Mathematical Model of the Essex Valley, St. Elizabeth
Introduction
Refining bauxite into alumina uses a so-called Bayer process in which bauxite is grounded, slurried with a solution of caustic soda (sodium hydroxide, NaOH), and impurities are removed. Excess sodium (Na) and impurities, called red mud (with heavy metals, such as Cd, Fe, Mn, Ti, As, Zn, Pb, etc.) are deposited into waste ponds.
If such waste pond is not properly constructed and/or is constructed on top of karstic limestone, it will leak and contaminate the ground water in limestone aquifers underneath.
This is the case of the alumina production at Nain in the St. Elizabeth parish. The setup is shown in the map. The following are the facts.
- Alumina Partners of Jamaica (ALPART) pumps the water north of the Nain bauxite plant and at the plant itself and uses this water in the production of alumina at Nain and for domestic purposes at the plant.
The wells in the vicinity of the plant at Nain were completed in 1967, and at Pepper in 1974.
- The industrial processing water is discharged into two waste ponds nearby the plant.
- National Water Commission pumps water from the Pepper-Goshen wells and supplies the town of Mandeville and its surrounding area.
- Waste ponds leak and Na (and eventually some heavy metals) travel with the ground water from the waste pond towards ALPART's wells at Pepper and eventually toward NWC wells at Pepper-Goshen.
The pollution by waste ponds is already a well documented fact. The map
Na distribution in 1999 highlights the extension of the sodium pollution. Individual wells show a sharp increase of Na after the bauxite-alumina operations started. This is the case of wells either at the Nain plant or at ALPART wells near Pepper.
Another example is shown for the well BR-031 at New
Forrest. This is a location more south towards Alligator Pond.
It also displays a sharp increase in Na. The increase in sodium implies that the contamination from the waste ponds at Nain has come that far south. There is also an increase in the Cl content coming from sea water intrusion.
ALPART wells at Pepper also display an increase in Na content. At the site of the well at ALPART 9 (Pepper 5) Na is used as a tracer to indicate at pollution reaching the well. The production started in 1969/70, and excess sodium arrived some 5 km north after 5 years.
The mathematical model of the Essex Valley is made to have a means to predict what may happen should Alpart stop the production (as it did in late 1980's). It is expected that if ALPART wells were not pumping, the contamination from waste ponds would have endangered the water supply wells (NWC) at Pepper. It is for the model to confirm and quantify this expectation.
The model is of preliminary nature. Its conclusions are valid but the model may need refinements, especially in recreating piezometric maps in the last 20 or so years. Using actual pumping volumes and schedules from all ALPART wells in the period under simulation (since the operations started), including the periods without operation, pumping, and sodium discharge, may correct some of results and modify conclusions. The more precise calibration of sodium in monitoring wells over the last 20 years may also modify the input of sodium as simulated in this model.
Modeled Area Grid Size
Two maps display the size and location of the modelled area.
The first map is a GWW-drawn presentation showing three groups of wells (NWC at Pepper-Goshen, ALPART at Pepper, and ALPART at Nain).
Shown is also the city of Mandeville which receives the water from NWC wells at Pepper-Goshen.
The second map is Visual Modflow produced map showing heads, velocity vectors, and general directions of ground water flow.
The grid is made of:
- 36 columns, each 500 m wide, from X coordinate 175,000 through 193,000, and
- 70 rows, each 500 m wide, from Y coordinate 135,000 through 170,000
Model Boundaries
- South: the coast, H=0 m, constant.
- North: no-flow across, H=variable, not assigned.
- East: no-flow across the line that represents the Spur Tree Escarpment. This is to say that the recharge on the Escarpment does not contribute ground water to the Essex Valley aquifer. This is a conservative assumption and not necessarily absolutely correct.
- West: no-flow across the column 1, being represented by Santa Cruz
mountain acting as a ground water divide. This would imply that the recharge
from columns one, two, etc. would contribute water to the Essex valley aquifer.
The recharge on a hypothetic column west of the column 1 would contribute to
the western part of the Santa Cruz mountain aquifer (and would flow toward
Pedro Plains).
- Several cells north of Santa Cruz and within the Upper Morasse are
declared as constant-head cells with H set at 6 m (AMSL). Ground surface in
the Upper Morasse is at elevations between 8 and 10 m.
- Although the modelled area is partly within the Manchester Parish (eastern
part), the ground water flow within the Essex Valley is entirely within the
St. Elizabeth Parish.
