I'm having difficulties trying to establish the best approach to create a mathematical model of a process that has a combined continuous and discrete (batch) element to it. I explain as follows: The system is a hopper (vessel), open to atmosphere, with dry granular material being fed in by conveyor (i.e. continous), the outlet at bottom of hopper has a valve that opens to discharge granular material initially discharging a lot of material quickly into a container below then a more slow gradual but constant outlet flow as the container is moved forward and filled. The hopper discharge valve then closes and waits a delay time until the next empty container is ready below (meanwhile the hopper is being filled), and the process repeats again. I have tried Integral Mass Balance approach but I don't think this is right. Ideally I need a Laplace transform expression for the system. I know the time values for the valve open discharge and rates of mass flow as well as material in-flow to hopper and hopper volume. If anyone has any ideas on the best way to approach this problem it would be gratefully received.