Flow and transport through fractured rock - numerical approaches to account for fracture heterogeneity

Abstract

Fractures and networks of fractures are relevant for a large number of subsurface engineering applications, such as geothermal energy utilization, drinking water supply, CO2 storage, and others. Fluid flow velocities in fractures often differ to those in the surrounding porous matrix by orders of magnitude and consequently, fractures largely govern the overall flow and transport characteristics of fractured reservoirs. Thereby, fractures can act as flow conduits, barriers, or a mixture of both. Moreover, due to the complex geometry of fractures and fracture networks, their impact on hydraulic properties can be very heterogeneous. To further complicate this issue the hydraulic properties are difficult to obtain from field experiments and subject to large uncertainties. Nonetheless, due to the relevance of fractures across subsurface applications, a detailed characterization of hydraulic properties is essential. Here, two possible approaches to improve the characterization of hydraulic properties are presented and discussed. First, the focus is on advancing our understanding of solute and heat tracer tests in single rough fractures. Secondly, an efficient numerical method to model flow through fractured porous media is presented. Hydraulic properties are commonly obtained by tracer tests in the field. A large number of artificial and natural solutes are used as tracers and heat as a tracer has increasingly been used in recent years. Due to the strong thermal interaction between the fracture fluid and the rock matrix heat tracer transport greatly differs from solute tracer transport. These differences show a characteristic behavior for simplified geometries, such as parallel plate with linear flow field, parallel plate with flow between two boreholes, and linear flow through channel(s). However, it remains unclear how these characteristic differences are affected by heterogeneous hydraulic properties of rough fractures. By numerical simulations of joint solute and heat tracer tests in a single rough fracture, we show that heat exchange in fractures with spatially variable apertures is closer to the parallel plate conceptual model than the channel(s) model. In summary, the relation of solute and heat tracer recovery varies strongly for fractures with variable apertures. The second part of this manuscript presents an efficient numerical method to model flow though fractured porous media. In such models fluid flow velocities and spatial scales range over several orders of magnitudes. Therefore, it is important that fractures are explicitly represented by discrete model domains, which results in discrete-fracture-matrix (DFM) models. Due to strong geometrical heterogeneities and uncertainties in fracture networks, efficient numerical models are necessary to perform stochastic studies with a large number of realizations. One of the limiting factors for such stochastic studies is the difficult and time consuming mesh generation for DFMs. To overcome this issue, non-conforming mesh methods have been developed over the past decades. One of these methods uses Lagrange multipliers and variational transfer for pressure coupling with non-conforming fracture and matrix meshes. By combining Lagrange multipliers with a 3D L2-projection variational transfer operator (LM–L2), we show the applicability of this method for large 3D DFMs. The method is validated with 2D benchmark cases and compared to reference results of complex 3D cases. The utilized space of dual Lagrange multipliers allows to reduce conditioning compared to other non-conforming methods. Taken together, the LM–L2 method is able to accurately compute pressure fields for large DFMs in 3D. Due to the complexity of 3D DFMs it is important to compare different numerical methods with each other. Therefore, we participated with the LM–L2 method in a large benchmark study where 17 different methods are compared. In this benchmark study flow through 3D fractured porous media was investigated. Additionally, advective transport is computed to facilitate comparison of the flow fields. So far, the LM–L2 method was employed to compute pressure fields. As such, it was necessary to extend the LM–L2 formulation for advective transport. The flow and transport results of the LM–L2 method are compared to all other methods for four benchmark cases, which test the general performance of the methods and their ability to represent challenging geometries and a large DFM. The results show that, due to the non-conforming meshes the LM–L2 method is advantageous for complex fracture geometries and the 3D variational transfer operator handles challenging setups naturally. The pressure fields for all benchmark cases show good agreement with the other methods. However, the concentration results are less accurate, which is due to the very coarse meshes and additional challenges such as numerical diffusion and mass conservation. Improvements could be made with local adaptive mesh refinement. In summary, the presented work improves our understanding of flow and transport processes in the context of subsurface fracture applications in two ways. To be more precise, the focus is on the impact of fracture heterogeneity in tracer tests and 3D DFMs. First, heat transfer characteristics in rough fractures are described in detail and information to refine the relationship between solute and heat tracers is given. This contributes to a better characterization of hydraulic properties of fractured systems. Additionally, a numerical, non-conforming mesh method for flow was examined and applied for challenging and complex networks of fractured porous media. The advantage of this method lies in the convenient mesh generation of geometrically complex fracture networks and its applicability for stochastic studies.