This theme issue covers topics at the forefront of scientific research on energy and the subsurface, ranging from carbon dioxide (CO2) sequestration to the recovery of unconventional shale oil and gas resources through hydraulic fracturing. As such, the goal of this theme issue is to have an impact on the scientific community, broadly, by providing a self-contained collection of articles contributing to and reviewing the state-of-the-art of the field. This collection of articles could be used, for example, to set the next generation of research directions, while also being useful as a self-study guide for those interested in entering the field. Review articles are included on the topics of hydraulic fracturing as a multiscale problem, numerical modelling of hydraulic fracture propagation, the role of computational sciences in the upstream oil and gas industry and chemohydrodynamic patterns in porous media. Complementing the reviews is a set of original research papers covering growth models for branched hydraulic crack systems, fluid-driven crack propagation in elastic matrices, elastic and inelastic deformation of fluid-saturated rock, reaction front propagation in fracture matrices, the effects of rock mineralogy and pore structure on stress-dependent permeability of shales, topographic viscous fingering and plume dynamics in porous media convection.
This article is part of the themed issue ‘Energy and the subsurface’.
A recent roundtable report from the US Department of Energy’s Office of Science identified the cross-cutting theme of ‘Controlling subsurface fractures and fluid flow’ as critical to achieving environmentally and economically sustainable energy growth . The report focused on developing scientific and engineering approaches to understanding and manipulating fluid flow through the fractured rock media that underlie the performance of diverse energy systems including the production of unconventional oil and gas (hydraulic fracturing) and enhanced geothermal energy generation as well as the long-term disposal of energy waste products through carbon dioxide (CO2) sequestration and in nuclear waste repositories. These problems remain challenging owing to the complex thermo-hydro-mechanical–chemical coupled processes involved across multiple spatial and temporal scales.
This theme issue explores the state-of-the-art of flow through fractured and porous media in a collection of experimental, theoretical and computational (or combinations thereof) articles at the intersection of the two major scientific disciplines relevant to issues of energy and the subsurface, namely fluid mechanics (specifically, multiphase flow through porous and fractured media) and solid mechanics (specifically, fracture and rock mechanics). However, given the inherently multidisciplinary nature of the current challenges that fall under ‘energy and the subsurface’, the contributions to this theme issue also interface with the fields of computational and applied mathematics, hydrogeology (or the equivalent of reservoir flow studies), chemistry (reactive flows) and geophysics. Figure 1, which is also the cover art of the theme issue, illustrates the inseparable nature of fluid and solid mechanics and computation in hydraulic fracturing. The triaxial direct-shear experiment shown in figure 1a illustrates fracture propagation coupled with fluid flow in shale that is accurately simulated in figure 1b using a finite-discrete element method that incorporates fluid pressure within the fractures.
The idea for and the contributions to this theme issue originated in a 2015 workshop on Grand challenges in geological fluid mechanics sponsored by the Center for Nonlinear Studies at Los Alamos National Laboratory, which the co-guest editors organized along with Robert Ecke and Duan Zhang. The goal of the workshop was to survey the latest developments in the field and to bring together theory and practice. In doing so, the workshop highlighted cross-cutting research in academia, industry and the US Department of Energy complex at the interface of hydraulic fracturing, geothermal energy production, carbon capture and sequestration, nuclear waste disposal, and the evaluation and reduction of the environmental impact of these processes. A subset of the invited speakers at Grand challenges in geological fluid mechanics were asked to contribute either regular or review papers to this theme issue on ‘Energy and the subsurface’ in order to establish a self-contained volume detailing both the state-of-the-art and the research directions of the field.
2. Theme issue contributions
The theme issue begins with an overview by Hyman et al.  of the characterization and analysis of flow and transport in shale formations across multiple spatial and temporal scales through integrated computational, theoretical, and experimental methods. At the field scale, discrete fracture network models are used to simulate production of a hydraulically fractured well in a shale gas reservoir. Meanwhile, at the core scale, triaxial fracture experiments are compared with computational results from finite-discrete element models to understand dynamic fracture/crack propagation in low permeability shale. Additionally, lattice Boltzmann simulations are combined with microfluidic experiments (using both synthetic and natural rock) to understand multiphase flow and mixing at the pore scale. Finally, a discussion is provided of the potential of CO2 as an alternative working fluid, both in fracturing and re-stimulating activities.
