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• Deep Carbon
• Past to Present
• Online publication date: October 2019
• pp 388-414
• Publisher: Cambridge University Press

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## Abstract

New instruments and approaches have revolutionized the analysis of stable isotopologues – especially for methane – which is changing our understanding of the biotic versus abiotic formation of carbon compounds in the subsurface. This chapter highlights recent developments in analytical approaches, and it synthesizes recent results regarding the biotic versus abiotic origins of carbon compounds in the subsurface.

## 13 A Two-Dimensional Perspective on CH4 Isotope Clumping Distinguishing Process from Source

### 13.1 Introduction

Isotope ratios have been used extensively to trace the origins of methane gases (e.g. Schoell 1980). For this purpose, the stable isotope ratios 13C∕12C and D/H have been paramount. These ratios refer to the atomic abundances of the rare isotopes of carbon and hydrogen relative to the more abundant isotopes, in aggregate, and inclusive of all of the methane isotopic molecular species in a sample of gas. We therefore refer to these ratios as “bulk” isotope ratios. The term “isotopologue” refers to specific isotopic versions of the molecules. For example, the “12CH3D isotopologue” refers to the 12CH3D + 12CH2DH + 12CHDH2 + 12CDH3 permutations of the D-substituted isotopic species of CH4 collectively. In the geosciences, the term “clumping” denotes more than one heavy isotope in a single molecule or molecular unit (e.g. 13C18O16O16O + 13C16O18O16O + 13C16O16O18O in the CO32– moiety within the CaCO3 crystalline structure). In this chapter, the results of recent studies of the relative abundances of the clumped methane species 13CH3D and 12CH2D2 measured at the University of California, Los Angeles (UCLA) are summarized.

We begin with a description of the goals of this research program. The original excitement about making use of the 13C–18O multiply substituted isotopologue of CO2, 13C18O16O + 13C16O18O, derived from acid digestion of carbonate was due to the prospect of removing the various logical degeneracies that have historically plagued our interpretations of the significance of 18O/16O (usually expressed as δ18O values, the per mil differences in 18O/16O from a standard material) in carbonates (Eiler et al. 2005). Marine carbonate oxygen isotope ratios can vary in response to temperature, ice volume, or secular variations in the δ18O of the oceans. By using the temperature-dependent propensity of 13C and 18O to form bonds as a homogeneous (as in a single-phase as opposed to heterogeneous fractionation between two separate phases, in this case carbonate and water) thermometer, the relationship between bulk δ18O in the carbonate and that in the water becomes irrelevant if the goal is to deduce temperature of formation. The goal, therefore, was to develop an isotopic tracer in which the bulk isotope ratios are normalized out.

The CH4 clumping project at UCLA, in collaboration with the Carnegie Institution of Science, began in 2008 with the prospects for funding by the Deep Carbon Observatory and an eye toward replicating the powerful aspects of carbonate clumping for methane. In particular, the group originally sought to distinguish biotic from abiotic methane based largely on temperature of formation, but also based on reaction pathways. Even before delivery of our unique mass spectrometer built for this purpose (Figure 13.1), methane experts (in particular Barbara Sherwood Lollar, University of Toronto) warned of the naivety of assuming that methane molecules would have simple, single-stage histories, and emphasized in particular the important role of mixing, the breadth of abiotic organic reactions over the range of temperatures that might be involved, and the complexity of microbial methanogenesis pathways and associated kinetic fractionation effects. In response, we developed predictions for these various phenomena in preparation for the new data to come.

Figure 13.1 Mass spectrometer used to separate the two rare mass-18 isotopologues of CH4 gas molecules. The instrument – the Panorama – is housed at UCLA and is the first of its kind (Young et al. 2016).

The work described herein is the realization of those original goals to use two mass-18 isotopologues of CH4 to disambiguate the multiple possible sources of methane gases using a process-oriented approach. Just as carbonate isotope clumping can break the degeneracy between seawater δ18O and temperature of formation, the use of two methane mass-18 isotopologues should remove the ambiguities arising from variations in the 13C∕12C and D/H ratios of the carbon and hydrogen sources of methane. We seek to eliminate, or at least mitigate, the uncertainties surrounding the use of δ13C and δD as the primary arbiters for the origin of methane gas. Even when combined with other important tracers of gas provenance like C1/C2+ (the ratio of CH4 to C2H6 + C3H8, etc.), ambiguities regarding the provenance of methane often remain when relying on bulk isotope ratios. Rules of thumb have been constructed based on years of observations. One example is that a decrease in 13C/12C (δ13C) with increasing carbon number for the alkanes can be evidence for abiotic formation. But these rules are, for the most part, empiricisms and fraught with exceptions. The goal of the studies described here is to make use of the relative concentrations of 13CH3D and 12CH2D2 together in methane gas to remove the uncertainties plaguing other tracers while avoiding adding just another layer of complexity. This means using what these isotopologues are telling us in order to gain a fresh vantage point for our views on the origin of methane and to find out if we might be led astray by some of the earlier criteria for provenance.

Perhaps the most succinct way to summarize this perspective is that the isotopic bond ordering, or clumping, traces process, while bulk isotope ratios trace both process and source isotopic compositions. By following the isotopic bond ordering, we are isolating process from variations in source material.

### 13.2 Temperature

The concept of using “clumping” of heavy isotopes in a molecule as a thermometer is understood by referencing the null condition of the purely stochastic distribution of isotopes among the molecules of interest. In the case of methane, one is concerned with the fraction of carbon that is composed of the heavy isotope, X(13C) = 13C/(13C + 12C), and the fraction of the hydrogen isotopes that is composed of deuterium, X(D) = D/(D + H). In the case of purely random distributions of isotopes among molecules, the products of fractional isotope abundances yield the joint probabilities, or predicted concentrations, for the isotopologues. For example, X(12CH3D) = X(12C)(X(H))3X(D), where the exponent accounts for the simultaneous occurrence of H at three positions. Isotopologue abundances are not generally random, however. The temperature-dependent exchange of isotopes between isotopologues occurs by reactions such as

13CH4 + 12CH3D ⇄ 12CH4 + 13CH3D.
${}^{13}C{H}_{4}+{}^{12}C{H}_{3}D\phantom{\rule{0ex}{0ex}}⇄\phantom{\rule{0ex}{0ex}}{}^{12}C{H}_{4}+{}^{13}C{H}_{3}D.$
(13.1)

The equilibrium constant for this reaction is

${k}_{\mathrm{Eq},{}^{13}CD}=\frac{\left({}^{13}C{H}_{3}D\right)\left({}^{12}C{H}_{4}\right)}{\phantom{\rule{0ex}{0ex}}\left({}^{13}C{H}_{4}\right)\left({}^{12}C{H}_{3}D\right)},$(13.2)

where the square brackets denote concentrations that can be equated with the fractional abundances of the isotopologues by number. At high temperatures (≥1000 K), the distributions of isotopologues are effectively random (stochastic) and substitution of the fractional abundances into the equilibrium constant in (13.2) yields (e.g. Richet et al. 1977):

${k}_{\mathrm{Eq},{}^{13}CD}=\frac{\left({}^{13}C{H}_{3}D\right)\left({}^{12}C{H}_{4}\right)}{\left({}^{13}C{H}_{4}\right)\left({}^{12}C{H}_{3}D\right)}=\frac{4X\left({}^{13}C\right)\phantom{\rule{0ex}{0ex}}{\left(X\left(H\right)\right)}^{3}\phantom{\rule{0ex}{0ex}}X\left(D\right)\phantom{\rule{0ex}{0ex}}X\left({}^{12}C\right)\phantom{\rule{0ex}{0ex}}{\left(X\left(H\right)\right)}^{4}}{4X\left({}^{12}C\right)\phantom{\rule{0ex}{0ex}}{\left(X\left(H\right)\right)}^{3}\phantom{\rule{0ex}{0ex}}X\left(D\right)\phantom{\rule{0ex}{0ex}}X\left({}^{13}C\right)\phantom{\rule{0ex}{0ex}}{\left(X\left(H\right)\right)}^{4}}=1.$(13.3)

