Here is my impression of the widely used in oil industry secondary crude oil distillation system, or high-temperature reformer (cocking machine). This kind of equipment is usually applying for processing of the crude oil remains. That is remaining after the main straight run of the crude oil when all naturally presenting fractions were removed. And the only heavy oil without any other portions was left behind.

 Thus to create some new fractions within the secondary crude, the substance is exposing to the extreme heating condition. That caused the molecules of the oil to move around and burst and crack into the smaller chains creating all over again new hydrocarbon fractions from coke to diesel and petrol distillates.

 Now I can agree that not every one of us has access to real crude oil. Still, everyone can get the used automotive or hydraulic oils. In fact, by comparison with the secondary crude, the used automotive oil is a much better choice because it was already treating once. It was made free of sulfur and other harmful components; thus, you are technically dealing with the crude that was preparing for automotive use.

 What does it mean? - it means that the fuel obtained by processing the WMO is technically neutral and can be treated and cleaned without using any potentially dangerous methods that involve some chemicals that can be dangerous for the back-yard researcher and environment. 

 In the beginning, I was thinking about the waste vegetable oil processing into biofuel. But a simple comparison of operations and chemicals involved in two separate processes of diesel production using the reformer and veggie oil processor gave me the next idea. And thus, for bio-diesel production, one will need to clean the oil first, then settle it in a reactor with strong alkali and methanol (both are dangerous and toxic), then after conversion, you'll need to separate the glycerol and the fuel. You'll need to wash the fuel using some water and dry it after all, and despite all of this, your fuel will be a short living substance that was not designed for any long-time storage, plus it can turn solid at temperatures close to the 0c. Not convenient - too many operations, harmful chemicals (plus not free as well) possible water pollution, short life of the fuel that not reliable at colder temperatures.

Now let see what the automotive waste oil would involve and what kind of results can be obtaining. The oil should be free of water, also better to have it filtered - just like veggie oil, then you run it once through reformer and settle in an airtight container for three days to allow the bitumen to separate and deposit on the bottom of the container. 

 Then the resulting fuel can be transferred to the storage/settling container where it is settling with the addition of some silica gel, which is a neutral substance (even used as a moisture absorber in the food packs) for at least three days. After that, it can be either used in the diesel engine or stored as long as you want (if stored with silica - getting even better over the time). 

 Also, this kind of fuel will not freeze at +5c simply because the source oil was made the way to stay liquid despite the negative temperature. Moreover - there is no need to wash it with water; the used silica can be placed to the log burner on the metal tray where can be reactivated and used again.

As you can see, the processing of the waste automotive (mineral and synthetic) oils is friendlier than the production of the biofuel that requires the harmful and expensive chemicals, water washing, and drying.

 Anyway, here is the small piece of equipment that is capable of producing enough for personal use, of running your diesel gen-set agricultural machinery or diesel car (not suitable for common rail systems).