Mitigation of ventilation air methane (VAM) using novel methanotrophic coating materials: a technical analysis

Ventilation air methane (VAM) is a potent greenhouse gas source originating from geological wells, current and extinct mineshafts and other terrestrial conduits venting methane to the atmosphere, contributing to global methane emissions and disproportionate warming potential. Herein, we introduce the concept of the methanotrophic material as an engineering solution. Such materials should be capable of converting methane at ambient temperatures and pressures to a binder product, capturing and permanently sequestering the methane while simultaneously restricting its further emission. While such materials are currently under research development, this goal is supported and facilities by the mathematical framework, introduced and used herein, to evaluate the ability to convert methane, using currently published activity data. We include a case study of the conversion of a characteristic stream of VAM (0.6% methane in air, 1.7 × 108 l hr−1 equivalent to 100 000 standard cubic feet per minute). We show that when appropriately designed, such systems require a surface coverage of less than 1000 m of mine tunnel length (equivalent to 20 000 m2 areal coverage) in order to reduce the methane emission from this stream by over 99%. Finally, we highlight formaldehyde as a reactive intermediate of methane oxidation which may itself be incorporated into these coating materials. As a component of binders and polymers already used ubiquitously in commercial products, this intermediate ultimately allows these systems to sequester the carbon from methane in a stable and solid form. The results presented here are easily extended to the treatment of other methane streams—either more concentrated or dilute—and the results herein will guide the design and development of a new class of carbon-negative materials.


Introduction
Methane is recognized as a potent greenhouse gas which has been responsible for over 20% of the increase in global temperatures since the industrial revolution [1].In the first 20 years of emission, methane contributes 80 times more warming than the equivalent mass of CO 2 , where today methane emission contributes half as much warming as CO 2 emissions [2].Compared to CO 2 however, methane emissions are relatively dispersed and dilute-coming from many low-concentration sources such as leaks from fossil fuel infrastructure, livestock, and landfills [3].To address these dilute and distributed streams, we introduce what we assert is a concept of significant utility in the form of a methanotrophic coating or material.This in theory can be applied in a thin layer to a variety of natural and industrial surfaces and is capable of converting gaseous methane as well as carbon sequestration into a solid form with useful functions.An overview schematic of such a coating is shown in figure 1.
Ventilation air methane (VAM) is a methane emission stream found in extinct and operational mine, for example.During coal and other types of mining, methane gas is emitted from the naturally methane-containing fossil fuel [4].This methane poses a safety and health hazard for mine workers, and active coal mines require ventilation with large amounts of fresh air to sweep the gas away and keep its concentration typically below one percent [5].Fire suppressant dust is coated onto the walls of Figure 1.Schematic of a methanotrophic coating material of thickness L applied onto a heterogeneous surface.Methane from the atmosphere is adsorbed by a selective methane adsorbent.This is followed by methane oxidation over a catalyst which is interfaced with the adsorbent.Either of the adsorption or oxidation processes can limit the ultimate rate of methane conversion within the system.Carbon-containing products produced from methane oxidation can potentially be polymerized into a solid coating.
the mine to act as heat sinks for an emerging ignition event of the methane.VAM methane in the vented air represents approximately 70% of coal mine methane emissions [4], but its dilute nature makes it economically and technologically challenging to remediate.
Herein, we present a mathematical framework that allows the prediction of the methane conversion performance of these materials from streams of pure methane down to the ambient atmospheric methane concentration (∼1.8 ppm).We show that existing adsorbents and methane oxidation catalysts would be capable of converting 99% of a low-concentration methane emission stream (characteristic of VAM) with physically realistic areal coverage.Last, we discuss and evaluate several proposed chemistries capable of ambient-temperature reaction with formaldehyde to produce polymeric materials that can sequester the methane oxidation product into a solid material.We propose that these materials would be capable of growth, strengthening, and reinforcement through incorporating this carbon source with potential uses as gas-impermeable coatings, adhesives, thermal insulation, and structure materials.

