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Showing papers in "Reviews in Mineralogy & Geochemistry in 2015"


Journal ArticleDOI
TL;DR: There are a large number of methods for quantifying porosity, and an increasingly complex idea of what it means to do so as discussed by the authors, which is why it is important to quantify the relationships between porosity and storage, transport and rock properties, however, the pore structure must be measured and quantitatively described.
Abstract: Porosity plays a clearly important role in geology. It controls fluid storage in aquifers, oil and gas fields and geothermal systems, and the extent and connectivity of the pore structure control fluid flow and transport through geological formations, as well as the relationship between the properties of individual minerals and the bulk properties of the rock. In order to quantify the relationships between porosity, storage, transport and rock properties, however, the pore structure must be measured and quantitatively described. The overall importance of porosity, at least with respect to the use of rocks as building stone was recognized by TS Hunt in his “Chemical and Geological Essays” (1875, reviewed by JD Dana 1875) who noted: > “Other things being equal, it may properly be said that the value of a stone for building purposes is inversely as its porosity or absorbing power.” In a Geological Survey report prepared for the U.S. Atomic Energy Commission, Manger (1963) summarized porosity and bulk density measurements for sedimentary rocks. He tabulated more than 900 items of porosity and bulk density data for sedimentary rocks with up to 2,109 porosity determinations per item. Amongst these he summarized several early studies, including those of Schwarz (1870–1871), Cook (1878), Wheeler (1896), Buckley (1898), Gary (1898), Moore (1904), Fuller (1906), Sorby (1908), Hirschwald (1912), Grubenmann et al. (1915), and Kessler (1919), many of which were concerned with rocks and clays of commercial utility. There have, of course, been many more such determinations since that time. There are a large number of methods for quantifying porosity, and an increasingly complex idea of what it means to do so. Manger (1963) listed the techniques by which the porosity determinations he summarized were made. He separated these into seven methods for …

788 citations


Journal ArticleDOI
TL;DR: In this paper, the authors focus on how reactive fluids can move through "tight rocks" which have a very low intrinsic permeability and how secondary porosity is generated by fluid-mineral reactions.
Abstract: The term porosity is very widely used in geosciences and normally refers to the spaces between the mineral grains or organic material in a rock, measured as a fraction of the total volume. These spaces may be filled with gas or fluids, and so the most common context for a discussion of porosity is in hydrogeology and petroleum geology of sedimentary rocks. While porosity is a measure of the ability of a rock to include a fluid phase, permeability is a measure of the ability for fluids to flow through the rock, and so depends on the extent to which the pore spaces are interconnected, the distribution of pores and pore neck size, as well as on the pressure driving the flow. This chapter will be primarily concerned with how reactive fluids can move through ‘tight rocks’ which have a very low intrinsic permeability and how secondary porosity is generated by fluid–mineral reactions. A few words about the meaning of the title will help to explain the scope of the chapter: 1. “Fluid–mineral interaction”: When a mineral is out of equilibrium with a fluid, it will tend to dissolve until the fluid is saturated with respect to the solid mineral. We will consider fluids to be aqueous solutions, although many of the principles described here also apply to melts. The generation of porosity by simply dissolving some minerals in a rock is one obvious way to enhance fluid flow. Dissolution of carbonates by low pH solutions to produce vugs and even caves would be one example. However, when considering the role of fluid–mineral reaction during metamorphism the fluid provides mechanisms that enable re-equilibration of the rock, i.e., by replacing one assemblage of minerals by a more stable assemblage. This not only involves the dissolution of the parent mineral phases, but the …

