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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.

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Cement sheaths play an important role in providing zonal isolation and preventing the migration of formation fluids to aquifers and the surrounding environment. The condition of a cement sheath may change because of the imposed pressure and temperature alterations during a wellbore lifetime. Cement sheath mechanical failure may happen because of poor cement placement, development of cracks within the cement sheath and debonding at the cement sheath, casing and rock interfaces. A three-dimensional finite element framework, employing an appropriate constitutive model (Concrete Damage Plasticity, CDP) for cement sheath and a surface-based cohesive behaviour for the interfaces, is developed for integrity investigations. The incorporation of the CDP is very advantageous to model quasi-brittle materials due to its capabilities to simulate both compression and tensile damage. The effect of casing eccentricity on stress distribution within the cement sheath and the integrity of the cement sheath is investigated while enhancing the wellbore pressure. Three different degrees of casing eccentricity (30%, 50% and 70%) were considered. The huge stress concertation within the narrower part of the cement sheath makes this section susceptible to compression and tensile damage. The high magnitude of compression and tensile damage in the scenario with 70% casing eccentricity highlights the importance cement sheath centralisation.