As has already been said, yes you can, but you can't directly convert it to a "kWH" number without other measurements.
But what DanDel said above is just as valid. What I see you wanting is just a comparison. Since the power supply is going to be the same in both tests, the watts value is really unimportant. What you really want to know is the delta (difference) in the two tests, and current is a perfectly valid measurement tool all by itself in this instance.
For example, if it takes 2.2A when using oil #1, and 2.1A using oil #2, then the delta is 2.1/2.2, or .955 (95.5%), so oil #2 saves 4.45% energy compared to oil #1. If you then learn the kWH of either one at a later date, you can extrapolate the actual monitary value of the other or the savings by applying that ratio.
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