# Numerical Simulation of Improved Gas Production from Oceanic Gas Hydrate Accumulation by Permeability Enhancement Associated with Geomechanical Response

^{1}

^{2}

^{3}

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## Abstract

**:**

_{g}), followed by the TPL (23.54%) and the HBL (4.29%). The cumulative water-to-gas ratio (R

_{wgT}) gradually decreased during gas production, with the HBL exhibiting the highest value. Permeability enhancement can improve gas production, with the FGL being the most responsive to such enhancement. It increased V

_{g}by 87% and reduced R

_{wgT}to 85%. To achieve more realistic production schemes and better enhance energy recovery, it is advisable to conduct numerical investigations that incorporate geomechanical considerations due to the intricate nature of hydrate-bearing sediments.

## 1. Introduction

#### 1.1. Background

_{2}per unit of energy [2]. The potential reserves of hydrated gas are over 1.5 × 10

^{16}m

^{3}and are widely distributed throughout the earth [3], with over 230 hydrate deposits discovered globally in ocean floors and permafrost zones. To extract methane gas from hydrate reservoirs, the in-situ equilibrium condition (high pressure and low temperature) of NGH must be broken, allowing it to decompose and be produced as fluid. Four methods can be used for gas recovery from hydrate-bearing sediments, including depressurization [4,5], thermal stimulation [6], inhibitor injection [7], and CO

_{2}–CH

_{4}replacement [8,9,10,11]. National programs exist in many countries to research and produce natural gas from gas hydrate deposits in order to discover the commercialization possibility of methane hydrate resources, leading to various studies on the Alaska North Slope [12,13,14,15], the Mallik site in Canada [4,16,17], the Black Sea [18,19], the Krishna–Godavari basin in India [20,21], the Ulleung basin in Korea [22,23], the Nankai Trough in Japan [24,25,26], and the South China Sea [27,28,29] and Qilian Mountain [30] in China.

^{5}ST m

^{3}, averaging 5.15 × 10

^{3}ST m

^{3}/d [29]. This achievement marked the most significant amount of gas production and the longest production period in history. Recently, the China Geological Survey performed another production test using a horizontal well for the first time in the Shenhu Area, achieving a 30-day continuous gas production process. The total gas production reached 8.614 × 10

^{5}ST m

^{3}, averaging 2.87 × 10

^{4}ST m

^{3}/d [27]. The gas production rates in both production tests remain significantly below 5.00 × 10

^{5}ST m

^{3}/d, which is necessary for the commercial exploitation of NGHs [1].

#### 1.2. Targeted Accumulation

#### 1.3. Objectives

## 2. Methodology

#### 2.1. Coupled Numerical Simulators

#### 2.2. Governing Equations

#### 2.2.1. Flows of Fluid and Heat

_{2}O, m refers to CH

_{4}, and i refers to water-soluble inhibitor), $\varphi $ represents the porosity, ${S}_{\beta}$ represents the saturation of phase $\beta $, ${\rho}_{\beta}$ represents the density of phase $\beta $, and ${X}_{\beta}^{\kappa}$ represents the mass fraction of component $\kappa $ in phase $\beta $.

_{R}is the heat capacity of the dry rock, T is the temperature, and ${U}_{\beta}$ is the specific internal energy of phase $\beta $. The energy change of hydrate dissociation Q

_{diss}is

_{f}is 33.72995 J∙gmol∙kg

^{−1}∙cal

^{−1},

_{4}and H

_{2}O system) or (b) a kinetic reaction (the hydrate is regarded as a distinct component) [60]. The former was employed in this study. Interested readers can refer to Moridis [40,61] for in-depth information on the specifics of the two models and the associated thermodynamics.

_{2}O, CH

_{4}, and inhibitor) contributed by the aqueous and gaseous phases is defined as

**k**is the absolute permeability tensor, and

**g**is the gravity vector.

#### 2.2.2. Geomechanics

_{f}is the saturation-weighted fluid density, which is calculated using

**C**is the elasticity tensor, ${\sigma}^{\prime}$ is the effective stress tensor,

**I**is the identity matrix, and $\epsilon $ is the strain tensor. Biot’s coefficient α [62] is defined as

_{s}is the skeletal grain modulus, and K

_{dr}is the drained bulk modulus. The average mobile fluid pressure P

_{t}is calculated using

**u**is the displacement vector.

#### 2.2.3. The Coupling Method between Geomechanics and Flows of Fluid and Heat

_{dr}is the drained modulus, ε

_{v}is the volumetric strain, and $\delta {P}_{t}{}^{k-1}$ is the difference at the NR iteration k and k − 1.

