Comparison of the Organic Flash Cycle (OFC) to other advanced vapor cycles for intermediate and high temperature waste heat reclamation and solar thermal energy
Highlights
► The Organic Flash Cycle (OFC) is proposed to improve temperature matching. ► Ten aromatic hydrocarbon and siloxane working fluids are considered. ► Accurate equations of state explicit in Helmholtz energy are used in the analysis. ► The OFC is compared to basic ORCs, zeotropic, and transcritical cycles. ► The OFC achieves comparable power output to the optimized basic ORC.
Introduction
As energy demands continue to rise, researchers continue to search for alternative energy sources to generate electricity, as well as improve existing methods to maximize efficiency. In order to meet global energy demands, a greater reliance on electricity generated from renewable energy sources such as solar thermal and geothermal energy will become necessary. For solar thermal, energy is obtained from a heated fluid circulating in a solar field, whereas for geothermal, energy is obtained from hot brine that has been extracted from a geothermal well. In addition to renewable sources, thermal energy that in the past would have been released and lost to the ambient such as hot exhaust exiting a gas turbine and industrial waste heat, are now being reexamined as potential power sources. These aforementioned energy sources are often termed as finite thermal energy reservoirs because the reservoir temperature and its thermal energy decreases dramatically as heat is transferred from the source to the power cycle. In order to make the most of these finite sources, the design of an efficient and effective power cycle is crucial.
One of the major sources of irreversibilities for vapor power cycles stems from the heat addition process. The thermal source and working fluid must be separated by some temperature difference in order for heat transfer to occur; however, heat transfer across a finite temperature difference inherently causes irreversibilities. Therefore, it is important to maintain good temperature matching between the heat exchanger streams to minimize these types of irreversibilities [1], [2]. A large degree of temperature mismatching often does occur when the thermal source is single-phase and possesses a near linear temperature profile along the heat exchanger. For a vapor power cycle using a pure working fluid though, the working fluid is first heated as a liquid, undergoes liquid–vapor phase change, and if necessary, is further superheated as a vapor thereafter. Its temperature profile will first be near linear, then constant during phase change, and then near linear again, as shown in Fig. 1a. Temperature mismatching causes a pinch point to form, destroys potential work or exergy, and reduces the effectiveness of the heat exchangers [2]. To minimize temperature mismatching, researchers have proposed a number of possible solutions that include utilizing unconventional working fluids and innovative cycle configurations and designs.
The use of zeotropic mixtures as working fluids in vapor cycles has been proposed by a number of researchers as a possible method to improve temperature matching [3], [4], [5], [6], [7], [8], [9]. Zeotropic mixtures exhibit a unique characteristic known as a “temperature glide,” which results in a variation in temperature during isobaric phase change. Temperature gliding can produce a better temperature match to the finite thermal reservoir by avoiding isothermal phase change. As shown in Fig. 1b, the zeotropic working fluid's temperature glide follows the temperature profile of the thermal reservoir more closely. This reduces the irreversibilities in the heat addition process and can potentially improve the net power output and utilization efficiency [10].
Another method that has been suggested is to avoid the phase change region completely by transferring heat at pressures above the critical pressure [11], [12], [13], [14], [15], [16]. This would essentially avoid the temperature mismatching encountered in the constant temperature phase change process. An illustration of the improved temperature matching is shown in Fig. 1c. A vapor cycle that operates partly under supercritical conditions is known as a transcritical cycle; working fluids that are often suggested for such cycles include carbon dioxide [13], [14], [15] and helium. Although theoretically the transcritical cycle has merit, the design of a suitable supercritical turbine for fluids other than water is still in the developmental phase [15]. A fluid under supercritical conditions can possess both liquid and vapor behaviors; thus tailoring a turbine specifically to one specific condition; i.e. liquid or vapor behavior, becomes problematic [17] and the development of an appropriate supercritical turbine design remains ongoing.
