Non-linear models for evaluating the residual opening of hydraulically stimulated fractures and its impact on well performance.

Abstract

Hydraulic stimulation techniques have been employed successfully over the past 60 years to enhance the productivity of oil and gas reservoirs. These techniques work by injecting a pressurised fluid into the wellbore to initiate and propagate an artificial fracture or to open a network of existing fractures. These techniques are also commonly known as hydraulic fracturing or fracking. The main objective of hydraulic stimulation is to create highly conductive pathways, which can significantly increase the permeability of the reservoir and, subsequently, improve the well productivity. An injection of small particles (usually known as propping agents or proppants) with the fracturing fluid is the most common method to prevent the stimulated fractures from full closure during the production stage because of confining stresses. To date, research has largely focused on the assessment of conditions and characteristics of fluid-driven fractures, as well as proppant transport and settlement mechanisms. The modern theory of hydraulic fractures is based on linear elastic fracture mechanics and theories of poro-elasticity, fluid flow in narrow openings and suspension flow in porous media. Despite numerous studies being carried out, few are devoted to the residual opening of hydraulic fractures, which has a significant effect on well productivity. There are many exciting potential applications and developments of hydraulic stimulation techniques for geothermal reservoirs and coal seam gas production. These all require new and more comprehensive theories, supported by analytical and numerical solutions capable of describing the non-linear effects of proppant placement and compressibility on the fracture residual opening profile and, ultimately, on the reservoir permeability and well performance. In order to address these needs and gaps, this thesis aims to develop: • a new mechanical model for predicting the mechanical response of saturated and unsaturated low-consolidated granular particles to compressive loading; • a new mathematical method and non-linear solutions for evaluating the residual aperture of fractures partially filled with unconsolidated compressible particles (proppant) and subjected to compressive loading; • a new mathematical model for evaluating the production rate of hydraulically stimulated wells taking into account the residual closure and various regions of distinct permeability along the fracture. These new models are all based on the classical theories of solid, fluid, contact, fracture, rock and soil mechanics, which provide a framework for evaluating the residual opening profiles (aperture) of hydraulically stimulated fractures, as well as the influence of the fracture residual aperture on the well performance. A number of simplifications are used to formulate the mathematical models and develop non-linear solutions. Many of these simplifications, such as two-dimensional problem geometry, plane strain conditions and linear elastic behaviour of the medium, represent a well-established foundation for analytical and numerical modelling in reservoir engineering. Accounting for other important phenomena, such as proppant flow-back and secondary cracking, is beyond the scope of this thesis but may be included in future work. The numerical results obtained within the developed models indicate that the residual openings and distribution of proppant along the fracture have a significant effect on well productivity (up to 50 per cent in the case of a relatively low level of confining stresses in the reservoir) and must be incorporated into the evaluation of the efficiency of hydraulic stimulation techniques and assessment of well productivity.