I think that a material or process flow, where the outputs of one process become inputs to other processes until no more processes have yet occurred, can be a poset or or a partially-ordered set, depending on the configuration. However, such a flow can also contain cycles (where byproducts feed back into previous processes, like food waste becoming compost which is used to grow more food). Here's a diagram of that flow: http://locecon.org/clusters/network/8/

[edit] per clarifications from Artur Grzesiak and David Tanzer on the next page, I now understand that the flow with the cycle is a preorder, but without the cycle, it would be a partial order. (Hope I understood correctly...)