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Numerical simulations on consolidation effects have been carried out for gas production from offshore methane hydrates (MH) layers and subsidence at seafloor. MH dissociation is affected by not only MH equilibrium line but also consolidation (mechanical compaction) depended on depressurization in the MH reservoir. Firstly, to confirm present model on consolidation with effective stress, the history matching on gas production and consolidation has been done to the experimental results using with synthetic sand MH core presented by Sakamoto
*et al.* (2009). In addition, the comparisons of numerical simulation results of present and Kurihara
*et al.* (2009) were carried out to check applicability of present models for gas production from MH reservoir in field scale by depressurization method. The delays of pressure propagation in the MH reservoir and elapsed time at peak gas production rate were predicted by considering consolidation effects by depressurization method. Finally, seabed subsidence during gas production from MH reservoirs was numerically simulated. The maximum seabed subsidence has been predicted to be roughly 0.5 to 2 m after 50 days of gas production from MH reservoirs that elastic modulus is 400 to 100 MPa at MH saturation = 0.

Methane hydrates (MH) has been expected to be the next-generation natural gas resources. Most of MH is reserved in marine sediments or permafrost in the offshore area of 900 km^{2} at Eastern Nankai Trough located at pacific coast of Honshu island in Japan. According to Fuji et al. (2008) [

As gas production methods from MH reservoirs, depressurization, thermal stimulation, inhibitor injection, N_{2}, CO_{2} or their mixing gases injection have been proposed and studied to enhance in-situ MH dissociation in considering MH equilibrium condition presented by Pooladi-Darvish (2004) [^{3} of natural gas was produced for six days. Moridis et al. (2010) [

For the case of depressurization method, bottom-hole pressure (BHP) at a producer is reduced by the lowering hydraulic head by pumping up water in the producer, and MH dissociation process in the reservoir begins after pressure propagation from the producer. Depressurization must be kept to maintain gas production rate or MH dissociation rate. The MH dissociation-rate is proportional to heat transfer rate to the MH from outside sands and water with available sensible heat which depends on the difference between present temperature and MH equilibrium temperature corresponding to the MH pressure after depressurization.

However, depressurization and the decrease of solid saturation by the MH dissociation induce consolidation of MH reservoir and nearby sediments. The seabed subsidence is summation of deformation propagated from the three dimensional consolidation in sediment layers lower than the seabed. The depressurization causes increasing effective stress and reducing fluids permeability that makes low pressure propagation speed and low gas mobility in the MH reservoir. As a result, MH dissociation and gas production are suppressed by those processes connecting each other.

The reservoir consolidation and seabed subsidence are important issues to keep gas production rate from MH reservoir and control stabilities of seabed, sediment layers and producer. In this research, the numerical model considering MH dissociation and consolidation has been presented by history matching with the laboratory experiments carried by [

Once depressurization method is applied for a reservoir, pore pressure is decreased, and effective stress (= confining stress-pore pressure) is increased simultaneously. Further MH reservoir at Eastern Nankai trough is an unconsolidated sand sediment-layer that makes easy to induce the consolidation with increasing effective stress. The coordinate system of numerical simulation model considering consolidation of MH reservoir and seabed subsidence is shown in

The reservoir simulator CMG STARS^{TM} was used for numerical simulations on gas production and consolidation based on MH dissociation and elasticity function of MH saturation. In the simulations, MH was defined as solid phase that saturation in MH reservoir porosity reduces absolute permeability with power function [

The increase of MH saturation (solid phase) results in sharply decrease of relative permeability due to decrease of apparent porosity in the MH reservoir. Conversely, apparent porosity and permeability increase rapidly by MH dissociation. In addition, porosity depended on congenital compressibility of MH reservoir is decreased by increase of effective stress with depressurization. In this numerical simulation, effective porosity, which depends on MH saturation, compressibility and depressurization, is defined by following Equations (2) and (3).

where

ϕ_{v}: Porosity [-]

ϕ_{i}: Initial porosity [-]

κ: Compressibility [MPa^{−1}]

p: Reservoir pressure [MPa]

p_{i}: Initial reservoir pressure [MPa]

