THEORY OF METHOD

In this procedure, dissolved CH4 concentrations are determined by normalizing measured gas void CH4 to another gas, such as N2 or Ar, that is stripped from the pore fluid but whose in situ concentration is known. The in situ concentrations of the normalizing gases are assumed to be established by atmospheric equilibrium at the temperature at which local bottom water formed. These gases are assumed to be unreactive in sediments. Claypool and Threlkeld (1983) considered a method based on normalization to CO2.

Although it is unequivocal that Ar is unreactive, N2 pore fluid concentrations can be influenced by microbially mediated denitrification and nitrogen fixation. It is unlikely, however, that nitrogen fixation occurs in deeply buried marine sediments, as there is always dissolved ammonium available and the quantitative importance of denitrification is limited because the dissolved nitrate concentration in deep ocean waters is at most less than ~5% of that of dissolved N2 (Pilson, 1998).

Because the molar ratios of CH4, N2, and Ar in gas voids may differ from that in solution, we first develop theoretical relationships between the in situ dissolved CH4 concentration, [CH4]0, the measured vapor phase mole fractions of CH4, N2, and Ar in gas voids (XCH4, XN2, and XAr , respectively), and the in situ dissolved inert gas concentrations. Relationships are separately presented for three procedural variations depending on what is measured: (1) when only the gas phase mole fractions of CH4 and one inert gas are determined, (2) when total vapor phase pressure of the gas void along with the gas phase mole fractions of CH4 and one inert gas are determined, and (3) when the gas phase mole fractions of CH4, N2, and Ar are determined. The additional measurements in procedures 2 and 3 remove one source of uncertainty implicitly associated with procedure 1. We also address uncertainties related to corrections that account for sample contamination due to the entrainment of ambient air during sampling.

Fractionation of the dissolved gases between the vapor phase and the aqueous phase will occur during the ebullition of gases from the sediment during decompression and warming on deck due to differences in solubilites and diffusivities; dissolved gas molar ratios are not necessarily identical to gas void molar ratios. The relationships we develop for calculating [CH4]0 assume that fractionation is dominantly due to differences in solubility rather than diffusivity. This assumption is justified by the consideration of the dynamics of bubble growth (see the "Appendix").

With these assumptions we develop two models of vapor-phase formation that can be considered as physical end-members that describe the distribution of gas between pore fluid and gas voids: (1) equilibrium vapor phase degassing and (2) fractional vapor phase degassing. Because it is unclear which model more closely represents how gas is distributed, the uncertainty in calculated [CH4]0 due to the choice of degassing model is considered.

The equations that are derived for both models follow from mass balance. That is, the initial number of moles of gas in a volume of pore fluid is set equal to the sum in pore fluid and gas void following degassing. Additionally, Henry's law and ideal gas behavior are assumed.

In equilibrium degassing, it is assumed that there is chemical equilibrium between the entire vapor phase and the degassing fluid. The mass balance for each gas (ignoring the small amount of water in the vapor phase) is given by

MiwCi0 = [Vvapor (XiP/RT) + MiwCi], (1)

where

R = gas constant,
P = total pressure of the gas phase,
T = temperature (K),
Vvapor = volume of the vapor phase,
Miw = mass of interstitial water,
Xi = gas phase mole fraction,
Ci0 = dissolved gas concentration of i in situ, and
Ci = dissolved gas concentration of i following gas void formation.

Applying Henry's law,

Ci0 = [(Vvapor/MiwRT) + KHi]XiP, (2)

where

KHi = Henry's law constant for species i.

Substituting [CH4]0 and an inert gas, I, for Ci0 and eliminating P, the relationship between [CH4]0 and the vapor phase molar ratio, XCH4/XI, is then given by

[CH4]0 = (XCH4/XI){[KHCH4+ (Vvapor/MiwRT)]/[KHI + (Vvapor/MiwRT)]}[I]0. (3)

In the case of fractional degassing it is assumed that the vapor is no longer in contact with the fluid after it is released and each gas is in equilibrium with the fluid at the time it degassed. In this case, Ci varies with degassing as

(dCi/dVvapor) = –(XiP/MiwRT) = –(Ci/KHiMiwRT). (4)

