Striving to translate shale physics across ten orders of magnitude: What have we learned?
Introduction
The coming decades are poised to undergo a transition away from fossil-based energy resources towards renewables, driven primarily by ecological and political pressures induced by climate change. The success of this transition, however, is contingent upon the sustainable production of low-carbon fuels from shales as well as the utilization of geological formations, sealed by shale, to sequester anthropogenic CO2 and to potentially store renewable energy (e.g., hydrogen). During the past decade, shale formations have grown steadily in importance due to their significant contribution to the global energy supply and security. The low-carbon intensity fuels extracted from these formations, called shale gas and tight oil, have already displaced several carbon-intense fuels like coal for electricity generation. The impact has been especially dramatic in the U.S. Over the last decade, the U.S. has gone from scarce supplies of natural gas to abundance, and in 2018 became the world's largest producer of oil since the 1970s (Yergin, 2020). The International Energy Agency (IEA) has even projected that the U.S may become a net oil exporter within another decade (IEA, 2017). The result has been a marked reduction in the U.S carbon emissions and air pollution (Yergin, 2020).
Despite shale's promise, its engineering challenges are immense not only because the well-understood physics of conventional porous media are no longer applicable, but also because shales exhibit a much greater degree of heterogeneity than conventional reservoirs. The term “shale” refers loosely to ultrafine-grained rock types such as mudstones, marlstones, chalks, and others, which are nanoporous and exhibit chemical and structural heterogeneity at scales ranging from a few nanometers to several meters (Loucks et al., 2012) (Fig. 1); altogether accounting for 10 orders of magnitude. The nanoporosity renders shales nearly impermeable, and it is only through the advent of horizontal drilling and hydraulic fracturing that production from shales has been made possible. Their working principle is to increase the accessible surface area between wellbore fluids and the rock, and thereby production. Despite the success of these technologies, only about 5% of the original oil in place and about 25% of the gas in place is recovered, with production rates decreasing markedly after a few months (Patzek et al., 2013). Moreover, questions about the impact of production on the environment (e.g., fugitive methane; Howarth et al., 2011) and groundwater supplies remain open. Addressing these challenges is key to sustainable field operations (Hemminger et al., 2015), and it requires a fundamental understanding of the physics and chemistry of shales, as well as their manifestation at multiple length and time scales. To appreciate the difficulty, consider that the productivity of a given well is directly tied to the rate at which individual gas molecules desorb from the walls of a nanoscale pore and then diffuse into the nearest microcrack whose aperture is sensitive to geomechanical stresses and the presence of liquids. Other interactions between clays and water further confound the picture by introducing swelling (Wang et al., 2017) and mineral reactions (Harrison et al., 2017).
Nanopores are comparable in size to fluid molecules, rendering classical continuum (or Darcy-scale) descriptions of fluid dynamics and phase behavior invalid; most of which also neglect key molecular forces between minerals and fluids (Jin and Firoozabadi, 2016). What is more, shales seem to lack a clear separation between scales. This makes describing (or closing) the physics at a single scale of observation nearly impossible (Section 2.1). The above challenges can be recast into two broad questions: (1) how do we describe the nanoscale physics and chemistry of shales? And (2) how do we translate such knowledge across spatiotemporal scales? This review explores the latter question, while the former will be addressed in separate publications (Khan et al., 2021; Jew et al., 2020).
We distinguish the “scale” question from the “physics” question because the former is not exclusive to shales, but all geologic porous media. Scale translation, which we define as transforming data or information from one observation scale to another, has been a long-standing challenge in geosciences. Shale development has just stirred a more acute need for it. A massive body of literature already exists on scale translation, describing classical methods such as homogenization (Hornung, 1996; Whitaker, 2013; Gray and Miller, 2014) and numerical upscaling (Durlofsky and Chen, 2012; Farmer, 2002; Renard and de Marsily, 1997; Christie, 1996) that allow small-scale measurements or simulations to be transformed into large-scale decisions about the development of a petroleum reservoir or the fate of a contaminant plume. But these methods, while indispensable, have limitations. For one, they translate geologic information in a unidirectional fashion: from small to large, called upscaling. Another is that they require spatiotemporal scales associated with structural/chemical heterogeneities of the porous medium, as well as the physical/chemical processes occurring in them, to be separated, which may not hold for shales (Section 2.1).
What is promising about today is that significant progress has been made in three areas since the turn of the century: (1) increase in computational power and the development of algorithms that are scalable on parallel machines, (2) high-resolution imaging instruments (e.g., hyperspectral, X-ray micro/nano-CT) that generate massive amounts of data, and (3) the development of machine learning methods able to recognize patterns among such data. However, these methods have largely evolved in isolation and while geoscientists now have a wider array of experimental and computational tools at their disposal, no single tool can probe the full gamut of heterogeneity present in shales. The gap must, therefore, be filled by an ability to translate one data type into another, and from one spatiotemporal scale to another. As we will describe later, such tasks require not only upscaling, but also downscaling, which converts large-scale data into small-scale information; something traditional methods do not address. We believe it is only through such a combination of multi-modal data acquisition and high-powered computation and pattern recognition that a full picture of shales, among other challenging geomaterials, can be constructed.
