freshwater/saltwater response to the reduction in the freshwater head (h f ) in order to

Transcription

1 100 Seawater enters the pumping wells when (h f ) approaches sea level at 0 m. The freshwater/saltwater response to the reduction in the freshwater head (h f ) in order to attain hydrostatic equilibrium is slow (Howard, 1987). However the low permeable fractures or conduits along the South Coast Fault Zone and wells drilled to intercept the saltwater interface (Rushton, 1980) will allow the aquifer to reach equilibrium conditions at a much faster rate. Therefore, it is pertinent to simulate cells at the saltwater/freshwater interface along the southern coastline with the equivalent freshwater head h f. The saltwater interface was simulated as a constant-head boundary along the coastline in these areas (Figure 4.10). Equivalent freshwater head was calculated is documented in Table 6. For the purposes of this study, the interface will be treated as a specified-head seepage boundary to the ground-water flow system. Submarine Discharge The quantity of discharge from the White Limestone to the sea along coastal areas south of the South Coast Fault is unknown. Geophysical investigations conducted by NASA (1971) failed to show any evidence of freshwater outflow from the White Limestone aquifer along the immediate coast. However, actual points of discharge into the sea may be some distance offshore where the White Limestone is exposed to the seabed. Under natural conditions, the length of the saltwater wedge is directly proportional to the hydraulic conductivity (K) and thickness of the aquifer (b 2 ) squared and inversely proportional to the flow of freshwater (q) to the sea. Analytical

2 101 Table 6. Calculation of freshwater head (m) along the constant head boundary at Bernard Lodge, Old Harbor, and Manchester Highlands, Rio Cobre and Rio Minho-Milk River Basins, Jamaica, West Indies. Basin Aquifer Location Thickness of Aquifer b (m) Fresh Water Head h f (m) Rio Cobre Alluvium Bernard Lodge Rio Cobre Alluvium Old Harbor Rio Minho-Milk River White Limestone Manchester Highlands

3 102 EXPLANATION CONSTANT-HEAD BOUNDARY Mandeville Linstaed Boundary of physiographic region Major Towns May Pen Old Harbour River channel CARIBBEAN SEA Figure 4.10 Map of study area showing the constant-head boundary.

4 103 calculations of submarine discharge from the White Limestone aquifer along the Manchester Highlands and the alluvial aquifers at Bernard Lodge and Old Harbor were accomplished using the following data provided by the WRAJ (Table 7-8): 1) width of the coastal boundary across which submarine discharge occurs, 2) the distance inland from the shoreline, 3) hydraulic conductivity values, 4) aquifer thickness and 5) the Ghyben Herzberg ratio (á = 0.025). Equation 6 was used to compute the submarine discharge from the coastline: ThW Q s = α (6) 2L where Q s is the submarine discharge of freshwater [L 3 /t] T is the aquifer the transmissivity [L/t 2 ] W is the width of the coastal boundary across which submarine discharge occurs [L] L á is the ldistance inland to the toe of the saltwater wedge [L] is the Ghyben-Herzberg ratio (á =0.025) [dimensionless] As pumpage reduces the flow of freshwater to the sea along coastal margins, the length of the intruded saltwater wedge increases. The length of the wedge (interface toe) during the discharge of fresh ground-water to the sea may be found through the relation: L ρ ρ Kb 2 s f = (7) ρ Q f s