108 citations


Journal ArticleDOI
TL;DR: The role of microstructures and their possible effects on flow and transport have long been neglected as discussed by the authors, and prediction of system response to chemical conditions requires understanding how individual processes that occur at the microscopic scale contribute to the observed large-scale flow, mechanical, and transport distribution patterns.
Abstract: Dissolution and precipitation reactions are the primary mechanisms that occur when a rock (i.e., a mineral assemblage) is in contact with a fluid out of equilibrium. They play a critical role in natural processes (e.g., weathering, compaction, meteoric and marine diagenesis) and anthropogenic processes (e.g., reservoir acidizing, CO2 sequestration, acid mine drainage, contaminant mobility, bioremediation). Such fluid–rock interactions result in complex changes in pore structure and mineral composition, leading in turn to changes in flow, mechanical, and transport properties, such as permeability, dispersivity, strength, and pore accessibility. Consequently, geochemical disequilibrium can lead to complex modifications of hydrodynamic and transport properties in porous and fractured rocks. Porous rocks are often characterized by complex textures and mineral compositions that are derived from their depositional and diagenetic environments. They typically have heterogeneous structures, the macroscopic physical properties of which depend on microscopic characteristics. Permeability, for example, is closely related to the microstructure, in particular the size and the spatial distribution of pore throats, pore roughness, and presence of fine clogging particles. The coupled hydrological, mechanical, and chemical (HMC) processes are highly non-linear and minor changes at the pore scale in one property can result in large modifications of the others properties. Prediction of system response to chemical conditions requires understanding how individual processes that occur at the microscopic scale contribute to the observed large-scale flow and transport distribution patterns. Predictive modeling remains challenging for the time and spatial scales involved in geological processes and because of the lack of information about how the physical properties of the porous medium evolve as a result of chemical reactions. In particular, the role of microstructures and their possible effects on flow and transport have long been neglected. Consequently, upscaling the flow and transport properties remains poorly constrained by pore-scale observations despite a multitude of experiments, …

105 citations


Journal ArticleDOI
TL;DR: Anovitz and Cole as mentioned in this paper proposed a pore-scale approach to understand and quantify the relationship between reaction-induced porosity and porosity change and the transport properties of subsurface materials.
Abstract: The recent profusion of microscopic characterization methods applicable to Earth Science materials, many of which are described in this volume (Anovitz and Cole 2015, this volume; Noiriel 2015, this volume), suggests that we now have an unprecedented new ability to consider geochemical processes at the pore scale. These new capabilities offer the potential for a paradigm shift in the Earth Sciences that will allow us to understand and ultimately quantify such enigmas as the apparent discrepancy between laboratory and field rates (White and Brantley 2003) and the impact of geochemical reactions on the transport properties of subsurface materials (Steefel and Lasaga 1990, 1994; Steefel and Lichtner 1994; Xie et al. 2015). It has only gradually become apparent that many geochemical investigations of Earth materials have suffered (perhaps inadvertently) from the assumption of bulk or continuum behavior, leading to volume averaging of properties and processes that really need to be considered at the individual grain or pore scale. For example, a relationship between reaction-induced porosity and permeability change can perhaps be developed based on bulk samples, but ultimately a mechanistic understanding and robust predictive capability of the associated geochemical and physical processes will require a pore-scale view. The question still arises: Do we need pore-scale characterization and models in geochemistry and mineralogy? The laboratory–field rate discrepancy (or enigma) is a good example of where a pore-scale understanding may provide insights not easily achievable with bulk characterization and models. If the reasons for this apparent discrepancy between laboratory and field rates cannot be explained, then it appears unlikely that scientifically defensible and quantitative models for a number of important Earth Science applications ranging from chemical weathering and its effects on atmospheric CO2, to subsurface carbon sequestration, to nuclear waste storage, to contaminant remediation and transport, …

92 citations


Journal ArticleDOI
TL;DR: In this paper, a pore-scale model is proposed to study biogeochemical reactions in the context of reactive flow and multicomponent transport in the subsurface environment.
Abstract: Important geoscience and environmental applications such as geologic carbon storage, environmental remediation, and unconventional oil and gas recovery are best understood in the context of reactive flow and multicomponent transport in the subsurface environment. The coupling of chemical and microbiological reactions with hydrological and mechanical processes can lead to complex behaviors across an enormous range of spatial and temporal scales. These coupled responses are also strongly influenced by the heterogeneity and anisotropy of the geologic formations. Reactive transport processes can change the pore morphology at the pore scale, thereby leading to nonlinear interactions with advective and diffusive transport, which can strongly influence larger-scale properties such as permeability and dispersion. Therefore, one of the greatest research challenges is to improve our ability to predict these processes across scales (DOE 2007). The development of pore-scale experimental and modeling methods to study reactive processes involving mineral precipitation and dissolution, and biofilm dynamics allows more fundamental investigation of physical behavior so that more accurate and robust upscaled constitutive models can be developed for the continuum scale. A pore-scale model provides fundamental mechanistic explanations of how biogeochemical processes and pore-scale interfacial reactions alter flow paths by pore plugging (and dissolving) under different geochemical compositions and pore configurations. For example, dissolved CO2 during geological CO2 storage may react with minerals in fractured rocks, confined aquifers, or faults, resulting in cementation (and/or dissolution) and altering hydrodynamics of reactive flow. This can be observed in a natural analogue where primary porosity in sandstone is cemented by carbonate precipitates, affecting dissolved CO2 flow paths at the Little Garde Wash Fault, Utah (e.g., Fig. 1a–b). Several other examples demonstrating macroscopic characteristics of calcium carbonate (CaCO3) precipitation in Figure 1 include an elongated concretion along the groundwater flow direction, CaCO3 precipitation along the vertical pathway sealed …

