The blast furnace relied on the fact that the unwanted sulfur-iron compounds were lighter than the pure iron and iron-carbon mix, pig iron, that was its main product. The furnace was built in the form of a tall chimney-like cauldron lined with refractory brick. Coke and iron are poured in the top, which would normally burn only on the surface. Air was blown into the middle, thus the "blast", allowing combustion in the middle of the mixture. The results of this localized burning was a liquid that sank to the bottom of the furnace, with the lighter materials on top. A valve was opened to allow the slag to pour out, and once emptired, another valve at the bottom opened to remove the pig iron.
The exact nature of the reaction is:
Fe2O2 + 3 CO => 2 Fe + 3 CO2
Air blown into the furnace reacts with the carbon in the coal to produce carbon monoxide, which then mixes with the iron oxide, reacting chemically to produce pure iron and carbon dioxide, which leaks out of the furnace at the top.
CaCO3 => CaO + CO2
The calcium oxide reacts with various acidic impurities in the iron (notably silica) and floats with the slag, thereby further purifying the iron.
The pig iron produced by the blast furnace is not very useful directly due to its high carbon content, around 4-5%, making it very brittle. Further processing was needed to reduce the carbon content for use as a construction material. For some time the products of the blast furnace was used almost directly as wrought iron after additional processing, the conversion to steel using the crucible technique was too expensive to operate on a large scale. However with the introduction of the Bessemer process the conversion to steel was also dramatically improved, and by the turn of the late 1800s almost all iron was being converted to steel before use.
The blast furnace remains an important part of modern iron production. Modern furnaces include a heater to pre-heat the blast air to high temperatures in order to avoid cooling (and thus having to re-heat) the mix, and use fairly complex systems to extract the heat from the hot carbon dioxide when it escapes from the top of the furnace, further improving effeciency. The largest blast furnaces produce around 60,000 tonnes of iron per week, enough for about four cars per minute.