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What is the difference between energy-from-waste (EFW) and cogeneration, and why is the latter more efficient (let's compare electricity to electricity)? Aren't both essentially incineration?

See below from pages 9 and 12 (respectively) from "The Environmental Impact of Paper Waste Recycling: A Comparative Study" (emphasis added):

Net energy from paper waste management options (one cycle)

In fact, due to the energy requirements of paper production, combustion of unusable fibre can be used even more effectively when integrated into milling. Because a significant portion of the energy required for paper production is thermal, combustion of waste paper can be used directly to fuel the process. Wood fibre cogeneration plants, which generate both electricity and useable thermal energy, obtain efficiencies of 25-30% for electrical generation (mean of 27.5%), and up [to] 75% overall when heat is recovered (FAO 1990). So if the average thermal content of paper is assumed to be 17.3 GJ/T (Morris 1996), a maximum of 2.60 GJ/T could be recovered as electricity through EFW, but 4.76 GJ/T could be recovered through cogeneration, plus an additional 8.23 GJ/T in thermal energy (see Appendices 2, 3). This represents an improvement of 2.16 GJ/T in electrical production, and 10.4 GJ/T overall.

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Cogeneration is a more specialized process with specific fuel requirements which is used to produce electric and heat energy. Energy from waste is a general process whereby any mix of waste is burned to produce electric energy only. This is explained further in the paper. From page seven:

It is important to note the efficiency level of EFW generation. Because these plants operate by burning all household wastes: organics, plastics, glass, aluminum, etc. as well as paper, it is difficult to optimize plant design for generation due to the variability of the combustibles (Ekvall and Finnveden 2000). As a result of this, and the normal inefficiencies involved in energy conversion, burning garbage to produce electricity is able to capture only 15% of the waste’s intrinsic energy (Morris 1996), significantly lower than other fuels (such as coal, which averages approximately 38% efficiency) (Taylor et al. 2008). This could be improved if further sorting were carried out in the waste-fuel stream, with specific incinerators for different fuels, but this would largely undermine the simplicity advantage conferred by such a catch-all disposal method.

Note that when cogeneration is introduced in the quote included in the question it is referred to as wood fibre cogeneration, meaning that the authors are looking at one specific type of cogeneration, and comparing it to a broad array of EFW processes.

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The thing about producing electricity using a thermal engine is that thermal engines have a maximum efficiency that cannot exceed the Carnot efficiency. Example: discard heat at 30 degrees Celsius, use 300 degree Celsius steam, the Carnot efficiency is (1-(273.15+30)/(273.15+300)) * 100% = 47%. That's the maximum that no engine can exceed given the temperatures. Usually you would find that the true efficiency is far lower, something like 37%.

Cogeneration works as follows: you discard the heat at 90 degrees Celsius instead. That gives efficiency of (1-(273.15+90)/(273.15+300)) * 100% = 37%. In practice that would be far lower, something like 28%. But this time you can utilize the waste heat at 90 degrees Celsius to heat buildings in a cold climate. Thus, the total efficiency can be said to be even 90% or higher. However, do note if you lose 9 units of the electric energy, a heat pump with COP=4 could produce 36 units of heat with that, giving 27 units of 'free' heat. So the 'true total' comparable efficiency of non-cogeneration would be 37% + 27% = 64% if the 9% extra is used for additional heating. Yet, the 64% is still below 90% of cogeneration.

Cogeneration can be used with any heat source, waste, coal, fuel oil, natural gas, hydrogen, diesel, gasoline, etc. Every car is essentially using cogeneration as they have a heater powered by the engine waste heat. Even nuclear can use cogeneration but typically due to safety requirements the distance of nuclear is far away from population centers, so cogeneration would require so long heat transfer pipelines that it might not be economically efficient. Also you can't make any plant a cogeneration plant, it has to be taken into account at the plant design stage to allow discarding 90 degree Celsius water instead of 30 degree Celsius water.

District heating networks are what make large-scale cogeneration feasible. With no district heating network, you might not have a way to transfer the heat from large centralized plants to individual buildings.

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