Golmshtok-2014-The impact of faulting on the s(6)

and radial heat flow qr+ρ(r)

r=?λe?T?wCwvvwT are farsmaller in absolute values than the velocity 0 of waterconstantly inflowing through the base of the layer andthe initial flow q0 at the same level, respectively. Byvarying the values of R when solving our problem, we

IZVESTIYA, PHYSICS OF THE SOLID EARTH Vol. 50

established that (r)

w < 5 × 10–4 cm/yr and

qr<0.4mW/m2 for any ?H≤z≤0 even atr=7000m when R = 8000 m. Therefore, we assumethe additional boundary conditions which requirethat ?pw?r = 0 and ?T?r = 0 on the surface r =RThe faulting??induced temperature disturbance atthe axis of the channel at z=z0ph=?430 m, which wascalculated by solving the discussed problem (see belowfor the method of numerical solution) without consid??ering the latent heat of hydrate dissociation, is denoted

by δT0

(t). Clearly, this temperature disturbance at anytime is higher than its counterpart corresponding tothe conditions of phase transformation.

Using δT0

(t) as a boundary condition for tempera??ture at the base of the layer, we again numerically solveproblem (20) and (24) of Section 3 with h = 430 m,δ0maximum pressure increment h=0.1, and p=107 Pa. The dependence of theΔp on permeability κresulting from this solution is shown by the dashed line0in Fig. 1. As follows from this dependence, with κ0 =5× 10?13 m2 previously assumed for the Central BaikalBasin, the maximum pressure increment in the layer isat most 20 kPa. However, with allowance for the factthat permeability in the channel sharply increases at its

formation (see the assumed values of κ(c)

and facilitates the gas escape from the hydrate dissoci??0 and porosity)ation zone, the effective κκ0 can significantly exceed0= 5 × 10–13 m2. This results in the gas pressure incre??ment Δp of a few kPa at most.

Considering this, in our analysis of the impacts offaulting on the gas hydrate stability in the studied seg??ment of the axial zone of the Central Baikal Basin, weneglect the excess pressure of gas released due to gashydrate decomposition (since it is small) and onlysolve the joint hydrodynamic and heat transfer prob??lem (described by Eqs. (19a) and (24)) for the sameboundary and initial conditions presented above.

The coupled heat transfer and fluid filtration prob??lems described by the cited equations, together withthe cited boundary and initial conditions were jointlysolved by the finite element method using the COM??SOL Multiphysics (COMSOL, 2008). In order toachieve the required accuracy of calculations andensure the convergence of iterative process of solvingEqs. (19a) and (24), we used a significantly denser gridnear the surface of phase transition from methanehydrate to methane gas.

Hydrates during Channel Formation. Numerical Results4.2. The Changes in the Stability Conditions of Gas During the formation of the fluid pathway conduit,pressure decreases both inside the conduit and in itsvicinity. This causes horizontal filtration of water from

No. 4 2014

538

Filtration rate, cm/yr5432

0210.5010GOLMSHTOK543200400600800100012001400

Distance from the channel axis, m

Fig. 3. Vertical velocity of water filtration at the bottom ofthe lake. The numbers on the curves indicate the time afterthe onset of faulting (ka).the ambient rocks into the channel almost throughoutits entire length. This water inflow is later rearrangedinto the additional vertical flow, which leads eventually

(z)to the increase in the vertical filtration velocity vw. As

follows from Fig. 3, as early as starting from t≈4 ka,the vertical velocity of water filtration at the lake bot??

Temperature disturbance ΔT = T – Tst, K

1020304050

301000

2000

3000

Depth, m4000510153050100500

024ΔT, K68

50010

5000

6000

7000Depth, m10020030074005500

60012341015

Fig. 4. Temperature disturbance on the channel axis due tofaulting. The numbers on the curves indicate the time afterthe onset of faulting (ka).tom within the channel is higher than the maximumvelocity vm=v0+va at the base of the sedimentarylayer at the initial time instant. At t ≈ 10 ka, the verticalflow velocity within the channel reaches its maximum(at point r=0, the maximum value is by a factor of 1.3higher than vm). After having reached the maximum,the vertical velocity insignificantly decreases and sta??bilizes at the steady??state values corresponding to thetime interval long after the onset of conduit formation.Far from the axis of the channel, the radial component(r)of the velocity vw becomes vanishingly small, and the(z)vertical component vw becomes indistinguishablefrom its initial value v0 over all time scales.The changes in the hydrodynamic regime in thesediment layer promote the enhancement of the bot??tomward heat and mass transfer within the channeland adjacent regions, leading to the rise in tempera??ture inside and close to the heterogeneity. The exam??ple in Fig. 4 illustrates the temperature incrementΔT=T(r,z,t)?Tst(z) relative to its initial value on thechannel axis for different time t as a result of the for??mation of the fluid flow channel. This figure and, par??ticularly, the inset clearly demonstrate the dramaticchange in the curves of temperature increments in theupper part of the channel (the appearance of localminima—sharp bends of the curves) due to the heatremoval from the medium at phase transition frommethane hydrate to methane gas. The anomalousbehavior of temperature curves fades with time afterthe onset of channel formation.The character of the changes in temperature incre??ments, along the vertical profiles inside the channeland within its closest proximity (r≤1000 m), isapproximately the same as on the axis. Farther awayfrom the axis and after a longer time after the begin??ning of channel nucleation, the areas appearwherein the temperature increments are negative(ΔTmin=?0.12 K). This effect is accounted for bythe reduction of the convective component of the heattransfer due to the water outflow into the channel andslowdown of the vertical fluid filtration. The cooling ofthe sediments compared to their initial temperatureshifts the base of the methane hydrate stability zonedownwards. However, methane gas is absent in thepores of the sediment at z≤z0ph in our model, andcrystallization of the hydrates and thickening of thehydrate??bearing layer do not occur here. As the timeincreases, the channel??surrounding domain where thetemperature increments are nonnegative (ΔT) pro??gressively expands along the radius and involves theentire area of computations at t≥150 ka.An even more strikingly pronounced manifestationof the phase transition than that shown in Fig. 4 isobserved in Fig. 5, which illustrates the changes in theconductive component of the vertical heat flow alongthe channel axis. The negative jumps in the heat flow

No. 4 2014IZVESTIYA, PHYSICS OF THE SOLID EARTH Vol. 50

THE IMPACT OF FAULTING ON THE STABILITY CONDITIONS OF GAS HYDRATES539

mark the position of the phase boundary at each timeinterval shown in the figure. The amplitudes of thejumps rapidly decrease with time, although remainingnoticeable up to t = 500 ka and even longer. Thesejumps agree with the well??known Stefan condition andclearly demonstrate that in the solution of the phasetransition problem, the inclusion of the termLρhφδhδ(T?Tph) in expression (5) for volumetric heatcapacity is equivalent to the direct application of thiscondition.

The formation of the fluid flow channel manifestsitself in Fig. 5 by the anomalous increase of the axialheat flow down to the lake bottom, where its conduc??tive component at t = 1 Ma is slightly higher than600mW/m2, which exceeds its initial value on thissurface by a factor of 15. The character of changes inthe vertical component of the conductive heat flowacross the lake bottom is shown in Fig. 6. Outside thechannel at all t > 0, the flow on the lake bottom quitesteeply decreases with distance from the axis andapproaches the initial value. Unfortunately, we cannotvalidate the calculated distribution of the conductiveheat flow at the lake bottom by the correspondingobservations because such measurements were notconducted in the region of study.