Interface Control Volume Finite Element method for modelling fluid flow in heterogeneous porous media

Modelling fluid flow in highly heterogeneous and fractured reservoirs is a challenging task. These reservoirs typically have a complex structure with large and sharp variations in their material properties. Node Control Volume Finite Element (NCVFE) has been used to model those types of reservoirs at the fracture scale for the last decade. However, since the control volumes are constructed around the nodes and the material properties are assigned on elements, there is a loss of accuracy and associated fluid smearing when modelling multi-phase flows. We present a new numerical method to improve the modelling of multi-phase fluid flow in these reservoirs, called Interface Control Volume Finite Element (ICVFE). The method drastically decreases the smearing effects observed with other CVFE methods, such as NCVFE, while being mass conservative and numerically consistent. The pressure is computed at the interfaces of elements, and the control volumes are constructed around them, instead of at the element nodes. This assures that a control volume straddles, at most, two elements, which decreases the fluid smearing between neighbouring elements when large variations in their material properties are present. Lowest order Raviart-Thomas vectorial basis functions are used for the pressure calculation, and Lagrange basis functions are used to compute fluxes. The method is a combination of Mixed Hybrid Finite Element (MHFE) and FE methods. Its accuracy and convergence are tested using three dimensional tetrahedral elements to represent heterogeneous and fractured reservoirs. Our new approach is shown to be more accurate than current methods in the literature. Significance • The ICVFE produces less unphysical flows than NCVFE while honouring the material properties of the domain. • It also models more accurate fluid saturation profiles than NCVFE. • The ICVFE method defines the primary variables (pressure and saturation) on the interfaces of elements. Therefore, it computes a high resolution of the primary variables over the finite element mesh (the number of interfaces is larger than the number of elements). This down-scaling is attractive and convenient since the truncated numerical errors decrease with the increase of degrees of freedom, and conventionally this is achieved by refining the mesh.