SWEETWATER TECHNOLOGY
DIV. TEEMARK CORPORATION
1132 Air Park Drive
AITKIN MN, 56431
PHONE: 218 - 927 - 2200  FAX; 218 - 927 - 2333
TOLL FREE: 800 - 428 - 9900

ALUMINUM DOSE CALCULATION

FOR APPLYING ALUM (OR ALUM and SODIUM ALUMINATE)
TO INACTIVE PHOSPHORUS RELEASE FROM LAKE BOTTOM SEDIMENTS
Revised 11/97
The following calculations and example give a method of calculating the total aluminum dose and application rate required to treat internally recycled phosphorus.
Upon request, we can e-mail a Microsoft Excel file (sweetwater alum dose calc.xls) that performs the alum dose calculations.
E-mail your request to teemark@aitkin.com or submit an information request.
The dose is the total amount of aluminum, in the form of Al2O3, to be applied. This calculation takes into account the maximum internal phosphorus release rate, the number of years the treatment will last, the variation of phosphorus release rates from deep to shallow waters, the efficiencies of the application method and the alkalinity of the water.
The application rate is the concentration of aluminum (in ppm) to be applied to the lake to properly distribute the dose.
The examples are for the application of aluminum in the form of aluminum hydroxide Al2O3. This is done by treating with alum (aluminum sulfate) or a combination of alum and sodium aluminate which might be necessary in lakes with low alkalinity. Alum and sodium aluminate form an aluminum hydroxide floc on contact with the lake water. The floc settles to the bottom to form an aluminum hydroxide blanket over the sediment.
All sediments go anoxic and release phosphorus into the lake water. The rate of release increases as water depth increases and dissolved oxygen in the water decreases. Therefore it is desirable to apply the material to the water proportionately to the water depth, (i.e. volumetrically) in order to distribute more material in deeper waters. Because wind and wave action would disturb the alum blanket in shallow waters, usually only waters deeper than 4 to 10 feet are treated.
However, a strictly volumetric application might result in a disproportionate amount of aluminum being applied to the deepest parts of the lake. To avoid overdosing the deep holes and to achieve a more uniform aluminum hydroxide blanket, a maximum depth is used in the calculation of the volume of water to be treated
This maximum depth is the point below the thermocline on the midsummer dissolved oxygen curve where DO becomes somewhat uniform. This depth, TZ is usually 1.5 times the depth of the thermocline.
Therefore we will base the application rate calculation on the volume of water in the treatment area using a maximum depth of TZ. This is VD as shown below.
lake profile

Parameters:
H = Depth at which treatment begins.
H will range from 4 to 10 feet. It should be the shallowest point at which the sediments and subsequent alum blanket will not be significantly disturbed by wind, waves or other activities. The treatment area will be all waters with a depth greater than H.
PL = Total phosphorus recycled from the sediments in one year.
PLcan be determined by mass balance calculation, sediment release experiments, or other methods.
Y = The number of years the alum treatment should be expected to last.
Y will vary from 3 to 15 years with 7 to 10 years being typical. The choice of Y will depend upon the sedimentation rate.
Ka = Ratio of molecular weight of aluminum to molecular weight of phosphorus = .89
Kd = The distribution efficiency of the application equipment.
Kd will range from 0.4 for poor guidance of the application vessel and manual metering controls to 0.95 for equipment with precise guidance and automatic metering.
Ki* = Insitu efficiency of aluminum binding with sediment phosphorus.
Aluminum not only reacts with phosphorus but it will also react with other elements in the water. Ki is the portion of the aluminum that reacts with the phosphorus.
Kr* = The ratio of maximum sediment release rate of phosphorus to average sediment release rate.
The release rate of phosphorus will vary substantially from one area of lake bottom to the next. Without the ability to identify these zones of rich and poor sediments form the surface, the whole lake bottom must be treated as if it were rich sediments.
Kr is estimated to be 2.5. (Cooke, Kennedy)
TZ* = 1.5 times the midsummer thermocline depth.
VL = The total water volume of the lake.
VH = The volume of water in the shallows (depth less than the treatment depth "H").
VTZ = The volume of lake water that lies below TZ.
VD = The volume of lake water in the treatment area down to TZ, used for the application rate calculation.
= VL - VTZ - VH
WD = The weight of the water volume VD.
*These figures are estimates and many of them depend on the characteristics of the particular lake.
Further research is needed to better define these variables.


