Stationary Combustion Systems Chapter 6

Transcription

1 Stationary Combustion Systems Chapter 6 Stationary combustion systems presently supply most of the earth s electricity. Conversion will take time, so study of these systems in order to improve them is appropriate. Such systems have 3 main components. Combustion chamber or boiler to burn fuel Turbine - Means of converting heat to mechanical energy Generator - Means of converting mechanical to electrical energy No fuel conversion is required for Hydro powered systems, and nuclear uses nuclear fuel to heat the working fluid. Existing fossil fuel plants are being up-fitted and new ones are being built because: 1. Modernization of old plants increases efficiency, which increases output and reduces CO2 emissions. This is a necessary step because a rapid move to solar/wind/biomass is unreasonable. 2. Modern plants will be able to accommodate a mix of biomass in their fuel to further cut CO2 emission. Biomass is carbon neutral since the carbon needed to grow the fuel was taken from the atmosphere. 3. Modern plants can include hooks for sequestration. 6-3 COMBUSTION CYCLE CALCULATION FUNDAMENTALS Classical thermodynamics is the branch of physics that deals with the mechanical actions or relations of heat. Heat quantity is characterized as enthalpy or energy per unit mass. Intuitively, higher enthalpy means higher energy concentration. Heat quality is characterized as entropy or energy per unit mass-temperature. Classically we think of low entropy as high order and high entropy as high disorder and thus discuss the ever increasing entropy of the universe. HOWEVER in

2 thermodynamics higher entropy results when a working fluid like water has a higher quality of heat, being at higher pressure or temperature. THE GOOD NEWS we pull most of our enthalpy and entropy values from tables. First law of Thermodynamics: Thermal processes conserve energy. Energy not transferred from the working fluid to the turbine, for example, is lost into the materials of the system, but still exists. Second law of Thermodynamics: A combustion cycle cannot experience a reduction in entropy. The best case is break even. Simplification discusses isentropic cycles, where entropy remains constant. The Carnot limit sets an upper expectation for combustion cycle efficiency. η carnot = (T H -T L )/T H This says that the rejection temperature (low temperature) must be 0K if a system has an efficiency of 1. Increasing the high temperature and decreasing the low temperature result in a more efficient system. Enthalpy quantity of energy (units of energy per unit mass), measured in kj/kg or BTU/lb. Entropy quality of energy (units of energy per unit of mass-temperature), measured in kj/kg.k or BTU/lb.degree R. (K = C and R = F ) The objective of a combustion cycle is to get the maximum energy out of the combusting fuel. The thermal efficiency of the combustion system is: η th = (ω out ω in )/q in When we look at actual cycles, we will see that we add complexity to increase efficiency. Thus all such improvements must be economically justified.

3 6-3-1 RANKINE VAPOR CYCLE Developed by William J. M. Rankine in Same guy for which the Rankine degree is named. (K = C and R = F ) : Note the numbered stages: 1-2 pumps (compresses) fluid (work in), 2-3 the boiler heats the fluid (heat in), 3-4 steam spins turbine (work out), 4-1 steam is condensed back to fluid (heat out). ω pump = υ f (P 2 P 1 ) where υ f is the specific volume (volume per unit mass) of the fluid.

4 An ideal Rankine cycle will have isentropic (no increase in entropy) compression and expansion steps, which yield high quality liquid (no vapor) after compression, and high quality vapor (no liquid) after expansion. The quality of the fluid at the turbine exit (a mix of vapor and liquid) is expressed as a ratio of the change in entropy from S4 to fluid, to the maximum possible change in entropy between pure steam and pure liquid. x = fluid quality = (s 4 s f )/(s g s f ) Since the change in enthalpy is proportional to the change in entropy, this can be used to calculate the enthalpy of state 4 and enable a Rankine cycle efficiency evaluation. Example 6-1 in metric units Isentrophic compression and expansion no worries about heat leaks. Specific energy of the 4 MPa steam at turbine entry (h 3 ) enthalpy of kj/kg (Appendix B, p500) Specific energy of the 100 kpa water after the condenser (h 1 ) enthalpy of kj/kg (Appendix B, p 496) s 3 = s 4 due to isentropic expansion = kj/kg.k (Appendix B, p500) From ω pump = υ f (P 2 P 1 ) we calculate the pump work, knowing the specific volume of water at 100 kpa to be m 3 /kg (Appendix B, p 496), to be 4 kj/kg. Thus the specific energy of the water after the pump (before the boiler) is h 2 = h 1 + ω pump = = kj/kg We need to know h 4 to arrive at the work extracted output of the turbine. This requires a knowledge of the fluid quality (entropy) of the liquid/vapor leaving the

