Okay, welcome back. So we were considering what was the best operating condition for our fictional manufacturing facility. So we had our electrical energy target, and we had our heat energy target. If we work in quadrant A we make excess heat so we don't want that condition because excess heat simply gets rejected to the environment so that's a complete loss in the system. So that really eliminates both A and B from consideration, because both of those are again on the high side of the heat energy target. Up in quadrant C we regenerate more electrical energy than what we need. Now you'll often hear people talk about oh, well I'll install solar panels or wind turbine on my property and if I generate more energy than I need I'll sell it back to the grid. Well at this point in time I've yet to hear that that has ever been successful. So while in principle that can be a feasible operating mode to generate enough of electrical energy for yourself and more so you could put that energy back into the grid, it doesn't tend to be that successful. And that's primarily because we're still trying to figure out how to have these components interact with the grid. So often what I hear is instead people generate excess energy and they just put it back into the grid and they're not paid for that. And again that's just because we're still trying to figure out how to how the power companies can actually monitor that, how can they use that energy because it's not dependable it's very intermittent. So it makes it very challenging, very transient system. So, while in principle, quadrant C could be a good place to operate. In practice, it's not. It's a hard place to be. So that really says is that you want to undershoot both your heat and electrical energy needs. So what you have to identify is, essentially, what's the steady baseline electrical energy needs for your company or your home, and what are the steady baseline heat energy needs. And then, what you would do is supplement. So if this is your target, you would supplement this energy difference from the grid, and you would supplement this heat difference from some sort of supplementing hidden heating. So if it's a boiler or a furnace or something like that, but hopefully this got you thinking about how this is a pretty hard system to design for because we not only have these kind of, these are average operating conditions. But now imagine that you would have di-annual variation and seasonal variations that you would have to consider too. So again hopefully it got you thinking about all these issues. Okay, so let's step back into this waste heat recovery business. So we talked about waste heat recovery for combined heat and power. And we saw our little example of that. In principle again that's a great thing to do. In practice we have to be pretty thoughtful about how to do that effectively. Combine cycles are another form of waste heat recovery. And in this case what we're going to do is realize that my air standard braking cycle or if you prefer, my gas turbine power system generates a lot of waste heat. So let's go ahead and sketch that up here, and I'll show you how we're going to take that excess energy and we're going to use it effectively, so again we have our compressor. We compress air from the ambient. So this is typically this state, I label this state one. This is going to be typically just drawing in air from outside. So 298 Kelvin and pressure it state one. It's typically going to be atmospheric, right? So we draw this from the ambient. We compress that air to state two, we add heat by burning natural gas, propane, whatever our combustion sources is from state two to three and then again as we've done before, as we harness that energy to generate work out through the turbine. So this is my work in for the compressor. And what we recognize again is this is a high energy, high enthalpy, high temperature fluid at state four. So what we're going to do is take those exhaust gases, and here's where we're going to be pretty clever, and we are going to couple the exhaust energy of my braking cycle with a ranking cycle. So let's show you how we're going to do that. So remember the basics of our ranking cycles say we have to have work in, that as pump. And then, remember, we had our steam generator here. And then, we would expand that high temperature steam through a steam turbine. And then we would condense the water back to liquid phase through my condenser. And what we're going to do in this system is we're going to take this high-energy fluid from the exhaust of my gas turbine and what we're going to do is pass that through a heat exchanger to heat the steam. So this is also referred to as a heat recovery steam generator, so this is heat recovery, and then we'll exhaust those gasses out the stack, dump that heat to the environment, now, so this is going to be exhaust, to environment. Okay, this heat transfer is going to occur without mixing the fluid, I don't want to mix the air with the water, so this is a two fluid heat exchanger where there's no mixing between fluids. So this is air, and this is water. And in this heat recovery steam generator, there is no fluid mixing. Okay. Now, the pressure of these two systems are different right, because we're going to exhaust the gas turbine here nominally to some pressure that's above the ambient. So this will be greater than the atmospheric condition. At the exit here this will be, let's go ahead and label these as a, b, c d, and this is going to be exit state five. So the exit state is going to have a pressure of about one atmosphere. So when we look at the work out of the cycle, what we have here is the network for the cycle. We have work in through the compressor. So this is work in for the compressor. We have work out from the gas turbine. We have work in from the pump, to the pump I should say. And then we have work out of the steam turbine. Okay. So we know that the work ins are less than zero. I'll, sorry, I'll put that as work in comma. This pump is work in. So this is less than zero, this is greater than zero, this is greater than zero but you can see. That we have four work transfers in the system. So now if we consider the net heat transfer for the system, and remember we're considering the cycle which includes essentially if we were to draw a dash line around this entire system. So we have key transfer in from the combuster of the braking cycle, right, so we know that's going to be greater than zero. I'll draw a line so we understand that these inequalities refer to the work transfer and these are the inequalities for the heat transfer, and then we come over here and let's go ahead and. Label that we know we have Q out, or heat transfer out of the condenser. So we have plus Q, condenser, out, and we know again that's going to be less than zero. And here's where we want to be thoughtful. The heat transfer here that occurs between the air, the hot air, which is the exhaust of the Brayton cycle, and the steam in the Rankine cycle is entirely within the overall cycle. So that key transfer doesn't appear in the accounting for the overall combined cycle. Okay. So these are again, these are combined cycle values, okay, for both of these. So now typically that's not going to be