5 104 Distances of 150m from Bernard Lodge, 120m from Old Harbor, and 750m from the Manchester Highlands along the coast to the seepage face (L) were divided by the model cell width of 160m to determine the number of cells from the coastline to the saltwater interface (saline front) (Figure 4.11, Table 7). In order to estimate freshwater exploitable ground-water resources in the coastal aquifer, knowledge of the amount ground-water discharge into the sea is required. Values used to determine Q s for the alluvium aquifer at Bernard Lodge and Old Harbor and the White Limestone aquifers at Manchester Highlands are provided by the WRAJ and modified in (Figure 4.11, Table 7-8). SOURCES AND SINKS Estimates of Aquifer Recharge Natural recharge to the saturated zone in a ground-water reservoir may come from a number sources that include: 1) deep percolation of precipitation, 2) streambed percolation, 3) subsurface inflow from neighboring basins, and 4) leakage from ponds, lakes, and reservoirs. Direct recharge, that is precipitation that contributes to soil moisture content and crosses the water table as recharge to the ground-water system, may be expressed as: RE = P R AE ± S (8) where, RE P is the direct recharge is the precipitation

6 105 Table 7. Estimated values used in the determination of submarine discharge from coastal aquifers of the Rio Cobre and Rio Minho-Milk river basins, Jamaica, WI (Source: Water Resources Authority of Jamaica). Hydrologic Basin Aquifer /Location Transmissivity - T (m 2 /d) Distance to Toe Of Seawater L (m) Aquifer Thickness h (m) Rio Cobre Alluvium at Old Harbor Rio Cobre Alluvium at Bernard Lodge Rio Minho-Milk River White Limestone at Manchester Highlands

7 106 Table 8. Calculation of submarine discharge in the Rio Cobre and Rio Minho-Milk River basins, Jamaica, West Indies. (After Ghyben and Herzberg; 1901). Location in Coastal Aquifer Aquifer Thickness b Length of Saltwater Wedge L Submarine Discharge Q s Submarine Discharge Q s Length of Model Cell Ratio of L/Width of Model cell No of Model Cells used to simulate L (m) (m) (m 3 /d) (m 3 /d) (m) (m) WRA (1990) WRA (1990) WRA (1990) This study Alluvium at Bernard Lodge ,500 1,216, Alluvium at Old Harbor ,694 1,250, White Limestone at Manchester Highlands , , Total 472,143 2,874,000

8 107 EXPLANATION Spauldings Mandeville Linstead Spanish Town SUBMARINE DISCHARGE Submarine discharge point from The White Limestone aquifer Submarine discharge points from alluvial aquifer Old Harbour Bernard Lodge Major Towns Constant-Head Boundary Manchester Highlands CARIBBEAN SEA Figure 4.11 Map of coastal areas where ground-water is discharged to the sea from coastal aquifers.

9 108 R AE S is the surface runoff is the actual evapotranspiration is the change in storage However the net ground-water recharge rate to the Rio Cobre and Rio Minho- Milk river basins within the time interval (e.g. 1 year) may be estimated using equation 9 and the change in storage is neglected for steady-state conditions (Maidment, 1992): P = R + ET + G + I (9) where, P I R G ET is the precipitation is the irrigation is surface runoff is deep percolation leading to ground-water recharge is the evapotranspiration Major sources of recharge to the alluvial and White Limestone aquifers within the study area include infiltration from precipitation, natural or induced infiltration from surface water, irrigation water, and ground and surface water runoff. Mean annual precipitation rates based on the Jamaica Meteorological Service s (JMS) 30-year annual mean for the period were obtained from the WRAJ (Appendix 1, Tables 17-18). Evapotranspiration from the Rio Cobre and Rio Minho-Milk river basins is approximately 69% or x 10 9 m 3 /yr of the total precipitation of x 10 9 m 3 /yr (Table 9). Net recharge rates from precipitation to the water table (i.e. after the removal

