Recall that non-self-regulatory variables behave like "pure integrators".  The most common examples of process variables behaving this way are liquid levels whose outputs are pumped.   The non-self-regulating variables for this process are described in the following.

L1 - Perhaps the most obvious non-self-regulatory variable is the liquid level in the reactor. If  the flow rate F2 was increased, the reactor would eventually overflow if there were no control.

L2 - The liquid level in the flash separator is also non-self-regulatory.  If two of the valve settings v8, v6 and v4 were not controlled and mismatched, the liquid level in the flash would either rise or fall and not attain steady state.

Remember, a draining tank without a pump is self-regulating.  (See Example 3.7 for the draining tank.)