Equation (13.3) shows that an equilibrium constant of unity in this case corresponds to a purely random distribution of isotopes among the molecules. At lower temperatures, the stabilizing effects of two heavy isotopes bonded together take hold and the equilibrium constant in (13.2) gets progressively larger as temperature decreases. This enhancement in rare multiply substituted isotopologues, or clumping, can be expressed in delta notation and in per mil units as

${\Delta }_{{}^{13}C{H}_{3}D}={10}^{3}\left(\frac{X\left({}^{13}C{H}_{3}D\right)}{\phantom{\rule{0ex}{0ex}}X{\left({}^{13}C{H}_{3}D\right)}_{\text{Stochastic}}}-1\right).$(13.4)

Similarly, internal isotope exchange leading to doubly deuterated methane can be described by the reaction

212CH3D ⇄ 12CH2D2 + 12CH4,
$2{}^{12}C{H}_{3}D\phantom{\rule{0ex}{0ex}}⇄\phantom{\rule{0ex}{0ex}}{}^{12}C{H}_{2}{D}_{2}+{}^{12}C{H}_{4},$
(13.5)

with the equilibrium constant

${k}_{\mathrm{Eq},{\mathrm{CH}}_{2}{D}_{2}}=\frac{\left({}^{12}C{H}_{2}{D}_{2}\right)\left({}^{12}C{H}_{4}\right)}{{\left({}^{12}C{H}_{3}D\right)}^{2}}.$(13.6)

The stochastic value for the equilibrium constant for reaction (13.6) is

${k}_{\mathrm{Eq},{}^{12}C{H}_{2}{D}_{2}}=\frac{\left({}^{12}C{H}_{2}{D}_{2}\right)\left({}^{12}C{H}_{4}\right)}{{\left({}^{12}C{H}_{3}D\right)}^{2}}=\frac{6\phantom{\rule{0ex}{0ex}}X\left({}^{12}C\right)\phantom{\rule{0ex}{0ex}}{\left(X\left(H\right)\right)}^{2}\phantom{\rule{0ex}{0ex}}X{\left(D\right)}^{2}\phantom{\rule{0ex}{0ex}}X\left({}^{12}C\right)\phantom{\rule{0ex}{0ex}}{\left(X\left(H\right)\right)}^{4}}{{\left(4\phantom{\rule{0ex}{0ex}}X\left({}^{12}C\right){\left(X\left(H\right)\right)}^{3}\phantom{\rule{0ex}{0ex}}X\left(D\right)\right)}^{2}}=\frac{3}{8},$(13.7)

such that a stochastic distribution of isotopes leads to an equilibrium constant of 3/8. Per mil departures from this stochastic ratio are quantified using

${\Delta }_{{}^{12}C{H}_{2}{D}_{2}}={10}^{3}\left(\frac{X\left({}^{12}C{H}_{2}{D}_{2}\right)}{\phantom{\rule{0ex}{0ex}}X{\left({}^{12}C{H}_{2}{D}_{2}\right)}_{\text{Stochastic}}}-1\right).$(13.8)

The two parameters Δ12CH2D2 and Δ13CH3D are independent intramolecular thermometers where thermodynamic equilibrium applies. The relationships between temperature and both Δ12CH2D2 and Δ13CH3D are calculable (e.g. Ma et al. 2008; Webb and Miller 2014; Liu and Liu 2016) and loci of thermodynamic equilibrium in plots of Δ12CH2D2 versus Δ13CH3D serve as useful references in the plots to follow (Figure 13.2).

Figure 13.2 Plot of thermodynamic equilibrium among methane isotopologues as a function of temperature in Δ12CH2D2 versus Δ13CH3D space

(after Young et al. 2017).

### 13.3 Criteria for Intra-CH4 Thermodynamic Equilibrium

Criteria for establishing whether or not methane molecules are in isotopologue equilibrium with one another is a first-order requisite for making use of these new data. A datum for a sample of methane gas that plots on the curve in Figure 13.2 would be regarded as representing thermodynamic equilibrium at the indicated temperature by virtue of the concordant temperatures recorded by both clumped species. However, in the absence of data for both Δ13CH3D and Δ12CH2D2, Figure 13.2 cannot be used to establish equilibrium or nonequilibrium.

While the large-geometry mass spectrometer that permits use of Figure 13.2 was being built for UCLA, two other groups published several papers based on application of the single mass-18 isotopologue 13CH3D, or unresolved 13CH3D and 12CH2D2, where the two species are lumped together in one measurement (Stolper et al. 2014, 2015; Wang et al. 2016). Their conclusions were reviewed by Douglas et al. (2017), who describe the “reversibility of methanogensis” hypothesis that was used in several of these papers to explain why temperatures derived using the relative abundances of 13CH3D are not always reasonable (Wang et al. 2015). However, our studies of Δ13CH3D and Δ12CH2D2 suggest that the rate of methanogenesis is not the primary factor that controls isotope clumping in microbialgenic methane.

The reversibility of the methanogenesis concept is based on earlier work relating D/H and 13C/12C in microbial methanogenesis to the chemical potential gradient between reactants H2, CO2, or methyl groups and the product CH4 (Valentine et al. 2004; Penning et al. 2005). This hypothesis posits that the degree of isotopic equilibrium among CH4 molecules will depend on the rate of methanogenesis (see below). In these studies, the primary tool for establishing whether or not Δ13CH3D (or the similar parameter Δ18, which is used where the two mass-18 species are unresolved, since normally 13CH3D ≫ 12CH2D2 in abundance) represents equilibrium is whether or not the observed D/H partitioning between water and methane, αD/H (H2O–CH4) (the fractionation factor αD/H between water and methane is defined as D/H of water divided by D/H of methane), is consistent with the temperature deduced from the single mass-18 clumping temperature. In this scenario, if Δ13CH3D is out of equilibrium but progresses toward equilibrium, there will be a correlation between the Δ13CH3D (Δ18) and δD of the methane (unless, by coincidence, the methane is already in equilibrium with water). Of course, the obvious disadvantage of this approach as the primary criterion for intra-methane equilibrium is that one has to have the δD of water coexisting with the methane of interest, and there are circumstances where water samples are either impractical to obtain or nonexistent.

In addition to being inconvenient, the water δD criterion for methane isotopologue equilibrium is not universal, as illustrated using Δ13CH3D and Δ12CH2D2 data from the Kidd Creek Mine, Timmins, Ontario, Canada (Young et al. 2017). Figure 13.3 shows Δ13CH3D versus δD and versus Δ12CH2D2 for CH4 from Kidd Creek. Because the δD values of the waters in the mine are generally within a few per mil of –30‰ standard mean ocean water (SMOW), the δD of CH4 is a measure of αD/H (H2O–CH4). One sees that while Δ12CH2D2 shows a clear progression toward equilibrium, δD does not. At this location, δD is not especially useful as an indicator of equilibrium, but Δ12CH2D2 is. This confirms that heterogeneous (water versus gaseous CH4) disequilibrium in D/H can persist even as homogeneous equilibrium (exchange among gaseous CH4 molecules) is approached.

Figure 13.3 Kidd Creek Mine CH4 data showing the Δ13CH3D versus two different potential measures of the degree of intra-CH4 isotopic equilibrium, δD, and Δ12CH2D2. Curves show equilibrium (at fixed δD water = –32‰) from 0ºC to 350ºC. The stars represent equilibrium at 30ºC. The data show a time evolution toward equilibrium in Δ12CH2D2

(Young et al. 2017).