10 109 of evapotranspiration) were estimated by the WRAJ to be 9.26 x 10 8 m 3 /yr, or approximately 21 % of the total annual precipitation (Table 9). The equivalent rate of volumetric recharge to the study area is x 10 6 m 3 /d. Recharge is assigned in units of mm/yr and the conversion represents an average rate of mm/yr. Recharge was assigned to the Rio Cobre and Rio Minho-Milk river basins based on differences in slope, topography, and relief as used by Torres-Gonzalez et al. (1996) and by Sepulveda (1996) in similar geologic provinces in Puerto Rico. Steep slopes and well-drained sinkholes characterize the highland regions of the Rio Cobre and Rio Minho-Milk river basins. Alluvial sediments with moderately drained overlying soils cover the irrigated plains. The assignment of weights based on the percent slope calculated in a GIS using spatial analysis, relief, and topography were used to demarcate net recharge zones in the model (Figure 4.12). The estimated net recharge value of mm/yr was applied to 6 zones ranging from 0% slope greater than 12.85% slope. For example, the highest weight of 1.2 was assigned to highland plateaus, 0.7, 0.5 was assigned to the irrigation plains, and 0 assigned to no-flow boundaries (Table 10). Ground-water recharge of upland areas was initially assumed to be influenced primarily by slope, with steep-sloped regions having lower recharge than low-sloped regions of the lowlands. A map of the distribution of simulated recharge for the Rio Cobre and Rio Minho-Milk river basins is shown in figure 4.13.

11 110 Table 9. Water Balance, Water Use and Future Demands of the Rio Cobre and Rio Minho-Milk River basins, Jamaica In MCM/yr (after Water Resources Authority of Jamaica, 1990). ITEM RIO COBRE RIO MINHO TOTAL Rainfall Evapotranspiration Surface water Runoff Ground-water recharge (Exploitable surface) Water runoff Exploitable ground-water NON AGRICULTURAL SEC TOR: Present Use Expected Demand AGRICULTURAL SECTOR: Present Use 589 Possible demand

12 111 EXPLANATION PERCENT SLOPE (%) Major TownS Major highways CARIBBEAN SEA Slope calculated using GIS ArcView Spatial Analyst, Base from United Nations Development Program/OAS Government of Jamaica, Underground Water Authority of Jamaica (now WRAJ) Map of Watershed Management. Digitized by the author from 1:250,000 scale, Lambert Conical Orthomorphic Projection, UTM Zone 18. Figure 4.12 Map of percent slope used in the assignment of recharge in the study region.

13 112 Table 10. Assignment of net recharge zones applied to the three-dimensional ground-water-flow model Model Recharge Zones A Xi ΣArea B % Area C Weight Wi D (WiXi) E WiXi WiXi F %AreaWiXi WiXi G CF CF * Vol RchRt H CF CF I No-flow boundary Urban Centers 1.93E E Irrigated Coastal Plains 1.40E E (Slopes < 4.28) and river reaches Upland regions (slopes 4.08E E ) Hilly Terrane (slopes > 3.00E E Highland Plateaus 4.45E E Total Recharge 2.55E E C is based on slope (See Figure 4. 13)

14 113 Simulated Rivers River interaction with ground-water-flow was simulated with the River Package in MODFLOW (McDonald and Harbaugh; 1988). A total of 1650 river cells were used in the simulation and specified in model layer 1 (Figure 4.14). The Rio Cobre was divided into 384 reaches; Rio Minho into 938, Pindars River into 141, Milk River into 129, Rio D'Oro into 73, Rio Magno into 118, and Rio Pedro into 114. The River Package (RIV) requires that a known river head and a streambed conductance be specifed by the user. The model simulates leakage to and from the river based on the head in the river and the simulated head in the model. The rate of leakage between the river and the aquifer (Q RIV ) is calculated from (Source: Anderson and Woessner, 1992): Q RIV ( H h) = C h>rbot (10a) RIV RIV where HRI h RBOT C RIV is the head in the source reservoir is the head in the aquifer directly below the surface reservoir is the bottom of the streambed is the stream conductance When the water table falls below the bottom of the streambed (RBOT), the leakage stabilizes and QRIV is calculated from: Q RIV ( H RBOT ) = C hrbot (10b) RIV RIV

15 114 EXPLANATION RECHARGE Values expressed in mm/yr 0 mm/yr (no-flow cell) 3 mm/yr 3.4 mm/yr 87 mm/yr 110 mm/yr 150 mm/yr CARIBBEAN SEA Boundary of physiographic region River Figure 4.13 Aquifer recharge used in the model analysis.

