I made a graphene solution with PH around 9. In this solution particles were well dispersed but after I added some HCl the black carbonaceous solid started to sediment.
I don't know what this solid is. Could it be graphene?
Acidic treatment makes positively charged groups on the graphene layers, and it cleaves the C-C bonds by making C=O and C-H bonds on it. Since it attacks the carbon residues by being a nucleophile and cleaves bonds, there is a very low possibility for it to form pure carboneous structure as a sediment, if it is not the part broken down from the graohene sheet. There is a paper below explaining it, I hope you can find more information there.
Wish you luck.
Cheers.
Article Defect formation in graphene nanosheets by acid treatment: A...
In order to determine the surface chemistry of your powders you should measure zetapotential, from my experience with other carbon based materials (graphites, cokes, activated coal etc.) the surface charge such that the zetapotential becomes high enough to get a stable dispersion (approximately -30-5 mV) 0 at pH > 8, this is exactly what you observed. In the acidic range the dispersions become instable.