In the book Ship Breaker by Paolo Bacigalupi, one of the characters falls into crude oil and state that one cannot swim in crude oil. The character can swim in water.
If true, why would you not be able to swim in crude oil?
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Dead Sea† 1240 kg/m3 Sea Water 1025 kg/m3 Water 1000 kg/m3 Crude oil, Mexican 973 kg/m3 Crude oil, 48° API 790 kg/m3
The Human body has an average density of 1062 kg/m3 ‡ This is why (most) humans float in the Dead Sea without any swimming effort and do not sink.
Lighter forms of crude oil would support the human body less, this can make staying afloat difficult or impossible.
Buoyancy depends on the weight of the volume of displaced fluid compared to the weight of the object displacing the fluid. To stay afloat you have to provide a swimming force that is equal to the force of gravity on the mass difference. The greater the deficit in density, the greater force you have to provide, at some point this force exceeds that which a human can provide for any significant time.
Lighter forms of crude oil should have a greater proportion of volatile hydrocarbons. The vapours of these hydrocarbons will displace air at the surface of the oil and make it difficult or impossible to obtain oxygen by breathing.
In general, oil on seawater (for example) quickly spreads into a thin film, so buoyance may not be an issue. But the difficulties in swimming and breathing can be potentially fatal
To followup a comment to RedGrittyBrick's question:
I'd +1 this answer if you were to include figures on whether a typical human swimmer could provide that additional force (could an Olympic gold-medallist?).
Per RedGrittyBrick's reference data the density of crude oil varies from 0.79 to 0.97. The second-highest density of all the oils listed is 0.915.
The density of fit young man is about 1.08 (very close to 1). A 70kg man swimming in oil whose density is 0.915 would therefore experience negative buoyancy of about
(1 - 0.915) x 70 = 6 kg.
This weight increases to 12 kg if you choose the 2nd-lightest crude (density 0.825) instead of the 2nd-heaviest.
These numbers imply that it would be like swimming in water with a 6..12 kg weight attached, which may be feasible for some but is not easy: Lifeguard Certification FAQs says that the hardest part of the test to become a lifeguard is the lifting a 10 pound (approx 4.4 kg) brick.
The amount of swim force you could theoretically (assuming for example that you can breathe in the fumes) generate is IMO slightly greater in oil than water, because oil has a higher kinetic viscosity ... but not very much more: approximately 50 SSU for crude compared with 38 SSU for water.
A simple numerical analysis, to @Sklivvz's pont, would be off-topic.
Experimentation would be dangerous/unethical so the theory is all there is.
Assuming (based on common sense) that the metabolic differences work against and not in favour of swimming in crude oil as opposed to water, the 6..12 kg of negative buoyancy would not be compensated for by any increased metabolic capacity.