Golmshtok-2014-The impact of faulting on the s(3)

Qw=–ωρw????????T????t

W, Qgas=ρg??φ??????eT????s????g+UW??????????T????t,S=??φ=α–φ

(22)

K??????+????????K????????????,

wsUw=βw+(1–?δh)ω,U=(1–γ)ρ??ρ??????h+γρ??????h

??–1+ω,

(23)

gρw

W=δhφδ(T–Tph),

where Ks≈4×1010 Pa is the bulk modulus of the min??

eral skeleton material, Kw=2.2×109 Pa is the bulkmodulus of water, is Biot’s coefficient (for poorlyconsolidated terrigenous sediments ≈0.75 (Riceand Cleary, 1976)).

When deriving Eq. (20), we took into account thatgas compressibility is typically by a few orders of mag??nitude higher than the compressibility of porousmedium; therefore, the changes in porosity comparedto the changes in the gas density and gas saturation can

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be neglected by placing porosity φ outside the sign ofthe derivative ?(ρgφesg)t in the continuityequationTemperature T in (19)–(23) is determined by solv??ing the energy conservation equation. Neglecting theJoule–Thomson effect, the viscous friction in waterand gas, and their adiabatic heating at compression(the estimates show that these effects are negligible inour case), we obtain this equation in the form

?Te??????????–??(λe?T)

= –(ρwCwvw+ρgCgvg)??T.

(24)

Expressions (19) and (20), thermal conductivityequation (24), and relationship (13) form a closed sys??tem. With the appropriate boundary and initial condi??tions, this system of equations can be solved for thepressure fields in the liquid and gas phases (pw and pg),distribution of temperature T, and saturations of thepore space with water sw and gas sg in the conditions ofphase transformation from methane hydrate to meth??ane gas.

If the water mass flow is low or the water is immo??bile, we can eliminate the terms containing vw and?t in the right??hand sides of (20) and (24), assumethe water and gas saturations in (16) to be sw=w, andsg=g from (17), respectively, and only solve the sys??tem of equations (20) and (24).

If, however, the properties of the gas hydrate??bear??ing sediments imply that the methane gas released atthe phase change boundary at hydrate dissociation isswept out of the reaction zone and the anomalous gaspressure is almost negligible, then, instead of (19), wehave

κwpw?w?S????????????+??–????????????(?pw+ρwgez)=0.

?tμw

(c)

release at hydrate dissociation in the real geological

environment. These key parameters include sedimentpermeability and the degree of thermal impact on themedium containing gas hydrates (Nigmatulin et al.,1999). Clearly, the saturation of the pore space by gashydrate δh should also have a considerable effect.

Let us solve the problem of phase transition frommethane hydrate to methane gas in the horizontallayer with thickness h, which is composed of sedimentswith constant porosity φ=φ0. We place the origin ofcoordinates on the base of the layer and orient thezaxis upwards. As previously, the fraction of methanehydrate in the total pore volume is δh. Before timet=0, pressure p and temperature T in the layer wereconstant and equal to p=p0 and T=T0. Since t = 0,temperature at the base of the layer (z = 0) rapidlyincreases by δT to exceed the phase transition temper??ature, thus triggering the reaction of methane hydratedissociation. Temperature and pressure at the top ofthe layer (z = h) keep being p=p0 and T=T0. Theabsolute permeability for the gas phase is described bydependence (3).

Just as in the study of Nigmatulin (1999) men??tioned above, we assume that the pore water is immo??bile (vw = 0) and the base of the layer is impermeableto gas, i.e., (?pz)z=0 = 0 in accordance to Eq. (12).transfer due to the free gas flow by equating the right??hand side of (24) to zero. Since we are interested in theupper bound on the gas pressure, we also disregard gassolubility in water by assuming cH = 0.

In order to numerically solve Eqs. (20) and (24), wereplace the Heaviside and Dirac functions by their

x,Δx) smoothed over the(x,Δx)intervals (2Δx), where, for example

?0,x<–Δx,?

