 When we had introduced the regenerator to the Brayton cycle, we had tapped into the wasted heat that would have been left over from the turbine outlet and allowed some of that heat to be transferred into the stream prior to the combustion chamber, meaning that we would get the same network out for less Q in or more network out for the same Q in. That addition of the regenerator improved our thermal efficiency by essentially retrieving some of the heat that would have been wasted. When we consider regeneration for Rankine cycles, we are looking at something a little bit different. First, we have the option of allowing our fluids to mix together. I mean, in the Brayton cycle, we are separating these two streams from one another and our goal of trying to optimize the amount of heat exchanged is a function of how much surface area and how optimized we can make the convection on the inside surface of the regenerator to try to get as much heat transferred over. But the best heat transfer would occur by just mixing the streams together. When we do that, we get something that looks like this. Furthermore, I will point out that the regenerator in the Rankine cycle is referred to a feed water heater. It is heating the feed water, which is the water that goes into the boiler. So we are heating the feed water in a feed water heater. And one option here is to allow them to mix together. When we do that, we have to maintain a constant pressure across the mixing process, which means that we have to establish a medium pressure in our analysis. We have the high pressure prior to the expansion process, we have the low pressure at the end of the expansion process, and then we have an intermediate pressure. So what we do here is extract some of the steam early out of the turbine. We run it through a regenerator, either of the open feed water heater or closed feed water heater variety, depending on whether it mixes or not. And we reunite it with the stream that it was extracted from before it goes around into the boiler again. So when we analyze open feed water heaters, what we are doing is extracting some of the steam early, we are mixing it at an intermediate pressure before it gets compressed all the way back to the high pressure before going into the boiler. In order to mix together, that means we have to bring the low pressure up to the intermediate pressure, which means that we're looking at an additional pump for each open feed water stage. The advantage of an open feed water heater is that you get the best heat transfer characteristics possible, which means that you're going to have a higher thermal efficiency. If we were to keep the streams separate, we get something that looks like this or this, depending on if we want to reunite the stream at the high pressure or the low pressure. Because we're not mixing the stream together at the intermediate pressure, it has to mix together with the leftover steam in the turbine. And that mixing process has to occur at the same pressure. So in this variety of closed feed water heater, we are mixing at the high pressure, which means we are pumping the intermediate pressure back up to the high pressure, allowing them to mix before we go into the boiler. Or in this case, we are taking that intermediate pressure, we are using an expansion valve to expand it down to the low pressure before mixing it and using a single pump to drive it up from the low pressure all the way to the high pressure before entering the boiler. Essentially what we're doing by adding a feed water heater is raising the average temperature at which heat is added, which is improving our thermal efficiency. Again, the open feed water heater is the best in terms of thermal efficiency, the manufacturing complexity and mixing efficiency. The closed feed water heater though has the advantage of not necessarily requiring a pump. So depending on the circumstances, you might save money in the long run by taking advantage of economies of scale in your pump design. So a little bit more money into pumps for more thermal efficiency to get a return on that investment versus perhaps a little bit less money for a slight drop in thermal efficiency so as to not quite get as much return on that investment. But if you save some money here versus saving some money there, depending on the circumstances, one might be more favorable than the other. Your job as the engineer would be to determine the optimum arrangement and use of your resources. Let's try an example of all three varieties.