Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Universal Scaling Laws of Hydraulic Fracturing

Version 1 : Received: 9 June 2020 / Approved: 11 June 2020 / Online: 11 June 2020 (12:10:13 CEST)
Version 2 : Received: 12 October 2020 / Approved: 13 October 2020 / Online: 13 October 2020 (14:16:33 CEST)

How to cite: Sun, B. Universal Scaling Laws of Hydraulic Fracturing. Preprints 2020, 2020060138 (doi: 10.20944/preprints202006.0138.v1). Sun, B. Universal Scaling Laws of Hydraulic Fracturing. Preprints 2020, 2020060138 (doi: 10.20944/preprints202006.0138.v1).

## Abstract

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.

## Subject Areas

hydraulic fracturing; scaling law; fracture

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