### 13.4Kinetics

An understanding of the effects of kinetics on methane isotope clumping is also crucial for interpreting these new data. The idea that the rate of methanogensis controls the degree of departure from thermodynamic equilibrium among methane isotopologues has been put forward several times in the literature, perhaps in most complete form in the supplement to Wang et al. (2015) in which the authors invoke “Michaelis–Menten” kinetics for the H addition steps to build methane. This kinetic formalism is commonly used in the biochemistry of enzymes. The equations represent simple transition state-like kinetics where the transition state is replaced by the enzyme–substrate complex:

$E+S\phantom{\rule{0ex}{0ex}}\underset{{k}_{r}}{\overset{{k}_{f}}{⇄}}\phantom{\rule{0ex}{0ex}}\mathrm{ES}\phantom{\rule{0ex}{0ex}}\stackrel{{k}_{\mathrm{cat}}}{\to }\phantom{\rule{0ex}{0ex}}E+P,$(13.9)

where E is the enzyme, S is the substrate, ES is the substrate bound to the catalyzing enzyme (the enzyme–substrate complex), and P is the product. The forward and reverse rate constants for binding are shown in (13.9), and the subscript “cat” signifies the catalyzed rate constant. The binding of the substrate to the enzyme by a reversible (equilibrium) process is the foundation of Michaelis–Menten kinetics, just as it is foundational for transition state theory. For this equilibrium, the forward and reverse rates are by definition equal:

kf[E][S] = kr[ES].
${k}_{f}\left(E\right)\left(S\right)={k}_{r}\left(\mathrm{ES}\right).$
(13.10)

Mass balance requires [E] = [E]0 – [ES], where the “0” subscript signifies the initial concentration. After some manipulation, (13.10) leads to the simple first-order rate equation for product P:

$\frac{d\phantom{\rule{0ex}{0ex}}\left(P\right)}{\mathrm{dt}}={k}_{\mathrm{cat}}\frac{{\left(E\right)}_{o}\left(S\right)}{\left(\frac{{k}_{r}}{{k}_{f}}\right)+\left(S\right)}.$(13.11)

Comparing the above to the often-cited Michaelis–Menten equation for an enzyme-catalyzed reaction:

$\frac{d\phantom{\rule{0ex}{0ex}}\left(P\right)}{\mathrm{dt}}=\frac{{V}_{\mathrm{max}}\left(S\right)}{{k}_{m}+\left(S\right)},$(13.12)

where km is the “affinity” for the enzyme plus substrate, one sees by inspection that (13.11) is equivalent to (13.12), where the “affinity” for the bound substrate is here equivalent to kr/kf and the maximum rate used in the Michaelis–Menten formulation, Vmax, is kcat[E]0. Notice that when the substrate is plentiful such that [S] ≫ kr/kf, the rate of product production is maximized since d[P]/dtVm = kcat[E]0. Conversely, where the concentration of the substrate is very small, leading to starvation and thus [S] ≪ kr/kf, we have d[P]/dtkcat[E]0[S]/(kr/kf), which is the maximum rate multiplied by [S]kf/kr, and so smaller than the maximum rate of reaction. What is more, in this case, both the forward and reverse reactions to form the ES complex are involved, leading to the suggestion that reversibility, or equilibrium, controls the attachment of the substrate to the enzyme.

While (13.11) and (13.12) are handy for describing how the rate of product formation depends on three postulated rate constants, they offer little or no fundamental insights into the effects on isotope clumping. For example, we do not know a priori which reaction in the sequence of steps leading to CH4 formation is properly described by (13.9). Importantly, the kinetic isotope effects (KIEs) and/or equilibrium isotope effects (EIEs) for each of the steps in (13.9) can be adjusted to fit the data, but this relegates (13.11) and (13.12) to little more than a framework for applying fit parameters. Measurements of both Δ13CH3D and Δ12CH2D2 suggest that the “reversibility of methanogenesis” hypothesis is not the best explanation for the clumping of isotopes into methane of microbial origin.

Here, we consider an alternative approach to explaining the effects of microbial methanogenesis on methane mass-18 isotopologue abundances based on the large degree of disequilibrium exhibited by the low Δ12CH2D2 values characteristic of microbialgenic gas in combination with highly variable Δ13CH3D values. For this purpose, we take the reaction scheme used by Young et al. (2017) as an analogue for hydrogenotrophic methanogenesis and the steps leading to the net reaction CO2 + 4H2 → CH4 + 2H2O. Young et al. (2017) used the reaction scheme for the Fischer–Tropsch synthesis of methane on a cobalt (Co) catalyst suggested by Qi et al. (2014). Methanation of CO2 can occur by conversion first to CO, with the subsequent steps being the same as those for direct methanation of CO (Wang et al. 2011). The kinetic model presented here is therefore relevant to methane production from CO2 as well. We added isotope exchange between methane molecules on the surface, desorption and adsorption of CH4 gas, and attack of CH4 by OH to the elementary steps leading to methane formation. The set of reactions can be represented by these basic reactions and their isotopically substituted equivalents:

$\begin{array}{c}{\mathrm{CO}}_{g}\to {\mathrm{CO}}^{\ast }\\ {H}_{2\phantom{\rule{0ex}{0ex}}g}\to 2{H}^{\ast }\\ {\mathrm{CO}}^{\ast }+{H}^{\ast }\to {\mathrm{HCO}}^{\ast }\\ {\mathrm{HCO}}^{\ast }+{H}^{\ast }\to {\text{HCOH}}^{\ast }\\ {\text{HCOH}}^{\ast }\to {\mathrm{CH}}^{\ast }+{\mathrm{OH}}^{\ast }\\ {\mathrm{CH}}^{\ast }+{H}^{\ast }\to {{\mathrm{CH}}_{2}}^{\ast }\\ {{\mathrm{CH}}_{2}}^{\ast }+{H}^{\ast }\to {{\mathrm{CH}}_{3}}^{\ast }\\ {{\mathrm{CH}}_{3}}^{\ast }+{H}^{\ast }\to {{\mathrm{CH}}_{4}}^{\ast }\\ {\mathrm{OH}}^{\ast }+{H}^{\ast }\to {H}_{2}{O}_{g}\\ {{\mathrm{CH}}_{4}}^{\ast }+{\mathrm{OH}}^{\ast }\to {H}_{2}{O}^{\ast }+{{\mathrm{CH}}_{3}}^{\ast }\\ {{\mathrm{CH}}_{4}}^{\ast }⇄{{\mathrm{CH}}_{4}}^{\ast }\phantom{\rule{0ex}{0ex}}\left(\text{isotope exchange}\right)\\ {{\mathrm{CH}}_{4}}^{\ast }\to {\mathrm{CH}}_{4g}\\ {\mathrm{CH}}_{4g}\to {{\mathrm{CH}}_{4}}^{\ast },\end{array}$(13.13)

where an asterisk signifies a surface-adsorbed species and a subscript “g” refers to a gas species. With all isotopologues and isotopomers, the model consists of 124 species and 796 reactions. The rate constants for the reactions are of the form

${k}_{f}={Q}_{\mathrm{Tun}}\frac{{k}_{b}T}{h}\frac{{q}^{+}}{\prod _{r}{q}_{r}}\left(\frac{-\mathrm{Ea}}{{k}_{b}T}\right),$(13.14)

where kb is the Boltzmann constant, h is the Planck constant, Ea is the activation energy, qr are the partition functions for reactant species r, q+ is the partition function for the transition state, and QTun is a correction for quantum tunneling. The 124 ordinary differential equations comprising the model are solved numerically using the Lawrence Livermore ordinary differential equation solver (DLSODE). Activation energies for the methane formation reactions were taken from Qi et al. (2014). Values for Ea for the reaction CH4 + OH were taken from Haghnegahdar et al. (2015). The tunneling correction is from Bell (1959, 1980).

