What is the maximal possible soil methane uptake?

The spread of published values of the rate of methane uptake by soils makes up several orders of magnitude from 0.0001 to 1 mg·m^-2·h^-1, which is comparable in magnitude to the spread of estimates of the release of CH₄ out of waterlogged soils. The high values of CH₄ emissions out of waterlogged soils are well explained, since with high methane production, it can be removed from the soil at almost any speed through a convective (most often bubble) transport mechanism. But when being absorbed by the soil, methane can penetrate in it only due to an apparently slow diffusion mechanism. Thus, the question arises of the maximum theoretically justified assessment of methane consumption by the soil. The aim of our work was to try to quantify the maximum possible amount of CH₄ consumption by the soil relying on a strict basis of soil biokinetics and physics.

To estimate the maximum specific absorption flux of CH₄ by the soil, we used the "mass conservation equation" [Walter et al., 1996; Zhuang et al., 2004; Глаголев, 2006, p. 316; 2010, p. 35-36]:

¶C/¶t = -¶F/¶z + Q_ebull + Q_plant + R_prod + R_oxid,

where C (mg/m³) is the concentration of methane at time t at depth z; F (mg·m^-2·h^-1) is the specific flux of methane due to diffusion; Q_ebull and Q_plant (mg·m^–3·h^-1) are the rates of change in methane concentration at time t at depth z due to the formation of bubbles and drainage through the roots of plants, respectively; R_prod and R_oxid (mg·m^-3 · h^-1) are the rates of formation and consumption of methane, respectively.

Since we going to estimate the flux of CH₄ only at its maximum possible consumption, the equation is simplified, as far as its terms accounted for the formation and transport of methane (R_prod, Q_ebull, Q_plant) will be equal to 0. Finally, we will consider the system in a steady state, i.e. ¶C/¶t = 0. Thus:¶F(t,z)/¶z = R_oxid(t,z).

Using Fick's first law to calculate the diffusion flux (used with a modified sign compared to its traditional form):

F(t,z) = D(z)·¶C/¶z,

where D(z) is the diffusion coefficient [Zhuang et al., 2004]; and the modified Michaelis-Menten equation for calculating methane oxidation is:R_oxid(t,z) = -V_max·(C - C_Th)/(K_M + C - C_Th), where C_Th (mg·m^-3) is the threshold concentration [Panikov, 1995, p. 151]; V_max (mg·m^-3·h^-1) is the maximum specific consumption rate; K_M (mg·m^-3) is the half–saturation constant, and also under assumptions, (i) the concentration of CH₄ is approximately equal to atmospheric (C_A = 1.29 mg/m³) at the upper boundary (soil/atmosphere); (ii) the flux of CH₄ can be assumed to be zero at an infinitely great depth [Born et al., 1990]; (iii) D, V_max and K_M >> (C- C_Th) do not change with depth. Therefore, the absolute value of the specific flux from the atmosphere to the soil is:

|F(0)| = (C_A-C_Th)·(V_max·D/K_M)^½.

The maximum value of the diffusion coefficient can be estimated by the Penman equation: D = D _o·P_a·0.66, where D_o is the diffusion coefficient in air; P_a is the porosity of aeration [Смагин, 2005, p. 165]. Since we are going to estimate the maximum value of diffusion, we will take the limit value of porosity, which is 1, but as far as the proportion of pores of stable aeration accounts for half of the total pore volume [Растворова, 1983, p. 52], then for further calculations we will take P_a = 0.5, hence D = D _o·0.33. According to [Arah and Stephen, 1998], for CH₄

D_o = 1.9·10^-5∙(T/273)^1.82 m²/s = 6.8·10^-2∙(T/273)^1.82 m²/h,

where T is temperature (K). When solving our diffusion problem, we assumed that the temperature is the same throughout the soil profile, and is 293 K. then D = 6.8·10^-2∙(293/273)^1.82·0.33 = 2.55·10^-2 m²/h.

The maximum rate of CH₄ oxidation by soil was experimentally estimated in [Bender and Conrad, 1992] and was 57.3 mg/(h·m³), which is in good agreement with the value of V_max = 47 mg/(h·m³) obtained at T = 32 °C according to the temperature dependence for automorphic soils of boreal forests V_max = 1.5^{(T ‑5.4)/10} mmol/(h·L), given in the work of Zhuang et al. [2004].

The half–saturation constant is the concentration of the substrate, at which the specific growth rate of microorganisms takes a value equal to a half of the maximum.  Summaries of the values K_M have been repeatedly published (see, for example, [King, 1992, Tab. II; Segers, 1998, Tab. 4; Глаголев, 2006, pp. 324-325]). For our purposes, we should take the K_M obtained directly in the experiments with substrate concentrations (CH₄) closest to those found in natural conditions. The minimum value (3·10^-8 mol/L) is given in [Bender and Conrad, 1992]. This value corresponds to the methane concentration in the air of about 20 ppm (14.3 mg/m³). This К_М value will be taken for further calculations.

The threshold concentration of CH₄ for methanotrophs in the upper soil layer, given in the scientific literature, varies from 0.1 to 3.5 ppm [Crill, 1991; Bender and Conrad, 1992; Kravchenko et al., 2010]. Since we are interested in the minimum value of this indicator, we will bring it to the minimum temperature (273 K or 0 °C): C_Th = 0.0714 mg/m³.

Now, having all the necessary numerical values, we can estimate the maximum intensity of methane consumption by natural soils:

|F(0)| = 1.2186·(57.3·2.55·10^-2/14.3)^½ ≈ 0.39 mg/(m²·h).

Thus, for a certain "ideal" soil (evenly warmed throughout the profile, perfectly aerated, and at the same time containing enough moisture to create optimal living conditions for methanotrophs, which, by the way, are extremely numerous in the soil, and their methane half–saturation constant is very low, etc.) we obtained an absorption intensity of CH₄ of about 0.39 mg/(m²·h). Since the combination of optimal values of all factors affecting methane consumption is very unlikely (or, rather, even improbable) in real soils, the resulting value can be considered extremely possible. And in view of this, the empirical generalization made in [Crill, 1991] becomes clear: "From the Amazon floodplain to the Arctic, the most rapid rates rarely exceed 6 mgCH₄·m^-2·d^-1" i.e. 0.25 mg/(m²·h).

Conclusion. So, we considered the absorption of methane as a biochemical process (following the Michaelis-Menten law with certain kinetic parameters), limited by diffusion in porous medium (soil). Based on this theoretical analysis, we came to the conclusion that the extremely large values of the specific absorption flux of CH₄ (about 0.4 mg·m^-2·h^-1 and more), which are sometimes found in the literature, are unrealistic, if we are talking about the soils, which are always under methane concentrations no greater than atmospheric – 1.8 ppmv. This applies to the vast majority of soils – almost all, except for wetlands and soils covering landfills, underground gas storage facilities or other powerful sources of methane.