_{H}has a higher value. However, there is a scarcity of research on how the properties are related to the hydrate phase. Rutqvist and Moridis [50] proposed a standard approach that utilizes linear interpolation equations as follows:

_{H}= 0, and subscript 1 denotes S

_{H}= 1.

## 3. Numerical Model

#### 3.1. The Geologic Model

#### 3.2. Domain Discretization

_{w}< r ≤ 1 m, while that of 0.20 m was used for 1 m ≤ r ≤ 21 m. For distances greater than 21 m but less than 300 m (r

_{max}), Δr increased logarithmically for r > 0.20 m. The segment length in the vertical direction (Δz) was 0.5 m in the hydrate accumulation area and was larger in OB and UB. A mesh representation of the domain used in this study is presented in Figure 5a, while a more detailed representation of the grid near the wellbore is given in Figure 5b.

_{2}O, CH

_{4}, and NaCl) as well as the heat balance of the system. Previous research has demonstrated that a chemical equilibrium reaction provides an accurate result during hydrate formation/dissociation in gas production [60]. To account for the scale of the problem, a total of 560,000 equations were formulated, consisting of approximately 380,000 equations in pT+H V1.5 and 180,000 equations in the RGMS. Consequently, the problem sizes necessitated the use of pT+H V1.5 and the RGMS to provide practical solutions.

#### 3.3. Well Description

^{−9}m

^{2}, the porosity was 1, the capillary pressure was 0, the irreducible gas saturation was 0.005, and the relative permeabilities had linear relationships with phase saturations. This approach was able to simulate the pressure drop in a steel wellbore, which was validated in a previous study [66]. The bottomhole pressure (P

_{bh}) was 3 MPa [67] at a gridblock above the topmost well gridblock.

#### 3.4. System Properties

#### 3.5. Initial Conditions

#### 3.6. Model Validation

^{5}ST m

^{3}[29]. Using the constructed model, a simulation was performed to replicate the 60-day production, taking into account the geomechanical responses. The simulation resulted in a total gas production of 3.08 × 10

^{5}ST m

^{3}, as depicted in Figure 6. This successful replication serves as validation for the constructed model.

#### 3.7. Simulations Cases

_{s}within the region from 0 to the stimulated radius (r

_{s}) within a specific layer. To assess the effectiveness of permeability enhancement, a permeability enhancement ratio (f

_{k}= k

_{s}/k

_{0}) was proposed, in which k

_{0}is the original permeability of the layer. There are four different values of r

_{s}(0.3 m, 0.5 m, 1 m, and 2 m) and three different values of f

_{k}(2, 4, and 8), combined with three layers, resulting in a total of thirty-six cases.

## 4. Results and Discussion

_{G}), hydrate saturation (S

_{H}), the production rates of CH

_{4}and H

_{2}O (Q

_{g}and Q

_{w}, respectively), and the cumulative production of CH

_{4}and H

_{2}O (V

_{g}and M

_{w}, respectively), The water-to-gas ratio was also monitored, both instantaneously (R

_{wg}= Q

_{w}/Q

_{g}) and cumulatively (R

_{wgT}= M

_{w}/V

_{g}). Geomechanics-related parameters monitored were radial and vertical displacements (u

_{r}and u

_{z}, respectively) at key locations. To evaluate the influence of permeability enhancement, the key parameters are V

_{g}and R

_{wgT}. Specifically, more gas and less water are desired after permeability enhancement, so larger V

_{g}and smaller R

_{wgT}values are better.