Young et al. (2017) used forward rate constants throughout the reaction network to characterize the effects of the kinetics alone on product methane isotopologues. We concluded in that work that the very negative Δ12CH2D2 values were due either to the influence of quantum tunneling or to the combinatorial effect of accessing multiple sources of hydrogen produced by very different fractionation factors involving D/H during the assembly of methane. We favored tunneling in particular for our measurements of products from the Sabatier reaction in the laboratory (CO2 + 4H2 → CH4 + 2H2O) mainly because invoking a slight difference in tunneling for 13C–H bonds versus 12C–H bonds could account for the combination of very positive Δ13CH3D values along with the negative Δ12CH2D2 values (note: an error in that paper has the ratio of tunneling length scales aD/aH = 1.005, when in fact it is the ratio of a13C–H,D/a12C–H,D that was fit to 1.005 to explain the high Δ13CH3D values in the Sabatier reaction; see below). We noted that a combinatorial effect (e.g. Yeung et al. 2015; Rockmann et al. 2016; Yeung 2016) may be important for microbial methanogenesis, but we also expressed concern that the required differences in D/H between pools of hydrogen would need to be very large.

However, Cao et al. (2019) have argued recently that adding certain equilibrium steps into our reaction network can indeed produce the requisite large differences in D/H among pools of hydrogen that can reproduce the very low Δ12CH2D2 values observed in microbialgenic methane gases. Here, we take their suggestion and investigate the effects of reversibility on the clumping in the reaction network. For these calculations, the KIE and EIE fractionation factors for each reaction step provided by Qi et al. (2014) are used.

Why would a metal-catalyzed reaction scheme have anything to do with the microbial production of CH4? What advantage is there in trying to use this reaction scheme to address the microbialgenesis of methane? The basic conceit is that the metal surface simulates the enzymes that afford catalyzed transfer of electrons and protons back and forth during the reaction scheme, and that it is the nature of the various C1 C–H moieties and their bond stiffness that actually control the isotope effects, regardless of the molecule to which they are bound. This may be useful insofar as at least we are using well-characterized KIE and EIE fractionation factors rather than making them up to explain the data. The logic is that despite the potential failings of the analogy, there is benefit in using a real physicochemical model to try to explain what we are seeing. This model is used in lieu of a detailed understanding of the isotope effects attending each step of the enzymatically catalyzed reactions.

With this in mind, one can observe that the steps of building CH4 molecules from CO2 + H2 by enzymes and from CO + H2 on metals are broadly similar. The reaction pathway for hydrogenotrophic addition of hydrogen to form methane as given by Lieber et al. (2014) for Methanococcus maripaludis is

$\begin{array}{c}{\mathrm{CO}}_{2}\stackrel{\left(1\right)\mathrm{Fwd}}{\to }\phantom{\rule{0ex}{0ex}}\mathrm{COH}‐\mathrm{MF}\stackrel{\left(2\right)\mathrm{Ftr}}{\to }\phantom{\rule{0ex}{0ex}}\mathrm{COH}‐{H}_{4}\mathrm{MPT}\stackrel{\left(3\right)\mathrm{Mch}}{\to }\mathrm{CH}\equiv {H}_{4}\mathrm{MPT}\stackrel{\left(4\right)\mathrm{Hmd}}{\to }\phantom{\rule{0ex}{0ex}}\\ {\mathrm{CH}}_{2}={H}_{4}\mathrm{MPT}\stackrel{\left(5\right)\mathrm{Mer}}{\to }\phantom{\rule{0ex}{0ex}}{\mathrm{CH}}_{3}-{H}_{4}\mathrm{MPT}\stackrel{\left(6\right)\mathrm{Mtr}}{\to }\phantom{\rule{0ex}{0ex}}{\mathrm{CH}}_{3}-\mathrm{CoM}\phantom{\rule{0ex}{0ex}}\stackrel{\left(7\right)\mathrm{Mcr}}{\to }\phantom{\rule{0ex}{0ex}}{\mathrm{CH}}_{4}\end{array},$(13.15)

where the facilitating enzymes are shown above the arrows (e.g. Ftr = formyltransferase; numbers are for reference only) and the C1 carriers are shown as the molecule acronyms (e.g. H4MPT = tetrahydromethanopterin). As described by Shima et al. (2002), these steps comprise a series of C1 molecules that act as terminal electron acceptors (oxidants that themselves are reduced) where carbon is progressively reduced, with each transfer of C1 facilitated by the indicated enzyme. For example, COH is transferred from the methanofuran molecule to the next C1 carrier H4MPT by the enzyme Ftr. The subsequent conveyance of COH to CH (step (3)) is facilitated by methenyl-H4MPT cyclohydrolase (Mch). The last step in which the CH3 in methyl-coenzyme M (CH3–CoM) is reduced to methane is facilitated by the methyl-coenzyme M reductase (Mcr); Mcr is the focus of a lot of attention because it is common to methanogens and anaerobic methanotrophs and is involved in that last step that is common to both. Now compare this with the reaction network in (13.13) written in similar fashion:

$\begin{array}{c}\mathrm{CO}\stackrel{\left(1\right)}{\to }\phantom{\rule{0ex}{0ex}}\mathrm{CO}\ast \stackrel{\left(2\right)}{\to }\phantom{\rule{0ex}{0ex}}\mathrm{HCO}\ast \stackrel{\left(3\right)}{\to }\text{HCOH}\ast \stackrel{\left(4\right)}{\to }\phantom{\rule{0ex}{0ex}}\\ \mathrm{CH}\ast \stackrel{\left(5\right)}{\to }\phantom{\rule{0ex}{0ex}}{\mathrm{CH}}_{2}\ast \phantom{\rule{0ex}{0ex}}\stackrel{\left(6\right)}{\to }\phantom{\rule{0ex}{0ex}}{\mathrm{CH}}_{3}\ast \phantom{\rule{0ex}{0ex}}\stackrel{\left(7\right)}{\to }\phantom{\rule{0ex}{0ex}}{\mathrm{CH}}_{4}\ast \end{array}.$(13.16)

The reactions in (13.15) and in (13.16) both utilize H2 as the main source of electrons for reduction. In both reaction sequences, C1 passes from oxidized carbon through an alcohol/formyl molecule to a formaldehyde-like molecule followed by progressive reduction by proton addition.

The effects of kinetics versus equilibrium for each of the steps that produce methane are investigated by using the reactions in (13.16) as analogues for the reactions in (13.15) and examining the consequences of imposing various combinations of equilibrium versus kinetics for each step. Borrowing terminology suggested by Cao and Bao, we can refer to this using the vector [0, 0, 0, 0, 0, 0, 0] to signify where all seven steps are kinetic, or [1, 1, 1, 1, 1, 1, 1] to indicate where all seven steps are completely reversible. Intermediate circumstances are represented accordingly; for example, where the first three steps are equilibrium, we have [1, 1, 1, 0, 0, 0, 0]. For comparison, note that Stolper et al. (2015) assume that the rate-limiting step, the only kinetic step, is step (7) in (13.15), which is mediated by Mcr, corresponding to [1, 1, 1, 1, 1, 1, 0]. This seems to be a common assumption.

The results of this exercise are summarized in Figure 13.4. The results for different assumptions about reversibility based on this reaction scheme show clearly that the very low Δ12CH2D2 values and moderately low Δ13CH3D values of the gases produced by microbial methanogenesis are well explained by scenarios in which equilibrium for the first two or three steps in the reaction sequence in (13.16) obtains, with subsequent steps being kinetic. Indeed, Qi et al. (2014) suggested that step (3) in (13.16) is the likely rate-limiting step, with steps (1) and (2) being reversible. We note that the EIEs (defined as the reaction rate constant for hydrogen only divided by the rate constant for deuterium only) have typical values of order 0.6 compared with the KIEs defined similarly for the same reactions, which usually have values >1. The result is the production of extreme D/H ratios for the various pools of hydrogen atoms along the reaction sequence. For example, in the successful model [1, 1, 0, 0, 0, 0, 0], δD relative to the reactant hydrogen gas (0‰ in this case) is +125.6‰ for CH, 0.4‰ for CH2, and −104.9‰ for CH3 in this reaction scheme. Quantum tunneling of protium (H) and deuterium (D) may also play a role in the enzymatically catalyzed reactions, but we find that we can use a more conservative tunneling distance to fit the data than was used previously for the Sabatier reaction (see the caption to Figure 13.4). Notice that the results with all irreversible steps cannot explain the microbial methanogenesis data (Figure 13.4). Also, the [1, 1, 1, 1, 1, 1, 0] scheme in which the final step is rate limiting gives nonsensical results, with Δ12CH2D2 and Δ13CH3D values of +138.4 and +11.3, showing that this scheme, analogous to that used by Stolper et al. (2015), is unlikely to be correct.

