Multiple Rankine Topping Cycles Offer High Efficiency
Jon D. McWhirter, Idaho State University
The Efficiency of a Rankine Cycle is Primarily
determined by the temperatures of heat addition and
heat rejection. However, no working fluid has been identified that will operate in a Rankine cycle over an extremely wide temperature range. Multiple Rankine topping cycles offer a technique for achieving high thermal efficiencies in power plants by allowing the use of several working fluids to span larger temperature ranges.
Rankine topping cycles have been employed in the past, using mercury as the working fluid in the topping cycle. Figure 1 shows a typical temperature-entropy (T-S) diagram for such a plant.1 Utilities built six of these plants in the United States between 1928 and 1949. The best of these plants, the Schiller Station, had a design efficiency of 36 percent, based on a mercury turbine inlet temperature of 958 F. The toxicity hazards of working with mercury, coupled with some technical difficulties, eliminated the cost advantages of employing higher efficiency mercury topping cycles, however, and led to their disfavor compared with steam-only systems. Germany reportedly built and operated a multiple Rankine topping cycle plant in the first half of this century–using mercury, water and ammonia–but details are not available.
In the 1970s, engineers devised Rankine cycles employing potassium as topping cycles for supercritical steam systems (Figure 2).2,3 Cycle analyses indicated achievable efficiencies of 53 percent, which would have been around 10 points higher than the efficiencies of contemporary plants. This efficiency gain, however, probably was too small to justify the increased plant hardware costs and safety concerns associated with employing potassium as a working fluid.
In the 1980s, a consortium comprised of representatives from Austria, the Federal Republic of Germany and The Netherlands evaluated a three-module multiple Rankine topping cycle concept.4 The proposed system employs potassium in the high-temperature portion, diphenyl in the intermediate-temperature section and steam in the low-temperature section, with a reported net efficiency of 51 percent. A coal-fired potassium boiler delivers saturated potassium vapor at 1,598 F to an intermediate-pressure potassium vapor turbine and then through three low-pressure potassium vapor turbines, at an exhaust temperature of 891 F. The system requires three low-pressure turbines, arranged in parallel, because the relatively high specific volume of potassium vapor (900 ft3/lb) results in high volumetric flow rates as saturation pressure approaches vacuum conditions. The potassium cycle employs a single feed liquid heater. The condensing potassium delivers heat to the boiling diphenyl at 851 F. The potassium condenser/diphenyl boiler then delivers saturated diphenyl vapor to a turbine with extraction lines for four feed liquid heaters. The remaining vapor at the turbine exhaust condenses at 549 F to vaporize steam at 518 F. The chosen fluids and arrangements for the three-module cycle dictated a high cost with relatively little performance advantage over gas-turbine combined-cycle plants.
The efficiency gains achievable with the topping cycles discussed above, although significant, are not revolutionary. The limitations can be explained in terms of basic thermodynamics. The efficiency of a heat engine is primarily determined by the average temperatures at which heat is added and rejected. When the heat engine is comprised of sections with different working fluids, the area on a T-S diagram between the heat rejected from one cycle and the heat added to another cycle bears heavily upon the efficiency. That is, if a larger temperature difference exists between the heat rejection temperature of the hotter cycle and the heat addition temperature of the cooler cycle, greater irreversibility results, with a concomitant reduction in the overall cycle efficiency.
For the mercury topping cycle (Figure 1), the mercury boiler outlet temperature is about 950 F, with heat rejected from the mercury at about 500 F and heat added to the water at about 450 F.1 The 50 F temperature difference between heat rejection and heat addition represents an acceptable, medium temperature difference and corresponds to the temperature difference achieved at the commercial mercury topping cycle plants. Conversely, for the potassium topping cycle (Figure 2), with a boiler outlet temperature of about 1,500 F, poor use is made of the area between the steam heat addition section and the potassium heat rejection section: the potassium cycle heat rejection temperature is set at about 1,100 F, while the supercritical steam cycle heat input temperature varies from 550 F to 1,050 F, including reheats.2 The potassium cycle heat rejection temperature is limited primarily by the vapor pressure and vapor specific volume. Further reductions in the temperature could result in excessive in-leakage of air (due to the lower corresponding saturation pressure) and would increase the volumetric flow rates at the potassium turbine outlet and potassium condenser inlet for a given potassium mass flow.
