (2013) who provided inspiration for this endeavour. 7.

References

Brown, C. J., Motz, L. H. (2007). Analysis of canal pumping test adjacent to everglades national park using a one-dimensional flow model considering storage and skin effect in a finite-width sink. Restoring Our Natural Habitat World environmental and water resources congress 2007. Retrieved from https://blackboard.unf.edu/courses/1/2014SPRING.CGN6933.12598.01.MULTI/groups/_432 72_1//_1884017_1/Motz and Brown 2007 40927(243)186_ASCE_Congress.pdf Chin, D.A., Price, R.M., DiFrenna, V.J., (2009). Non-linear flow in karst formations. Groundwater v. 7(5): 669-674. Cunningham, K.J., Wacker, M.A., Robinson, E., Dixon, J.F., Wingard, G.L., (2006). A cyclostratigraphic and borehole geophysical approach to development of the three-dimensional hydrogeologic model of the karstic Biscayne aquifer, southeastern Florida. US Geological Survey Scientific Investigations Report 2005-5235, 69 p. DiFrenna, V. J., Price, R. M., Reza Savabi, M. (2007). Identification of a hydrodynamic threshold in karst rocks from the Biscayne aquifer, south Florida, USA. Hydrogeology Journal, doi: 10.1007/s10040-007-0219-4 Genereux D., Guardiario J. (1998). A canal drawdown experiment for determination of aquifer parameters. Journal of Hydraulic Engineering, 3:294-302. doi:580 10.1061/(ASCE) 10840699(1998)3:4(294) Ghasemizadeh, R., Hellweger, F.,Butscher,, C., Padilla, I., Vesper, D., Field, M., Alshawabkeh, A., (2012). Review: Groundwater flow and transport modeling of karst aquifers, with particular reference to the North Coast Limestone aquifer system of Puerto Rico.Hydrogeology Journal.20(8), 1441-1461, doi: 10.1007/s10040-012-0897-4 Makuch, D. S., Carlson, D. A., Cherkauer, D. S., Malik, P. (1999). Scale dependency of hydraulic conductivity in heterogeneous media. Ground Water, 37(6), 904-919. Shapiro, A. M., Renken, R. A., Harvey, R. W., Zygnerski, M. R., Metge, D. W. (2008). Pathogen and chemical transport in the karst limestone of the Biscayne aquifer: 2. chemical retention from diffusion and slow advection. Water Resources Research, 44, doi: 10.1029/2007WR006059 Sukop, M. C., Huang, H., Alvarez, P. F., Variano, E. A., Cunningham, K. J. (2013). Evaluation of per-meability and non-darcy flow in vuggy macro porous limestone aquifer samples with lattice Boltzmann method. Water Resources Research, 49, 1-15. doi: 10.1029/2011WR11788 Zechner, E., Frielingsdorf, W. J. (2003). Evaluating the use of canal seepage and solute concentration observations for aquifer parameter estimation.Journal of Hydrology, 289(2004), 62-77. doi: 10.1016/j.jhydrol.2003.11.002.

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