Figure 13.4 Summary of modeling reactions in (13.13) and (13.16). The stars represent model results for different combinations of equilibrium (signified by a 1 in the square brackets) or kinetic (signified by a 0 in the square brackets) steps during methane formation for the seven steps numbered in (13.16), as described in the text. Black dots denote equilibrium in +50°C intervals starting with 0ºC at the upper right. Circles show natural (open) and laboratory culture (crossed) data for microbial methanogenesis. The H tunneling distance used in the model that includes tunneling is 3 × 10–10 m with no carbon isotope effect. For the [1, 1, 0, 0, 0, 0] calculation, only steps (1) and (2) include isotopic equilibrium.

The reaction schemes resembling the microbial data in Figure 13.4 also give realistic CH4 δD and δ13C bulk values for the product methane. For example, for the [1, 1, 0, 0, 0, 0, 0] scheme, we obtain CH4 δD = −161.2‰ and δ13C = –44.1‰ relative to the hydrogen and carbon substrates.

Gruen et al. (2018) confirm that all four H atoms comprising CH4 from hydrogenotrophic methanogenesis are from water, and yet we see profound disequilibrium in ΔCH2D2. While this simple model explains the first-order Δ12CH2D2 and Δ13CH3D characteristics of microbial methanogenesis, there is more to the kinetic story with respect to methane formation. Also, it should be pointed out that the highest Δ12CH2D2 and Δ13CH3D values near the equilibrium curve in Figure 13.4 are boreal lake analyses that are evidently the result of methanotrophy (see below) rather than methanogenesis.

### 13.5 The Microbial Array

The positively sloping array in Δ12CH2D2 versus Δ13CH3D space defined by the in vitro and in vivo microbial methanogenesis data (Figure 13.4) cannot be explained easily by simply varying the degree of reversibility for the reaction steps. Quantum tunneling involving both D/H and 13C/12C seems to be required. The involvement of carbon isotopes may at first seem unlikely. However, Miller et al. (1981) point out that it is incorrect to think of hydrogen tunneling in isolation. It is the reacting system as a whole that experiences tunneling, and if carbon atoms are involved in the reaction coordinate, the isotopic composition of the carbon can have an effect on tunneling. Using the same model reaction sequence described above, I have explored the interaction between various reversibility scenarios and the effects of tunneling. Generalized vectors showing the effects of the various parameters based on this exploration of parameter space are shown in Figure 13.5. Disparities in reversibility, and thus large differences in fractionation factors at each step, cause decreases in Δ12CH2D2 at constant Δ13CH3D. This occurs with only moderately low δD for the product methane compared with the more extreme values caused by tunneling. Shorter hydrogen/deuterium tunneling distances increase the effects of quantum tunneling. Where the tunneling distance aH is greater for reactions involving 13C (as expected) than for 12C, the slope of the enhancement in tunneling in Δ12CH2D2 versus Δ13CH3D space is negative (Figure 13.5).

Figure 13.5 Vectors showing the effects of the key kinetic parameters controlling clumping during CH4 formation.

The effect of differences in tunneling distances involving 13C versus 12C can be visualized using a Marcus theory representation of tunneling shown in Figure 13.6; the lower energy of vibration for the 13C–H bond relative to the C–H bond, for example, will necessitate a greater tunneling distance. The effect of a13C–H/a12C–H > 1 on Δ13CH3D can be understood as follows: the longer tunneling distance for the 13C case gives less advantage to H relative to D in bonding with 13C relative to the 12C case, all else equal, and so 13CH3D is preferred relative to 13CH4. Thus, Δ13CH3D goes up.

Figure 13.6 Schematic illustrating the relationship between carbon isotope substitution and tunneling. The ordinate is potential energy and the abscissa is the reaction coordinate ζ representing the interatomic motions leading to the reaction. The parabolas represent the potential energy of reactants and products in terms of interatomic distances along the reaction coordinate. The gray arrows shows the “tunneling” of hydrogen through the energy barrier associated with the transition from reactants to products. 2aH is the tunneling distance for a hydrogen bonded to either 13C or 12C (see text). λ refers to the “reorganization” energy as defined in Marcus theory that depends on the force constant f and the separation between the two energy minima Δξ.

The principles described in Figures 13.5 and 13.6 can be used to describe the “kinetic array” that lies well below the equilibrium curve in Figure 13.4. There is a hint that these principles may have applications beyond just microbial methanogenesis. The methane gases from the deeper levels of the Kidd Creek Mine study fall on the high Δ12CH2D2 and Δ13CH3D end of the microbial array (Young et al. 2017). These gases are confidently regarded as abiotic with no connection to microbial methanogenesis, as far as we know (Sherwood Lollar et al. 2007). Therefore, their continuity with the microbialgenic gases implies a fundamental kinetic link.

The high end of the kinetic array occupied by some of the microbial data and the Kidd Creek data can be explained by a larger role for both kinetics and tunneling. Removing the reversibility in all but step (1) and adjusting aH and a13C–H/a12C–H to 5.2 × 10–11 m and 1.016, respectively, yields a fit to the Kidd Creek data and the high end of the microbial kinetic array (black star in Figure 13.7). The 13C/12C tunneling effect of 1.016 is squarely in the range found by Miller et al. (1981). The δD obtained in this model is −470.7‰ relative to the source of hydrogen, similar to the low values for the Kidd Creek methane.

Figure 13.7 Comparison between the “kinetic array” in Δ12CH2D2 versus Δ13CH3D space and several relevant reaction rate models based on the reaction scheme shown in (13.13) and (13.16). The array may be defined by a “mixing” of the processes, similar to those depicted by the blue and black stars. See text for discussion. KC = Kidd Creek.

Taken together, the two results for the two ends of the “kinetic array” based on the analogue model for methane formation suggest that the positively sloping array in Δ12CH2D2 versus Δ13CH3D space can be explained by a gradation from reversibility in some early key steps and a more limited role for tunneling on the lower end toward less reversibility and a larger role for tunneling on the higher end, including more participation of carbon in the reaction coordinate. In the case of the Kidd Creek data, it may make sense that catalysis of methane formation by metal surfaces would permit more of a role for carbon motions than in the case of the C1 host molecules facilitating microbial methanogenesis.

### 13.6Is This New Information Helping?

Is this new information about processes orthogonal to differences in isotopic reservoirs actually helping us determine the provenance of methane gases? We examine this question with the aid of Figure 13.8. Here, we plot ~170 natural CH4 samples analyzed and vetted in our laboratory at UCLA to date as well as the culture experiments and several high-temperature Fischer–Tropsch experiments in Δ12CH2D2 versus Δ13CH3D space on the left and in the traditional Schoell plot (δD versus δ13C) on the right. Based on the clumping diagram, three groups of samples are selected as examples of “process end members” as a sort of test of the efficacy of considering process as a means of deducing provenance. Two of the three groups are easily defined and substantiated by laboratory experiments. The first of these are the natural samples that represent purely microbial methanogenesis based on their similarity to the combination of Δ12CH2D2 and Δ13CH3D values obtained in our in vitro culture experiments (in most cases these are from boreal wetlands). The second group comprises gases produced at high temperatures (meaning >100°C) that lie at or near to isotopologue thermodynamic equilibrium. While many of these gases are thermogenic, we are purposefully avoiding the traditional classification terminology at this stage because these terms can connote both process and the sources of carbon and hydrogen (e.g. Sherwood Lollar et al. 2006; Etiope and Sherwood Lollar 2013). The third group represents “abiotic” methane. Here, we have immediately deviated from the strategy outlined in the previous sentence and introduced a measure of circularity into the classification by convolving it with source material. This is justified because of the overwhelming geological and geochemical evidence suggesting that the Kidd Creek Mine gases owe their origins to abiotic processes deep in the crust.

