Modeling flow and transport in fracture networks using graphs.

Fractures form the main pathways for flow in the subsurface within low-permeability rock. For this reason, accurately predicting flow and transport in fractured systems is vital for improving the performance of subsurface applications. Fracture sizes in these systems can range from millimeters to kilometers. Although modeling flow and transport using the discrete fracture network (DFN) approach is known to be more accurate due to incorporation of the detailed fracture network structure over continuum-based methods, capturing the flow and transport in such a wide range of scales is still computationally intractable. Furthermore, if one has to quantify uncertainty, hundreds of realizations of these DFN models have to be run. To reduce the computational burden, we solve flow and transport on a graph representation of a DFN. We study the accuracy of the graph approach by comparing breakthrough times and tracer particle statistical data between the graph-based and the high-fidelity DFN approaches, for fracture networks with varying number of fractures and degree of heterogeneity. Due to our recent developments in capabilities to perform DFN high-fidelity simulations on fracture networks with large number of fractures, we are in a unique position to perform such a comparison. We show that the graph approach shows a consistent bias with up to an order of magnitude slower breakthrough when compared to the DFN approach. We show that this is due to graph algorithm's underprediction of the pressure gradients across intersections on a given fracture, leading to slower tracer particle speeds between intersections and longer travel times. We present a bias correction methodology to the graph algorithm that reduces the discrepancy between the DFN and graph predictions. We show that with this bias correction, the graph algorithm predictions significantly improve and the results are very accurate. The good accuracy and the low computational cost, with O(10^{4}) times lower times than the DFN, makes the graph algorithm an ideal technique to incorporate in uncertainty quantification methods.

Where Does Water Go During Hydraulic Fracturing?

During hydraulic fracturing millions of gallons of water are typically injected at high pressure into deep shale formations. This water can be housed in fractures, within the shale matrix, and can potentially migrate beyond the shale formation via fractures and/or faults raising environmental concerns. We describe a generic framework for producing estimates of the volume available in fractures and undamaged shale matrix where water injected into a representative shale site could reside during hydraulic fracturing, and apply it to a representative site that incorporates available field data. The amount of water that can be stored in the fractures is estimated by calculating the volume of all the fractures associated with a discrete fracture network (DFN) based on real data and using probability theory to estimate the volume of smaller fractures that are below the lower cutoff for the fracture radius in the DFN. The amount of water stored in the matrix is estimated utilizing two distinct methods-one using a two-phase model at the pore-scale and the other using a single-phase model at the continuum scale. Based on these calculations, it appears that most of the water resides in the matrix with a lesser amount in the fractures.

Understanding hydraulic fracturing: a multi-scale problem.

Despite the impact that hydraulic fracturing has had on the energy sector, the physical mechanisms that control its efficiency and environmental impacts remain poorly understood in part because the length scales involved range from nanometres to kilometres. We characterize flow and transport in shale formations across and between these scales using integrated computational, theoretical and experimental efforts/methods. At the field scale, we use discrete fracture network modelling to simulate production of a hydraulically fractured well from a fracture network that is based on the site characterization of a shale gas reservoir. At the core scale, we use triaxial fracture experiments and a finite-discrete element model to study dynamic fracture/crack propagation in low permeability shale. We use lattice Boltzmann pore-scale simulations and microfluidic experiments in both synthetic and shale rock micromodels to study pore-scale flow and transport phenomena, including multi-phase flow and fluids mixing. A mechanistic description and integration of these multiple scales is required for accurate predictions of production and the eventual optimization of hydrocarbon extraction from unconventional reservoirs. Finally, we discuss the potential of CO2 as an alternative working fluid, both in fracturing and re-stimulating activities, beyond its environmental advantages.This article is part of the themed issue 'Energy and the subsurface'.

Relationship between pore size and velocity probability distributions in stochastically generated porous media.

We perform a set of detailed numerical simulations of single-phase, fully saturated flow in stochastically generated, three-dimensional pore structures with diverse porosities (ϕ) and degrees of connectivity, and analyze the probability density functions (PDFs) of the pore sizes, S, and vertical velocity components, w, which are aligned with the mean flow direction. Both of the PDFs are markedly skewed with pronounced positive tails. This feature of the velocity PDF is dictated by the pore structure and determines the shortest travel times, one of the key transport attributes that underpins the success or the failure of environmental remediation techniques. Using a maximum likelihood approach, we determine that the PDFs of S and w decay according to an exponential and a stretched exponential model, respectively. A strong correlation between the key parameters governing the decay of the upper tails of the two PDFs is found, which provides a quantitative result for this analogy that so far has been stated only qualitatively. The parameter governing the concavity of the tail of the velocity PDF varies linearly with porosity over the entire range of tested values (0.2≤ϕ≤0.6). The parameters controlling the spread of the upper tails of the PDFs of S and w appear to be linked by a power-law relationship.