Hydraulic Conductivity and Storativity
- The hydraulic conductivity in x and y directions is taken as 20 m/day in
all of the model area except in the Essex Valley Fault system where it is made
30 m/day. Reports indicate that this fault system acts as a preferential way
for ground water flow, being more karstified than the rest of limestone. The fault system extends from the waste ponds (shown in red in the map). Its extension coincides with the two green lines starting between the north pond and Myersville and simulating pathlines.
Recharge to Limestone Aquifer
- The recharge from infiltrated rainfall is equal to 250 mm/year in the most of the model area, except north of Santa Cruz in a portion of the Upper Morasse where it is reduced to 200 mm/day or eliminated altogether.
- The rationale for this is the following. Annual rainfall is 57 inches (1450 mm), and the recharge coefficient of 17% is of correct order of magnitude or an underestimate. Considering the karstic nature of the terrain and lack of a thick and extensive soil cover, the order of magnitude of the recharge coefficient would be between 15 and 25%.
- The Upper Morasse is the final recipient of the ground water flowing through the Essex Valley aquifer to the north and north-west. From there, the water either evaporates or transpires supporting the growth of swamp-kind of vegetation or feeds tributaries of the Black River system. Assigning the recharge to the Upper Morasse and evaporation in the same time would not change the outcome of the simulation. Only the water balance would be different.
Evapotranspiration from Aquifer
- Maximum rate of evapotranspiration is assigned at 2000 mm/year, with the extinction depth set at 2 m below ground surface. The model does have the ground surface elevations assigned to each cell according to real topography.
- The extinction depth is interpreted in the following way. When the elevation of the water table is beneath the surface elevation less the 2 m (extinction depth), evapotranspiration from the water table is curtailed. When the water table is at or above the ground surface, evaporation loss from the water table occurs at the maximum rate (2,000 mm/year, in this model).
Abstraction from Limestone Aquifer
The ground water information system that was recently established for the Black River Basin has the following cumulative volumes for major groups of wells within the Essex Valley:
Q is the total abstraction volume from one of well groups in one year. The first number is million cubic metres (MCM), the second number is million imperial gallons per day (migd).
It appears that all abstractions are underreported. In 1982, it was
reported that "actual abstraction from the Nain-Pepper section of the
Valley is about 13 migd" not including the NWC Pepper wells. The abstractions
(pumping) used in the simulation are:
- Alpart at Nain: 27,400 m3/day (6.0 migd)
- Alpart at Pepper: 28,800 m3/day (6.3 migd)
- NWC at Pepper: 18,000 m3/day (4.0 migd)
The heads (equipotentials) in the model were calibrated using the above
abstractions and 250 mm/yr recharge rates from rainfall. Higher abstraction
rates would demand a recharge coefficient greater than 17%, or recharge rates
higher than 250 mm/yr.
For comparison, shown are also daily abstractions as entered into the GWIS
of the Black River basin. There are many missing months, data appear to be
incomplete, so that the reported volumes are evidently underestimated.
N.W.C. abstracts from Pepper-Goshen area and supplies
Mandeville with about 33.5 MCM in the 6 year period, at an average daily rate of
15,310 m3.
ALPART's abstraction at Pepper in the same period
is reported at about 50.0 MCM, or an average daily rate of 22,836 m3.
ALPART's abstraction at Nain display the total
volume in the period from 1994 through 1999 about 39.6 MCM, or an average daily
rate of 18,096 m3.
Software Used for Modeling
- The Visual Modflow package from Waterloo Hydrogeologic Inc. was
used for the simulation of the Essex Valley aquifer. It is a proven standard
for 3-D ground water flow and contaminant transport modeling using MODFLOW,
MODPATH and MT3D. These packages are integrated with an intuitive and
powerful graphical interface.
- Most of graphics presented here is directly obtained from Visual Modflow.
The rest is obtained using Ground Water for Windows (GWW) as a
post-processor, with data exported from Visual Modflow runs and imported into
the GWW.
Phases of Modeling
- Phase One: simulating ground water flow using the parameters and
boundaries as described above. The map above and
an expanded (zoomed in) section showing the flow
pattern from the ponds northwards, is obtained by assuming no-pumping
conditions from either producer (ALPART at Nain, ALPART at Pepper, N.W.C. at
Pepper-Goshen, etc.). The map simply shows the directions of flow and
elevations of water table in the simulated aquifer. Such a distribution of
heads could have been a valid representation some 30 years ago when the
abstraction from limestone aquifer was in its infancy.
- Phase Two: simulating ground water flow in present days by adding
the abstraction from wells at Nain (ALPART's bauxite plant), at Pepper
(ALPART's industrial and domestic wells supplying the water to the bauxite
plant at Nain), at Pepper-Goshen (N.W.C. wells supplying Mandeville) and
other individual wells at Myersville, Southampton, etc.
