Corn stover (stalks, leaves, cobs but not grain) is being used to create ethanol

Question

Corn stover (stalks, leaves, cobs but not grain) is being used to create ethanol that meets the “cellulosic biofuel” requirement in the Renewable Fuel Standard.

A typical removal rate is 2.0 tons of stover per acre. Corn stover contains 0.50% nitrogen, 0.15% phosphorus, and 0.80% potassium by weight. When it is removed from the land, the nutrients must be replaced.

A particular corn producer is supplying corn stover to a biorefinery making ethanol. The producer has these fertilizers available:

• anhydrous ammonia nitrogen (82-0-0) @ $509/ton;

• diammonium phosphate or DAP (18-46-0) @ $425/ton; and

• potash or potassium (0-0-60) @ $318/ton.

Fertilizer nutrient content is designated as (N-P-K) where N = % nitrogen, P = % phosphorus and K = % potassium, all on a weight basis. Thus, anhydrous ammonia is 82% nitrogen by weight, 0% phosphorus and 0% potassium.

What is the nutrient replacement cost for this corn producer? Express your result in both $ per acre and $ per ton of stover removed. (Hint: DAP contributes both nitrogen and phosphorus – do that one first.

Explanation / Answer

The corn removal rate = 2 tonnes/acre. = 1815 kg/acre

So, Nitrogen removal rate = 1815*0.005 = 9.075 kg/acre

Phosphorus removal rate = 1815*0.0015 = 2.7225 kg/acre

Potassium removal rate = 1815*0.0080 = 14.52 kg/acre

For Potassiun we need 14.52/0.60 = 24.2 kg of potash which will cost, (24.2*315)/1815 = $4.2

While adding phosphorus we will add nitrogen also.

For phosphorus we need 2.7225/0.46 = 5.919 kg of diammonium phosphate which will cost, (5.919*425)/1815 = $1.39

and the nitrogen we will get will be, 5.919*0.18 = 1.066 kg

The remaining nitrogen will be, 9.075 - 1.066 = 8.009 kg

For that nitrogen we need, 8.009/0.82 = 9.78 kg of anhydrous ammonia nitrogen which will cost, (9.78*509)/1815 = $2.75

So total cost fornutrient replacement for the 2 tonne of corn is = 4.2 + 1.39 + 2.75 = $8.34

So the cost is, 4.17 $/tonne and the 1 acre produces 2 tonnes of corn stoves so it is 8.34$/acre.

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