5 turbine. s g and s f are from Appendix B, p 496. s 4 is from step one of this explanation. x = fluid quality = (s 4 s f )/(s g s f ) = ( )/( ) = 78.7% Knowing the fluid (vapor) quality, allows us to rearrange the corresponding enthalpy formula and solve for h 4. h 4 = kj/kg. The efficiency of the cycle will be the (work done by the steam as it expanded and cooled, minus the work expended by the pump) divided by the heat added in the boiler, or... η th = (ω out ω in )/q in = [(h 3 - h 4 ) - ω pump ]/ (h 3 h 1 ) = 25.3% As it should be, this is less than the Carnot limit of 28.8% (η carnot = (T H -T L )/T H ), using the temperatures of completely condensed water at 100 kpa and of saturated steam at 4 MPa. Make sure to convert to K. Irreversible losses (heat leak, friction in pumps and turbines, etc) lower cycle efficiency. A 15% turbine efficiency reduction (from 100% to 85%) in this case results in a 3.8% reduction in combustion cycle efficiency Brayton Gas Cycle Gasses (LNG) can be combusted directly to drive a turbine, rather than be used to heat a working fluid. Such a cycle requires compression on the input and

6 exhausts combustion products at the output. Mechanical coupling from the output turbine is often used to drive the input side compressor. This type of cycle is named after an American engineer, George Brayton who developed the continuous combustion cycle in the 1870s. The 4 state cycle is similar to, but different from the Rankine Vapor Cycle. 1-2 Work is added to compress atmospheric air. 2-3 Fuel is injected into the compressed air and combusted in a chamber. 3-4 Combustion products expand through a turbine creating work output in the form of a rotating shaft. Needed: Continuous supply of fresh air and fuel Exhaust products are either directly discharged to the atmosphere or recycled through a heat exchanger to extract some of the remaining thermal energy for other purposes. The work needed for compression in the Brayton Cycle is much greater than that needed for pumping the nearly incompressible fluid in the Rankine Cycle. Several methods can be used to calculate Brayton Cycle efficiency, but we will use the relative pressure method. We need the pressures before and after compression, or the compression ratio of the compressor and one of the pressures. pr 2 = pr 1 (P 2 /P 1 ) where P 2 /P 1 is the compression ratio. Example 6-4 in metric units Isentrophic compression and expansion no worries about heat leaks. 295K air at 95 kpa enters the compressor. The compression ratio is 6:1 and the compressed air is heated to 1100K in the combustion chamber before being expanded in the turbine. The air table on p502, Appendix B, directly provides enthalpy and relative pressure for state 1 and 3. We need to solve for h 2 and h 4 to calculate the turbine output and work input to the compressor.

7 We can multiply pr 1 by 6 to get pr 2 and then interpolate the air table to find h 2. Similarly, we can divide pr 3 by 6 to get pr 4 and then interpolate the air table to find h 4. Once we have all four h values, then we can calculate as follows: Heat in = q in = h 3 h 2 = = kj/kg Turbine work = ω turbine = h 3 h 4 = = kj/kg Compressor work = ω compressor = h 2 h 1 = = kj/kg η th = (ω turbine ω compressor )/q in = ( )/668.4 = 38.5% Understanding the irreversible losses in the Brayton Cycle are doubly important as these losses will increase the need for input work at the compressor and reduce the availability of output work at the turbine. Practical analyses should not presume isentropy unless these losses are known to be small. In our case, without considering irreversible losses, the compressor chewed up 43% of the work output of the turbine. 6-4 Advanced Combustion Cycles With efficiencies before losses of 25% and 38% of Rankine and Brayton, we naturally have explored other cycles. This discussion focuses on the combustion cycle rather than the efficiency of generation because modern generators are around 98% efficient Supercritical Cycle These cycles use higher pressures to increase heat capacity and thus efficiency. Such cycles require advanced materials to contain the higher pressures and temperatures. Rankine efficiencies improve by 10 15%, but the Carnot limit increases even more as the cycle temperature climbs. Narrowing the pressure swing can close the gap between actual and Carnot but this means that more, maybe all of the cycle must be at supercritical pressures, driving up material and component costs.

