Sounds like your tank float is not properly adjusted. After you fill up how many miles can you drive before the fuel gauge needle moves off the "F" mark? If it's more than about 75 I would say time to adjust the float arm or replace the fuel level sender.
You could run the tank dry and then see how much it takes to refill -- just make sure to carry a 5 gallon jug of fuel with you so you're not calling AAA for roadside assistance. Then run to the gas station and fill up, add in the five gallons from the jug into the equation and see what number you get. For your van I believe it should be 32 gallons.