The question posed in the title of this post is yet unanswered. We still do not know if we can build a fossil fuel power plant whose emission of greenhouse gases is zero across its entire life cycle (i.e. construction, operation, and deconstruction.)
But with that having been said, we still don't know if we can build a solar PV or a wind turbine with zero life cycle greenhouse gas emissions. Nobody yet has proven that a solar PV panel or a wind turbine can self-replicate without replying on the existing fossil fuel based economy. (For example, today's solar PV technologies and wind turbines rely on relatively cheap gasoline and fossil fuel based electricity during the construction phase of operations.)
This is a problem because we need to limit the concentration of carbon dioxide in the atmosphere. (While there is still uncertainty on what should be the maximum allowable concentration in the atmosphere, the likely maximum should probably be in the range of 400-800 ppm.) Given that we are currently increasing the concentration of CO2 at a yearly rate of ~3 ppm and given that we have yet to demonstrate a single 'modern' technology that has a zero lifecycle emission of greenhouse gases, we need to get out acts together and start demonstrating technologies that can self-replicate without reliance on an economy that emits greenhouse gases. This means that solar PV projects can't count as truly self-replicating and truly zero GHG-emitting until the electricity from the solar panel and only from the solar panel is used power the factory and build the factory that makes the solar panels.
So, let me know get to the main point of this post: I think that there are ways to design self-replicating coal power plants that don't emit greenhouse gases and that have positive growth rates. While there are a lot of people researching the topic of carbon capture and sequestration at coal power plants, most people in this field stop short at the power plant and don't address the question of how to limit CO2 emissions from factories and steel mills that make products used to construct the power plant. In other words, who cares if you can design a coal power plant that doesn't emit CO2 during operation if there are significant amounts of CO2 emissions during the construction and deconstruction phases of the lifecycle? You can't determine if the system can self-replicate without CO2 emissions until you design and model the whole system (not just the power plant.) This means including the cars that the workers drive into your model of the system.
Therefore, we must start thinking about designing self-replicating power plants cycles that don't emit CO2 emissions. As such, I think that there is one type of coal power plant that is more likely to be able to self-replicate without CO2 emissions than other types of coal power plant. This type of coal power plant goes by the acronym IGCC-CCS. The acronym stands for Integrated Gasification Combined Cycle with Carbon dioxide Capture and Sequestration. (Note: Sequestration here refers to storing CO2 under the ground. It should also be noted that there are a number of natural CO2 reservoirs in the U.S and there are plenty of locations to safely store CO2 in the U.S.)
One of the main components of this power plant is a coal gasifier. It should be noted that there are a wide variety of different coal gasifiers, and some of the fixed/m-bed types of coal gasifiers can also take municipal solid waste as input. In addition to the coal or waste input into the gasify, there is also an input of steam and/or oxygen. The output can be a mixture of hydrogen, carbon monoxide, hydrogen sulfide, carbon dioxide, steam, and methane, depending on the pressure, temperature, and input feedstock composition.
This intermediate step between solid feedstock and combustion product is crucial for the ability to self-replicate without CO2 emissions because the fuel gas leaving the gasifier is typically already at high pressure and can be converted fairly easily into three relatively pure streams of (1) hydrogen, (2) carbon dioxide, and (3) hydrogen sulfide. In addition, the ash in the coal and waste can be used throughout the plant, such as in the concrete or asphalt.
The key here is that the hydrogen can be used fuel the Brayton-Rankine combined cycle to generate electricity without generating CO2 emissions and the hydrogen can also be used in the steps required for construction and maintenance of the power plant. For example, the hydrogen would be used in the following processes: (a) operating the steel mill that converts iron oxides into steel; (b) operating the kiln that produces lime for making concrete; (c) fueling the hydrogen vehicles that move people and materials around the plant; (d) fueling the hydrogen vehicles that mine the coal or collect the municipal solid waste that enters that gasifier; (f) making ammonia that fertilizes the farms that make food for the workers of the plant; and (g) fueling the factory that builds the gasifier, the syngas turbine, steam turbine, pipes, chemical reactors, vehicles, etc...
Most of the carbon dioxide would be sequestered in saline aquifers; though, a portion of the carbon dioxide would be used in enhanced oil & gas recovery. The oil & natural gas would be used to make plastics used throughout the plant and in the vehicles, such as polymer membranes for separating H2 from CO2&H2S or for operating the hydrogen vehicles (PEMFC). Some of the oil and natural gas can also be used to make asphalt and some can be used to make food supplements such as vitamins, amino acids, and medicines. In other words, there will still be oil&gas drilling long after we cap CO2 emissions into the atmosphere (and this is why divesting from oil&gas companies is silly and morally suspect.) Don't get me wrong, I'm all for capping CO2 emissions, but I think that divesting from oil/coal/gas companies is morally suspect because it's like any other psychological disorder...it's an avoidance of the real problem and a propping up a paranoid delusion that it's evil companies (and not normal people like you and me) who emit CO2 into the atmosphere.
And now, that leaves us with the other gas specie that can be generated from the coal gasifier: hydrogen sulfide. The H2S can be used to make elemental sulfur (i.e. fertilizer for the farms) or can be mixed with lime (CaO) and oxygen to form gypsum (i.e drywall to line the buildings.)
My point here is that we can use all of the elements in coal (and municipal solid waste) in our economy. This is one of the advantages of a coal gasification power plant...it generates (nearly) all of the species that would be required to construction a new coal gasification power plant. A typical combustion coal power plant can't as easily create pressurized hydrogen, pressurized carbon dioxide, and elemental sulfur. (Like wise, a solar PV panel, a nuclear power plant, and a wind turbine can't as easily create the pressurized hydrogen, pressurized carbon dioxide, and elemental sulfur that would be required throughout the economy.)
So, one could fairly easily image a self-replicating coal gasification power plant out near Wyoming or North Dakota. The coal would be mined in the Power River Basin, WY (using hydrogen fueled trucks.) According to the USGS, there's ~162 billion short tons of recoverable coal in the Power River Basin and in Montana. (For comparison, the U.S. currently consumes less than 1 billion tons of coal per year.) The iron ore for the steel mine would be mined in Minnesota (using hydrogen fueled trucks) and shipped on hydrogen powered railcars, or perhaps a location for ore could be found closer to the power plant. The carbon dioxide would be sequestered in Wyoming or Alberta (as is currently done by the Dakota Gasification Company.) The ammonia and sulfur made at the plants (along perhaps directly with some of the coal fresh from mine) would be used to fertilize farm lands in North Dakota that are currently not able to grow crops due to poor soil.
So, while this is only a sketch of what such a self-replicating power plant would look like, it's good to know that we can continue to grow for some time into the future using coal as our main feedstock while having near-zero emissions of greenhouse gases from both the power plant and the wider economy. And just perhaps, we can use some of the steel and hydrogen from the power plant system to build spaceships and start colonizing the Moon & Mars with self-replicating solar auxons. The question is how best to turn this dream into reality...one step at a time.