A focused review of numerical modelling of hydraulic fracture propagation by Peirce  follows the overview by Hyman et al. . Peirce  addresses the difficulties encountered in developing numerical models of hydraulic fractures owing to the degenerate, hyper-singular nature of the governing coupled integropartial differential equations. The review discusses a class of numerical schemes developed to exploit multiscale asymptotic behaviour encountered near the fracture boundary. Specifically, locating the free boundary using tip asymptotics and imposing the latter asymptotic behaviour in a weak form are illustrated through two approaches to discretizing the governing equations: the displacement discontinuity boundary integral method and the extended finite-element method. Practical issues such as models for proppant transport that capture ‘tip screen-out’ are also discussed.
Next is a review of the role of computational sciences in the upstream oil and gas industry by Halsey . In particular, he discusses how computational sciences have reduced and led to management of the fundamental uncertainty of the subsurface formations from which the oil and gas industry produces hydrocarbons. Three applications are discussed at a non-technical level: (i) seismic imaging and the emergence of full wavefield inversion enabled by algorithmic advances and petascale computing, (ii) reservoir simulation being advanced through highly parallel computing architectures, and (iii) the role of data analytics.
The fourth and final review article by De Wit  describes recent advances in understanding chemohydrodynamic patterns in porous media. Fluids used in oil and gas recovery operations can be volatile or, at the very least, reactive with subsurface species. For example, supercritical CO2, which is used in carbon sequestration, is partially miscible with the brine encountered naturally in geologic formations. The interplay between chemical reactions, including mixing, and hydrodynamics can give rise to chemohydrodynamic instabilities that affect the spatio-temporal evolution of various injected and displaced species in the subsurface. Specifically, De Wit  describes the influence of chemical reactions on viscous fingering, which occurs owing to the Saffman–Taylor instability of displacing a more viscous fluid by a less viscous one and is ubiquitous in subsurface fluid mechanical processes. Buoyancy-driven fingering in miscible systems, convective dissolution, as well as precipitation patterns are also reviewed with an outlook towards understanding the feasibility and efficiency of CO2 sequestration.
Complementing the reviews are seven original research papers. Chau et al.  study the growth of two intersecting near-orthogonal systems of parallel hydraulic fractures, motivated by recent analysis of gas outflow histories at wellheads that show an optimal hydraulic crack spacing. Chau et al.  argue that, while flow in lateral cracks branching from a primary crack can be modelled as viscous flow of a compressible (proppant-laden) fluid, the model must be complemented with the pressurization of a sufficient volume of micropores by Darcy-type diffusion into the shale, which generates tension along existing crack walls. By enforcing equilibrium of the stresses in the fractures, pores and water, with the generation of tension in the solid phase, a new three-phase medium concept (between Biot’s two-phase medium and Terzaghi’s effective stress) emerges. The new model is validated through simulations that combine finite elements for deformation and fracture with volume elements for fluid flow.
Lai et al.  present an experimental study of the dynamics of fluid-driven cracks in an elastic matrix made from gelatin. They measure the crack shape as a function of space and time and identify a dimensionless parameter that determines the relative competition between toughness and viscous effects. By properly choosing the Young’s modulus of the gelatin, the viscosity of the injected liquid and the injection flow rate, viscous effects in the flow can be tuned to be negligible compared with toughness effects. Then, the crack dynamics can be described, theoretically, by a set of scaling laws, in particular for the crack radius as a function of time. Experiments using gelatin verify these theoretical predictions by showing self-similar collapse under the proper dimensionless rescaling, thus enabling the practical use of the scaling laws.
Makhnenko & Labuz  discuss elastic and inelastic deformation of fluid-saturated rock. Fluids saturating in situ rock affect both the elastic parameters and the inelastic response of the rock. Obtaining accurate measurements to specify constitutive models for such mechanical response is difficult. To this end, Makhnenko & Labuz  develop techniques for testing fluid-saturated porous rock under the limiting conditions of drained (long-term), undrained (short-term) and unjacketed (solid matrix) response in hydrostatic, axisymmetric and plane strain compression. Through measurements across a range of mean stress values, enough data are gathered to fully calibrate an elastoplastic constitutive model’s parameters.
Rajaram & Arshadi  derive a similarity solution for reaction front propagation in a fracture matrix system based on a new composite similarity variable, assuming quasi-steady advection in the fracture and a sharp reaction front in the rock matrix. The reaction front location is found to depend linearly upon the distance along the fracture and to propagate along the fracture ‘diffusively’ (i.e. time dependence is as the square root of time). Rajaram & Arshadi  show that their similarity solution is applicable to a broad class of reactive transport problems in fracture–matrix systems, and that it reproduces the approximate solutions for non-reactive solute and heat transport in a fracture. The similarity solution is benchmarked against numerical simulations for nonlinear reactive transport of a mineral-laden aqueous species in the rock matrix, showing good agreement, especially in the diffusion-limited (long-time) limit.
