(Modified from McAvoy, 1983). A decanter shown in Fig. E18.14 is used to separate a feed that consists of two completely immiscible liquids, a light component and a heavy component. Because of the large difference in their densities, the two components form separate liquid phases very rapidly after the feed enters the decanter. The decanter is always full of liquid. The level of the interface I between the two liquid phases is measured by a DP cell. Each liquid flow rate can be adjusted by using a control valve, which is connected to a standard PI controller. The control valve equations relate flow rates, pressures, and controller output signals \left(m_{1}, m_{2}, m_{3}\right):
\begin{aligned}&F_{1}=m_{1}\left(P_{0}-P_{1}\right) \\&F_{2}=m_{2}\left(P_{1}-P_{2}\right) \\&F_{3}=m_{3}\left(P_{1}-P_{3}\right)\end{aligned}
Using the following information, propose a pairing of controlled and manipulated variables for a conventional multiloop control configuration based on physical arguments. It is not necessary to calculate a RGA.
Available Information
(a) Pressures P_{0} and P_{2} are constant:
P_{0}=250 psi \quad P_{2}=30 psi
(b) The feed composition can vary. The nominal value is w_{H}=0.99, where w_{H} is the weight fraction of the heavy component.
(c) The densities of the pure components are
\rho_{H}=9 lb / gal \quad \rho_{L}=3 lb / gal
(d) At the nominal steady state,
F_{1}=2093 gal / min , \quad F_{2}=60 gal / min , \quad P_{1}=180 psi
(e) The transmitters and control valves have negligible dynamics compared to the process dynamics.
