Gas Processing Expert

I am trying to understand the demethanizer bottoms temperature control strategy that manipulates the flow split through the BAHX/exchanger paths. This is a typical control scheme used in Cryo Gas Processing facilities. Could you explain the this control particularly w.r.t: How does this control determine how much flow to send to each exchanger? What is the expected cause-and-effect relationship between the split ratio and demethanizer bottoms temperature? How does this control scheme actually work - Is the temperature controller working in some sort of cascade control to split the flow? I need a detailed controls explanation on how this control works. A PFD is attached.