Drying and storing a bin of grain

grain bin capacitygrain drying costmoisture shrinksafe storage timeaeration airflow

Filling, drying and storing a bin: the volume and mass of grain, the water to take out, the fuel it costs, aeration air and safe storage time.

Round Bin Capacity

V = \pi \left(\frac{d}{2}\right)^{2} h

The volume of grain in a round bin, from the inside diameter and the depth of grain. Answered in bushels or cubic metres — the conversion between them is geometry, not agronomy.

Grain Cone Volume

V = \frac{\pi}{3} \left(\frac{d}{2}\right)^{2} h

The volume of a cone of grain: the peak above a level fill in a bin, or a whole pile dumped on the ground. One third of the cylinder that would enclose it, which is more than most people guess.

Grain Mass from Volume

m = \rho \, V

The mass of grain filling a known volume, from its bulk density. The step between a bin measurement and a quantity that can be sold, hauled or insured.

Water Removed in Drying Grain

W_w = W_1 \, \frac{M_1 - M_2}{100 - M_2}

The mass of water that has to leave a lot of grain to take it from one moisture to another — the quantity a dryer is actually sized, fuelled and costed against.

Grain Weight at a New Moisture

W_2 = W_1 \, \frac{100 - M_1}{100 - M_2}

What a lot of grain weighs once its moisture changes, holding the dry matter constant. This is the core of every grain contract, every drying invoice and every elevator settlement.

Grain Drying Energy

E = \frac{m_w \, \lambda}{\eta}

The fuel energy a dryer needs to evaporate a given mass of water, once its efficiency is accounted for. The calculation behind a propane bill in a wet harvest.

Aeration Airflow Requirement

Q = q \, M

Total fan airflow for a stored quantity of grain, from the aeration rate per tonne. The first number in sizing an aeration fan — though not the last, because static pressure decides the rest.

Safe Storage Time

t = t_0 \cdot 2^{-\Delta M} \cdot 2^{-\Delta T / 5.56}

How long grain will keep before spoilage, as a halving rule: storage life halves for every percentage point of moisture above the reference condition, and halves again for every 10 F° of warming.

How they fit together

Start with what is in the bin, because every later number is per tonne. Round bin capacity handles the cylinder and grain cone volume handles the peak on top of it, and that cone is not a rounding error — on a typical farm bin it is 8 to 12% of the total, which is a full truckload you would otherwise have failed to account for. Grain mass from volume converts with bulk density, and bulk density is a real property of a real load rather than a table value: wet grain packs differently from dry, and the same wheat can vary several percent between a gently filled bin and one filled through a spreader.

Then the water. Water removed in drying and weight at the new moisture are two different questions and confusing them is the classic and expensive error in this whole area. Water removed is the mass of water the dryer has to evaporate, and it sets your fuel bill. Shrink is what the load weighs afterwards, and it sets what you get paid. They are not the same number, because when you take water out you lose that weight from a sale that was priced by weight. Take 200 tonnes of corn from 20% to 15% and you evaporate about 11.8 tonnes of water, and the load you sell is about 188 tonnes. Budget the fuel against the first figure and the cheque against the second, and never let one stand in for the other.

Drying energy converts that water into fuel: mass times latent heat, divided by dryer efficiency. The efficiency term is where the honest surprises live, because a continuous-flow dryer running 50 to 60% means nearly half the propane is going up the stack heating outside air. Aeration airflow requirement is a different job that gets confused with drying, and the distinction is worth stating plainly: aeration cools and equalises grain at perhaps 0.1 cfm/bu and cannot dry it, while drying air is 1 to 2 cfm/bu, an order of magnitude apart. Sizing an aeration fan and expecting it to take three points out is a spoiled bin. Safe storage time is the formula to run first in practice even though it sits last here, because it is the one that tells you whether any of the rest was necessary: it is measured in days rather than months at high moisture and warm temperature, and it falls off a cliff. Corn at 20% and 25 °C has a couple of weeks; the same corn cooled to 5 °C has a season. Cooling often buys you the time to dry more cheaply later, or to not dry at all.