How do you remove old black adhesives off of concrete?

A little more investigation as to what that "Old Black Adhesive" was is in order before you commence. It may be a petroleum based product that is dissolved with mineral spirits? Or it may be that a water soaked blanket applied to the surface will cause it to loose any bond it still has.

Absent that, a hot water pressure wash, 3000 lb# wash, citric or phosphoric acid bath are all pretty benign and may work. Grinding with a rotary device is also a possibility? If water disposal or protection is important to you a more expensive water recovery and or dust capture system may be needed.

Avoid acid washes at all cost! We see them recommended by uneducated trades people all the time!! Not only are they caustic, they degrade a concrete surface instantly and will cause other failures in short order