Analytical methodology
For any methane oxidation in the adsorbed phaseeither on a solid catalyst or in solution-the rate of the adsorption may limit the overall rate of methane oxidation.Methane is first required to be adsorbed at or on an active material from the ambient atmosphere.The rate of this adsorption and accompanying conversion are analyzed in tandem in order to understand any limitations which this adsorption may present.Such adsorption-reaction analysis has been used to analyze other systems of greenhouse gas conversion within similar materials [6].For a generic methane adsorbent, the rate of methane adsorption onto it can be modeled as a first-order process: where q is the amount of adsorbed methane in units of moles of methane per mass of adsorbent, q e is the amount of adsorbed methane at equilibrium with the same units, k ads is the rate constant for methane adsorption in units of inverse time, and t is the corresponding time.The total amount of methane adsorbed in the system is a function of the mass of adsorbent present, m ads , as follows: When the adsorbent is paired with a catalyst capable of methane conversion, a consumption term is introduced to the equation (2): Here k c,sat is the rate of methane conversion of the catalyst when the system is saturated with methane, assuming that this rate is linearly proportional to the amount of adsorbed methane, and m cat is the mass of catalyst present.Then the steady-state amount of adsorbed methane, as well as the rate of methane adsorption and conversion of the system is found by setting equation (3) equal to zero and solving for q, which gives the following: The rate of methane adsorption and conversion at steady-state is then found: q SS q e m cat k c,sat = m ads m cat q e k ads k c,sat m ads q e k ads + m cat k c,sat .( To simplify the above expression, a Damköhler number, Da, for the system, given as the ratio of the rate of methane conversion to the rate of methane adsorption is defined as: If Da ≫ 1 then the rate of methane conversion is much more rapid than the rate of methane adsorption, and the system is ultimately limited by this adsorption.Whereas if Da ≪ 1 then the system is limited by the rate of methane conversion, with the gas being able to adsorb more rapidly than it can be converted.The steady-state rate of adsorption and conversion can then be simplified by introducing this dimensionless constant into equation (7) as follows: In this work, we explore three catalytic routes for methane oxidation: enzymatic conversion with methane monooxygenase, heterogeneous conversion with zeolite-based Fe-ZSM-5, and photocatalytic conversion with titania-based nanoparticles.These catalytic systems were chosen because they span a range of routes of methane oxidation, requiring differing oxidants and energetic inputs, and because of their proven activity at or near ambient temperature.We propose that these systems may be coupled with various methane adsorbent materials such as: activated carbon, metal-organic frameworks, and zeolites.A summary of catalyst, adsorbents, and their relevant characteristics is shown in table 1.
Depending on the choice and amount of methane oxidation catalyst and adsorbent, the system may ultimately be limited by either the rate of the gas' oxidation or adsorption.The ratio of the rate of adsorption and rate of conversion, given as the Damköhler number is shown below in figure 2(A), assuming an equal mass loading of both adsorbent and catalyst.The Damköhler number for several theoretical methanotrophic material systems at varying mass loadings and ratios is shown in figure 2(B).
Any system designed with too extreme a Damköhler number ends up wasting mass and volume-which otherwise could be optimized to yield higher overall methane conversion rates.As such, care must be taken when choosing an appropriate adsorbent, catalyst, and mass loadings of each within a combined system in order to avoid these limitations.For example, methane monooxygenase converts methane rapidly on a per-mass basis.Coupling this enzyme with an equal mass of any of the methane adsorbents presented here would result in a system strongly limited by adsorption rate (Da ≫ 1).Such a system would make inefficient use of the enzyme, where either more adsorbent would be needed to increase the overall methane conversion rate, or less enzyme could be added, in order to convert the same amount of methane with an overall lower mass of catalyst present.
The concentration of methane as well as other gases can play a role in affecting the adsorption and conversion rate in all systems presented in this work.
Here, the adsorption capacity of any adsorbent is taken as a function of the partial pressure of methane.Table 1 includes the adsorption capacities for each adsorbent at one atmosphere of methane partial pressure.The dependence of adsorption capacity on methane partial pressure is taken to be linear with respect to the partial pressure of methane, following a simplified Freundlich isotherm [14]: where P CH4 is the partial pressure of methane, and K, is the Freundlich constant for the adsorbent.The above expression captures the linear range of the adsorption isotherm at partial pressures of methane below one atmosphere.We recognize that effects such as competitive adsorption, adsorption selectivity, and adsorbent poisoning may have large effects on any adsorbent's capacity.We note that this analysis is easily adapted to incorporate such non-idealities, but is not included here for generality and simplicity.