Al Ismail & Zoback  present novel pulse-decay permeability experiments on Utica and Permian shale samples, revealing the effects of rock mineralogy and pore structure on the stress-dependent permeability of shale. They show that, even though the permeability of samples, whose pores resided in kerogen, positively correlates with organic content, the absolute value of the permeability is not affected by the mineral composition of the samples. For clay-rich samples, meanwhile, higher pore throat compressibility is observed, leading to permeability reduction at larger effective stress. This finding highlights the need to model permeability of clay-rich shale reservoirs as stress-dependent.
Woods & Mingotti , like De Wit , study a new variation on the classic problem of viscous fingering. Unlike De Wit , however, the fluids involved are not reactive but, instead, there is a topographic variation in the flow conduit’s geometry. Specifically, the thickness and permeability decrease away from the centreline, which represents a simple model of the cross-channel variations in channelized reservoirs. It is found that the cross-channel variations tend to focus the flow along the centre of the channel if the displacing and displaced fluids have the same viscosity. If the viscosity of the displacing fluid is smaller, then the flow focusing intensifies, leading to a very poor sweep of the system. If the ratio of the viscosities of the displacing to displaced fluid is sufficiently large, then a blunt nose may develop at the leading edge of the fluid–fluid interface, whereas the remainder of the interface becomes stretched out along the edges of the channel, which leads to a more efficient sweep of the system. Nonlinear solutions for the evolution of the fluid–fluid interface are shown to compare favourably with laboratory experiments.
Last, but not least, Ecke & Backhaus  present experimental results on mass transport through molecular diffusion and plume dynamics in multispecies flows in porous media, which has applications to CO2 sequestration. They study a water–propylene glycol system enclosed in a Hele-Shaw cell with variable permeability, which captures the essential physics of porous media convection. Using optical shadowgraph, Ecke & Backhaus  track the interface between the two miscible fluids in their artificial porous medium. Through these measurements, it is possible to determine the mass transport rate and the spatial separation and the velocity and width characteristics of solutal plumes. From the latter data, it is shown that the plume dynamics is closely related to the mass transport rate, pointing to quantitative differences between miscible (such as supercritical CO2 and brine) and immiscible (such as oil and water) interfaces in porous media convection.
Given the broad implications of improving the efficiency and mitigating the environmental impact of novel energy production strategies, as succinctly summarized by the US Department of Energy’s SubTER initiative’s goal of ‘mastering the subsurface for energy production and storage’ , we hope that this theme issue will, at the very least, stimulate wider interest in the subject and guide research directions that are currently at the forefront of many national and international governing and scientific bodies’ agendas.
As is evident in the articles collected for this theme issue, a cross-disciplinary approach is necessary for the development of new methodologies for characterizing and analysing subsurface fluid flow and transport problems relevant to the energy sciences. Fluid mechanics is needed to interpret the complex flow environment that ranges from nanopores to tortuous fracture networks with and without proppant particles. Meanwhile, fracture mechanics governs the formation, geometry and persistence of the stimulated and natural fracture network. All of these processes are embedded within a multiphase hydrogeological environment pervaded by geochemical and geophysical phenomena. Recent advances in experimental methods (such as the direct observation of fracture processes), high-performance computing (including high-fidelity fracture growth and transport simulations), and theoretical modelling of fracture systems have significant promise for integrating these disciplines and meeting the goal of ‘mastering the subsurface’.
I.C.C. and H.S.V. conceived and drafted the manuscript. All authors gave final approval for publication.
We declare we have no competing interests.
We gratefully acknowledge support from Los Alamos National Laboratory’s Laboratory Directed Research and Development (LDRD) programme through the Center for Nonlinear Studies and grant no. 20140002DR. Los Alamos National Laboratory is operated by Los Alamos National Security LLC for the National Nuclear Security Administration of the US Department of Energy under contract no. DE-AC52-06NA25396.
We thank Bailey Fallon, the Commissioning Editor of this theme issue of Philosophical Transactions A, for his expert assistance in organizing it. We are grateful to Bill Carey for providing feedback on this introductory article. We also thank all the authors for their contributions, without which this theme issue would not have been possible. Last, but not least, we acknowledge the efforts of the numerous anonymous referees who vetted the manuscripts in this theme issue and provided constructive feedback to us (the guest editors) and the authors.
One contribution of 12 to a theme issue ‘Energy and the subsurface’.
- Accepted July 12, 2016.
- © 2016 The Author(s)
Published by the Royal Society. All rights reserved.