89 citations


Journal ArticleDOI
TL;DR: Weathering of bedrock to produce porous regolith, the precursor to biologically active soil and soluble mineral nutrients, creates the life-supporting matrix upon which Earth's Critical Zone (the thin surface layer where rock meets life) develops.
Abstract: Weathering of bedrock to produce porous regolith, the precursor to biologically active soil and soluble mineral nutrients, creates the life-supporting matrix upon which Earth’s Critical Zone—the thin surface layer where rock meets life—develops (Ollier 1985; Graham et al. 1994; Taylor and Eggleston 2001). Water and nutrients locked up in low porosity bedrock are biologically inaccessible until weathering helps transform the inert rock into a rich habitat for biological activity. Weathering increases the water-holding capacity and nutrient accessibility of rock and regolith by increasing porosity and mineral surface area, affecting the particle-size distribution, and enhancing ecosystem diversity (Cousin et al. 2003; Certini et al. 2004; Zanner and Graham 2005). Especially in areas where soils are thin and climate is dry, the water stored in weathered rock is essential to ecosystem productivity and survival (Sternberg et al. 1996; Zwieniecki and Newton 1996; Hubbert et al. 2001; Witty et al. 2003). Removal of soluble material during weathering decreases the concentrations of major elements such as Ca, Na, and Mg and the overall mass of the solid, decreasing the bulk density and increasing porosity. These chemical and physical changes result in decreased uniaxial compressive strength and elastic moduli of the rock and increased infiltration of water through the weathered rock (Tugrul 2004). Porosity in intact bedrock is comprised of inter- and intra-granular pores developed during (re-) crystallization in igneous and metamorphic rocks or diagenesis in sedimentary rocks. As we conceptualize it, the conversion of low-permeability bedrock to regolith generally begins due to the transport of meteoric water into protolith through the large-scale fractures that are present as a result of regional tectonic factors or exhumation (Wyrick and Borchers 1981; Molnar et al. 2007). In zones near the fractures, water can infiltrate into the low-porosity rock …

89 citations


Journal ArticleDOI
TL;DR: In the field of hydrology where transport behavior is more routinely considered, clays and clay-rich shales were largely relegated to a minor role because of their low hydraulic conductivity as mentioned in this paper.
Abstract: The mineralogical and chemical properties of clays have been the subject of longstanding study in the research community—in fact, entire journals are devoted to the topic. In the field of hydrology where transport behavior is more routinely considered, clays and clay-rich rock were largely relegated to a minor role because of their low hydraulic conductivity. However, this very property explains in part the renewed interest in the behavior of clays and clay rocks in several important subsurface energy-related applications, including the long-term disposal of nuclear wastes in geological repositories and the storage of CO2 in subsurface geological formations. In these applications and environments, the low permeability of the clay-rich formations or engineered barriers provides at least part of the safety functions for radionuclide contaminants confinement and subsurface CO2 sequestration. From a geochemical and mineralogical point of view, the high adsorption capacity of clay minerals adds to the effect of low hydraulic conductivities by greatly increasing the retardation of radionuclides and other contaminants, making clays ideal where isolation from the biosphere is desired. The low permeability of clay-rich shales also explains why hydrocarbon resources are not easily exploited from these formations, thus requiring in many cases special procedures like hydraulic fracturing in order to extract them. Clay properties remain also topic of intensive research in the oilfield industry in connection with their swelling behavior, which has an adverse impact on drilling operations (Anderson et al. 2010; Wilson and Wilson 2014; De Carvalho Balaban et al. 2015). While the low permeability and high adsorption capacity of clay minerals are widely acknowledged, it is clear nonetheless that there is a need for an improved understanding of how the chemical and mineralogical properties of clay rocks impacts transport through them. It is at the pore-scale that the chemical properties …