Next, the rate of methane conversion of each of the methane conversion catalysts explored in this work may also be a function of the amount of methane and other atmospheric gases present.Methane monooxygenase oxidizes methane to methanol through the use of oxygen and NAD(P)H [15]: Assuming an otherwise available supply of NAD(P)H, the activity of the enzyme is dependent only on the available concentration of methane and oxygen.This activity is taken to follow a form similar to other oxidoreductase enzymes such a glucose oxidase [16]: Table 1.Summary of methane conversion catalysts and methane adsorbents.
b All adsorbents are taken to follow a simplified Freundlich isotherm, where the maximum capacity for gas adsorption is taken to bel linearly proportional to the partial pressure of methane at and below one atmosphere.This coefficient is equal to the equilibrium methane adsorption, qe, when the partial pressure of methane is one atmosphere.where the Michaelis constants for methane, K M,CH4 , and oxygen, K M,O2 , are 3.0 and 16.8 µM respectively [7].The concentration of these gases dissolved in the aqueous reaction mixture is given as following, assuming the amount of dissolved gas is directly proportional to the partial pressure of the gas, following Henry's law: With these constants taken as 1.4 mmol l −1 atm −1 and 1.3 mmol l −1 atm −1 for methane and oxygen respectively.
The rate of photocatalytic conversion of methane is also a function of methane concentration and oxygen concentration within the liquid phase reaction mixture [17], where the reaction follows the general form [12]: Further, the rate may also be a function of wavelength and strength of illuminating light, pH, temperature, catalyst identity and morphology, and presence of contaminants among others [18]however these dependencies are not incorporated.
Here, we take the rate of methane oxidation to only be proportional to both methane and oxygen concentration for ease of use, with a first order dependance assigned to oxygen, and a second order dependence to methane.This dependence captures the major and obvious dependence of faster conversion rate at higher methane concentrations as well as the fact that excess oxygen partial pressure attenuates this conversion rate [12,19,20], Here, the rate of maximum methane conversion is when the ratio of methane to oxygen partial pressure is just greater than two to one.As such, the value of k photo,sat is taken as the conversion rate under these optimal conditions.Additionally, we recognize that the photocatalytic conversion of methane can and often does have complicated and diverse reaction kinetics [17,21].Other kinetic expressions incorporating the relevant variables may easily be input into the model presented here to refine the analysis for a specific system.
Finally, the H 2 O 2 -mediate rate of methane oxidation over iron-based zeolites is accomplished as follows [22]: The rate of this reaction is taken to be directly proportional to concentration of methane within the reaction (assuming a constant supply of peroxide) as has been reported previously up to ∼5 atmospheres of partial pressure [23]: Here, we compute the rate of methane conversion that may be achieved by such composite systems if incorporated into a coating material.Taking the steady-state rate of methane conversion for any of these systems as presented in equation ( 5), and given some area coverage of the system, we introduce a term for density of system, where a portion of the coating may consist of an adhesive, a binding agent, or a chemically inert support for the adsorbent and or catalyst.A methane adsorbent and catalyst are incorporated into a coating with a thickness, L. The volume fraction of each of these within the coating is given as: where ϕ ads is the volume fraction of the adsorbent, ϕ cat is the volume fraction of the catalyst, and ϕ i is the remaining volume fraction.The total mass of methane adsorbent with density, ρ ads , and catalyst with density, ρ cat , within the coating over a given area, A, are given as: The steady-state rate of methane conversion by the coating (assuming no mass transfer limitations within) is then given as: For a system which makes efficient use of its catalyst (with a sufficiently small Damköhler number) the above expression can be simplified to the following: The methane conversion rate of a given coating can then be calculated.The rate of one potential Comparison of activity of methanotrophic coating for varying chemistries of methane conversion as well as partial pressure of methane in air.Each coating is taken to be 1.0 mm thick with an overall density of 1.0 g cm −3 and a ratio of catalyst mass to adsorbent mass such that the system's Da = 0.05.Here, assuming uniform density of each methane oxidation catalyst, the mass fraction of catalyst is taken to be 0.02, 0.86, and 0.97 for the enzymatic-, zeolite-, and photocatalyst-based systems respectively.No mass fraction is assigned to inert material.As a reference, the rate of carbon conversion for a general plant such as maize, normalized to the area of its active photosynthesizing leaves, is also shown as the dashed grey line at a value of 36 000 µmol m −2 hr −1 [24].methane conversion of a given coating, comprising over a range of thicknesses and methane partial pressures is shown in figure 3 below.The coating is taken to be 1 mm thick, with any overall density of 0.5 g cm −3 .The relative mass loadings of each catalyst and adsorbent (taken here to be the activated carbon, Norit RB2 in all cases) are set as to have each system with Da = 0.05.Here, this low Damköhler number ensures that the catalysts loaded within the material are operating under near saturation conditions.This optimizes the conversion rate per mass of the methane oxidation catalyst, something which is beneficial here as in the catalyst will cost (enzyme, or transition metal-based) than the activated carbon adsorbent.
