How Long to Dry Calculations

You asked me how long it would take to dry your grain.  I don’t think I gave you a very good answer, so I will try to explain this.  I will use the WGRF final report as a reference.
1. On page 6 I explain the black box approach to drying. If one measures the amount of water going in, and out of the bin, the difference would indicate the amount of drying taking place. The Absolute humidity is the amount of water in the air. The absolute humidity can be determined from the psychrometric graph of Fig 4 or from an equation or from an online calculator. www.planetcalc.com/2167/  One simply enters the Temperature  and Relative Humidity of the air, and out pops the Abs Humidity. We can get the Temp and RH of the outside air from any weather station.  However getting the temp and RH of the air exiting a bin is a little more involved.   It will be assumed that the temp of the exiting air will be the same as the temp of the top layer of grain.  I think that’s a reasonable assumption; but what about the RH of the exiting air — where do we get it from?   We could have a RH sensor at the exiting port; but most of us don’t have that.   So, we will again assume that the exiting air will have the same temperature and the same RH of the air in the top layer of grain. 
2. What is the RH of the air in the top layer of grain.  We will use EMC (Equilibrium Moisture Equations) equations to determine the RH. If we know the moisture content and the temp of a specific type of grain; an EMC equation will give what the RH of the air will equalize to. We can use my calculator to do this at www.planetcalc.com/4959/   Enter the moisture content of the grain, as well as the grain temp.  For the outside air temp, DO NOT enter the outside temp, but, rather the grain temp.  Then the EMC RH will be the resulting threshold RH for your specific grain.   Use this RH and grain temp of the top layer to calculate the absolute humiidity of the exiting air.3. The measurements made on the air entering and leaving the bin are all that is necessary to determine the amount of drying that is taking place.  If the absolute humidity of the air entering is 20 gr./m^3 and the abs hum of the air exiting was 25 gr./m^3; then for every cubic meter of air that flows through the bin there will be 5 grams of water removed.4. Let’s say that the fan is pushing 3,000 CFM.  For every cubic meter of air that goes through the bin, there are 5 grams of water removed, as above. There are 35.31 cubic feet in a cubic meter, so there are  3000 / 35.31 = 85 m^3 /min or 5098 m^3/hour x 5 gr/m*3 =25,488 gr/hr  or 25.488 kg/hr  or 56.17 pounds per hour of water removed. (There are 2.204 lbs in a kg)
5. So, how long would it take to remove 1% of moisture.   Let’s assume that we have 5000 bushels of wheat at 16.5% moisture and 60 lbs. per bushel. Above we see that we are removing 56.17 lbs/hr from the bin of 5000 bushels.   or  56.17/5000 = 0.01235 lbs/bu/hr.    But we want to remove  1%  or 0.01 x 60 = 0.6 lbs. Therefore, it will, with the conditions and the rate above, will be  0.6 / 0.01235 = 48 hours  or two days.  The problem is that the outside air is changing in both temp and RH and therefore to give an accurate time, this calculation must be done every hour.
Let’s go through an arbitrary example: The question is:  How much drying, in terms of % moisture content per bushel, occurs in one hour given that we have a bin of 5000 bushels of wheat at 16.5% moisture.  The aeration fan puts out 3500 CFM.  The outside temp. is 0 deg C and the relative humidity, RH, is 66%. The top layer of grain in the bin is 6 C, the middle is 5 C, and the bottom is 4 C.
1. What’s the abs. humidity of the air entering the bin?   Using the abs humidity cal  www.planetcalc.com/2167/   and enter 0 C for temp and 66% RH  yields  3 gr./m^32. What is the RH of top layer? using grain drying calc, www.planetcalc.com/4959/  enter 16.5% for grain moisture, and 6 for both grain and air temp. gives RH of 75.1%3 What is absolute humidity of exiting air? Using the abs humidity cal  www.planetcalc.com/2167/   and enter 6 C for temp and 75.1% RH  yields  5 gr./m^34. For every cubic meter of air that passes through the bin,  5 – 3 gr = 2 grams of water are removed.5  3500 CFM /35.31 = 99.12 cubic meters per min     x 60  = 5,947 cubic meters per hour     x 2 grams = 11,894 gr/hr   0r  11.894 kg/hr   x 2.204 = 26.22 lbs of water removed per hour6. How much water are we removing from one bushel of wheat per hour?    26.22 / 5000 = 0.005243 lbs of water removed per bu. per hour7. In terms of % moisture, how much is it reduced?   Assuming wheat is 60 lbs/bu.   (  0.005243 / 60 ) x100 = 0.00873%  At this rate it will take 114 hours ( ~ 5 days) to remove 1% MC ( 16.5- 1  to 15.5%)
I hope this example will help to give one the ability to calculate how long it will take to dry grain.