Figure 13.8 Comparison of data categorized by process in Δ12CH2D2 versus Δ13CH3D space (left panel) to their positions in the bulk isotope “Schoell” plot (right panel). Details are discussed in the text. Fields on the left are from the mass-18 isotopologue work, while the fields in bulk isotope space are from Etiope and Schoell (2014) and Etiope (2017). Gray symbols are data not categorized explicitly in this plot. The data labeled “microbial methane” are dominantly, although not entirely, from boreal lakes. PDB = Pee Dee Belemnite standard.

The three end-member processes are well separated on the left-hand panel of Figure 13.8. Those same data points, with the same color coding, are plotted on the Schoell plot on the right in Figure 13.8. I have added two major methane source fields, biotic and abiotic, as inspired by the fields shown in Etiope and Schoell (2014) and Etiope (2017). The microbial and thermogenic process subfields of the biotic field are also shown. Overall, the microbial gases as defined by the isotopic bond ordering plot in the microbial subfield for biotic gases in the Schoell plot. The high-temperature equilibrium gases tend to plot in the thermogenic subfield of the biotic field in the Schoell plot, and the Kidd Creek abiotic gases are at the lower edges of the abiotic field in the Schoell plot. Have we learned anything?

The answer appears to be yes because the isotopologue fields separate process from source material unambiguously. For example, the vertical (δD) positions of boreal wetland microbial methanogenesis data in the Schoell plot are lower than those for many “typical” microbial gases because the water δD values for these arctic environs are approximately −200‰ (e.g. Douglas et al. 2016 and references therein), rather lower than for waters from lower latitudes. The [1, 1, 0 … 0] kinetic model (blue star in Figure 13.7) predicts a downward shift in δD of ~160‰ relative to the source hydrogen, yielding bulk δD values of about −360‰, consistent with the boreal wetland data in Figure 13.8. The breadth of the microbial field in the Schoell plot is therefore dictated in part by the range of source hydrogen and carbon samples independent of process. In isotopic bond ordering space, this effect is normalized out.

The importance of normalizing away reactant bulk isotopic compositions is best exemplified by the fact that there are instances where data falling squarely in the microbial field in Δ13CH3D–Δ12CH2D2 space are not in the biotic field on the Schoell plot. The reasons for this can be traced to unexpected source materials (as enumerated in publications in preparation). Similarly, gases equilibrated at relatively high temperatures as evidenced in the Δ13CH3D–Δ12CH2D2 plot span the biotic and abiotic fields in the Schoell plot.

Most of the other data points that appear in Figure 13.8 (undifferentiated data are shown in gray) that do not fall within one of the fields in Δ13CH3D–Δ12CH2D2 space are the result of mixing, fractionation by molecular mass (e.g. Giunta et al. 2018), or possibly processes that are still under study (see Section 13.7).

As an illustrative example of both the high information content and the complexity afforded by CH4 isotopologue data, we consider here a methane sample from a seafloor vent from the North Atlantic. It is generally thought that aqueous alteration of ultramafic rocks can produce abiotic methane as a by-product of serpentinization that releases hydrogen gas by a reaction resembling 3Fe2SiO4 + 2H2O → 2Fe3O4 + 3SiO2 + 2H2(g). However, the process is less clear than once thought due to severe kinetic limitations (McCollom 2016). The temperatures or kinetic pathways of methane formation in serpentinizing systems would be valuable arbiters for competing hypotheses for CH4 formation in these settings. One well-studied site for methane production associated with active serpentinization is the Atlantis Massif that lies east of the intersection of the Mid-Atlantic Ridge and the Atlantis transform fault on the North Atlantic Ocean seafloor. The Lost City hydrothermal field from the southern Atlantis Massif has been of particular interest as the archetypical example of an off-axis seafloor hydrothermal alteration zone (Kelley et al. 2005). Fluids are venting at temperatures of ~30–90°C and both archaeal methanogens and methanotrophs are evidenced in the system (Kelley et al. 2005). Earlier studies indicated that serpentinization at the site was seawater dominated at temperatures of ~150–250°C (Allen and Seyfried Jr. 2004; Boschi et al. 2008). Proskurowski et al. (2006) used apparent D/H partitioning between CH4, H2, and H2O to suggest that methane formation linked to serpentinization occurred at temperatures of ~110–150°C. Wang et al. (2018) used Δ13CH3D to estimate methane formation temperatures for several seafloor vent systems, including Lost City. Their Δ13CH3D value for the Beehive vent at Lost City is 1.84 ± 0.60‰ (95% confidence), from which they derive a methane formation temperature of 270 +104/−68°C. These authors discuss the evidence supporting this temperature, which is higher than many previous estimates.

At UCLA, we measured a methane sample from the Beehive vent at Lost City (collected in 2005 and provided by Marvin Lilly, University of Washington) and obtained Δ13CH3D = 1.95‰ ± 0.40 (2σ) and Δ12CH2D2 = 11.6‰ ± 1.2 (2σ) (Figure 13.9). This Δ13CH3D value is indistinguishable from the Wang et al. (2018) value, and thus at face value it is consistent with the high formation temperature (260 +58/–45°C in our case) obtained in the Wang et al. study. However, the Δ12CH2D2 value is 7.5‰ higher than the equilibrium value at that temperature. Since the datum is displaced from the equilibrium curve (Figure 13.9), the Δ13CH3D value of 1.95 cannot be taken a priori as a direct measure of methane bond formation temperature.

Figure 13.9 The mass-18 isotopologue data and bulk δ13C and δD values for a sample from the Beehive vent of the Lost City hydrothermal field and two possible mixing scenarios to explain the data discussed in the text. Stars show end-member compositions for the missing scenario involving microbial gas described in the text. Solid dots on the mixing curve mark proportions in 10% increments. The Lost City data are the gray circles in both plots. Error bars are 2σ. PDB = Pee Dee Belemnite standard.

The position of the Lost City sample above the equilibrium curve in Figure 13.9 suggests that the gas is a mixture. One mixture that fits the datum within error is composed of 20% microbial gas and 80% high-temperature (~350°C) abiotic gas (blue curve in Figure 13.9). The bulk isotopic compositions of these two end members and the associated mixing curve in bulk isotope ratio space are shown in the inset in Figure 13.9. The end-member δ13C and δD values required by the fit to the Δ13CH3D and Δ12CH2D2 data are reasonable, if imperfect, representatives of microbial methanogenesis and abiotic gas, respectively. In this case, the methane isotopologue data may be indicative of a microbial methanogenesis component to the Lost City gas, whereas any temperature information for the mixture end members is model dependent. While the mixing scenario described above is plausible, the Lost City datum by itself does not lead to an entirely unique interpretation. For example, a fit to the isotopologue data can also be obtained by mixing 375°C and 75°C gases with abiotic-like δ13C and δD values of −20 and −60‰ and −3.5 and −183‰, respectively (green curve in Figure 13.9).

Possible explanations for the Lost City data other than mixing are: (1) the bulk isotopic composition of the gas was altered by a process that fractionates isotopologues by molecular mass, moving the gas along a slope-1 line in Figure 13.9 and thus suggesting a low formation temperature of ~75°C by extrapolation back to the equilibrium curve; or (2) combinations of mixing and fractionation.

The Lost City example shows at once the potential power of the methane isotopologue data, but also the complexity in the interpretations that can arise, especially where the data are sparse. Of course, suites of data representing ranges in composition are more diagnostic than individual data points. Among the data shown in Figure 13.8 are examples of linear trends in Δ12CH2D2 versus Δ13CH3D space with slopes of unity that are telltale signs of fractionation by molecular mass, for example.