As a case-study in the use of these materials to address real streams of methane emissions-their ability to convert the methane within a stream of VAM is explored.During mining, methane gas is emitted from geological formations therein [4].This methane poses a safety and health hazard for mine workers, and active coal mines require ventilation with large amounts of fresh air to sweep the gas away and keep its concentration typically below one percent [5].This dilute stream represents approximately 70% of coal mine methane emissions [4], but its remediation is complicated by the low concentration range.
To determine the required surface area to mitigate an example VAM effluent stream (1.7 × 10 8 l hr −1 or 100 000 scfm at 0.6% methane), as an approximation the gaseous atmosphere within the mine is assumed well-mixed-that is there a constant concentration of methane gas everywhere.This concentration then represents the methane concentration within the VAM effluent.Thus, for a desired methane concentration in the VAM effluent (and correspondingly a total conversion of VAM methane), the required surface area of the methanotrophic coating to achieve this conversion can be calculated.
The coating is assumed to be applied to all walls of some passage within the mine.The shaft is modeled as an isothermal, constant density plug flow reactor [25], where the concentration of methane within the stream is governed by the following equation: Here P CH4 is the partial pressure of methane within the stream, x is the coordinate of distance along the shaft, u is the velocity of air flow, and r CH4 (P CH4 ) is the rate of conversion of methane within the coating given the current partial pressure of methane in the stream (as shown for example in figure 2).We assume no mass transfer limitation between the methane within the gas phase and that of the coating.Here, the passage where the coating is applied is assumed to be a square tunnel with side lengths of five meters, generally representative of the size of gate-roads within a coal mine, but the coating may also be applied to any surface within the coal mine [26,27].This geometry also gives air velocity values representative of real airflow within similar mines [28].Through integration of equation ( 22) the partial pressure of methane present in the mine effluent-given that the air stream has traveled along a given length of mine-is computed.The results are shown below in figure 4 for a representative coating of each catalytic system.
We find that enzymatic and Fe-ZSM-5-based systems are capable of converting 99% of the methane within the stream with only less than 2500 m of tunnel length coated.The enzymatic coating performs the best, requiring only 240 m of tunnel to reach 99% conversion of the methane, whereas the Fe-ZSM-5 based coating requires 2400 m.These dimensions are well within what would be available in the average coal mine.For reference, within a representative longwall mine, the mined panel can reach 4 km in length, with a width of nearly 0.5 km.Where the tail road length, that leading out and away from the mined face, would be most representative of the model presented here-assuming most methane emission is a result of the face of coal being mined.These results suggest that the two most active methane converting systems would be appropriate The coating is taken to be applied to each wall of a 5-by-5 square meter passageway.Here, each coating is taken to be 1.0 mm thick, where the mass ratio of catalyst to adsorbent present gives a Damköhler value of 0.05 the same as in figure 2. For the MMO, Fe-ZSM-5, and CoOx/TiO2 coating systems, lengths of 240 m, 2400 m, and 6376 000 m respectively are required to convert 99% of the methane stream.Here, the photocatalytic system requires more than a 1000 times longer than the other systems to reach this same benchmark, which is attributed to the poor scaling of its methane oxidation activity at low partial pressures of the gas.
to treat current low concentration streams of methane emission, whereas the photocatalytic-based conversion of methane is exceedingly unfavorable at low partial pressure.However, this system may be appropriate at intermediate partial pressures of methane, between 0.5 and 0.8 atm of methane in air as shown figure 3, where its activity exceeds that of enzymatic based conversion.

