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:(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Mathematical model of continuous and batch (discrete) system combined

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