62 citations


Journal ArticleDOI
TL;DR: The pore scale can be defined as the largest spatial scale at which it is possible to distinguish the different fluid and solid phases that make up natural subsurface materials.
Abstract: Darcy-scale simulation of geochemical reactive transport has proven to be a useful tool to gain mechanistic understanding of the evolution of the subsurface environment under natural or human-induced conditions. At this scale, however, the porous medium is typically conceptualized as a continuum with bulk parameters that characterize its physical and chemical properties based on the assumption that all phases coexist in each point in space. In contrast, the pore scale can be defined as the largest spatial scale at which it is possible to distinguish the different fluid and solid phases that make up natural subsurface materials. Because the pore scale directly accounts for the pore-space architecture within which mineral reactions, microbial interactions and multi-component transport play out, it can help explain biogeochemical behavior that is not understood or predicted by considering smaller or larger scales (Fig. 1). Specifically, the nonlinear interaction between the coupled physical and geochemical processes may result in emergent behavior, including changes in permeability, diffusivity, and reactivity that is not captured easily by a Darcy-scale continuum description. Reactive processes in porous media such as microbially mediated reduction–oxidation (Fig. 1) or mineral dissolution–precipitation (Fig. 2) take place at interfaces between fluid and solid phases. Because the different phases are distinguishable at the pore scale, experimental and modeling studies need to consider these interfaces so as to accurately determine reaction rates. An interface is the surface between two phases that differ in their physical state or chemical composition. Depending on the scale of observation, the appearance of the interface can vary. Sharp interfaces are those in which the physical and chemical characteristics change abruptly across the interface. Diffuse interfaces are those in which the characteristics change smoothly over a layer of varying thickness. Reactive processes themselves can change the appearance of the interface. For example, mineral heterogeneity can …

61 citations


Journal ArticleDOI
TL;DR: A review of the recent research in which geochemists have examined precipitation of solid phases in porous media, particularly in pores a few nanometers in diameter (nanopores), can be found in this paper.
Abstract: The purpose of this article is to review some of the recent research in which geochemists have examined precipitation of solid phases in porous media, particularly in pores a few nanometers in diameter (nanopores). While this is a “review,” it is actually more forward-looking in that the list of things about this phenomenon that we do not know or cannot control at this time is likely longer than what we do know and can control. For example, there are three directly contradictory theories on how to predict how precipitation proceeds in a medium of varying pore size, as will be discussed below. The confusion on this subject likely stems from the complexity of the phenomenon itself: One can easily clog a porous medium by inducing a rapid, homogeneous precipitation directly from solution, or have limited precipitation occur that does not affect permeability or even porosity substantially. It is more difficult to engineer mineral precipitation in order to obtain a specific outcome, such as filling all available pore space over a targeted area for the purposes of contaminant sequestration. However, breakthrough discoveries could occur in the next five to ten years that enhance our ability to predict robustly and finely control precipitation in porous media by understanding how porosity and permeability evolve in response to system perturbations. These discoveries will likely stem (at least in part) from advances in our ability to 1) perform and interpret X-ray/neutron scattering experiments that reveal the extent of precipitation and its locales within porous media (Anovitz and Cole 2015, this volume), and 2) utilize increasingly powerful simulations to test concepts and models about the evolution of porosity and permeability as precipitation occurs (Steefel et al. 2015, this volume). A further important technique to isolate specific phenomena and understand reactivity is also microfluidics cell …