16 EXPLANATION SIMULATED RIVER LEAKAGE BOUNDARIES Inactive cell CARIBBEAN SEA Figure 4.14 Simulated river leakage in the Rio Cobre and Rio Minho-Milk River Basins, Jamaica, WI. 1 Milk River, 2 Danks at Rio Minho, 3 Pindars River, 4 Rio Pedro, 5 Rio D Oro, 6 Rio Pedro, and 7 Rio Cobre.

17 116 Streambed hydraulic conductivity is unknown. The streambed commonly consists of unconsolidated cobble, gravel, sand, clay, minor limestone, and volcanogenics on the inside of meanders or impoundments. The initial value of streambed hydraulic conductivity was set to m/d for all reaches, based on values computed from variable head permeameter and field tests conducted on various materials (Rosenshein et al., 1968). Since there were no data available on stream conductance values, the simulated values of the streambed hydraulic conductivity are within the range of reported values for unconsolidated stream sediments (Rosenshein et al., 1968). Thickness of streambed sediments is often assumed to be 1ft in most modeling studies. The thickness of the streambed sediments in the Rio Cobre and Rio Minho-Milk river basins was assumed to be 1 m because there is mostly a thick accumulation of cobbles, gravel, and sand. The area of the river was estimated by choosing the widths of rivers (20 m to 100 m) and using 200 m as the length per model cell. River conductance values ranging from to 20 m/d were calculated for the area of the river channel in the model cell, the thickness of the streambed sediments, and the vertical streambed hydraulic conductivities. AQUIFER PARAMETERS USED IN MODEL SIMULATION Computed Hydraulic Conductivity Specific-capacity tests conducted in the Rio Cobre and Rio Minho-Milk river basins by several previous investigators (Versey, 1962); FAO, 1974; H. Humphrey s Limited, 1974, and Botbol, 1982) were performed to determine aquifer transmissivity. The distributions of transmissivity in the alluvial and White Limestone aquifers are

18 117 shown in Figures The transmissivity value at a given well was obtained using the Theis equation below: h o h = Q 4πT u u e du, u 2 r S u = (11) 4Tt where Q h h o h - h o T t is the constant pumping rate [L 3 /t] is the hydraulic head [L] is the hydraulic head before pumping started [L] is the drawdown [L] is aquifer transmissivity [L 2 /t] is the time since pumping began [t] r is the radial distance from the pumping well [ L] S is aquifer storativity [dimensionless] Aquifer transmissivity (T) values for the alluvial and White Limestone aquifers in the Rio Cobre and Rio Minho-Milk river basins were divided by aquifer thickness to compute the hydraulic conductivity (K) values (T/b = K) (Appendix 1, Tables 23-26). Thicknesses of both layers were determined from well logs. Thickness ranges from 1 m to 150 m in layer 1 and 2 m to 260 in layer two. Due to variations in lithology and thickness associated with the alluvial and White Limestone aquifers of the Rio Cobre and Rio Minho-Milk River basins, it was necessary to assign a number of hydraulic

19 118 EXPLANATION RIO MINHO-MILK RIVER BASIN RIO COBRE BASIN WELL LOCATION specific capacity transmissivity in meters squared per day Boundary of physiographic region CARIBBEAN SEA Figure 4.15 Transmissivity estimates from specific-capacity tests in the alluvial aquifer in the Cobre and Rio Miho-Milk River Basins.

