Numerical optimization of steam cycles and steam generators designs for coal to FT plants
Introduction
Advanced integrated energy systems typically include a heat recovery steam cycle (HRSC) fed with waste heat from gas turbines and/or a number of process units. Besides generating power for auxiliary systems and (optionally) for electricity export, the HRSC can also supply heat to endothermic processes and steam to external users, taking advantage of the integration between the heat recovery steam generator (HRSG) and other heat exchangers. For instance, given the large amount of process waste heat, the HRSC of integrated gasification combined cycles (IGCCs), integrated reforming combined cycles (IRCCs) and coal to Fischer–Tropsch liquids plants may take large advantage of the integration between the HRSG tube banks and those of the syngas coolers. However, existing simulation codes are not well-matched to the task of optimizing complex integrated steam cycles. In such cycles, the HRSG is connected (in a potentially very complex manner) with a heat recovery steam network, a set of process coolers with multiple options for heat recovery, and a process with various demands for heat and steam. Existing simulation codes for power plants cannot determine the most advantageous options of heat recovery within the process coolers, the most efficient options for supplying heat and steam to the process, or the most efficient integrations between the steam generator and the external steam network. For instance, when using GT PRO (Thermoflow, 2012) or GATE CYCLE (GE Energy, 2012), the arrangement of the steam network, the options for heat recovery within the syngas coolers, and the connections between the process and the steam generator must first be determined by the designer according to his experience and thermodynamic considerations. Once these are fixed, the simulation code can be applied to model the steam generator and steam cycle to find the optimal design parameters. However, when there are multiple attractive integration options that offer the potential for increased efficiency and/or lower costs, the designer is forced to simulate and optimize each HRSC configuration. A large number of possible configurations can make this procedure both time consuming and potentially unsuccessful. Indeed, the most advantageous options may be overlooked by the designer.
On the other hand, the optimal design and synthesis of steam cycles, steam networks and utility systems for chemical plants have been attracting attention for more than 30 years. For example, a systematic methodology to optimize the design of utility steam cycles is proposed by Nishio et al. (1980), which couples linear programming with a set of thermodynamic rules to determine the best plant structure and the intensive steam cycle parameters, Papoulias and Grossman (1983) and Bruno et al. (1998), which propose respectively a Mixed Integer Linear Programming (MILP) and a Mixed Integer Non-Linear Programming (MINLP) model to select among all the alternative units included in the utility superstructure, Colmeranes and Seider (1989), which combine the temperature interval method of Linnhoff and Flower (1978) with a superstructure of Rankine cycles capable of generating complex configurations, and Marechal and Kalitventzeff, 1997, Marechal and Kalitventzeff, 1999, which combine the heat cascade problem of pinch analysis with a MILP superstructure of Rankine cycles capable of considering multiple external heat/steam sources/users. However, these methods are not suitable for carrying out the detailed design of a heat recovery steam cycle for the following reasons:
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the design of the steam generators (either HRSG or boiler type) is not considered in the models but reduced to the assumption of a boiler thermal efficiency;
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the prediction of the turbines performance is either left out by assuming a constant isentropic efficiency or simplified (e.g., Bruno et al., 1998) by neglecting the moisture losses (i.e., efficiency losses due to the formation of water droplets at inlet of the last stages) and the labyrinth seal losses;
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steam can be generated in both the steam generator and external heat exchangers (HXs) but no integration is allowed between the tube banks of the two systems.
A rigorous design approach must simultaneously optimize the heat recovery, heat supply and steam supply options, the steam network, the steam/water mass flow rates, the pressure levels and temperatures, and the steam generator design variables. This approach was chosen by Martelli et al. who developed an automatic optimization methodology called the “HRSC Optimizer” (Martelli, 2010, Martelli et al., 2011a). This software couples a rigorous mathematical representation of the HRSC with a two-level optimization algorithm, and is capable of reproducing all physically feasible HRSC arrangements. The methodology simultaneously optimizes the design of the HRSG, the mass flow rates, pressures, and temperatures of all the steam/water flows (in both the HRSG and the external heat exchangers), as well as the mass flow rates of fuel used for supplementary firing (SF). The HRSC Optimizer has been successfully applied to the design of Shell based IGCCs (Martelli et al., 2011b), coal to substitute natural gas processes (Martelli, 2010), integrated reforming combined cycles (Martelli et al., 2012), and integrated gasification fuel cells (Lanzini et al., 2012). In all the instances, the comparison with the HRSCs designed by expert engineers has shown that the optimized designs are significantly more efficient.
In this work, the HRSC Optimizer has been applied to the design of HRSCs for coal gasification-based Fischer–Tropsch synthesis processes, often termed “Coal-To-Liquids” (CTL) plants. We focus here on CTL plants designed and simulated by Liu et al. (2011), from which we have selected two configurations:
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CTL-RC-CCS: a high (99%) fraction of the unconverted syngas exiting the FT synthesis reactor is recycled to maximize the production of liquid fuels, and
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CTL-OT-CCS: a once-through design where unconverted gases are not recycled but instead burned in a gas turbine to generate electric power.