#### 4.1. Base Case

#### 4.1.1. Fluid Production

_{g}produced at the well from the HBL, TPL, and FGL and all layers in the base case. The value of Q

_{g}has an initial peak after production begins, followed by a decline and minor fluctuations within a certain range in the subsequent production period. The initial peak is caused by the rapid dissociation of hydrates near the wellbore region and a subsequent surge in gas production rate after the bottomhole pressure drops. In addition, the free gas in the TPL and FGL contributes to the initial peak of Q

_{g}. The average gas production over the entire production period is 0.074 ST m

^{3}/s, which is far below the gas production rate of 0.579 ST m

^{3}/s (=5.00 × 10

^{5}ST m

^{3}/d) required for the commercial exploitation of NGHs [1]. Compared with hydrate deposits in Mount Elbert, Alaska North Slope, where there exists a lag time before substantial gas production [14], the hydrate deposit at well SHSC-4 does not exhibit such a lag phenomenon but instead has the highest gas production rate in the early stage of production, indicating that this class of hydrate deposit is conducive to exploitation. The contribution of each layer to the total gas production rate was ranked from highest to lowest as FGL, TPL, and HBL, indicating that the FGL is the primary source of gas production. This suggests that the FGL is the most important layer for gas production in the studied area.

_{g}produced at the well from the HBL, TPL, and FGL and all layers in the base case. As shown in the figure, in the later production period, since Q

_{g}fluctuates within a certain range, V

_{g}, which is the integral of gas production over time, shows a nearly linear relationship with time. After 120 days of production, the FGL, TPL, and HBL accounted for 72.17%, 23.54%, and 4.29% of the total cumulative gas production, respectively. This also indicates that the FGL is the most important layer for gas production because it has the highest contribution to the total cumulative gas production. It is anticipated that the FGL will exhibit the most pronounced response to permeability enhancement.

_{wg}and R

_{wgT}produced at the well from the HBL, TPL, and FGL and all layers in the base case. Apart from directly evaluating production via Q

_{g}and V

_{g}, R

_{wg}and R

_{wgT}can also be used to indirectly characterize production performance. In real practice, more gas and less water are desired, so smaller R

_{wg}and R

_{wgT}values are better. R

_{wg}produced from the HBL, TPL, and FGL and all layers decreased gradually during production. Among the three layers, the HBL has the highest R

_{wg}with the smallest contribution to gas production observed in Figure 8. Moreover, R

_{wg}produced from the HBL is tens of times higher than those from TPL and FGL. If permeability enhancement is carried out within HBL, gas production may increase, while water production may also increase. R

_{wgT}reaches a short-term peak in the first two days of production and then shows a decreasing trend throughout the entire production period. R

_{wgT}produced from the FGL and all layers tends to stabilize in the later period of production. Due to the large R

_{wgT}produced from HBL, the total R

_{wgT}was far higher than those from TPL and FGL.

_{r}and u

_{z}at key locations in the base case. As P

_{bh}is lower than the pressure of the formation, the reservoir is “squeezed” and moves toward the vertical well in the radial direction, but the compaction is not significant. Although the location with the largest radial displacement occurs at (r, z) = (1 m, −201 m), the absolute value does not exceed 0.01 m when the simulation ends. In the vertical direction, the subsidence at the top of the HBL and the uplift at the bottom are observed. As the gridblock that was set to the bottomhole pressure is closer to the top of the HBL, the subsidence at the top of HBL is more obvious, with a maximum level of no more than 0.08 m. Overall, the displacement within the formation is not significant.

#### 4.1.2. Spatial Distributions

_{H}in the base case. Hydrate dissociation occurs in the area where the significant pressure drop is shown in Figure 11 and the low temperature is presented in Figure 12. Hydrates gradually dissociate during production, but the unevenness of hydrate dissociation progress in each layer becomes apparent. The dissociation rate of the HBL is relatively uniform, while the lower part of the TPL undergoes hydrate dissociation, followed by hydrate formation. Moreover, in the FGL, the hydrate forms and dissociates alternatively. This phenomenon may be caused by the Joule–Thomson cooling effect, the capillary effect, the “upstream weighting” approach applied in the simulator [72], and the equilibrium model used in this study. The cyclic process of hydrate formation and dissociation in the FGL ultimately led to the temperature reaching 0.01 °C, resulting in the simulation stopping.