Discussion of chemistry
All methane oxidation catalysts in this work were chosen for their relatively active and unique chemistry.The oxidation of methane can and does produce a wide range of carbon-containing products such as methanol, formic acid, formaldehyde, carbon monoxide, as well as CO 2 .While methanol is commonly the desired product industrially due to its value as a potential liquid fuel and versatile chemical feedstock [29], its reactivity is limited at ambient temperature and pressures.Alternatively, formaldehyde is a flexible chemical reagent, capable of homopolymerization [30] and condensation with alcohols and amines to form solid materials and hydrogels even at ambient temperatures [31,32].We propose that such chemistry can be used to capture formaldehyde as reactive intermediate incorporated ultimately into useful polymer systems, sequestering the carbon from methane, and producing a growing Industrially, these materials can be engineered to produce strong structural components [36], adhesives and binders [37], and insulating foams [38].material.Several schemes for this reactivity are shown in figure 5, including reaction with urea, melamine, and phenol, reactions of which can be driven rapidly to produce high molecular weight materials through modulating pH and or temperature [33][34][35].
The photocatalytic and heterogeneous methane oxidation catalysts investigated in this work are already capable of directly producing formaldehyde from methane-albeit with variable selectivity.On the other hand, methane monooxygenase produces methanol selectively.However, coupling methane monooxygenase with an additional enzyme, methanol dehydrogenase [39], would allow for the generation of formaldehyde and continued regeneration of the necessary NADH substrate, as shown in the following reaction: We note that the optimal chemical environment for these enzymes and formaldehyde condensation and material growth may differ.For example, the activity of methane monooxygenase and methanol dehydrogenase are affected by pH [40], with the latter losing nearly 90% of its activity at pH 7.5 or below [41].However, formaldehyde condensation is exceedingly more rapid at extreme pH values-acidic or basic [42].Additionally, non-specific chemical reactions such as oxidative or photocatalytic degradation of any polymeric material produced remain a possibility [43], so care must be taken with adsorbent, catalyst, and reactant integration in order to minimize the possibility of these undesired and unproductive reactions.As photocatalytic activation would be limited to the surface of the photocatalytic material, one could envision a system where the photocatalyst remains on the material's surface, exposed to ambient or direct illumination, whereas the generated formaldehyde diffuses inward, growing and strengthening the material underneath.Such a design scheme could also be employed with the other catalyst chemistries and methods, understanding that methane concentration may be the highest directly at the surface of the material.
For these systems which rely on an initially loaded co-monomer, material growth would necessarily stop once all of this co-reagent is consumed.At this point, instead of accumulating reactive and potentially hazardous formaldehyde (or even methanol, formic acid, or carbon monoxide), it would be beneficial to have the systems shift selectivity CO 2 .CO 2 is unreactive and non-toxic and a less potent greenhouse gas as compared to the methane it would be formed from.Again, the photocatalytic and zeolite-based catalysts are capable of further methanol oxidation to products of higher oxidation state-and would potentially be able to drive selectivity completely towards CO 2 themselves.In contrast, the enzymatic pathway for methane oxidation would have near-perfect selectivity to methanol and subsequently formaldehyde.The system could be modified again through the addition of other enzymes, such as formaldehyde dehydrogenase and formate dehydrogenase [44,45], converting the formaldehyde to CO 2 as follows: Last, for these systems to operate independently and robustly, their ability to adsorb methane and catalytically convert the gas must be maintained for as long as possible.While the photocatalytic and heterogeneous catalyst systems explored in this work are composed of highly chemically and thermally stable materials [46,47], the opposite is true of the enzymatic system, where care must be taken to avoid deactivation and long lifetime.For this, covalent stabilization and or immobilization could protect the enzymatic system from degradation due to any changes in the chemical environment-such as changes in pH-or natural environment-such as changes in ambient temperature and humidity [48].It is known the tethering enzymes to the surface of nanoparticles imparts enhanced stability [48].Additionally, any fouling of the adsorbent or catalyst due to the accumulation of dust, debris, or other chemical contamination would be deleterious to their ability to convert methane.Application of the coatings in locations designed to minimize or prevent this fouling (such as on ceilings or higher up on walls) would be appropriate.Or periodic maintenance to remove any fouling layer could be employed including chemical or physical methods [49].These treatments also have the potential to generate beneficial methane and or formaldehyde during this process which could be naturally incorporated into the coating [50].Additionally, such coatings could be designed to incorporate anti-fouling behavior, as enzymatic, photocatalytic and zeolite-based oxidation systems have been employed in anti-fouling applications [51-53].

