A comparison of fractal methods for evaluation of hydraulic fracturing surface roughness
Abbas Movassagh A C , Xi Zhang A , Elaheh Arjomand A and Manouchehr Haghighi BA CSIRO Energy, Melbourne, Vic. 3168, Australia
B University of Adelaide, Adelaide, SA 5005, Australia
C Corresponding author. Email: abbas.movassagh@csiro.au
The APPEA Journal 60(1) 184-196 https://doi.org/10.1071/AJ19058
Submitted: 16 December 2019 Accepted: 23 January 2020 Published: 15 May 2020
Abstract
Surface roughness is a crucial parameter in the hydraulic fracturing process, affecting rock toughness, fluid flow and proppant transport; however, the scale-dependent nature of hydraulic fracture surfaces is not well studied. In this paper, we examined four fractal methods, compass, box-counting, variation and roughness-length, to evaluate and compare the fractal dimension of the surface roughness profiles created by laboratory hydraulic fracturing. Synthetic surface profiles were generated by the Weierstrass-Mandelbrot function, which was initially used to test the accuracy of the four methods. Each profile had a predefined fractal dimension that was revisited by these methods. Then, the fractal analysis was performed for experimental fracture surfaces, which were created by a hydraulic fracturing experiment in a true triaxial situation. By comparing fractal analysis results, we found that for both synthetic and laboratory fracture height profiles, the roughness-length method provides a relatively more reliable estimation of the fractal dimension. This method predicts the dimension for synthetic surface within an error of less than 1%, considering a wide range of surface heights from centimetres down to micrometres. By increasing the fractal dimension of surface profiles, the error of fractal estimation increased for all four methods. Among them, the variation method provided the closest results to the roughness-length method when considering both experimental and synthetic surfaces. The evaluated fractal dimension may provide a guideline for either field- or laboratory-scale hydraulic fracturing treatments to evaluate the effects of surface roughness on fracture growth.
Keywords: box-counting, experimental fracturing, fractal dimension, roughness-length, variation method, Weierstrass-Mandelbrot function.
Abbas Movassagh is a research scientist with CSIRO, and his research focuses on hydraulic fracturing experiments and modelling, including roughness and surface asperities analysis. He is seeking a PhD degree from The University of Adelaide and has gained more than 10 years’ experience in well intervention and reservoir engineering while working at the Middle-East coordinating numerous completion and treatment design and feasibility studies. |
Xi Zhang is a principal research scientist with the CSIRO Energy Business Unit. He has over 18 years’ experience in hydraulic fracture modelling. He holds a PhD degree from the University of Sydney. |
Elaheh Arjomand started her post-doc fellowship with CSIRO in mid-2019 and her research is mainly focused on the integrity of wells after decommissioning and abandonment. Elaheh received her PhD on the integrity of the cement sheath after being subjected to pressure and temperature variations from the University of Adelaide in 2018. |
Manouchehr (Manny) Haghighi is Associate Professor of Petroleum Engineering at the University of Adelaide. His research and teaching focus is on unconventional reservoirs, reservoir simulation, well testing and formation evaluation. He has supervised more than 40 MSc and 10 PhD students. Manouchehr has published more than 100 articles in peer reviewed journals and presented at numerous international conferences. |
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