_{G}in the base case. The evolution of gas saturation in the base case is also presented. The gas saturation in the HBL and TPL gradually expands, and some gas migrates from the TPL to the HBL. Gas dissociated from hydrate in the lower part of the TPL migrates toward the wellbore radially and toward the HBL vertically at a very slow rate due to the low permeability of the TPL (1.5 mD), resulting in gas accumulation in the lower part of the TPL. In the FGL, a large amount of gas flows into the wellbore because of the significantly lower wellbore pressure compared to the formation pressure and higher formation permeability. The Joule–Thomson effect caused by the rapidly migrating gas may have caused the low temperature in the FGL, meeting the conditions for hydrate generation. Thus, hydrates are formed, hindering the radial gas migration in the FGL and causing the gas to accumulate on the side away from the wellbore.

#### 4.2. Effect of Permeability Enhancement

#### 4.2.1. Fluid Production

_{g}with permeability enhancement and its ratio relative to that in the base case after 120-day production, respectively. For reference, the V

_{g}in the base case (V

_{g,}

_{0}) is 620,668 ST m

^{3}following 120 days of production. The permeability enhancement of three different layers (i.e., the HBL, TPL, and FGL) shows that the larger the values of r

_{s}and k

_{f}, the more significant the increase in gas production. When (k

_{f}, r

_{s}) = (8, 2 m), the V

_{g}values, predicted by improving the permeabilities of the HBL, TPL, and FGL, are 711,590, 706,541, and 1,160,649 ST m

^{3}, respectively. Compared to the base case, the production was increased by 15%, 15%, and 87% corresponding to the modification in the HBL, TPL, and FGL, respectively. In order to reach higher production, the permeability of the FGL should be enhanced.

_{wgT}with permeability enhancement and its ratio relative to that in the base case after 120-day production, respectively. For reference, the cumulative water–gas ratio (R

_{wgT}

_{,0}) is 2.84 kg H

_{2}O/m

^{3}CH

_{4}following 120 days of production. The results of permeability enhancement in the HBL show that the larger the values of r

_{s}and k

_{f}, the larger the R

_{wgT}. The increase in permeability near the wellbore area in the HBL results in a greater increase in water production than gas production, leading to a larger R

_{wgT}. The results of permeability enhancement in the TPL and FGL show that the larger the values of r

_{s}and k

_{f}, the smaller the R

_{wgT}. When (k

_{f}, r

_{s}) = (8, 2 m), the R

_{wgT}values, determined by permeability enhancement in the HBL, TPL, and FGL are 4.03, 3.17, and 2.41 kg H

_{2}O/m

^{3}CH

_{4}, respectively. The resulting ratios of R

_{wgT}to R

_{wgT}

_{,0}are 1.42, 1.12, and 0.85 when the permeabilities of the HBL, TPL, and FGL are increased, respectively. To reduce the amount of separated water required for unit gas production, the FGL should be treated to enhance its permeability.

#### 4.2.2. Spatial Distributions

_{H}, and S

_{G}with permeability enhancement after 120 days of production are arranged in a manner where the r

_{s}values increase from left to right and the k

_{f}values increase from top to bottom. The highest V

_{g}and the lowest R

_{wgT}are achieved after increasing the permeabilities of the FGL, and only the spatial distributions with permeability enhancement in the FGL are discussed.

_{f}is small, augmenting r

_{s}has an insignificant effect on the area of pressure drop, and the spatial distributions of P remain relatively unchanged compared to the base case. Conversely, when the value of k

_{f}is large, the increasing r

_{s}results in a narrower area of pressure drop in the upper section of the FGL and the lower section of the TPL, which is closer to the wellbore.

_{f}is small, the varying r

_{s}has a negligible effect on the spatial distributions of T compared to the base case, which is comparable to the area of pressure drop presented in Figure 15. However, when k

_{f}equals 4, an increase in r

_{s}results in a shrinkage of the low-temperature area within the FGL, with a gradual shift of the lowest temperature from the upper to the middle section of the FGL. Furthermore, when (k

_{f}, r

_{s}) = (8, 2 m), the low-temperature region within the FGL becomes exceedingly small.