The aim of this review is to place the foregoing new developments within the context of the more traditional approaches for scale translation and to highlight how they complement, rather than conflict with, each other. In Section 2, we generalize the definitions of well-established concepts such as scale translation, scale separation, tyrannies of prediction, upscaling, downscaling, and data translation. The goal here is to provide the necessary background for later sections and to broaden the classical definitions used in conventional porous media. In Section 3.1, we provide a brief, but self-contained, review of analytical homogenization methods. They consist of mathematical techniques used to derive macroscopic governing equations from their microscopic counterparts. While we discuss several such techniques, we highlight that all of them require “scale separation” as a central assumption. Understanding them, however, is crucial for making appropriate use of the computational methods presented next. In Section 3.2, we discuss hybrid methods, which aim to model porous-media problems when scale separation is absent. In Section 3.3, we review numerical upscaling and its more recent extensions. A discussion of the upsides and pitfalls of numerical upscaling, and the potential avenues for improvement, is presented. Section 3.4 discusses multiscale computing, to which a large portion of this review is devoted. First, we discuss older techniques that were developed purely at the Darcy scale, such as multiscale finite element (MsFE), mixed multiscale finite element (MxMsFE), multiscale finite volume (MsFV), and mortar multiscale finite element (MoMsFE). We then discuss straightforward extensions of these methods to the pore (or micro) scale, followed by a presentation of more recent and specialized methods for solving pore-scale problems.
Next, we discuss traditional pore-scale modeling approaches, like pore network models (PNM), and formalize their algorithms by placing them within the context of numerical upscaling and multiscale computing. The main reason for our emphasis on multiscale methods in this paper is that not only do they bear many similarities with hybrid and numerical upscaling methods, as outlined throughout the paper, but they also possess additional properties that are computationally attractive such as the ability to downscale and quantify prediction errors. In Section 3.4.4, we propose a new algorithmic framework for bridging between pore- and Darcy-scale physics that combines several of the preceding methods. The anticipated limitations of the framework are also detailed. In Section 3.5, we discuss recent advances and trends in high-resolution and multi-modal imaging that are changing how geologic porous media are being characterized. Such images serve as crucial inputs to either the computational methods covered earlier or the machine learning algorithms discussed in the following Section 3.6.
The exposition style of this paper is pedagogical, and while mathematical details are certainly discussed, they are done so at a sufficiently high level so as not to distract from the main points. We use simple examples to convey the algorithmic details of each method presented. While the governing equations used in the examples describe conventional porous media (not shales), the reader should note that the algorithms themselves remain unaltered for shales. The only difference lies in the specific differential operators describing shale physics to which the algorithms would be applied. The validity of these operators, however, is a separate “physics” question actively being explored (Center for Mechanistic Control of Unconventional Formations (CMC-UF)). The paper concludes with Section 4, where we present two case studies that exemplify some of the methods presented.
Section snippets
Scale translation
We define scale translation as the process of using data at one spatiotemporal scale to infer needed information at another scale. An example is to use pore-scale data, such as X-ray μCT images, to derive Darcy-scale data, such as permeability (Wildenschild and Sheppard, 2013; Blunt et al., 2013). Another is to use core-scale measurements of organic content to reconstruct millimeter-scale variabilities of thermal conductivity (Mehmani et al., 2016a). Scale translation is bidirectional. If
Homogenization
Homogenization is the process of deriving governing equations that apply at the coarse scale from those that apply at the fine scale. The designations “coarse scale” and “fine scale” are relative to each other but arbitrary in absolute terms. For example, they may correspond, respectively, to the range O(10 μm) and O(1 mm) or O(1 cm) and O(10 m). Despite the arbitrariness, a common choice for the fine scale is the pore scale, which is the scale at which the porous medium appears as an aggregate
Case studies
The Center for Mechanistic Control of Unconventional Formations (CMC-UF) is an Energy Frontier Research Center, funded by the U.S. Department of Energy, whose mission is to understand the fundamental interactions between fluids and unconventional source rocks, such as shales. As members of this center, we grapple with challenging questions related to scale and data translation in shales, and part of our activities rely on developing disparate representations of the same physics that correspond
Summary
This review was motivated by the need to describe physicochemical processes in geologically challenging porous media, such as shales, that display large disparity in length and time scales. We showed that such geomaterials generally do not exhibit scale separation and therefore cannot be described with a closed set of equations at only one scale. Instead, the processes observed at large scales are intimately coupled to those occurring at small scales. Homogenization, consisting of a set of
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This work was supported as part of the Center for Mechanistic Control of Unconventional Formations (CMC-UF), an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science under DOE (BES) Award DE-SC0019165.
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