ALBERT

Description: A new approach to upscaling two-dimensional fracture network models is proposed for preserving geostatistical and geomechanical characteristics of a smaller-scale “source” fracture pattern. First, the scaling properties of an outcrop system are examined in terms of spatial organization, lengths, connectivity, and normal/shear displacements using fractal geometry and power law relations. The fracture pattern is observed to be nonfractal with the fractal dimension D ≈ 2, while its length distribution tends to follow a power law with the exponent 2 〈 a 〈 3. To introduce a realistic distribution of fracture aperture and shear displacement, a geomechanical model using the combined finite-discrete element method (FEMDEM) captures the response of a fractured rock sample with a domain size L = 2 m under in-situ stresses. Next, a novel scheme accommodating discrete-time random walks in recursive self-referencing lattices is developed to nucleate and propagate fractures together with their stress- and scale-dependent attributes into larger domains up to 54 m × 54 m. Advantages of this approach include preserving the non-planarity of natural cracks, capturing the existence of long fractures, retaining the realism of variable apertures, and respecting the stress-dependency of displacement-length correlations. Hydraulic behavior of multiscale growth realizations is modeled by single-phase flow simulation, where distinct permeability scaling trends are observed for different geomechanical scenarios. A transition zone is identified where flow structure shifts from extremely channeled to distributed as the network scale increases. The results of this paper have implications for upscaling network characteristics for reservoir simulation.

Description: Accurate simulation of multiphase flow in fractured porous media remains a challenge. An important problem is the representation of the discontinuous or near discontinuous behaviour of saturation in real geological formations. In the classical continuum approach, a refined mesh is required at the interface between fracture and porous media to capture the steep gradients in saturation and saturation-dependent transport properties. This dramatically increases the computational load when large numbers of fractures are present in the numerical model. A discontinuous finite element method is reported here to model flow in fractured porous media. The governing multiphase porous media flow equations are solved in the adaptive mesh computational fluid dynamics code IC-FERST on unstructured meshes. The method is based on a mixed control volume – discontinuous finite element formulation. This is combined with the P N +1 DG-P N DG element pair, which has discontinuous (order N+1) representation for velocity and discontinuous (order N) representation for pressure. A number of test cases are used to evaluate the method's ability to model fracture flow. The first is used to verify the performance of the element pair on structured and unstructured meshes of different resolution. Multiphase flow is then modelled in a range of idealised and simple fracture patterns. Solutions with sharp saturation fronts and computational economy in terms of mesh size are illustrated. This article is protected by copyright. All rights reserved.