Many, many, many, burned oil for the same reasons that locomotives in the Western Hemisphere did. One famous example is the Dampf Plus (formerly Deutsche Reichsbahn) 18-201, three cylinder pazifik type, built at Meiningin Dampflokwerks for testing passenger cars built for high speed electric lines of the Soviet bloc countries at the Gorlitz passenger car factory. Another example is the rack locomotive built by Winterthur at the end of the 20th century for the Schafbergbahn on Austria's Mount St Wolfgang. I rode the cab of this one, she burns diesel. Then there is the Super Kreigslok, a Winturthur conversion of a traditional German 52 class, also burns diesel. The list is endless.... Many engines were switched between coal and oil firing depending on fuel prices, again a specialty of the Meiningin Dampflokwerks, which was at one time the main backshop for the DR.

Greetings:
As I recall, some locomotives in Rumania burned oil and a few set up to burn coal and oil.
J.David

Russia had a lot of oil burners, too, including some Chinese QJs built to five foot gauge for use north of the Mongolian border at Manzhouli.

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The range by energy density of gaseous fuels is an issue. That is for sure, there are some safety concerns but modern practices can mitigate the risks. I definitely would make sure combustion and emissions are under thought or perhaps alternative fuel.

I know I got some funny looks on my way back to Germany from Copenhagen when I had an injector issue on my 7.3 power stroke f350

To be fair, most steam engines in Europe burn coal. But even 10% of the them (just picked that number out of thin air) is a lot of locomotives. If one is curious, Germany's Rio Grande Video has documentation of a number of present day examples, but before buying any of their excellent DVDs, you might want to make sure that your system can handle the PAL to NTSC format conversion.

Also, to be fair, a number of tourist or amusement railroads bring their oil burning engines up to changeover pressure using either straight propane or natural gas. While some may feel that "modern day practices can mitigate the risks", it still takes nothing more than a pinhole and a spark. Oil experienced firemen routinely clear any gas from the firebox because that's how we prevent flashbacks and/or explosions. I ask you man to man, what's safer, using some kind of gas for bringing up pressure, or the old method of atomizing and dafting an idle oil fire with either steam or compressed air ???

Nope. That is why my colleagues get such big eyes when we discuss the topic.

Oil is rare in Europe. Before the discovery and development of North Sea oil in the 1960s, oil was an expensive import item. That is why coal fired steam lasted about 10-20 years longer in Europe than in America (as well as a focus on electrification instead of diesel, which again delayed the conversion).

In spite of this, Denmark was a major innovator in internal combustion engines. Frichs locomotive works developed diesel locomotives and railcars in the 1920s, and many branch lines dieselized in the 1930s. Copenhagen is home to the world's largest diesel engine (during the period 1932 - 1962), Burmeister and Wain 2000, which drove an alternator for Copenhagen's city supply. This engine remained in backup and connected to the grid until 2004. During a dramatic blackout in 2003, all of eastern Denmark and southern Sweden was without power due to a network failure. The Diesel engine was started because it was the only power source that did not require external power to jumpstart and join the network.

The enginehouse is now a museum, and the engine started for short periods on select days. It is no longer connected to the net. It is in really bad condition and I can't see it generating power. It leaks exhaust everywhere.

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SWLM / Sulzer created a very fine and efficient vaporizing oil fired system they used in their modern rack locomotives that is probably going to be an easier find and easier sell than the dirtier atomizing systems, even if it needs to burn more refined oil it does it more cleanly and efficiently.

Gas firing is a non-starter for any steam locomotives of particular size. It can 'technically' be done, even with some control over turndown, but the fuel expense will eat you alive and the very probable critical-mixture issues will not make you happy.

Likewise, the general industrial-butner adaptation has to be done with care -- all I really have to do is mention the number 2100.

I was very kindly pointed (by someone here) to a Southern Pacific Facebook group that has provided online the full text of the SP's study of oil burning in the early Fifties (including actual description of the design and operation of the Gyro-Jet burner). I'd strongly recommend that you read through this before re-inventing firing combustion practice with either heavy or light oil.

Meanwhile, I suggest we start establishing a 'working group' here on potential zero-net-carbon and full zero-carbon alternatives for firing steam locomotives. The first option overlaps development of B100 boidiesel, including ways to make its entire supply chain zero-net-carbon. The second is more complicated if 'carrier carbon' is no longer a potential fuel element.

There are gas controls like automatic pressure stops.
It was just a consideration based off of optics of combustion fuel. Perhaps also costs, while I live in Europe now and have off and on for most of the last decade, I'm truly lucky that I don't pay pump prices for petrol or diesel, the price I pay with out tax is significantly cheaper than what my neighbors pay, including a few I know who have dyed fuel for their tractors. Lpg cars are significantly cheaper in several of my postings for the local nationals, but my tax avoidance scheme doesn't cover gas for cars only for houses where I escape the VAT

With great sarcasm I suggest the firing of steam engines from thermal runaway Tesla batteries...

Something that goes hand-in-hand with an "oil conversion" -- upon reflection -- is the necessary community organizing and political action (I intentionally stop short of calling it 'lobbying;, but draw your own conclusions on how to proceed) regarding:

Continuing access to sources of zero-net-carbon fuel of suitable characteristics. (This might well include long-term contracts with people willing to keep sourcing it)

Political tolerance for steam and its emissions in public policy, most particularly avoiding surprises a few years down the line should it begin to look 'expedient' to limit historic preservation from operating historic or preserved equipment.

Political efforts to reduce or eliminate 'road tax', especially punitive tax rate or income recovery for infrastructure, from "railroad" fuel. The most logical way to implement this would be to dye it a distinctive color, or introduce trace identifiers such as odorants, as for ag fuel, and then perhaps require more secure provisions against 'diversion' to other uses that a government might want to restrict (home heating is one current bugbear du jour).

Granted, this may be after the discovery of North Sea oil (and I won't argue this with folks who live in the EU), but the DR had plenty of oil burners. I suggest the program "18 201" by Rio Grande Video and Bahn Epoche, as well as another Rio Grande Videothek program, "Die Baureihe 01.5" which shows plenty of br 44 three cylinder 2-10-0 "Jumbo" types, and also br 01.5 pazifik engines in regular service. Eisenbahn Kurier also has a fine program with this same title, "Die Baureihe 01.5", which has extensive cab ride coverage. (Note that I edited this post in order to revise my suggestions.) For a real good look at oil burners in West Germany, check out "Hamburger Dampfreisen", another Rio Grande video.... Yet another Rio Grande video, "Die Baureihe 52.80" has coverage of the Kriegsloks updated by Meiningen, mostly coal burners to be sure. But, toward the end of the program is a chapter on the "Super Dampflok" of the Zollernbahn, a Winterthur rebuild of 1998 which I think uses the Sulzer firing system that Dave mentioned. Whatever kind of fuel they use (I had guessed diesel), this engine burns completely clean and pulls very strong and smooth in a series of runbys. Those of you with better German skills than mine will learn more from the interview with the lady fireman.

I'd be willing to bet that Meiningin could give you a much more detailed and accurate account than I can of the use of oil fired steam engines in Germany. They would probably be glad to do so if they thought you might be a potential customer for such a setup. Best of luck with your gorgeous Danish 4-4-0.