Solving for Ci and applying mass balance (equation 1) leads to

Ci0 = (PXiVvapor/MiwRT){1 – exp[–(Vvapor/MiwRTKHi)]}. (5)

Thus, [CH4]0 is related to the vapor phase molar ratio XCH4/XI and [I]0 by

[CH4]0 = (XCH4/XI)({1 – exp[–(Vvapor/MiwRTHi)]}/
{1 – exp[–(Vvapor/MiwRTKHCH4)]})[I]0. (6)

For both degassing models, if only one inert gas is measured, there is uncertainty in [CH4]0 because the Vvapor/Miw ratio is not determined. However, the magnitude of the uncertainty can be examined by considering the magnitudes of the terms and the limits of equations 3 and 6 as a function of Vvapor/Miw . Equations 3 and 6 have the same limits. When Vvapor/Miw >> RTKH,

[CH4]0 = (XCH4/XI)[I]0, (7)

and when Vvapor/Miw << RTKH, it follows that

[CH4]0 = (XCH4KHCH4/XIKHi)[I]0. (8)

That is, if either equilibrium degassing or fractional degassing occurs, [CH4]0 must have an intermediary value between (XCH4/XI)[I]0 and (XCH4KHCH4/XIKHi)[I]0. KHCH4/KHN2 is ~2 and KHCH4/KHAr is ~1.5 (Stumm and Morgan, 1981; Pilson, 1998).

Thus, if only the mole fraction of CH4 and one inert gas are determined, no knowledge of Vvapor/Miw creates an uncertainty of ±33% in the calculated mean concentration based on equations 7 and 8 when N2 is the inert gas and ±20% when Ar is the inert gas.

This limitation can be eliminated, in principle, if an additional inert gas mole fraction or the total pressure is determined. For the case of equilibrium and known total vapor pressure, Pvapor, it follows from equation 2 that

[CH4]0 = [I]0(XCH4/XI) + PvaporXCH4 (KHCH4KH I), (9)

and if two inert gases are measured,

[CH4]0 = ([I1]0XCH4/XI, 1)({KHCH4+ [([I1]0XI, 2KH I, 2– [I2]0XI, 1KH I, 1)/
([I2]0XI, 1 – [I1]0XI, 2)]}/{KH I, 1+ [([I1]0XI, 2KH I, 2– [I2]0XI, 1KH I, 1)/
([I2]0XI, 1 – [I1]0XI, 2)]}), (10)

where the sub- and superscript 1 and 2 refer to the two inert gases.

For the case of fractional degassing, [CH4]0 and [I]0 are given by equation 5. This pair of equations can be solved numerically for [CH4]0 if P is determined. If two inert gases are measured, P can be eliminated by numerically solving the three equations given by equation 5 for CH4 and the two inert gases.

We examined the sensitivity of calculated [CH4]0 on the choice of the model used in the calculation. Calculated [CH4]0 values as a function of Vvapor/Miw for each model were compared. The maximum difference in [CH4]0 for the two models was found to be small, only 9%, if the reference gas is N2, and approximately half of this value if Ar is used instead of N2. This sensitivity results from the fact that the solubility of Ar is more similar to that of CH4 than is the solubility of N2.

During sampling of the vapor, it is difficult to avoid contamination with N2 or Ar from ambient air. However, the extent of contamination can be quantified and subtracted from what is measured based on measured O2 because methanogenic sediments do not contain any dissolved O2. The uncertainty because of this correction can also be quantified by conventional methods of propagating errors. The corrected mole fraction, XIcorr, is given by

XIcorr = XImeasXO2measR, (11)

where

XImeas = the measured mixing ratio of N2,
XO2meas = the measured mixing ratio O2, and
R = the atmospheric N2/inert reference gas molar ratio.

It is important to minimize the amount of contamination because the relative uncertainty of the calculated [CH4]0 becomes unacceptably large as the mole fraction of inert gas due to contamination approaches XImeas/R. For example, if it is assumed that all of the relative errors associated with the measurement of CH4, N2, or Ar and O2 are 5%, then in order to keep the uncertainty in the calculated [CH4]0 below 30%, the measured inert gas/O2 ratio should be >4.8 for N2 and 0.073 for Ar (equivalent to ~80% of the inert gas due to contamination).

NEXT