ALUMINUM DOSE AND APPLICATION RATE CALCULATION:
Wa = The total aluminum dose. It is the weight of aluminum as Al2O3 to be applied.
= PL x ((K a x Kr)/(Kd x Ki)) x Y
Da = The application rate in parts per million by weight.
= Wa /WD x 106ppm
When applying the aluminum to the lake, it is applied by volume at the rate Da to the treatment area, treating waters deeper than TZ as if they had a depth of TZ.


ALUMINUM APPLICATION MATERIALS
In well buffered lakes, the aluminum dose can be applied using aluminum sulfate (Al2(SO4)3), commonly known as alum. In lakes that have low alkalinity, a buffering agent might be necessary to prevent the pH of the water from dropping below 6.0 during treatment.
The following test can be used to determine if buffering is necessary:
Da = Calculated aluminum dose in ppm.
DM = The maximum aluminum (Al+++) dose in the form of alum that a unit volume of lake water can support and still maintain a pH above 6.0 (determined by titration or alkalinity tables).
If Da is less than or equal to DM then straight alum can be used.
If Da is slightly greater than DM then the aluminum dose must be reduced to DM with a corresponding shorter expected life of the treatment.
If the difference between Da > DM is great, reducing the dose will compromise the effectiveness of the treatment. In this case the most cost effective method is to apply sodium aluminate and alum in the lake simultaneously. Sodium aluminate (Na2Al2O4) is a buffering agent which also contributes aluminum thereby reducing the amount of alum that is necessary for phosphorus inactivation. The ratio of alum to sodium aluminate to maintain neutral pH is 2 parts alum to 1 part sodium aluminate by volume.


ALUM and ALUM/SODIUM ALUMINATE DOSE CALCULATIONS

Parameters:
- Liquid alum weighs 11.1 lb/gal and contains 4.4% Al+++
- Liquid sodium aluminate weights 12.1 lb/gal and contains 10.38% Al+++
(Caution. There are other concentrations of sodium aluminate on the market. The preferred concentration contains twenty percent Al2O3.
- One gal. sodium aluminate will buffer two gallons alum
- Kc = 2.3 pounds to gallon molecular weight conversion factor


A. Straight Alum Application, (DM < Da)
Total pounds alum required
= Total aluminum required / lbs Al+++ per lb alum
= Wa/.044 pounds
Gallons alum required = Total pounds alum / 11.1 lbs/gal
= Wa/.044 pounds
= 2.05 xWa
B. Alum And Sodium Aluminate Application, (DM > Da)
@ neutral addition of 2 parts liquid alum to 1 part liquid sodium aluminate by volume:
Total pounds alum required = Total aluminum required / (Kc x lbs Al+++ per lb alum)
= Wa/(2.3 x .044)
= 9.9 Wa
Gallons alum required = Total pounds alum / 11.1 lbs/gal
= 9.9 Wa/11.1
= .89 Wa
Gallons sodium aluminate required = Gallons alum / 2
Pounds sodium aluminate = Gallons sodium aluminate x 12.1 lbs/gal.


EXAMPLE
"BLUEGREEN POND"
ALUMINUM DOSE and APPLICATION RATE CALCULATION
Parameters for treatment of Bluegreen Pond (an 1800 acre lake):
H = 6 ft (Depth at which treatment begins - defines the treatment area)
Y = 7 years (Treatment life)
Ka = .89 (Molecular wt ratio Al to P)
Kd = 0.9 (Distribution efficiency. The value .9 assumes computer controlled application with differential GPS guidance)
Ki = 0.6 (Institu reaction efficiency of Al to P - from previous history)
Kr = 2.5 (Ratio of Max to Avg phosphorus sediment release rate)
TZ = 25 ft. (1.5 times midsummer thermocline depth)
VL = 42,591 acre ft. (total water volume of lake)
VH = 1,057 acre ft. (water volume of waters outside the treatment area (i.e. shallower than H))
VTZ = 12,159 acre ft. (water volume below TZ)
VD = VL - VH - VTZ (water volume for application rate calculation) = 29,375 acre ft.
Water weighs 2.72 x 106 lb/acre ft.
Total Aluminum Dose Calculation:
          Aluminum Dose Wa = Y x ((Ka x Kr)/(Kd x Ki)) x PL
Wa = 7 yr ((.89 x 2.5) / (0.9 x 0.6)) x 15,000 lbs phosphorus/yr
= 432,639 lbs aluminum