22-Mec-B3 Energy Conversion and Power Generation · May 2018
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. 16-Mec-B3 Energy Conversion and Power Generation, National Examinations, May 2018. Three hours, closed book. Two sections: Section A is calculative (Questions 1–5) and Section B is descriptive (Questions 6–8). Candidates answer four questions from Section A and two from Section B; six questions of 10 marks each constitute a complete paper (60 marks). Reference data for individual questions are bound in as attachments on pages 9–15, reference formulae and constants on pages 16–19, and Granet & Bluestein steam tables are supplied. All eight questions are solved below, because the set is a study resource rather than a timed attempt.
Reference texts.
Wherever the paper's own attachments carry a value that duplicates a computed result — the Koeberg terminal temperature difference and back pressure on page 10, the gas-turbine output quoted in the preamble to Question 2, the published rating of the Oconee unit — that printed value is used as an independent check and the agreement is quoted in the answer.
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
(a) Why both enhancements beat the simple cycle. A simple open gas turbine rejects its exhaust at 450 °C to 600 °C, and that stream carries roughly two thirds of the fuel energy. Nothing in the cycle can use it, so the efficiency is capped near 30 % to 40 %. Both enhancements attack the same loss: they interpose a heat recovery steam generator in the exhaust and convert part of that rejected heat into additional work, without burning any more fuel. Because the fuel input is unchanged and the output rises, the efficiency must rise. For a bottoming cycle the arithmetic is a simple series cascade, $$\eta_{cc} = \eta_{gt} + (1-\eta_{gt})\,\eta_{hrb}\,\eta_{st} ,$$ so a 35 % machine whose boiler recovers 80 % of the exhaust heat into a 33 % steam cycle reaches $0.35 + 0.65 \times 0.80 \times 0.33 = 52.2$ %. Steam injection reaches a similar place by a different route: the injected steam is raised from waste heat but then expands through the existing turbine, so it adds mass flow and hence work without adding compressor duty — the compressor never has to handle it. In both cases the gain comes from recovering exhaust heat, and the ceiling is set by how far the gas can be cooled before the stack, which in turn is limited by the steam pressure chosen and by the acid dew point.
(b) Steam injection compared with steam bottoming. The steam-injected machine is much the simpler of the two. It needs a heat recovery boiler, a feedwater treatment plant and injection piping, but no steam turbine, no condenser, no cooling water system and no second generator, so its capital cost per kilowatt and its plot area are far smaller and it can be installed as a retrofit to an existing unit. It also raises the specific output of the gas turbine sharply — injecting five to ten per cent of the air flow as steam can lift output by twenty per cent or more — and the excess steam in the combustor lowers flame temperature, which suppresses thermal nitrogen oxide formation. Its response to load change is fast, because there is no steam drum to follow.
Against that, every kilogram of injected steam leaves up the stack as vapour. The plant therefore consumes high-purity demineralised water continuously, at a rate that on a mid-sized machine runs to tens of tonnes an hour, which rules the scheme out wherever water is scarce or expensive to treat. The latent heat carried away in that vapour is also lost, so the peak efficiency of an injected machine is a few points below a well-designed combined cycle: injection typically reaches the mid-forties per cent where a modern combined cycle reaches the high fifties. Injection additionally constrains the gas turbine itself, since the extra mass flow through the turbine raises its pressure ratio and can push the compressor towards surge, and it exposes the hot section to a more oxidising, more thermally conductive gas that shortens blade life.
The bottoming cycle is the opposite trade. It is expensive, slow to start and needs a condenser and its cooling water, but it recovers the working fluid in a closed loop, so make-up water is a small fraction of a per cent of the circulating flow, and it delivers the highest efficiency of any thermal plant in commercial service. It also decouples the two machines: the steam turbine can be sized, controlled and maintained independently, and multi-shaft arrangements allow the gas turbine to run alone when the steam plant is out. In short, choose injection where capital cost, footprint, rapid response or emissions dominate and water is cheap; choose bottoming where fuel cost and annual output dominate and the plant will run at high load factor.
(c) The heat recovery steam generator and its profiles. A typical unfired heat recovery boiler is a rectangular casing through which the gas passes horizontally or vertically over three tube banks arranged in counterflow to the water. Taking them in gas order: the superheater is nearest the gas inlet and raises the saturated steam to the turbine inlet temperature; the evaporator follows, and is the only bank with a drum, connected to it by unheated downcomers and heated risers so that a natural or assisted circulation carries a multiple of the steaming rate through the tubes; the economiser is at the cold end and heats the incoming feedwater to just short of saturation. The drum carries the steam separators and the chemical dosing and blowdown connections, and the feedwater is delivered to the economiser from a deaerator, which is often integrated into the same drum on smaller units.
The temperature diagram on the right shows why the arrangement must be in that order. The gas cools along an almost straight line, because its specific heat is nearly constant, while the water line has three distinct slopes: a steep rise through the economiser, a horizontal plateau through the evaporator at the saturation temperature of the drum pressure, and a second steep rise through the superheater. The closest approach between the two lines, the pinch, always occurs at the point where the water reaches saturation, and it is the single number that fixes the design: for a chosen steam pressure, the pinch fixes the gas temperature at that point, which fixes the steam flow, which fixes the stack temperature and hence the heat recovered. Lowering the steam pressure lowers the plateau and lets the gas be cooled further, recovering more heat but with less work per kilogram of steam; that trade is why large units use two or three pressure levels, each with its own economiser, evaporator and drum, so that the water line follows the gas line as closely as the pinch allows.
