The idea that a non detergent oil is required in an air or water pump, is in essence not true.
In fact, in some tests, the use of Mobil 1 extends air compressor life considerably. If you look around, you'll find that some brands of pumps and compressors specify Mobil 1, and other brands specify Non Detergent 30 viscosity oil, the compressor unit itself being identical between brands.
There have been claims of carbon buildup in compressor valves when using conventional motor oil with additives. Nonsense, oil is made of hydrocarbons and the additives are not responsible for carbon deposits. Carbon buildup in a compressor's valves, is due to low quality oil and poor oil control.
There are also claims that ND oil will allow water to settle to the bottom, where it will remain and not foam up. Also nonsense. The oil will mix with the water, any time the pump or compressor is used, with either oil. A good reason to change your pump or compressor oil before it saturates with water.
The reality of the situation is that for many of us, who maintain our equipment well, the use of a synthetic oil results in better cold weather operation of air compressors and high quality lubrication for pressure washer pumps.
I use M1, 15W-50 in highly loaded pressure washer pumps and hydrostatic drives. Works well. I use M1 10W-30 or 15W-50 in my air compressors.