Modeling the closure behavior of natural fractures in porous media using high aspect ratio interface elements

Abstract

Many reservoirs consist of fully saturated rock masses containing a very complex natural fracture network. In such cases a decrease in the fracture fluid pressure reduces its aperture due to an increase in the effective stresses. In order to tackle the influence of fracture permeability on the pressure field and fluid flow, this paper proposes a Discrete Fracture-Matrix (DFM) model based on the finite elements to simulate coupled flow and geomechanics in porous media containing fractures with known position and properties (e.g. DFN realizations and fracture networks interpreted from outcrops). The proposed model is based on the use of triangular finite elements with high aspect ratio (HAR) to explicitly represent the fractures. These HAR elements have been successfully used to deal with cracks in concrete structures, desiccation cracks in soils and hydraulic fracturing in geo-reservoirs. This work demonstrate that these HAR elements equipped with a simple continuum (stress-strain) constitutive contact model that mimics the discrete (stress-displacement) Barton-Bandis joint model are able to properly describe the closure behavior associated with natural fractures. The constitutive model is integrated by means of the IMPL-EX scheme, which is a robust and stable technique used to achieve faster convergence. Darcy's law establishes the relationship between the fluid flow and the pressure field, and a fully coupled hydro-mechanical formulation comprises the mathematical framework. The proposed approach is based on continuous mechanics concepts and the implementation is made at constitutive level, and therefore it is simple and easy to be included in any existing FE program. To show the efficiency and accuracy of the proposed model, three numerical examples are conducted in this work: (i) benchmarks involving a medium with a single natural fracture, (ii) three reservoirs with different discrete fracture networks, and (iii) a transient analysis of a reservoir under different fracture conditions, such that the behavior of a intact reservoir, a reservoir containing fractures with constant aperture, and a reservoir in which the fractures aperture depends on the stress state are compared in terms of pore pressure, displacement field and fluid loss. In the first example, the results obtained with the proposed methodology are validated against the Barton-Bandis model. The agreement between the results is very satisfactory. The analysis of the latter two cases show the Barton-Bandis contact model is able to reproduce the effects of fracture permeability on pressure field in the reservoir, showing the capacity of the model to reproduce the main trends associated with the closure of natural fractures.