Conclusion
This work introduces and explains a mathematical framework for evaluating the conversion of lowlevel methane at ambient temperature and pressures within methanotrophic coating materials.We consider three distinct chemistries for methane oxidation including enzymatic, heterogeneous, and photocatalytic routes, and introduce the novel concept of methanotrophic coatings-wherein oxidized methane could be converted into a growing and strengthening material system.We show that such coatings would be capable of treating a characteristic VAM stream to remove 99% of its methane content at areal coverages easily achieved within current coal mines.
Last, we identify formaldehyde as a key reactive intermediate for incorporation into stable polymers for the generation of these coating materials-allowing for diverse chemical reactivity at ambient conditions in order to produce methanotrophic materials in practice.This work and these concepts will form the basis for the design, engineering, and optimization of this new class of materials to treat a range of concentrated and dilute streams of methane emission.

Figure 2 .
Figure 2. (A) Damköhler number of systems designed with equal mass of catalyst and adsorbent for methane adsorption and conversion.The white dashed line represents Da = 1.(B) Comparison of Damköhler number of several hypothetic systems incorporating varying adsorbents and catalysts are a range of mass loadings of each.Depending on the catalyst and adsorbent present, differing but optimal mass loadings of each component are required in order to optimize the systems performance and remove any limitations in the rate of adsorption or conversion.

Figure 3 .
Figure 3.Comparison of activity of methanotrophic coating for varying chemistries of methane conversion as well as partial pressure of methane in air.Each coating is taken to be 1.0 mm thick with an overall density of 1.0 g cm −3 and a ratio of catalyst mass to adsorbent mass such that the system's Da = 0.05.Here, assuming uniform density of each methane oxidation catalyst, the mass fraction of catalyst is taken to be 0.02, 0.86, and 0.97 for the enzymatic-, zeolite-, and photocatalyst-based systems respectively.No mass fraction is assigned to inert material.As a reference, the rate of carbon conversion for a general plant such as maize, normalized to the area of its active photosynthesizing leaves, is also shown as the dashed grey line at a value of 36 000 µmol m −2 hr −1[24].

Figure 4 .
Figure 4. Performance of methanotrophic coating for the conversion of a characteristic stream of ventilation air methane.The coating is taken to be applied to each wall of a 5-by-5 square meter passageway.Here, each coating is taken to be 1.0 mm thick, where the mass ratio of catalyst to adsorbent present gives a Damköhler value of 0.05 the same as in figure2.For the MMO, Fe-ZSM-5, and CoOx/TiO2 coating systems, lengths of 240 m, 2400 m, and 6376 000 m respectively are required to convert 99% of the methane stream.Here, the photocatalytic system requires more than a 1000 times longer than the other systems to reach this same benchmark, which is attributed to the poor scaling of its methane oxidation activity at low partial pressures of the gas.

Figure 5 .
Figure 5. Overview of potential chemistry for the production of methanotrophic coating materials.(A) Scheme for urea-formaldehyde generation.(B) Scheme for melamine formaldehyde generation.(C) Scheme for polyoxymethylene formation.(D) Scheme for phenol formaldehyde resin generation.Formaldehyde serves as a reactive intermediate, which through homopolymerization or copolymerization with a variety of monomers is capable of producing a diverse range of materials.Industrially, these materials can be engineered to produce strong structural components[36], adhesives and binders[37], and insulating foams[38].

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