The distribution of equipotentials from phase two
is used in contaminant (sodium) transport modeling phases.
- Phase Three: simulating contaminant transport or fate of sodium
(Na) under the real conditions. This is, five wells at the Nain plant
(Nain 1,3,4,5,6) pump a cumulative total of 27,400 m3/day (6 million IGPD)
throughout the period of 20 years; four wells at ALPART's well field south of
Pepper pump a total of 28,800 m3/day (6.3 million IGPD) also throughout the
period of simulation of 20 years; and three N.W.C. wells at Pepper-Goshen pump
a cumulative total of 18,000 m3/day (4 million IGPD) in the last ten years of
the simulation.
- Phase Four: hypothetic scenario of ALPART's wells stopped pumping
and the only abstraction coming from N.W.C. wells (3 wells, each pumping at
6,000 m3/day) throughout a period of ten years. The purpose of this simulation
is to predict what may happen should ALPART's wells stop intercepting the
contaminant plume (in other words, stopped doing their "scavenging" work).
- Phase Five: hypothetic scenario with N.W.C. wells at Pepper-Goshen
pumping at total of 18,000 m3/day throughout a ten year period (between
11th and 20th year, with the first ten years being idle or nonexistant), and
then at about 10 million IGPD rate in the remaining 10 years (45,000 m3/day).
This apears to be the reported water demand for Mandeville. In the same time,
the ALPART's wells stopped pumping after 20 years of continuous operation.
Waste ponds stopped contributing Na after 20 years.
Simulating Transport of Sodium
Sodium in this model is treated as a conservative substance. In other words,
the only process of importance is advection. Sodium travels with ground water
and is neither sorbed, retarded, or decayed. It is only diluted. There is a
different conclusion from a master thesis on "Nonconservative Behaviour of
Sodium" by Taraszki (University of South Florida, Tampa, 1993). The author
comes to the conclusion that "chemical reactions possibly responsible for
sodium fixation include precipitation of sodium carbonates and gibbsite and
sorption of sodium onto aluminum species. Trona and dawsonite are the most
likely sodium carbonates to form upon evaporation in South Pond. Sodium will
co-precipitate with gibbsite, and amorphous aluminum species and gibbsite
crystals may also provide sorption sites for sodium."
The code used for simulation is MT3D, and upstream finite difference is the advection method selected.
Results
Phase Three (Real Case)
Sodium is being introduced at concentrations of 4,000-4,500 ppm (4 to 4.5 g/l)
at 5 model cells, and at 12,000 ppm (12 g/l) in one model cell. The total
area occupied by ponds is 1.75 sq.km. The recharge of waste water into the
aquifer from ponds is 2000 mm/yr. The total annual recharge of waste water
from ponds is equal to 2 m/yr * 1.75 * 1,000,000 m2 = 3.5 million cubic metres
(MCM/yr). The total mass of sodium being introduced annually into aquifer is
about 17,500 t/yr.
The extension of the Na plume after 5, 10, 15, and 20
years shows that the plume (at concentration of 50 ppm) reaches the Alpart
wells at Pepper after some 10-12 years. It never reaches the NWC wells at
Pepper-Goshen. Rather than continuing to the north, the plume is being
intercepted by Alpart's wells at both Pepper and Nain. The actual deviation from
the background concentration of sodium of some 10 ppm was noticed much earlier.
Pathlines in a map indicate that most of the
contaminant from the pond will end in Alpart's wells at Nain. A smaller
portion will bypass the Nain wells and will terminate in Alpart's wells at
Pepper.
The time evolution of the sodium content is shown in three points.
- At the Nain site, the Na content becomes
elevated almost instantly after the plant started working. Near the end of
the 20-year period, the Na content is almost steady above 1300 ppm. This
model output may be compared with the actual Na content in the well
BR-073 (Nain-3) in which the Na content in December
1999 was 1320 ppm.
- At the Alpart's site at Pepper, the Na content
becomes elevated after 6 years in Alpart 8 and after 9 years in Alpart 9.
The model output may be compared with actually observed in the field at
BR-079 (Alpart 9) and at BR-078
(Alpart 8). In both wells, the real rise starts in 1989 and continues at
an average rate of 3 to 4 ppm in each year until the end of 1999.
This was a consequence of ALPART's plant at Nain stopping its operation in
late 1980's due to economic constraints on aluminum production. With reduced
or eliminated inflow of red mud and sodium carried with it, the ground water
reacted by dilution and rebound to the original sodium background concentration.
The sodium content was reduced to less than 10 ppm. Yet, with resumed
operations, the sodium quickly fille in the aquifer and monitoring wells
started showing increase above the 10-ppm threshold.