48 citations


Journal ArticleDOI
TL;DR: In this article, the pore-scale dynamics of flow and reactive transport are modeled at the micro/pore scale and the macro/continuum scale, respectively, and the authors develop a model to predict flow and transport at any scale of interest.
Abstract: Fluid flow and reactive transport is relevant to many subsurface applications including CO2 sequestration, miscible/immiscible displacements in enhanced oil recovery, wellbore acidization, pollutant transport, and leakage/remediation of nuclear waste repositories. In all these scenarios, one or more fluid phases flow through the complicated geometry of the pore space, while advecting one or more chemical species along their flow streamlines. Simultaneously, the chemical species undergo molecular diffusion, due to their Brownian motion, allowing them to randomly jump from one streamline to the next. In the case of fluid–fluid or fluid–mineral reactions, chemical species may be transformed, potentially leading to precipitation and/or dissolution of solid minerals that alter the geometry/topology of the pore space. This in turn affects the velocity field of flow, and thus transport via advection/diffusion. Such complicated feedback between these pore-scale processes could give rise to “emergent” manifestations at larger scales. These manifestations are referred to as “emergent” because they cannot be foreseen from the behavior of the individual pore-scale mechanisms involved. In order to make reliable predictions of flow and transport at any scale of interest, accurate models need to be developed. Two spatial scales are commonly identified with a porous medium: the “micro/pore scale” (1–100 μm) and the “macro/continuum scale” (>1 m). The former is the fundamental scale in which physical processes (flow, transport, and geochemistry) take place, and the porous medium is regarded as discrete in nature (void space vs. grain space). The latter is a more practical scale, where we would ultimately like to have a reliable description of flow and reactive transport, and the porous medium is regarded as a continuum. The macroscopic parameters appearing in the description of continuum models, such as permeability or dispersion coefficient, are typically extracted from experiments or stand-alone pore-scale simulations. While such a “hierarchical” upscaling approach is …

44 citations


Journal ArticleDOI
TL;DR: In this paper, a Discrete Element Model (DEM) is used to analyze how the resulting pattern and the rate and progress of reaction depend on the initial porosity of the rock.
Abstract: In this article we attempt to shed some light on the factors that determine whether volume-increasing reactions and growth in pores will reduce or increase permeability. We will start by describing fi eld-scale examples of reaction-driven fracturing, and use a Discrete Element Model (DEM) to analyze how the resulting pattern and the rate and progress of reaction depend on the initial porosity of the rock. Ultimately, however, stress generation is related to growth processes taking place at the pore scale. We will therefore zoom in and describe pore-scale growth processes and how these are associated with fracturing and the production of new reactive surface area and new transport channelways for migrating fl uids. Stress generation by growth in pores requires that crystals continue to grow even after having ‘hit’ the pore wall. This implies that the fl uid from which the crystals precipitate is not squeezed out from the reactive interface by the normal stress generated by the growth, but can be kept in place as a thin fi lm by opposing forces that operate at very small scales. To understand the dynamics of crystal growth against confi ning pore walls, we need to zoom in even further and examine interface processes taking place at the nanometer scale. Hence, the last part of this chapter focuses on the nanometer-scale morphology of the reacting interface and the mechanical and transport properties of the fl uids confi ned along reactive grain boundaries.

Journal ArticleDOI
TL;DR: The pore space in rocks, sediments, and soils can change significantly as a result of weathering (see Navarre-Sitchler et al. 2015, this volume), diagenetic, metamorphic, tectonic, and even anthropogenic processes as mentioned in this paper.
Abstract: The pore space in rocks, sediments, and soils can change significantly as a result of weathering (see Navarre-Sitchler et al. 2015, this volume), diagenetic, metamorphic, tectonic, and even anthropogenic processes. As sediments undergo compaction during burial, grains are rearranged leading to an overall reduction in porosity and pore size (Athy 1930; Hedberg 1936; Neuzil 1994; Dewhurst et al. 1999; Anovitz et al. 2013). In addition, geochemical reactions can induce the precipitation and dissolution of minerals, which can either enhance or reduce pore space (e.g., Navarre-Sitchler et al. 2009; Emmanuel et al. 2010; Stack et al. 2014; Anovitz et al. 2015). During metamorphism too, mineral assemblages can change, altering rock fabrics and porosity (Manning and Bird 1995; Manning and Ingebritsen 1999; Neuhoff et al. 1999; Anovitz et al. 2009; Wang et al. 2013). As the pore space in geological media strongly affects permeability, evolving textures can influence the migration of water, contaminants, gases, and hydrocarbons in the subsurface. Although models—including the Kozeny–Carman equation (Kozeny 1927; Bear 1988)— exist to predict the relationship between porosity and permeability, they are often severely limited, in part because little is known about how pore size, pore geometry, and pore networks evolve in response to chemical and physical processes (Lukasiewicz and Reed 1988; Costa 2006; Xu and Yu 2008). In the case of geochemical reactions, calculating the change in total porosity due to the precipitation of a given mass of mineral is straightforward. However, predicting the way in which the precipitated minerals are distributed throughout the pores remains a non-trivial challenge (Fig. 1; Emmanuel and Ague 2009; Emmanuel et al. 2010, Hedges and Whitlam. 2013; Wang et al. 2013; Stack et al. 2014; Anovitz et …

