I think this is making things too complicated with the water calculations, namely the 1:1 ratio. Adipose tissue is almost completely fat, which in turn is hydrophobic. See the picture on this wikipedia page for reference: https://en.wikipedia.org/wiki/Adipocyte. The excess fluid (if any relevant amount exists in the body at the beginning of the diet) is lost fast (days) and early in the course of diest and the key is to have a constant, relatively slow (2-4 kgs / month) weight loss.