Both plants perform CO2 capture and storage (CCS), and employ commercially available technologies like the GE-Energy gasifier with a total water quench. Plant CTL-RC-CCS is an example of gasification based plants that generate synthetic fuels from coal (with minor electricity export), while plant CTL-OT-CCS represents polygeneration systems that produce both FT fuels and a significant electricity co-product.
Designing an efficient HRSC for a complex CTL plant is a challenging task for many reasons:
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The process involves three strongly exothermic reactions (oxygen blown gasification, water-gas shift, and FT synthesis) that produce a significant amount of waste heat whose efficient conversion to electricity is critically important in order to maximize the overall plant efficiency.
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The process steam network is complex, with more than 20 units exchanging (heating/condensing/absorbing) steam and a set of forbidden and imposed heat exchange matches (steam can be generated in some process coolers depending on its pressure and temperature for a number of technical issues).
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A large fraction of the recoverable thermal power is concentrated at low temperatures (below 250 °C) and only a small fraction can be used to superheat steam.
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Compared to up-to-date natural gas combined cycles and pulverized-coal-fired steam cycles which employ very high superheat and reheat temperatures (e.g., 565–600 °C, see Martelli et al., 2012), CTL plants can superheat and reheat steam up to limited temperatures because of the large flow of saturated steam generated by the FT reactor, and the relatively small amount of high temperature heat suitable for steam superheating. This leads to relatively low steam turbine inlet temperatures, and consequently the turbine expansion can reduce steam quality below optimal levels (<88%) which, in turn, yields large expansion losses due to the formation of water droplets in the last turbine stages.
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It must be determined whether it is advantageous to burn the FT off-gases in a boiler (e.g., in Liu et al., 2011) or in a gas-steam turbine combined cycle.
The systematic approach developed by Martelli et al. (2011a) is first upgraded by including a detailed boiler model, and then applied to the two CTL plants in order to determine optimal HRSC configurations and design criteria.
Section snippets
Plant configurations
The two plants are fed with the same coal type (Illinois No. 6 with lower heating value, LHV, 25.86 MJ/kg) and mass flow rate (278.9 kg/s) and share the same gasification section comprising a cryogenic air separation unit (ASU), a coal dryer and pulverizer, a slurry-feed GE-Energy gasifier with total water quench, and a wet syngas scrubber. In both CTL plants, the scrubbed syngas is partially shifted in a single-stage sour water-gas shift (WGS) unit and a WGS bypass stream whose flow is adjusted
HRSC optimization methodology
The mathematical model and details of the optimization algorithm are described in Martelli et al. (2011a). The problem tackled by the HRSC Optimizer can be formally stated as follows.
Given:
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one or more gas turbines or industrial furnaces followed by one or more HRSGs,
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a set of heat sources (HS) which can supply a given thermal power to the HRSC over a limited temperature range,
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a set of heat users (HU) which demand a given thermal power at a minimum temperature,
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a set of mechanical users, such as
Optimization of HRSC designs
The optimization of the HRSCs for the three plants was based on the techno-economic constraints (discussed in Martelli et al., 2012) and assumptions reported in Table 3. The constraints underpin the HRSC designs developed by Liu et al. (2011), thus enabling a fair comparison between their original HRSC designs and those obtained here by optimization. No constraints related to off-design operation were considered here, and it was further assumed that the steam turbines were designed specifically
Analysis of results
Fig. 6, Fig. 7 plot the composite curves (CC) (Linnhoff and Hindmarsh, 1983) of the recoverable process waste heat versus the CC of the HRSC for the three plant options. These curves are very useful in understanding the relative performances of the optimized HRSCs. The CCs in Fig. 6, Fig. 7 take into account not only process heat exchangers but also the boiler and the HRSG flue gases. It is worth noting that these CCs have been specifically modified to represent the effective temperatures at
Conclusion
Our analysis reveals that, using the HRSC Optimizer, designing efficient HRSCs for the CTL-OT-CCS plant is relatively straightforward, while designing the HRSC for the CTL-RC-CCS option is very challenging; in the latter plant, the recoverable thermal power is concentrated at low temperatures (i.e., below 260 °C) and only a small fraction can be used to superheat steam. To span the space of all the interesting steam cycle configurations, a new boiler model was developed and included in the HRSC
Acknowledgments
We are grateful to Prof. Guangjian Liu, North China Electric Power University (Beijing, China), for providing the plant data needed to design the steam cycles, and to Princeton University's Carbon Mitigation Initiative and LEAP (Laboratorio Energia Ambiente Piacenza) for financial support.
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