The ability to use rare isotopologue abundances rather than bulk isotope ratios as means of tracing the origins of methane gases could have important applications elsewhere in the solar system. Measuring Δ12CH2D2 and Δ13CH3D in methane from the atmospheres of Mars or Saturn’s moon Titan, for example, would provide powerful evidence for the formation mechanisms of Martian and Titanian methane even where the meaning of bulk 13C/12C and D/H in the methane is hampered by unknown chemical cycles on those bodies.

### 13.7The Effects of Oxidation on Δ12CH2D2 and Δ13CH3D

It appears that the combination of values for Δ12CH2D2 and Δ13CH3D provides a signature of microbialgenic methane (the microbial array) that is independent of bulk isotope ratios, and therefore independent of sources of carbon and hydrogen. The uniqueness of the low Δ13CH3D and extremely low Δ12CH2D2 values that in combination signify microbial methanogenesis depends on whether other processes might mimic this effect. We have in vitro evidence that anaerobic oxidation of methane (AOM) tends to drive isotopologue compositions of methane toward equilibrium and away from the microbial array. However, at time of writing, the effects of bacterial aerobic oxidation of methane remain unknown.

The data clustered near the equilibrium curve in the upper right of the Δ12CH2D2 versus Δ13CH3D diagram (e.g. left panel of Figure 13.8) present a vexing problem. At face value, these gases are in near isotopologue equilibrium at <50°C. Two prominent examples are a few of the boreal wetland samples and some of the deep mine samples. However, it seems unlikely that CH4 gas would equilibrate at such low temperatures absent a reaction that breaks and reforms methane molecules (as opposed to isotope exchange with water, for example, which is slow; e.g. Sessions et al. 2004). What is this process?

Young et al. (2017) postulated that the evolution of CH4 effusing from the Kidd Creek Mine fluids over several years from the disequilibrium abiotic field toward the equilibrium curve is the result of cycling between microbial methanogenesis and methanotrophy. The shifts over time are seen mainly in Δ12CH2D2, which is initially in gross disequilibrium, but not in Δ13CH3D, where the latter is in apparent equilibrium from the start (Figure 13.3). This cycling may or may not be distinct from the “cryptic methane cycle” described recently by Maltby et al. (2018) and Xiao et al. (2017); the cryptic methane cycle refers to high SO4 noncompetitive environs, while experiments suggest that methane reemitted by AOM is driven by low concentrations of the electron acceptor (e.g. SO4; see below). In addition, based on samples from Baltic Sea sediments, Ash et al. (2019) find evidence that isotopic bond-order equilibrium in these sediments is the result of AOM. Stolper et al. (2015) had hypothesized that AOM might yield thermodynamic equilibrium among methane isotopologues, suggesting that isotopic equilibrium between CH4, H2, and CO2 would ensue. The Baltic Sea results suggest that CH4 equilibration occurs without equilibrium with water. The concept that AOM has the capacity to yield methane in isotopic bond-order equilibrium builds on the earlier work of Holler et al. (2011) and Yoshinaga et al. (2014) showing that AOM can lead to 13C/12C equilibrium. AOM shares enzymatic machinery with microbial methanogenesis, leading to the notion that AOM is a reversal of methanogenesis (Scheller et al. 2010; Timmers et al. 2017). Indeed, Yan et al. (2018) report Fe-based AOM by the methanogen Methanosarcina acetivorans in which oxidation of methane occurs by the reversal of the biochemical pathway for acetoclastic and CO2 reduction to methane (see (13.17)). The influence of AOM on the isotopologue composition of CH4 in nature seems plausible; Yoshinaga et al. (2014) point out that methanogens represent a small contingent of the microbial communities in AOM-active sediments and that 14CO2 is converted to 14CH4 in sulfate–methane transition zones (Orcutt et al. 2005).

Confounding the identification of the CH4 isotopologue signature of AOM in natural settings is the contradictory evidence for its bulk isotopic effects. While Holler et al. (2009) found increases in bulk 13C/12C and D/H in residual methane left behind by AOM in the laboratory, Yoshinaga et al. (2014) emphasized that methane from sulfate-limited AOM horizons has a relatively low δ13C value, not high as expected from simple classical kinetics. They suggest that this is due to equilibration of 13C/12C in the back reaction to convert dissolved inorganic carbon (CO2 dissolved in water) to CH4.

Douglas et al. (2017) refer to “differential reversibility of methanogenesis” in the context of explaining various degrees of apparent equilibration of Δ13CH3D (or Δ18) values for methane. They suggest that hydrogenotrophic, H2-limited methanogenesis (Valentine 2011) causes reversibility. They attribute the equilibrium to rapid H/D exchange with water. This interpretation is in the context of the “reversibility of methanogensis” hypothesis rather than reversibility in AOM. These earlier suggestions notwithstanding, the Δ12CH2D2 versus Δ13CH3D data suggest that interspecies (e.g. CH4 versus H2O) equilibration is not a requisite for intraspecies (CH4 alone) equilibration.

Because of the difficulty in equilibrating isotopologues at low (near room) temperatures and because of the circumstantial evidence for AOM in several of the sites where low-temperature equilibration in methane gas is evidenced in the isotopologue data, experiments are underway attempting to characterize the Δ12CH2D2 versus Δ13CH3D effects of AOM. These include experiments by J. Gregory Ferry’s group at Penn State University that comprise exchange of the methyl moiety in methyl-coenzyme M (CH3-SCOM) and CH4 by the reaction couple

$\begin{array}{c}{\mathrm{CH}}_{4}+\phantom{\rule{0ex}{0ex}}\mathrm{CoB}‐S‐S‐\mathrm{CoM}\to \text{HSCoB}\phantom{\rule{0ex}{0ex}}+\phantom{\rule{0ex}{0ex}}{\mathrm{CH}}_{3}‐\text{SCoM}\\ {\mathrm{CH}}_{3}‐\text{SCoM}\phantom{\rule{0ex}{0ex}}+\phantom{\rule{0ex}{0ex}}\text{HSCoB}\to \mathrm{CoB}‐S‐S‐\mathrm{CoM}\phantom{\rule{0ex}{0ex}}+\phantom{\rule{0ex}{0ex}}{\mathrm{CH}}_{4},\phantom{\rule{0ex}{0ex}}\end{array}$(13.17)

where HSCoB is coenzyme B that provides the proton and CoB-S-S-CoM is the heterodisulfide of coenzymes M and B that serves as the oxidant in the reaction. Reaction (13.17) is catalyzed by the Mcr enzyme and is a reversible instance of the final step in (13.15). This experiment is particularly informative as it isolates the step that is often cited as the source of equilibration. The hypothesis is that the reversibility of this step might capture the mechanism for CH4 isotopologue equilibration by AOM. Accordingly, the expectation was that we would see reactant methane in the headspace for this cocktail of coenzymes progress toward isotopologue equilibration.

Some preliminary results from the Penn State experiments are shown in Figure 13.10. The data define two trends. At temperatures below those optimal for the Mcr used in the experiments (near room temperature), there is a trend toward equilibrium values for Δ13CH3D but little change in Δ12CH2D2. At 60°C, the optimal temperature for the thermophile-derived enzyme, there are modest but discernible increases in both Δ13CH3D and Δ12CH2D2 values (Figure 13.10). The higher-temperature experiments presumably involve greater turnover of methane by enzymatic activity and thus more exchange of hydrogen. Based on the modeling summarized in Figure 13.4, the positive shift in Δ13CH3D at relatively constant Δ12CH2D2 observed in the low-temperature experiments suggests that carbon played a larger role than hydrogen in affecting the isotopologue abundances resulting from exchange.