φ_{e}: Effective porosity [-]

S_{MH}: MH saturation [-]

The initial permeability of MH reservoir is remarkably low at the initial condition which has high MH saturation over 50%, however the apparent permeability of MH reservoir is improved rapidly with MH dissociation [

where

k: Apparent permeability [m^{2}]

k_{ab}: Absolute permeability [m^{2}]

N: Permeability reduction index (=6) [-]

In present research, the experimental results by [

The relative permeabilities were presented by Sakamoto et al. (2010) [

where

k_{rg}: Gas relative permeability [-]

k_{rw}: Water relative permeability [-]

c: End point for gas relative permeability [-]

b: End point for water relative permeability [-]

m: Index of gas relative permeability k_{rg} [-]

n: Index of water relative permeability k_{rw} [-]

The numerical block models in cylindrical coordinate were made for the laboratory experiments. Outer radius and height of the stainless cell are 89.4 mm and 144 mm (see

Equations (4) and (5) presented by [

Porosity, | 38.1 |
---|---|

Absolute Permeability, ^{2}] | 8.33 × 10^{−12} |

Initial MH Saturation, | 57.7 |

Initial Water Saturation, S_{w}_{0} [%] | 40.4 |

Initial Gas Saturation, S_{g}_{0} [%] | 1.9 |

Initial Temperature, T_{i} [˚C] | 10.7 |

Initial Pressure, p_{i} [MPa] | 10.0 |

Outlet Pressure, p_{out} [MPa]_{ } | 3.3 |

in pores by capillary pressure. The values of m and n were set as 10 and 3 in the Equations (5) and (6) respectively in order to represent that water has higher mobility than gas in the region of high water saturation.

As shown in

where

κ: Compressibility [MPa^{−1}]

ν: Poisson’s ratio [-]

E: Elastic modulus of MH reservoir (

E_{0}: Elastic modulus of sands (Rock matrix) (

S_{MH}: MH saturation [-]

β: Increase rate of elastic modulus vs.

Seabed subsidence is induced by decrease of porosity of sediment layers and the MH reservoir consolidation. In this research, the amount of seabed subsidence was evaluated as summation of vertical compaction in a grid at each distance from the seabed to MH reservoir given by

where

Δh: Displacement of seabed [m]

z: distance from seabed [m]

α: Subsidence ratio [-]

ζ: Distance index of subsidence [1/m]

The subsidence ratio (α), that has the value from 0 to 1, is contributing ratio of each grid’s displacement at z on the seabed subsidence at z = 0 based on Aoki et al. (1991) [

Authors have done the comparisons of cumulative methane gas and water productions between the laboratory experiments and present numerical simulation (see

The displacement behavior was recalculated by using modified compressibility considering cohesive strength of MH with varying initial elastic modulus of rock matrix E_{0} = 100 to 200 MPa, Poisson’s ratio ν = 0.2 to 0.6

and increase rate of elastic modulus β = 600 to 1000 MPa based on experimental results presented by Masui et al. (2005) [_{0} = 200 MPa, ν = 0.217 and β = 700 MPa, were used, the numerical simulation result showed the best matching with the experiments by [_{0} + βS_{MH}, is better than that with E = E_{0} = constant.

The comparison of temperature distributions between the laboratory experiment and present numerical simulation is shown in

As shown in

It was confirmed that present numerical simulation model can be used for simulating MH dissociation process and consolidation behavior in laboratory scale based on the history matching results presented in [

Comparative studies on numerical MH model were done by [

In the comparative studies, typical properties of MH reservoir at Eastern Nankai Trough given in

pressure difference 10.2 MPa between initial reservoir pressure 13.2 MPa and bottom-hole pressure 3.0 MPa was applied for depressurization in the MH reservoir.

