Fully coupled elasto-plastic computational framework for fluid pressurised crack evolution in porous media - Hardcastle, Alex (2021)
A dual porosity damage model is developed with the intention for the efficient solving of complex hydrofracture problems. The model is developed by utilising two pre-existing methodologies and adapting them for the purpose of solving hydrofracture problems. The damage model uses a NeoHookean finite deformation elastic constitutive model to calculate internally stored elastic energy. The constitutive model is derived from the three strain invariants so that with volume change, mechanical behaviour maintains consistency, a property that will be discussed in the literature, important to the development of both fracture and hydrofracture framework. The energy required for material breakage is derived from the material property: fracture strength. The two energy values are calculated over the considered model domain and are used with the energy minimisation technique to find the global minimum energy that contains the sum of the two aforementioned energy types. While calculating the domain configuration which has the lowest energy sum, fracture behaviour can be deduced from the required energy releases from the system to achieve the global energy minimum. This fracture methodology is combined with a dual porosity methodology that is derived by considering the fluid interface between interconnected porous and fractured domains. Mass balance and effective stress concepts have been utilised to derive partial differential equations which model fluid flow through these two domains in an interconnected manner. This aspect of the model is used to model the fluid transfers that occur in hydrofractures. The set of equations that govern the coupled porous flow are solved using the finite element method. The Galerkin method of the spatial discretisation is applied and solved using a Eularian scheme to iterate the solution of the governing linearised equations utilising the Newton Raphson approach. The plastic behaviour of rock like materials has been described utilising Mohr Coulomb plastic model through the application of the Hencky strain conversion to apply the infinitesimal framework to the hydrofracture framework. A continuum damage model (CDM) method relying on the energy minimisation theory has been applied in a finite deformation context. The variable minimised within the considered domain is mechanical energy, in doing so fracture behaviour can be captured through the energy exchanges required to maintain a global minimum. Several methodologies from geomechanics and fracture mechanics have been considered to create a model that can simulate post fracture behaviour in terms of strength and fluid flow. Combining two pre-existing concepts one for fracture problem and another for fluid flow modelling, a simple practical computational framework for hydrofracture is produced. The developed minimisation methodology is proven suitable for modelling complex fracture behaviour, by comparing numerical outputs against experimental and numerical fracture paths. The minimisation approach produced is computationally inexpensive, flexible and simple to implement within existing framework. Section 5.2 and 5.2.1 also showed how leakage from fractures to the surrounding porous system dictate pressure changes within the continuum and the resultant mechanical changes further proving that leakage is an important consideration mechanically as well as environmentally. Section: 5.1 also showed that the developed methodology can capture geotechnical behaviour. All whilst maintaining fracture/ hydrofracture capability and suitability. The dual porosity coupling can be used to capture the flow properties of hydro fractures. The use of which has the potential to reduce the number of required variables. In Section 5.2 and 5.2.1 the issue of two dimensional consolidation in closely confined thin horizontal fractures that inhibit hydrofracture progress are classified. The considered thin fractures or "penny cracks" within a large domain are shown in section: 5.3, further verifying this behaviour trend.