gas hydrate - CCOP

Partial differential equations for solids and solutes were set-up following the classical
approach used in early diagenesis modeling (Berner, 1980; Boudreau, 1997):
Solutes:
Solids:
⎛ ∂C
⎞
∂ Φ D
C
⎜ ⋅
S
⋅
x
⎟
∂
∂(Φ
⋅ v ⋅ C)
Φ
⎝ ∂
⋅ =
⎠
− + Φ ⋅ R
(1)
∂t
∂x
∂x
∂G
∂((1-
Φ) ⋅ w ⋅G)
(1-
Φ) ⋅ = −
+ (1- Φ) ⋅ R
(2)
∂t
∂x
where x is depth, t is time, Φ is porosity, C is the concentration of dissolved species in pore
water, v is the advective transport of solutes, G is the concentration of solids in dry sediments,
w gives the burial velocity of solids, and R defines the reactions occurring in the simulated
sediment column. The model considers the decrease in porosity with sediment depth,
advective transport of solutes via burial, compaction and fluid flow, burial of solids modified
by steady-state compaction, molecular diffusion of dissolved species and various microbial
and chemical reactions.
Porosity is assumed to decay exponentially with depth (x) due to steady-state compaction
(Berner, 1980):
Φ = Φ
f
+
-p⋅x
( Φ − Φ ) ⋅e
0
f
The initial porosity at zero depth (Φ 0 = 0.74), the porosity at infinite depth (Φ f = 0.45), and the
attenuation coefficient (p= 0.0025 m -1 ) were adjusted to fit ODP observations in diatomaceous
clayey silt sediments as summarized in (Einsele, 2000).
Molecular diffusion coefficients (D M ) are calculated as a function of sediment temperature
and salinity (35) using equations given in (Boudreau, 1997). Dissolved inorganic carbon
(DIC) is transported using the diffusion coefficient of HCO 3 - because bicarbonate is the major
DIC species at the near-neutral pH conditions prevailing in anoxic sediments.
Advective transport of dissolved species (v) is calculated considering steady state compaction
and upward fluid flow using the approach described in (Luff and Wallmann, 2003):
Φ
v =
f
⋅ w
f
− v
Φ
0
⋅ Φ
0
where w f is sedimentation rate and v 0 is the interstitial fluid flow velocity at zero depth
induced by upward fluid flow.
A novel rate law is applied to describe the effect of metabolite concentrations on the anaerobic
degradation of particulate organic carbon (POC) in anoxic marine sediments (Wallmann et al.,
2006):
R
POC
= K
C
⋅ k
x
⋅ POC
C(DIC) + C(CH ) + K
(3)
4
C
12
New Energy Resources in the CCOP Region - Gas Hydrates and Coalbed Methane