Figure 13.10 Summary of preliminary AOM in vitro experiments in Δ12CH2D2 versus Δ13CH3D space. Symbol shapes distinguish the two sets of experiments. The star shows the initial gas composition of the Santa Barbara slurry experiments. The Mcr experiments are migrated so that they are relative to the Santa Barbara initial gas composition. The arrows shows the two different trends that are evident in the data as described in the text. Equilibrium temperatures strictly apply only to the Santa Barbara experiments due to the migration of the Mcr data.

In a set of parallel experiments by Tina Treude’s laboratory at UCLA, methane headspace gas was consumed by SO4-limited AOM in in vitro marine sediment slurries using samples collected from active methane seeps in the Santa Barbara channel off the coast of Santa Barbara, California. Methane incubations lasted for various time intervals in the order of days to weeks with concentrations of SO4 ranging from 38 mM to <500 µM. The low-SO4 incubations resemble the low-temperature Mcr experiments in which the Δ13CH3D values of residual headspace methane increased toward equilibrium while Δ12CH2D2 remained relatively constant. However, the higher concentration of SO4 results resemble the higher-temperature Mcr experiments, with both Δ12CH2D2 and Δ13CH3D increasing with methane consumption (Figure 13.10). One datum from the Santa Barbara sediment slurry experiments lies above the equilibrium curve and might be explained by mixing between initial gas and equilibrated gas, as shown by the dotted curve in Figure 13.10.

These experiments are ongoing, and more detailed reports are in preparation, but our preliminary conclusion is that AOM can push residual methane toward Δ12CH2D2 and Δ13CH3D equilibrium on trajectories in Δ12CH2D2 and Δ13CH3D space that depend on the conditions. Where the enzymatically facilitated exchange is active, both Δ12CH2D2 and Δ13CH3D are affected, while under more restricted exchange activity, only Δ13CH3D is affected. Under no conditions do the effects of AOM resemble those for microbial methanogenesis in Δ12CH2D2 and Δ13CH3D space.

Aerobic microbial oxidation effects on Δ13CH3D were studied by Wang et al. (2016), in which Δ13CH3D values were observed to decrease by several per mil with methane consumption. The effects on Δ12CH2D2 are as yet not known from experiments. Oxidation of methane in the atmosphere by Cl or OH radicals was investigated experimentally by Whitehill et al. (2017) for 12CH4, 13CH4, 12CH3D, and 13CH3D (i.e. Δ13CH3D). The effects of Cl and OH oxidation of methane on 12CH2D2 (i.e. Δ12CH2D2) as well as on the other species was modeled by Haghnegahdar et al. (2017). The predictions for Δ12CH2D2 effects of Cl and OH oxidation have been verified by measurements of the experimental products produced by Whitehill et al. (2017) at UCLA. All of these results on the Cl and OH oxidation of methane indicate large shifts in clumping down to extremely low Δ12CH2D2 values (negative tens of per mil) and low Δ13CH3D values well below zero. What is more, in each of the studies, the isotopic KIE values (kinetic isotope fractionation factors) associated with the simple reactions CH4 + OH → CH3 + H2O and CH4 + Cl → CH3 + HCl closely approximate the “rule of the geometric mean” (RGM) (Bigeleisen 1955) in which the KIE for 13CH3D/CH4, for example, is the product of those for 13CH4/CH4 and 12CH3D/CH4, etc. Where the RGM applies, the relative abundances of the multiply substituted isotopologues – 13CH3D and 12CH2D2 in this application – are controlled entirely by the classical KIEs and not by the equilibrium zero-point energy effects specific to each of the isotopologues. The results of the classical kinetics in which the lighter isotopic species of methane react with Cl and OH more rapidly than the heavier isotopologues are increases in bulk 13C/12C and D/H in the residual methane left behind and concomitant decreases in Δ12CH2D2 and Δ13CH3D (see Question 1 in the “Questions for the Classroom” section for the proof of this behavior). One expects the RGM to apply for single-step kinetic reactions such as those that oxidize CH4 in the atmosphere. The RGM does not apply to the methane isotopologue effects of AOM. Whether the RGM applies to aerobic bacterial oxidation is at present not known, but experiments are planned.

### 13.8 Conclusions

Isotopic bond ordering in methane gas molecules traces process, while bulk isotope ratios trace both process and source isotopic compositions. By measuring the isotopic bond ordering in CH4 gas, it is possible to isolate processes from sources. The 13C/12C ratios of microbialgenic methane, for example, are controlled by the substrate carbon as well as by the processes of methane formation. The D/H ratios of methane are controlled by the source of hydrogen (often water), as well as the reaction path to formation. The combination of Δ13CH3D and Δ12CH2D2 yields a measure of the process of formation irrespective of the 13C/12C or the D/H ratios of the source carbon and hydrogen. While more experimental work is required to investigate all possible reaction pathways, thus far it appears that the position of a methane datum in Δ13CH3D versus Δ12CH2D2 space can be used to identify processes of formation independent of the uncertainties in the source material. One can predict that the ability to trace the origins of methane independent of bulk carbon and hydrogen isotope ratios could prove invaluable for assessing the origins of CH4 gas on other solar system bodies where the meaning of bulk isotope ratios would not be accurately known.

### 13.9 Limits to Knowledge and Unknowns

A known unknown is the effect of “cracking” of organics in Δ13CH3D versus Δ12CH2D2 space. Thus far, it seems that low – even negative – values for Δ12CH2D2 result from the multiple steps of building a CH4 molecule as in microbial methanogenesis. For comparison, Shuai et al. (2018) found that while nonhydrous pyrolysis of coal can generate methane with equilibrium Δ13CH3D (Δ18) values at temperatures ranging from ~400°C to ~500°C and from ~600°C to 700°C, disequilibrium in Δ18 by about 2‰ results from ~500°C to ~600°C. The degree of disequilibrium also depends on the rate of heating. Based on these results, an important question is whether such processes could ever lead to confusion between microbial methanogenesis and cracking in Δ13CH3D versus Δ12CH2D2 space. Hydrous pyrolysis of shale evidently leads to equilibrium isotopologue distributions in the product methane (Shuai et al. 2018). It is perhaps relevant in this context that the temperature window leading to disequilibrium in methane isotopologues due to pyrolysis seems to be rather narrow, suggesting that this may not be a generally important process. More experiments are required.

### Acknowledgments

This chapter is based on a compilation of work by a long list of collaborators, many of whom have been funded by the Deep Energy community of the Deep Carbon Observatory (Sloan Foundation). This chapter is not meant to replace the primary literature produced by these workers, but rather is an update on the status of results obtained with some novel new data. The author acknowledges the critical input and efforts (in no particular order) by Barbara Sherwood Lollar (University of Toronto), Gius Etiope (Istituto Nazionale di Geofisica e Vulcanologia), Thomas Giunta (University of Toronto), Jeanine Ash (UCLA, Rice University), Jabrane Labidi (UCLA), Issaku Kohl (Thermo Fisher Scientific), Douglas Rumble III (Geophysical Laboratory, Carnegie Institution for Science), Tina Treude (UCLA), Sebastian Krause (UCLA), Rachel Harris (Princeton University), James Gregory Ferry (Penn State University), Divya Prakash (Penn State University), Alexis Templeton (University of Colorado), Daniel Blake Nothaft (University of Colorado), L. Taras Bryndzia (Shell International Exploration and Production, Inc.), Marvin Lilly (University of Washington), Mojhgan Haghnegahdar (UCLA), and Edwin Schauble (UCLA), among many others. The conclusions put forward here are those of the author and may not be shared by all of the people engaged in the various studies.

### Questions for the Classroom

1

Why would partial consumption of isotopically light methane molecules leave the residual methane with lower Δ13CH3D and Δ12CH2D2 values relative to the initial isotopologue composition of the gas in the absence of isotopic exchange among the methane molecules?

2

Why do lower temperatures favor greater Δ13CH3D and Δ12CH2D2 values relative to the stochastic values of zero?

3

Why are Δ13CH3D and Δ12CH2D2 values independent of bulk isotope ratios?

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