Tensor analysis of the relative permeability in naturally fractured reservoirs

Fluid evidence shows that prediction of water breakthrough and oil recovery from fractured reservoirs cannot be performed accurately without upscaled relative permeability functions. Relative permeability is commonly assumed to be a scalar quantity, although the justification of that—specifically for naturally fractured reservoirs (NFRs)—is rarely attempted. In this study, we investigate the validity of this scalar-quantity assumption and how it affects fracture/matrix equivalent relative permeabilities, kri(Sw), achieved by a numerical simulation of unsteady-state waterflooding of discrete-fracture/matrix models (DFMs). Numerical determination of relative permeability requires a realistic-model, a spatially adaptive simulation approach, and a sophisticated analysis procedure. To fulfil these requirements, we apply the discrete-fracture/matrix modeling to well-characterized outcrop analogs at the hectometer to kilometer scale. These models are parameterized with aperture and capillary entry pressure data, taking into account variations from fracture segment to segment, trying to emulate in-situ conditions. The finite-element-centered finite-volume method is used to simulate two-phase flow in the fractured rock, while also considering a range of wettability conditions from water-wet to oil-wet. Our results indicate that the fracture/matrix equivalent relative permeability is a weakly anisotropic property. The tensors are not necessarily symmetric, and the absolute-permeability tensor is the most influential factor, determining the level of anisotropy of kri. The anisotropy ratio (AR) changes with saturation, is influenced by the fracture/matrix-interface wetted area (Awf), and differs for each phase. In addition, the diagonal terms of the equivalent relative permeability tensor (krii), determined using our novel approach, can be different from those obtained using the assumption that kri is scalar. The magnitude of the difference is controlled by the absolute permeability, wettability, flow rate, and orientation of the fractures in the model. It is worth mentioning that the type and direction of imbibition can be determined by off-diagonal terms of the kri tensor. Furthermore, krii largely depends on the direction of the waterflood along the i-axis

Consistent treatment of shear failure in embedded discrete fracture models using XFVM

Understanding deformations and fluid flow in fractured rocks is of central importance for many subsurface flow applications. Thus, numerical frameworks are needed that capture the coupled mechanical and hydraulic behaviour, including scenarios with complex fracture networks. This paper employs the extended finite volume method to represent fracture manifolds in a poroelastic matrix domain and to compute shear and tensile displacements of fracture segments. However, using embedded fractures with non-conforming grids can lead to severe convergence issues while computing shear slip and tensile opening of intersecting and parallel fractures, particularly if they have similar slopes. Our proposed solution of this problem is to slightly deform the fracture geometry by merging critical segments. We discuss and show examples of which attributes the merged segment has to adopt to ensure the correct slip behaviour at an intersection. Thereby it is crucial that the flow topology remains unaltered. Analysing failures of kinked fractures and fracture intersections show the flexibility of the devised algorithm. Moreover, it is demonstrated that deformation and opening patterns of a natural network with more than 200 fractures are qualitatively predicted very well. This method is a simple solution to treat multiple fracture segments in a grid cell, hence it can be used for any model embedding fractures in non-conforming grids.ISSN:0363-9061ISSN:1096-985

Multiphase thermohaline convection in the earth's crust: I. A new finite element - finite volume solution technique combined with a new equation of state for NaCl-H2O

ISSN:0169-3913ISSN:1573-163

Coupled heat and salt transport around cooling magmatic intrusions

ISSN:0016-7037ISSN:1872-953

An enhanced J-integral for hydraulic fracture mechanics

This article revisits the formulation of the J-integral in the context of hydraulic fracture mechanics. We demonstrate that the use of the classical J-integral in finite element models overestimates the length of hydraulic fractures in the viscosity-dominated regime of propagation. A finite element analysis shows that the inaccurate numerical solution for fluid pressure is responsible for the loss in accuracy of the J-integral. With this understanding, two novel contributions are presented. The first contribution consists of two variations of the J-integral, termed the JHFM$J_{HFM}$ and JHFMA$J_{HFM}A$-integral, that demonstrate an enhanced ability to predict viscosity-dominated propagation. In particular, such JHFM$J_{HFM}$-integrals accurately extract stress intensity factors in both viscosity and toughness-dominated regimes of propagation. The second contribution consists of a methodology to extract the propagation velocity from the energy release rate applicable throughout the toughness-viscous propagation regimes. Both techniques are combined to form an implicit front-tracking JHFM$J_{HFM}$-algorithm capable of quickly converging on the location of the fracture front independently to the toughness-viscous regime of propagation. The JHFM$J_{HFM}$-algorithm represents an energy-based alternative to the aperture-based methods frequently used with the Implicit Level Set Algorithm to simulate hydraulic fracturing. Simulations conducted at various resolutions of the fracture suggest that the new approach is suitable for hydro-mechanical finite element simulations at the reservoir scale.ISSN:0363-9061ISSN:1096-985

Multiphase thermohaline convection in the earth's crust: II. Benchmarking and application of a finite element - finite volume solution technique with a NaCl-H2O equation of state

ISSN:0169-3913ISSN:1573-163