The numerical simulations in considering field-scale sand consolidation were carried out by the considering model presented in the previous section based on matching with the laboratory experiments. Hereinafter simulations without consolidation or porosity change by setting E_{0} = ∞ are called as “base case” that was compared with ones considering consolidation in MH reservoir where E_{0} = 200, 140 and 80 MPa were given for sand layer, silt layer and mud layer, respectively, while ν = 0.217 was given for three layers that were presented by Yoneda (2013) [

As shown in ^{7} and 3.8 × 10^{7} m^{3} respectively. It is concluded that

Porosity, | 38.1 |
---|---|

Absolute Permeability, k_{ab} [m^{2}] | 8.33 × 10^{−12} |

Initial MH Saturation, | 57.7 |

Initial Water Saturation, S_{w}_{0} [%] | 40.4 |

Initial Gas Saturation, S_{g}_{0} [%] | 1.9 |

Initial Temperature, T_{i} [˚C] | 10.7 |

Initial Pressure, p_{i} [MPa] | 10.0 |

Outlet Pressure, p_{out} [MPa]_{ } | 3.3 |

present model has almost applicability for gas production from MH reservoirs in field scale, because little differences in modelling of relative permeability, heat capacities and pressure-temperature equilibrium between two models made effects on pressure propagation, MH dissociation and gas production.

_{0} in the consolidation model on gas production behaviors. It was confirmed that time showing the peak rate was approximately 530 days that is longer than 290 days of the base case, while the gas peak rate decreased to 45% of the base case. The decrease of absolute permeability by sand consolidation makes delay of pressure propagation and gas peak rate, however, the cumulative gas productions at 1825 days were approximately same value of 32 × 10^{6} m^{3}. After 1600 days, bottom-hole pressure propagated to whole reservoir region, therefore gas production rate or MH dissociation rate depends on reservoir permeability and heat supply to MH reservoir from upper and lower sediment layers. The peak times of gas production rate delayed with decreasing value of E_{0}. The time showing the peak production rate was around 400 to 930 days for E_{0} = 100 to ∞ MPa. However, the differences of cumulative gas productions after 2200 days are much smaller than that of early stage after start of depressurization. Based on calculation results of absolute permeability and pressure distributions in radial direction, it was confirmed that pressure propagation has strong relation with MH dissociation process and gas production behavior.

Numerical simulation of seabed subsidence was done for the MH reservoirs with two models of elastic modulus expressed by E = E_{0} and E = E_{0} + βS_{MH}. To decide the subsidence ratio α, field measurement data are required. In this research, the value of water-dissolved gas field, ζ = 0.0012 which was reported by [

Seabed subsidence behaviors were simulated for two models of elastic modulus to predict the largest subsidence and the largest gradient of subsidence.

values of E_{0} at 50 days from start of depressurization. In both of the models, the maximum amount of the subsidence becomes larger with decreasing E_{0}. For the model of E = E_{0}, values of the largest subsidence, Δh_{max} = 1.4, 1.6 and 2.0 m for E_{0} = 100, 200 and 400 MPa, respectively, and radius boundaries, r_{B} showing the value of subsidence Δh = 0.1 m are calculated as r_{B} = 31.8, 40.0 and 47.0 m for E_{0} = 100, 200 and 400 MPa, respectively, while for the model of E = E_{0} + βS_{MH,} Δh_{max} = 0.50, 1.0 and 1.85 m and r_{B} = 30.2, 34.8 and 36.4 m for E_{0} = 100, 200 and 400 MPa, respectively. The differences of two models are caused by existence of residual MH biding sand grains. It is estimated that the residual MH increases appearance elastic modulus of MH reservoir, then the seabed subsidence is controlled.

In this study, the consolidation-permeability compound model has been applied for numerical simulations on gas production from offshore methane hydrates (MH) reservoir. The model has been constructed by numerical history matching with experimental results on MH dissociation and consolidation by depressurization using the synthetic sand core presented by [

In our next study, the methodology presented in this paper will apply to simulate seabed subsidence during gas production by a thermal production method with hot water injection using horizontal wells proposed by authors [

Hiroki Matsuda,Takafumi Yamakawa,Yuichi Sugai,Kyuro Sasaki, (2016) Gas Production from Offshore Methane Hydrate Layer and Seabed Subsidence by Depressurization Method. Engineering,08,353-364. doi: 10.4236/eng.2016.86033

md = 9.8E−16 m^{2}

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