Universal Scaling Laws of Hydraulic Fracturing

Hydraulic fracturing has been studied by using dimensional analysis. The universal scaling law of the problem has been formulated. From this investigation, it has found that the key control variable in the process is total damage number $J=\frac{p+\frac{1}{2}\rho U^2}{\sigma_Y}$. The crack length is satisfied with the geometric similarity law if no response time is concerned, otherwise, it would not satisfy the similarity.