20 119 EXPLANATION Rio Minho-Milk River Basin Rio Cobre Basin WELL LOCATION specific capacity transmissivity in meters squared per day Boundary of physiographic region CARIBBEAN SEA Figure 4.16 Transmissivity estimates from specific-capacity tests in the White Limestone aquifer in the Cobre and Rio Miho-Milk River Basins

21 120 conductivity zones for each model layer. The average hydraulic conductivity value for each zone was assigned by finding the geometric mean of all values within each zone. Because of the regional scale of the model, local variations in hydraulic conductivity are not simulated. Hydraulic conductivity ranges from 50 to 200 m/d in layer 1 and from 10 to 870 m in layer 2. Estimates of hydraulic conductivity in layer 1 range from 50 to 200 m/d and 10 m/d to 820 m/d in layer 2. Figures define each of the hydraulic conductivity zones in both layers. Table 11 lists a summary of the initial estimates of hydraulic conductivity assigned to each zone in the model. These values fall within the range of typical values of hydraulic conductivity reported for karst limestone and alluvial aquifers (Brahana et al., 1988) (Appendix I, Table 22). Vertical Hydraulic Conductance Vertical conductance was assigned as a function of the hydraulic conductivity values in each layer. Conductance refers to movement of water through a layer of material that has a vertical hydraulic conductivity lower than that of the aquifer. The vertical hydraulic conductivity, K z, assigned to cells in the model was initially set to 5 percent of the horizontal hydraulic conductivity. The ratio of horizontal to vertical hydraulic conductivity varies from 4:1 to 20:1 because there is heterogeneity in geology and permeability. The lowest ratio is associated with the highly permeable section in the White Limestone aquifer of the Rio Minho-Milk River basin. Vertical conductance was calculated for the leakance between the alluvial and White Limestone aquifers and the confining unit in the lower Rio Cobre and Rio Minho-Milk river basins. The vertical conductance, V c between these cells is computed from the equation:

22 121 EXPLANATION 1 ESTIMATED HYDRAULIC CONDUCTIVITY OF THE ALLUVIAL AQUIFER m/d 25 m/d 25 m/d m/d 40 m/d 135 m/d m/d CARIBBEAN SEA m/d 165 m/d 165 m/d 780 m/d` 222 m/d Figure 4.17 Distribution of hydraulic conductivity zones in model layer 1- alluvial aquifer. 10 Assigned hydraulic conductivity zone

23 122 EXPLANATION ESTIMATED HYDRAULIC CONDUCTIVITY OF THE WHITE LIMESTONE AQUIFER 25 m/d 25 m/d m/d 40 m/d 135 m/d 135 m/d m/d 165 m/d 165 m/d 222 m/d 780 m/d Figure 4.18 Distribution of hydraulic conductivity zones in model layer 2 White Limestone aquifer. 10 Assigned hydraulic conductivity zone

24 123 Table 11. Estimated values of hydraulic conductivity used in model analysis (m/d) (Source: WRAJ, 1997). Aquifer Zone Estimated Horizontal Hydraulic Conductivity Kx Estimated Vertical Hydraulic Conductivity Kz WHITE LIMESTONE (m/d) (m/d) Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone ALLUVIUM: Zone Zone Zone Zone Zone

25 124 2K K V c K b + K b 1 2 = (12) where K 1 is the vertical hydraulic conductivity assigned to model cell in layer 1 K 2 is the vertical hydraulic conductivity assigned to model cell in layer 2 b 1 is the corresponding thickness of cell in layer 1 b 2 is the corresponding thickness of cell in layer 2 Computed values of vertical conductance between the alluvial and White Limestone aquifer is listed in Table 12.

26 125 Table 12. Computed values for vertical conductance between the White Limestone and alluvial aquifers, Rio Cobre and Rio Minho- Milk river basins, Jamaica, West Indies (m/d). Conductivity Zone (Alluvial Aquifer) Hydraulic Conductivity K 1 (m/d) Thickness Layer 1 b (m) Conductivity Zone (White Limestone Aquifer) Hydraulic Conductivity K 2 (m/d) Thickness Layer 2 b (m) Conductance Zone x 10-1 Zone x 10-1 Zone x 10-1 Zone