Filling the gaps
To increase the efficiency of the potassium Rankine topping cycle, a plausible option is to fill in the gaps below the potassium cycle with the intermediate temperatures of a mercury cycle, and reject this heat to a non-supercritical steam cycle. The effect of the various component temperatures on cycle efficiency can then be evaluated.
The basis for an efficiency calculation is the ratio of the power output to the power input (or the rate of heat input). For energy production, this is written as:
h = net power output
net heat input rate
It can be shown that the overall efficiency is conveniently expressed in terms of the efficiencies of the individual cycle components:
hoverall = hht + (1 – hht)[hit + (1 – hit)hLt ]
where hoverall is the overall cycle efficiency, hht is the high-temperature cycle efficiency, hit is the intermediate-temperature cycle efficiency and hlt is the low-temperature cycle efficiency.
The current analysis utilized these relationships to calculate the efficiency of a three-component system using sodium as the high-temperature working fluid, mercury as the intermediate-temperature fluid and water as the low-temperature working fluid. Figure 3 shows a simplified schematic diagram for this system. Figure 4 shows a simplified representative T-S diagram. The choices of working fluids are somewhat arbitrary for the analysis, so fluids with well-known properties were selected. A steam condenser pressure of 1.0 psia is used, with a saturation temperature of 101.7 F. A temperature difference of 50 F is used between the components. The parameters to be varied include the sodium boiler outlet temperature and the mercury and water heat addition temperatures, Thigh,Hg and Thigh,steam, respectively. Thermodynamic properties are from Van Wylen and Sonntag,5 El Wakil6 and Howell and Buckius7 for mercury, sodium and water, respectively. Assumed throughout are pump efficiencies of 80 percent and turbine efficiencies of 90 percent. Only simple Rankine cycles are evaluated; cycles employing feed liquid heaters, reheat and/or superheat are not considered.
Figure 5 shows the results of the three-module Rankine topping cycle analysis. As expected, the cycle efficiency increases with increasing sodium temperature, reaching 67 percent at a sodium temperature of 2,000 F. The marked difference in efficiency for the two steam temperatures is primarily due to the high specific heat of saturated liquid water. This property causes the efficiency of the steam cycle to be significantly below the Carnot cycle efficiency between the same temperature limits. Similarly, the extremely low saturated liquid specific heats for mercury and sodium explain the very small effect that the sodium condensing/mercury boiling temperature has on the overall cycle efficiency. The low specific heats for these two fluids cause much less deviation from a Carnot cycle efficiency, with the imperfect turbine efficiency being the largest source of said deviation.
The rather high efficiencies predicted represent significant improvements in thermal efficiencies compared with present steam power plants. Unfortunately, the intermediate fluid used in the analysis, mercury, is probably not a viable power plant working fluid because of its toxicity. Actually achieving the higher efficiencies associated with multiple Rankine topping cycles is further complicated by the reactivity hazards associated with the alkali metals and difficulties associated with materials requirements. S
Author–Dr. Jon McWhirter is an Assistant Professor in the College of Engineering at Idaho State University, Pocatello, Idaho, and a special-term appointee at Argonne National Laboratory. His research interests are in magnetohydrodynamics and liquid metal applications in energy conversion. He is currently on leave of absence and serving as an International Fellow with Japan`s Power Reactor and Nuclear Fuel Development Corp., and assigned to the MONJU Fast Breeder Reactor, Tsuruga, Japan.
1 Hackett, H.N., “Mercury-Steam Power Plants,” Mechanical Engineering, July 1951, pp. 559-564.
2 Wilson, A.J., “Space Power Spinoff Can Add 10+ Points of Efficiency to Fossil-Fueled Power Plants,” Proceedings of the 7th Intersociety Energy Conversion Engineering Conference, San Diego, Calif., Sept. 25-29, 1972, pp 260-268.
3 Fraas, A.P., Engineering Evaluation of Energy Systems, McGraw-Hill Inc., New York, 1982.
4 Brockel, D., Lang, A., Schwarz, N., Stehle, H., Wolter, I., and N. Woudstra, “Treble Rankine Cycle Project Summary Report,” Report No. BMFT-FB-T-86-046, 1986.
5 Van Wylen, R.E., and G.J. Sonntag, Fundamentals of Classical Thermodynamics, John Wiley and Sons, New York, 1973.
6 El Wakil, M.M., Power Plant Technology, John Wiley & Sons, New York, 1984.
7 Howell, J.R., and R.O. Buckius, Fundamentals of Engineering Thermodynamics, McGraw-Hill Inc., New York, 1987.