(x,Δx)=?σ?(x,Δx),–Δx≤x≤Δx,

x>Δx,?1,?0,x<–Δx,

(x,Δx)=?δ?(x,Δx),–Δx≤x≤Δx,

0,x>Δx,?

(19a)

In this case, in the problem of phase transition of

methane hydrate to methane gas, only the system ofequations (19a) and (24) with vg = 0 are solved, and thewater and gas saturations are, as previously, sw=w,

??w=βwS, whereand sg=g. From this it follows that S

βw and S are determined by the corresponding formu??las in (15) and (22).

3. THE IMPACT OF THE HYDRATE CONTENT

AND SEDIMENT PERMEABILITY ON THE CHANGES IN GAS PRESSURELet us explore at which values of the key parame??ters of the medium it is necessary to solve the completesystem of equations (19), (20), (24), and (13), and atwhich values it is sufficient to only solve Eq. (19a),together with (24). In other words, we estimate theimpacts of various parameters of a porous medium onthe value of the excess gas pressure caused by gas

16+35y–35y+21y–5y,?(x,Δx)=??σ??????????????????????????????????????????????????????????????????????????????????????????????????????????????

32(1–y)x?(x,Δx)=35δ??????????????????????????????????????????; y=??????????.32ΔxΔx

The phase transformation temperature Tph(p) and

its pressure derivative ?Tph?p in our study were cal??According to the seismic and drilling data, thethickness of the subsurface bottom sediments contain??

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THE IMPACT OF FAULTING ON THE STABILITY CONDITIONS OF GAS HYDRATES533

ing gas hydrates is 200–300 m, very rarely exceeding400–500 m (Kvenvolden, 1993; Ginsburg andSoloviev, 1994). In our calculations, we assume h =400m for the thickness of the subbottom sedimentscontaining methane hydrates; φ0 = 0.6 for the porosity(which is close to average) of unconsolidated marine

sediments in the layer of such thickness; s0

= 0.02; p0=10 MPa; T = 284 K; and T0

0ph = 285.06 K is the tem??perature of the methane hydrate–methane gas phasetransition at pressure p0 and salinity 35‰ (Sloan,1998); ΔT = 0.1 K is the half??width of the transitionzone for the smoothed analogs of the Heaviside andDirac functions of argument is the amplitude of the temperature jump.

(T?Tph,ΔT); δT = 20 KWe express the sharp rise in temperature at thebase of the layer in terms of functionTz=0=T0+δT ×(t–t0,Δt), where t0 = 2500 years,which is commensurate with the duration of the initialphase of faulting.

The numerical solution of the boundary??valueproblem (20) and (24), together with the boundaryand initial conditions formulated above was obtainedby the finite element method in the COMSOL Multi??physics environment for numerical simulations andsolving the equations of mathematical physics (COM??SOL, 2008).

With any permeability κhighest pressure in the layer is achieved at its base shortly0 and gas saturation δh, theafter the sharp rise in its temperature. The calculateddependences of Δp=maxt≥0(p(z=0,t)?p0)

on per??meability κshown in Fig. 1.

0 for each of the above values of δh areAs seen in Fig. 1, the excess pressure caused by themethane gas release during hydrate dissociation slowlyincreases in the area of small κ0 with decreasing per??meability and reaches 25–50 MPa. In the entire ana??lyzed interval of variations in permeability (κ0), theexcess pressure is higher the higher the hydrate satura??tion of sediments (δh), because their absolute gas per??meability in the zone where the hydrate has not yetdissociated is proportional to (1?δh)3 in accordancewith formulas (1) and (3), which impedes gas filtrationfrom the area of dissociation. With the growth in per??meability, the excess pressure steeply decreases start??ing from δκ0≈10?16 m2. It almost entirely vanishes forh ≤ 0.25 when κ0 > 4 × 10–13 m2.

If the thickness of the layer and/or the temperaturejump at its base are lower than the values used in thecalculations (h = 400 m, δT = 20 K), the range of κ0 atwhich the excess pressure does not exceed a few kPaexpands towards the lower permeability area.