Journal ArticleDOI
TL;DR: Acharya et al. as discussed by the authors investigated the effect of pore structure heterogeneity on surface reactions at the pore-scale to provide physicochemical insights on factors that control macroscopic reaction kinetics in porous media.
Abstract: Heterogeneity in pore structure and reaction properties including grain size and mineralogy, pore size and connectivity, and sediment surface area and reactivity is a common phenomenon in subsurface materials. Heterogeneity affects transport, mixing, and the interactions of reactants that affect local and overall geochemical and biogeochemical reactions. Effective reaction rates can be orders of magnitude lower in heterogeneous porous media than those observed in well-mixed, homogeneous systems as a result of the pore-scale variability in physical, chemical, and biological properties, and the coupling of pore-scale surface reactions with mass-transport processes in heterogeneous materials. Extensive research has been performed on surface reactions at the pore-scale to provide physicochemical insights on factors that control macroscopic reaction kinetics in porous media. Mineral dissolution and precipitation reactions have been frequently investigated to evaluate how intrinsic reaction rates and mass transfer control macroscopic reaction rates. Examples include the dissolution and/or precipitation of calcite (Bernard 2005; Li et al. 2008; Tartakovsky et al. 2008a; Flukiger and Bernard 2009; Luquot and Gouze 2009; Kang et al. 2010; Zhang et al. 2010a; Molins et al. 2012, 2014; Yoon et al. 2012; Steefel et al. 2013; Luquot et al. 2014), anorthite and kaolinite (Li et al. 2006, 2007), iron oxides (Pallud et al. 2010a,b; Raoof et al. 2013; Zhang et al. 2013a), and uranyl silicate and uraninite (Liu et al. 2006; Pearce et al. 2012). Adsorption and desorption at the pore-scale have been investigated to understand the effect of pore structure heterogeneity on reaction rates and rate scaling from the pore to macroscopic scales (Acharya et al. 2005; Zhang et al. 2008, 2010c, 2013b; Zhang and Lv 2009; Liu et al. 2013a). Microbially mediated reactions have also …

Journal ArticleDOI
TL;DR: In this paper, a wide variety of macro-scale observations of isotope partitioning across fluid-solid phase boundaries are considered, and the authors define the continuum scale as a representation in which interfaces are averaged over elementary volumes, rather than the pore scale in which these interfaces are explicitly resolved.
Abstract: The distribution of stable and radiogenic isotopes within and among phases provides a critical means of quantifying the origin, residence and cycling of materials through terrestrial reservoirs (Wahl and Urey 1935; Epstein and Mayeda 1953; Johnson et al. 2004; Eiler 2007; Porcelli and Baskaran 2011; Wiederhold 2015). While isotopic variability is globally observable, the mechanisms that govern both their range and distribution occur largely at atomic (e.g., radioactive decay), molecular (e.g., the influence of mass on the free energy of atomic bonds) and pore (e.g., diffusive transport to reactive surface) scales. In contrast, the vast majority of isotope ratio measurements are based on sample sizes that aggregate multiple pathways, species and compositions. Inferring process from such macro-scale observations therefore requires unraveling the relative contribution of a variety of potential mechanisms. In effect, the use of isotopes as proxies to infer a specific parameter, such as temperature (Urey 1947) or residence time (Kaufman and Libby 1954), carries the implicit requirement that one mechanism is the primary influence on the measured isotopic composition of the composite sample. In the present chapter, we consider a wide variety of macro-scale observations of isotope partitioning across fluid–solid phase boundaries. For this purpose we define the continuum scale as a representation in which interfaces are averaged over elementary volumes, as opposed to the pore scale in which these interfaces are explicitly resolved. Throughout this review it will be demonstrated that observations of isotope partitioning across fluid–solid boundaries require some representation of the isotopic composition of the solid surface and surrounding fluid distinct from ‘bulk’ or ‘well mixed’ reservoirs. For example, this distinction is necessary in order to (1) quantify the partitioning of radioactive and radiogenic species, (2) describe transport limitations that may impact the macroscopic partitioning of isotope ratios, (3) explain …