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Ground-Water Movement in the Floridan Aquifer System in Southern Florida: Flow Patterns Based on Hydraulic Gradients

The maximum hydraulic gradient (dh/dl) along a flow path indicates the direction of ground-water movement, whereas the rate of movement is dependent on the hydraulic gradient and the hydraulic properties of an aquifer-specifically, hydraulic conductivity and porosity. The average effective linear velocity of ground water () in a homogeneous and isotropic porous medium is explained by Darcy's law, which is expressed by the following equation:

=	K (dh/dl)	(6)

where
= average effective linear velocity, in feet per day;
K = hydraulic conductivity, in feet per day;
dh/dl = hydraulic gradient ( I ) or unit change in head per unit length of flow line, in feet per foot; and
= effective porosity.

Where hydraulic conductivity and effective porosity are constant, changes in hydraulic gradient indicate relative changes in velocity. Velocity can also be determined by the equation

=	T x I	(7)
	m x

where
T = transmissivity, in feet squared per day;
m = aquifer thickness, in feet; and
I = hydraulic gradient (dh/dl), in feet per foot.

Upper Floridan Aquifer

Measurements of head in the Floridan aquifer system are chiefly confined to the upper part of the aquifer system, where most wells were constructed. Maps of the potentiometric surface of the Upper Floridan aquifer (see map for 1980, fig. 4) are periodically prepared by the U.S. Geological Survey and other government agencies from measurements of water levels in many wells throughout the State. The maps show the configuration of the contours representing the prevailing isopotentials, and ground-water movement is downgradient (that is, from areas of high potential to areas of low potential) and approximately normal to the contours if the aquifer system is assumed to be isotropic. Movement of ground water in the Upper Floridan aquifer is shown by flow lines radiating generally from the area of highest head in central Florida near Polk City (fig. 4). South of the Polk City potentiometric surface high, the head in the aquifer declines gradually along a flow line that divides flow to the Atlantic Ocean on the east and the Gulf of Mexico on the west.

Figure 18. Estimated predevelopment and May 1980 hydraulic gradients along flow lines from Polk City to Key Largo and Fort Lauderdale, Upper Floridan aquifer. (Location of segments shown in fig. 11.) [larger version]

To gain insight into the rate of ground-water movement southward from the Polk City potentiometric surface high in central Florida, estimates of velocities and transit times were calculated for estimated predevelopment hydraulic gradients along selected segments of flow lines from Polk City to Key Largo and to Fort Lauderdale (fig. 18).

The estimates are further based on the assumptions that (1) predevelopment hydraulic gradients were unaffected by changes in sea level and climate, (2) the transmissivity (T) of the Upper Floridan aquifer is distributed according to Bush (1982, fig. 6), (3) the thickness of the aquifer (m) is 500 ft, and (4) the effective porosity () is 0.30 (table 7) and vertical flow is negligible. Segment I represents the flow along 75 mi from Polk City to about the southernmost point of recharge by sinkhole lakes in central Florida. Segment II represents the flow along 72 mi from the southernmost point of recharge to the center of southern Florida. Segment III represents the flow along 80 mi from the center of southern Florida to Key Largo. Segment IV represents the flow along 47 mi from the center of southern Florida to Fort Lauderdale.

For estimated predevelopment gradients and an assumed average porosity of 0.30, a particle of water traveling 227 mi from Polk City to Key Largo (segments I through III) would be in transit for a time ranging from 159,000 to 779,000 yr, depending on the estimated transmissivity. A particle of water traveling 152 mi from the southernmost point of recharge in central Florida to Key Largo (segments II and III) would be in transit from 155,000 to 768,000 yr. A particle of water traveling 119 mi from the southernmost point of recharge to Fort Lauderdale (segments II and IV) would be in transit from 123,000 to 593,000 yr. Locally, a particle of water traveling 47 mi (segment IV) from the center of southern Florida (site 10) to Fort Lauderdale (site 9) would be in transit from 35,000 to 177,000 yr. Only the transit time between sites 10 and 9 (segment IV) is within the 40,000-yr useful range of carbon-14 dating. Therefore, the occurrence of measurable carbon-14 activity in the brackish ground water in southern Florida strongly suggests that infiltrating freshwater in central Florida is not the only source.

Table 7. Estimated transit times along flow lines from the Polk City potentiometric surface high to Key Largo and to Fort Lauderdale under predevelopment gradients, Upper Floridan aquifer [Based on aquifer thickness of 500 feet and porosity of 0.30. Location of flow segments shown in fig. 11]
Flow segment	Head difference (feet)	Distance (miles)	Transmissivity (feet squared per day)		Velocity (feet per year)		Transit time (years)
			Minimum	Maximum	Minimum	Maximum	Minimum	Maximum
I	60.5	75	100,000	250,000	37	93	4,300	11,000
II	8.2	72
	14.1	136	1100,000	1250,000	15.2	113	115,000	136,000
	14.1	136	110,000	150,000	10.5	12.6	173,000	1380,000
							88,000	416,000
III	21.8	80	10,000	50,000	1.2	6.3	67,000	352,000
I-III	90.5	227					159,000	779,000
IV	14.3	47	10,000	50,000	1.4	7.0	35,000	177,000
I,II,IV	83.0	194					127,000	604,000
1Segment II divided into two subsegments.