8 6-4-2 Combined Cycle The combined cycle uses the Brayton Cycle exhaust to heat the working fluid in a Rankine Cycle. Thus work is extracted from both the Brayton gas turbine and the Rankine steam turbine. In practice these facilities typically have several gas turbines (Brayton Cycle) in parallel and a smaller number of steam turbines (Rankine Cycle), also in parallel. The output of the gas turbine exhaust stream limits the amount of steam generation that can be supported. Combined cycles can employ superheated steam cycles (heating the steam beyond its saturation temperature at a given pressure). Superheated steam has a higher energy density (enthalpy) and thus can support a more efficient cycle. Superheating has the disadvantage of requiring another component, designed to heat steam, between the boiler and steam turbine, and the full value of the steam s increased enthalpy is not realized because the enthalpy at the turbine exit also rises, thus reducing the potential output of the turbine. All things considered, design efficiencies of 50-60% are being reported in North American, European and Asian modern fossil fuel sites (Table 6-1)

9 6-4-2 Cogeneration and Combined Heat and Power Cogeneration plants use the exhaust heat for purposes other than generating electricity. A common such plant combines heating and power generation, and are called CHP for combined heat and power. Regardless, they fall under the umbrella designation as a cogeneration facility. Cogeneration as depicted in Figures 6-9 and 6-10 require the addition of a thermal expansion valve reduce the pressure of steam before introduction into the process heater that extracts heat for other purposes and condenses the steam for passage through a pump to a mixing chamber before being returned to the boiler. Note that some of the high pressure steam is fully expanded to drive the steam turbine of the Rankine Cycle, some is partially expanded in the turbine to reduce its pressure to that of the process heater, and some is valved off through the thermal expansion valve before being introduced to the process heater. Those paths and the second liquid pump complicate the Temperature/Entropy curve in Figure 6-10, but it can be logically followed step by step.

10 Cogeneration fell out of favor during the middle part of the 20 th century due to low fossil fuel costs. Interest is rising again with the rise in fossil fuel prices and subsequent desire to harvest as much energy as possible. Cogeneration by nature works best if the process heated load is near the stationary fossil fuel fired plant. This means having an industrial plant next to a power plant, or having a community build adjacent to a power plant. Sometimes this works out, sometimes not. Smaller cogeneration plants are popping up as retrofits like the one at Cornell University. There the existing steam plant was fitted with a generator capable of producing up to 7.5 MW of the average 32 MWs required by the university. After expanding through the turbines, the steam continues to heat the campus building as it has been doing since Small scale cogeneration systems are popping up also. Diesel cycle combustion engines are employed where LNG is used for space heating or domestic hot water. Some of the generators are as small as 30 kw in primary or secondary schools or apartment buildings. 6-5 Economics The very nature of the problem demands multiple economic approaches. Considerations that complicate analyses to support a decision to build a new plant include uncertainty of 1) fuel prices, 2) the energy market, 3) regulatory impacts, and 4) technology shifts. Sensitivity analyses and probabilistic analyses are useful, if not required tools. Amortization period vs. useful life of the facility can be hard to predict. One would hope to pay off the investment in 20 years or so and that the site can generate energy competitively for several decades after the payoff, but no one can say for sure. The cost of production will include the capital costs of the land and facilities, the fuel costs per unit of energy produced and the other costs of labor, compliance, etc. These three components divided by the energy produced will yield one view of $/watt. Then you can start the sensitivity and probabilistic analyses. See case study if interested.

11 6-6 Environment Tradable emission credits helped the reduction of harmful gasses like NO x and SO 4. Carbon credits promise to be challenging as they are not likely to be enacted uniformly. Example 6-11 looks at the impact carbon credits could have on the cost of electricity. 6-7 Future of Fossil Fuel Combustion The authors anticipate fundamental technological change to support fossil fuel combustion in the not too distant future. Essentially they see little runway left for enhancing existing technology but instead predict a heavy adoption of cogeneration and pursuit of zero-carbon emission facilities, such as that being studied the FutureGen Industrial alliance. The alliance sees a cycle involving gasification of coal, separation of CO 2 and H 2, the use of H 2 in high temperature fuel cells, which output electricity and steam to drive a steam turbine for additional electricity output. The CO 2 will be sequestrated locally or remotely, but there will be no smokestacks for direct emission. 6-8 Systems View Do we bridge or backstop Plan now for cogeneration or other multiple use applications Maintain the use of infrastructure while transitioning between energy sources Smaller scale (distributed) applications Positing good investments by coupling purposes 6-9 Summary Combustion presently generates most of the world s electricity. Rankine and Brayton cycles rule, but operate at only 30% and 40% efficient. Combined cycle and cogeneration are considered radical but needed advancements to the status quo. Sound economic analyses and a systems view are critical to support the path forward.