The trilateral flash cycle [17], [18], [19], [20], another proposed method to improve temperature matching, faces similar challenges to that of the transcritical cycle. In the trilateral flash cycle, heat addition occurs while the working fluid is a single-phase liquid, thereby avoiding isothermal phase change as shown in Fig. 1d. Once the working fluid is heated to a saturated liquid state, work is then extracted using a two-phase expander. Similar to the transcritical cycle, the design of a reliable and efficient two-phase expander is still ongoing, though significant strides have been made recently for screw-type and scroll-type expanders and reciprocating engines [20]. To avoid the requirement of a two-phase expander though, the single-phase liquid could be throttled to a two-phase mixture after heat addition. The liquid and vapor components of the mixture can then be separated and work can be extracted from the saturated vapor using a conventional and readily available Organic Rankine Cycle (ORC) turbine. By using this type of configuration, a two-phase turbine is no longer necessary, while the advantageous temperature matching between streams shown in Fig. 1d is still achieved. This resulting cycle is somewhat similar to the flash steam cycle that utilizes high temperature and pressure geofluid that has been extracted in the liquid state from a geothermal well. Once extracted, the liquid geofluid is then throttled to a lower pressure or flashed to produce a liquid–vapor mixture [10]. One major disadvantage of the steam flash cycle though, is that the steam after expansion contains a significant amount of moisture because water is a “wet” fluid. Wet fluids exhibit a saturated vapor curve on a temperature-entropy (T-S) diagram that is negatively sloped [4]. Isentropic expansion of a “wet” fluid from its saturated vapor state will always produce a two-phase mixture with liquid droplets forming. Although in reality large steam turbines often have isentropic efficiencies of 80%–90%, saturated steam cycles in both geothermal and nuclear power industries still require special wet steam turbines. Wet steam turbines are constructed with expensive reinforcing materials to protect the blades from erosion and damage caused by the liquid droplets [10].
Expansion of a saturated vapor into the vapor dome can be avoided if a fluid with an infinite or positively sloped saturated vapor curve on a T-S diagram was used instead of steam [3]. These fluids are known as “isentropic” or “dry” fluids, respectively. Turbine cost would be significantly reduced for the Organic Flash Cycle (OFC) since blade reinforcing materials are no longer necessary. Although uncontrolled expansion of the working fluid generates considerable irreversibilities during the throttling or flashing process [21], the reduction in exergy destruction during heat addition could still provide a net gain in the OFC's exergetic efficiency as a whole. The present study uses thermodynamic and exergetic analysis to evaluate the effectiveness of the OFC employing an organic “isentropic” or “dry” fluid. A finite thermal source originally at 300 °C is considered as it represents typical temperatures for high efficiency gas turbine exhaust, high temperature industrial waste heat or geothermal wells, and solar thermal energy using 1-axis tracking concentrated collectors such as parabolic troughs. Comparisons based on the internal second law efficiencies, heat addition exergetic efficiency, and utilization efficiency are then made to other vapor power cycles that have been proposed for solar thermal and waste heat applications.
Section snippets
Description of the Organic Flash Cycle
In Fig. 2a and b, a basic ORC plant layout and its T-S diagram are shown. Also shown are the T-S diagrams for a Rankine cycle using a zeotropic mixture and for a transcritical Rankine cycle. A schematic of the proposed OFC configuration and its T-S diagram are shown in Fig. 3a and b, respectively. Note that in Fig. 2 a “wet” fluid had been assumed, as the slope of the saturated vapor curve is negative, whereas in Fig. 3, a “dry” fluid has been assumed as the slope of the saturated vapor curve
Equations of state explicit in Helmholtz energy
To determine the thermodynamic properties of different working fluids, accurate equations of state are necessary. Since increases in efficiency by even just a few percent is important, simple equations of state such as cubic ones do not possess enough accuracy for analysis in this study. Instead a combination of modern equations of state such as the semi-empirical BACKONE equations [22], [23], the empirical, multi-parameter Span–Wagner equations [24], [25], [26], [27], and the equations of
Results for the basic ORC
Aromatic hydrocarbon and siloxane working fluids have often been proposed for ORCs utilizing a high or intermediate temperature finite thermal source [6], [32], [40], [41]. A list of the fluids analyzed in this study has been compiled in Table 1, along with the equation of state that was used and its corresponding references. Note in Table 1, aromatic hydrocarbons are first listed and then siloxanes. The finite thermal source is modeled as hot water initially at 300 °C flowing at a steady rate
Conclusions
A comparison of the Organic Flash Cycle to the optimized ORC and other advanced vapor cycles for high and intermediate temperature finite thermal sources was presented. The OFC concept is based upon the design principle of increasing utilization efficiency by increasing temperature matching and reducing exergy losses during the heat addition process. REFPROP, BACKONE, and Span–Wagner equations of states were used in conjunction with a detailed thermodynamic and exergetic analysis to determine
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