The mass balance (input into and output from the ground water system)
is as follows (as an average daily rate in the first ten years of simulation;
migd = million imperial gallons per day):
- Input:
- Recharge = 305,000 m3/day (67 migd)
- From storage = 5,000 m3/day
- Output:
- Evapotranspiration = 150,000 m3/day (33 migd)
- Wells = 56,000 m3/day (12 migd)
- Constant head boundary cells = 104,000 m3/day (23 migd)
Phase Four (Hypothetical Case of Pumping from N.W.C. Wells Only)
Only N.W.C. wells (3) are pumping at 6,000 m3/day each. They start pumping ten
years after the Nain bauxite plant became operational. In other words, the
limestone aquifer between the ponds and the Pepper-Goshen area is already
enriched with sodium. The model should answer just how much the release of
sodium in ponds would affect the quality of drinking water in N.W.C. wells.
The plume after 20 years shows that the N.W.C.
wells at Pepper-Goshen would remain at the periphery of the plume. The plume
would spread mostly in the western direction from the ponds, and would reach
the Upper Morasse area, which is the discharge area for the ground water
system north of the ponds. As shown in one of concentration with time
diagrams, the concentration at one of N.W.C. wells would reach a maximum
of only 100 ppm.
Phase Four: Conclusions
If the geology and hydrogeology of the Essex Valley are correctly translated
into this model, then there will be not much danger to the N.W.C. wells at
Pepper-Goshen from Alpart stopping altogether its production. N.W.C. wells
appear not to be in the direct path of ground water flow.
Phase Five: Hypothetical Case of Abstracting 10 Million IGPD at
Pepper-Goshen
It was reported that the actual water demand for the Mandeville area was about
10 million Imperial gallons per day. This is equivalent to about 45,000 m3/d.
In this phase, a hypothetical scenario is tested. Three wells at Pepper-Goshen
are pumping in the additional 10 years (beyond what was tested in phase four)
about 15,000 m3/d each. Thus the total abstraction in the year 21-30 was about
10 million IGPD or 45,000 m3/d. In the same period (after the year 20), the
Alpart's wells stopped abstraction altogether. The model simulated also the
end of the sodium input at ponds to zero after the year 20.
The results are shown as a map with heads and velocity
vectors and as another map with heads and Na plume
after 30 years of simulation.
The drawdown at the Pepper-Goshen sites is acceptable. Water levels are
still high, at about 17 m (AMSL). The plume did cover the abstraction sites,
with a maximum of less than 300 ppm.
Phase Five: Conclusions
The redistribution of pumping from the Nain area to the Pepper-Gohen area
would not create an additional depression. In other words, if and when the
industrial use of ground water ceases, this could be taken as an opportunity
to increase withdrawals from the Pepper-Goshen area for domestic water supply.
The ground water system can sustain such a high production from such a
small area.
The concentration of sodium at the Pepper-Goshen wells would
be less than about 300 ppm because of the dilution
effect of waters filling the cone of depression. Near the end of the pumping
period, there would be a decrease in the Na content. This is explained by
dilution and by reduced inflow of contaminated-with-sodium ground water from
the south.
It appears that such a scenario would not have adverse effects on the
ground water system. The concentration of sodium in the drinking water of about
300 ppm (a maximum in one well, P-2, closer to the Goshen area) could be
reduced by blending this water with the water from two more eastern wells at
Pepper (P-1 and P-3). These two wells do not exhibit higher sodium content than
50 ppm.
Improvements to the Model
The following improvements may be considered to make this model a more viable prediction tool:
- Modify the boundaries to result with the ground water contours more curved toward the New Forrest and Alligator Pond. The well at New Forrest 2 (Figure 5) remains outside the simulated Na plume. In the field, the opposite was
observed and confirmed. The plume should also spread more toward the south-eastern corner of the modeled area. This can be accomplished by reassigning boundary conditions and recharge in that part of the model.
- Input as accurate as possible pumping rates and schedules for the entire period of simulation (starting with early 1970's). Include the cessation of abstraction in the second half of 1980's when the plant stopped operations.
Acquire correct and complete data from ALPART and consult some earlier reports (by Geraghty & Miller, e.g.).
- Obtain more information on chemical analyses of "red mud". Modify the input of sodium (concentrations and locations). Inspect the ponds and notice the sites of sinkholes and places where the mud may enter the subsurface. Use this in the model.
- Since sodium was simulated as a conservative substance, test the model using nonconservative behaviour of sodium including dispersion.
- Learn more about the actual abstractions at Pepper-Goshen (by N.W.C.) and plans for future supplies of Mandeville and surrounding areas.
Repeat the modeling using improved data and in consultation with ALPART and N.W.C.