Lower Floridan Aquifer

Estimates of movement of ground water in the Lower Floridan aquifer have chiefly been based on indirect evidence because measurements of representative head are difficult to obtain. Attempts to calculate hydraulic gradients between a few closely spaced wells for which data are available have largely been unsuccessful owing to the extremely high transmissivity of the water-bearing zones in the Lower Floridan aquifer, to the effects of short-term tidal-caused fluctuations in water levels, and to variations in water density (Meyer, 1974; CH₂M Hill, Inc., 1981; Singh and others, 1983).

In recognition that the hydraulic gradient for a transmissivity of about 2.5 x 10⁷ ft²/d (Singh and others, 1983) would be very small, the head in well G-2296 at site 10 near the center of southern Florida was compared with the head in well G-2334 at site 9 in Fort Lauderdale about 44.5 mi east of well G-2296 at site 10 (table 8). The water level in well G-2296 was measured at 7.0 ft above sea level during a packer test on March 4, 1981. It was assumed that fluctuations resulting from tides were insignificant at well G-2296 because of its great distance from the coast. The water level in well G-2334 was continuously recorded during May 16-20, 1983, after a performance test on May 10, 1983 (fig. 19). Semidiurnal tides caused the water level to fluctuate about 0.5 ft, but the daily mean water level rose about 0.6 ft during the period as the density of the water column decreased owing to heating. The water level was about 0.2 ft above sea level on May 26, 1981, when a temperature survey (log) of the water column was obtained (fig. 6).

Table 8. Comparison of pressure head and related data between well G-2334 at site 9 and well G-2296 at site 10, Boulder Zone of the Lower Floridan aquifer [Site locations shown in fig. 2]
Well No.	Site No.	Average temperature (°F)	Dissolved solids1 (milligrams per liter)	Salinity (per mil)	Density2 (grams per cubic centimeter)	Water level3 (feet)	Pressure head4 (feet)
G-2334	9	62.2	37,500	36.62	1.02683	0.2	2,875.3
G-2296	10	78.8	37,500	36.62	1.02427	7.0	2,875.1
1Assumed to be the same for both wells. 2At prevailing salinity and temperature. 3Referred to sea level. 4At 2,800 feet below sea level; density equals 1.00000 g/cm3 (gram per cubic centimeter).

The density of the borehole fluid in each well was calculated from oceanographic tables (U.S. Navy, 1962) based on measurements of salinity (dissolved solids) and temperature, and the pressure heads were calculated for each well at a common depth of 2,800 ft below sea level for a common fluid density of 1.0000 gram per cubic centimeter (g/cm³). Salinity was based on the dissolved solids residue upon evaporation at 180 °C in a sample of water from well G-2334 at site 9. The lack of precision in the dissolved solids analyses required an assumption of uniform salinity. The average temperature of the borehole fluid (salinity comparable to seawater) in each well was determined from temperature logs.

The pressure head at well G-2334, site 9, was about 0.2 ft higher than that at well G-2296, site 10. The apparent inland hydraulic gradient, I, was estimated by the equation

I =	0.2 foot	x	1 mile	(8)
	44.5 miles		5,280 feet
	= 8.5 x 10-7

The average water velocity, , was estimated by the equation

=	T x I	x 365   (9)
	m x

where
= average water velocity, in feet per year;
T = 2.5 x 10⁷ ft²/d;
m = 650 ft;
I = 8.5 x 10^-7; and
= porosity, ranging from 0.2 to 0.4.

Based on the estimated hydraulic gradient (8.5 x 10^-7), the average velocity of ground-water flow through the Boulder Zone from site 9 to site 10 ranges between 59.7 and 29.8 ft/yr for porosities ranging from 0.2 to 0.4, and the transit time ranges from 3,900 to 7,900 yr.

A comparison of the estimated hydraulic gradient, velocity, and transit time from water-level measurements at sites 9 and 10 with those estimated by radio carbon dating suggests that the calculated difference in head may be too high (table 9, measurement 1). The estimated gradients and velocities based on transit time from radiocarbon dating suggest a gradual decrease in gradient and velocity during the past 7,500 yr. The present-day gradient and velocity would probably be closer to 3.8 x 10^-7 and 17 ft/yr, respectively. The difference in head between the wells, located 44.5 mi apart, would then be only 0.09 ft-a relatively small value compared with the range of tidal fluctuations at the coast and with the corrections in head for differences in fluid density. Another possibility is that the ground-water velocity calculated by equation 9 is on the basis of porous-medium concept. However, ground-water flows through the Boulder Zone may be best described by conduit or fracture flow, which normally is faster than flow in porous media. No acceptable fracture flow equations are available to calculate such velocity.

Table 9. Estimated hydraulic gradients and related hydraulic data based on measured water levels and radiocarbon dating, Boulder Zone of the Lower Floridan aquifer [Based on transmissivity of 2.46 x 107 feet squared per day, thickness of 650 feet, and porosity of 0.30. Site locations shown in fig. 2]
Measurement No.	Referenced segment	Distance (miles)	Head difference (feet)	Hydraulic gradient (feet per foot)	Average velocity (feet per year)	Transit time (years)
1	Site 9 to site 101	44.5	0.2	8.5 x 10-7	39.0	6,025
2	Site 9 to site 102	44.5	.28	1.2 x 10-6	54.6	4,300
3	Subsea outcrop to site 92	10.5	.021	3.8 x 10-7	17.3	3,200
4	Subsea outcrop to site 102	55.0	.24	8.4 x 10-7	38.7	7,500
1Calculation based on fluid density, water-level measurements, and assumed aquifer characteristics. 2Calculation based on radiocarbon age and assumed aquifer characteristics.