Worksheet for Calculating Biosolids Application Rates in Agriculture

Dan Sullivan and Craig Cogger
Oregon State University and Washington State University-Puyallup

 

Equations for Calculating Application Rates

The following equations summarize the calculations in the worksheet. You can use them in place of the worksheet. These equations do the same calculation as the worksheet, so you do not have to use both. These equations will give results in dry tons of biosolids per acre. You will still need an additional calculation (Step 6 in the worksheet) to convert to an "as is" basis.

Bapp = (Nneed – Nother)/Bpan [1]
Bpan = [(TN – AN) * M/100 + AN * R/100 + NN] * C [2]
Nother = (0.225Nw * W) + S (Nppi * 2.8 * Di) + Ngm + Nbs + Nman + Nstart [3]

Where:

Bapp is the biosolids application rate in dry tons/acre

Nneed is the plant-available N needed to produce the crop yield goal in lb/acre

Nother is the plant-available N provided by other sources in lb/acre

Bpan is plant-available N in the biosolids in lb/dry ton

TN is biosolids total N in mg/kg or percent

AN is biosolids ammonium N in mg/kg or percent

NN is biosolids nitrate N in mg/kg or percent

M is the biosolids organic N mineralization rate in percent (Table 3)

R is the proportion of ammonium N retained in available form in percent (Table 2)

C is the conversion to lb/dry ton for biosolids N. For analyses in mg/kg, C = 0.002; for analyses in percent, C = 20.

Nw is the nitrogen content of irrigation water in mg/kg

W is the irrigation water applied in inches

Nppi is preplant nitrogen in layer i in mg/kg. (Layers must be sampled in 12-inch increments)

Di is soil bulk density in layer i in g/cm3

Ngm is nitrogen from the plowdown of a green manure or cover crop in lb/acre

Nbs is nitrogen released from previous biosolids applications in lb/acre (Table 1)

Nman is nitrogen released from previous manure applications in lb/acre

Nstart is nitrogen supplied by starter fertilizer in lb/acre

Table 6. Conversion Factors

1% = 10,000 mg/kg or ppm
= 20 lb/ton
1 mg/kg = 1 ppm
.0001 %
.002 lb/ton
1 wet ton = 1 dry ton / (percent solids x 0.01)
1 dry ton = 1 wet ton x (percent solids x 0.01)
1 acre-inch = 27,000 gallons

 

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Worksheet for Calculating Biosolids Application Rates in Agriculture, PNW 511-W
by Dan Sullivan and Craig Cogger
(Oregon State University and Washington State University-Puyallup)
March 2, 2000