enough heat transfer for us to get a whole lot of energy that we want for the entrance to the steam turbine so we might have to supplement that with another form of heat transfer that is external. Right, so if we have to add coal or whatever. But the heat transfer that occurs between the braking cycle, between the air and the steam is entirely within the cycle, so there's no, that doesn't appear within the cyclic accounting, okay. And then of course if we were to close the loop here, this is my fictional rejection of the heat transfer to the ambient. Then we conclude that in my system two, so we would have plus Q dot ambient. In reality that has to be so, just again I apologize to have these lines crossing like this, but that's how you would close the loop, so again this heat transfer that's rejected to the ambient is different. Than if we had directly connected from four to one, okay? We're actually connecting from five to state one, okay? So Q ambient just as a reminder, I will add that this is five comma one, okay? And this value, again and since it's heat out of the system is going to be less than zero. So if we don't have any make up heat, if we don't provide any supplemental heating within the steam generator, that's it. We only have these three heat transfer terms. If I do require, let's like, oh we'll be even more colorful here, we'll add another color to our cycle. If I do need to add more supplemental heat transfer here. So this is going to be let's call it Qn supplemental and again this would be typically coal or some other form of you could do coal. You could do nuclear or something like that. Maybe it's a solar power tower who knows. But there's additional heat transfer in here then we would have to include that heat transfer here. As a supplemental of the transfer and that would be in, okay? So, let's back up for a moment and consider that we've learned. We have high temperature fluid coming out of the gas turbine when we use a Brayton power cycle. Rather than just send that up the exhaust, we might as well couple that to a heat exchanger. And we can couple that to the heat exchanger within another power cycle, like a Rankine cycle and that's referred to as a combined cycle system. And that is going to give me a much higher efficiency than if I just had a simple cycle. Okay. So, more than 20% of the US in the United States over 20% of the total energy circa 1997 was wasted in just thermal losses, so that's essentially, all of that energy was just rejected to the environment. That energy if we could find a way to harness it appropriately could power almost the entire transportation sector. There is a lot of waste heat generated, not just in the United States, but everywhere, so combined cycles and combined heat and power co-generation plants. Are no brainers. So let's line them up next to each other. So here we have kind of my basic coal fire power plant, that's shown in the top here. So we have just for comparison purposes, we'll use a benchmark of 100% fuel comes into my coal fired steam powered plant. That's my Rankin cycle. 60% of that energy is rejected as waste heat. 40% is generated as electricity. That's the typical Rankine power efficiency, a cycle efficiency of 40%. A combined cycle takes my natural gas turbine, the Brayton cycle, which generates about 70% waste heat, so your Brayton cycle's about 30% efficient. So I have 30% electricity generated form my 100% fuel bench mark. 70% is generated as waste heat. I can take that 70% of the waste heat, put it into a Rankine power plant and again with my 40% efficiency and I can get 28% electricity out of that system. And 42% is then rejected as waste heat. That means your combined cycle has an efficiency for just electricity out of 55 to 60%. So that's a remarkable, that's a huge improvement in the electrical efficiency out of my combined cycle. Now if we compare combined cycles to co-gen, that's what we've got in this slide here. So remember, when we generate power we always reject heat, because these are heat engines. That's what these are based on. There are a few exceptions that we're not going to have time to get into in this class, and that's like, fuel cells for example can generate power. And they aren't heat engines. So they follow a different sets of limiting behavior. But for heat engines which are essentially power cycles that generate power because of the temperature difference, they always create heat at the same time we create power. So in combined heat and power cogen, remember we have heat transfer as the desired output. So I get to include that in my definition for thermal efficiency. We can use CHP systems at any scale. You can do this for your home, all the way up to industrial power plants. And most industrial facilities that use very high power output, like, anything that's glass processing, cement processing, metal processing. They've already invoked heating power, and have been doing for many, many years. Cause they've already realized that's a whole lot of energy that could be wasted otherwise. So these are very common to see combined heating power systems around the world. But your heat transfer has to be co-located. If heat transfer application has to be co-located. So like in my example of the University of Michigan power plant. We have a hospital right next door so we can generate that heat and use it literally right across the street. So we can't transfer that heat large distances, otherwise CHP is the right answer, because if we look at my little sketch that I've drawn here the combined heat and power plant, again if I take 100% fuel in, if I generate electricity and heat as the desired output. I get 90% of that fuel energy is effectively used to create electricity and heat. That's awesome. I only have stack losses of 10%. That's the right answer. Okay? But if I don't have a co-located application for heat transfer or if I can't quite hit the targets. If they're very different right. If the electrical energy target is very different than the heat transfer energy target, these systems can be very cumbersome and they aren't as efficient under those conditions. So instead, the combined cycle power plant is again. A sort of no brainer, that's where we got this 55 to 60% useful energy created. And I say it's sort of a no brainer because well you're adding an entire set of power plant equipment, right? You have heat exchangers, you have the piping, you have another turbine. A steam turbine you want to add to that system. So there's a lot of capital equipment involved. With creating a combined cycle power. But, if we compare that to our baseline, where we're only generating 30 to 40% of useful electrical energy, it seems like we really need to focus on making sure that we're smart about how we make our power plant, where we locate them, and how we design them to hit our energy and heat transfer target. Okay, that's going to be the end of our discussion of the technical details of how to analyze stationary power systems. Next we're going to move on to talking about the energy carriers and we're going to start with a discussion of the fossil fuel reserves. So I want you to think about the answer to this question. Are fossil fuel reserves scarce? And we'll start with that next time.
