Flow field and traverse times for fan forced injection of fumigant via circular or annular inlet into stored grain

• The gas pressure for a flow in stored grain satisfies Laplace’s equation.
• Leading order closed form solution for traverse time is reasonable for inlet close to the central axis.
• Time to advect the phosphine to almost the entire grain bed is approximately one hour.

Fan forced injection of phosphine gas fumigant into stored grain is a common method to treat infestation by insects. For low injection velocities the transport of fumigant can be modelled as Darcy flow in a porous medium where the gas pressure satisfies Laplace’s equation. Using this approach, a closed form series solution is derived for the pressure, velocity and streamlines in a cylindrically stored grain bed with either a circular or annular inlet, from which traverse times are numerically computed. A leading order closed form expression for the traverse time is also obtained and found to be reasonable for inlet configurations close to the central axis of the grain storage. Results are interpreted for the case of a representative 6 m high farm wheat store, where the time to advect the phosphine to almost the entire grain bed is found to be approximately one hour.