_{H}and S

_{G}with permeability enhancement in the FGL after 120 days of production, respectively. In Figure 17, as the k

_{f}and r

_{s}values increase, the formation and dissociation of gas hydrate transpire in closer proximity to the wellbore, thereby facilitating the production of gas dissociated from gas hydrate. Furthermore, Figure 18 demonstrates that the formation of gas hydrate is less likely to obstruct the flow of gas, resulting in less gas accumulating on the side of the gas hydrate that is farther from the wellbore. These two figures collectively suggest that augmenting k

_{f}and r

_{s}values is more conducive to gas production. This assertion is supported by Table 3 and Table 4, which indicate that larger k

_{f}and r

_{s}values yield higher cumulative gas production.

## 5. Conclusions

- To evaluate the effectiveness of permeability enhancement considering the geomechanical responses in the Shenhu area, a coupled simulation using pTOUGH+HYDRATE V1.5 and the RGMS (Reservoir Geomechanics Simulator) is implemented.
- Based on the geophysical surveys and analysis of core samples at well SHSC-4 located in the Shenhu area of the northern South China Sea, the established numerical simulation model is accurate, and the simulation results are highly consistent with the trial production data, ensuring the reliability of the outcomes obtained in this study.
- In the base case, the formation and dissociation of gas hydrates in the free gas layer (FGL) alternate, ultimately resulting in a low-temperature region near 0 °C and leading to the cessation of the simulation after 120 days of production. The cumulative gas production reached 6.2 × 10
^{5}ST m^{3}. - In the base case, the FGL contributes the most to gas production, accounting for 72.17% of the cumulative gas production (V
_{g}), followed by the three-phase layer (TPL), accounting for 23.54% of the cumulative gas production, and the hydrate-bearing layer (HBL) contributes the least, accounting for only 4.29% of the cumulative gas production. - In the base case, the cumulative water-to-gas ratio (R
_{wg}) from the HBL, TPL, and FGL gradually decreases during the production of gas hydrates. R_{wgT}from the HBL, which contributes the least to gas production, is the highest, with a value several times those from TPL and FGL. - In the base case, the gas production obtained without permeability enhancement is insufficient for commercial production. Permeability enhancement can be an option used to increase gas production.
- After increasing the permeabilities of the HBL, TPL, and FGL with the same permeability enhancement ratio (f
_{k}) and the same simulated radius (r_{s}), the improvement effect of modifying the FGL is the best, with a maximum increase of 87%. The required mass of water separated from a unit of gas is the lowest when applying permeability enhancement in the FGL, with a minimum value of 85% of the original separation mass. - The results of modifying the FGL show that the higher the degree of permeability enhancement, the deeper the impact of permeability enhancement and the closer the formation and dissociation of gas hydrates are to the wellbore, making it more difficult for gas to be obstructed by the formation of gas hydrates, which is more conducive to production.
- Although permeability enhancement is attempted in this study, it did not extend the production period as the simulation still ends due to low temperature in the FGL. Future research should focus on exploring methods to prevent such low temperatures from occurring in the FGL.
- The results obtained by considering geomechanical responses differ from previous numerical studies that only considered flow and thermal behaviors. This indicates that neglecting geomechanical responses may result in an incorrect natural gas hydrate production scheme. Therefore, future numerical studies should take geomechanical responses into consideration to obtain more realistic results.
- In future work, it is imperative to discover production schemes that effectively mitigate the occurrence of a low-temperature region after 120 days of production, which currently causes disruptions in numerical simulations, thus enabling the extension of the observation period. Moreover, new production schemes combined with permeability enhancement should be explored to facilitate the achievement of production rates that meet the necessary threshold for the commercial exploitation of natural gas hydrates.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

$\Delta ()$ | Change in the quantity in parentheses |

$\Delta {H}^{0}$ | Specific enthalpy of hydrate dissociation/formation (J∙kg^{−1}) |

$\nabla $ | Del operator |

C_{R} | Heat capacity of the dry rock (J∙kg^{−1}∙K^{−1}) |

dA | Differential surface (m^{2}) |

dV | Differential volume (m^{3}) |

E | Young’s modulus (Pa) |

G | Shear modulus (Pa) |

G_{0} | Shear modulus when the hydrate saturation is zero (Pa) |

G_{1} | Shear modulus when the hydrate saturation is one (Pa) |

h_{β} | Specific enthalpy of phase $\beta $ (J∙kg^{−1}) |

K_{dr} | Drained bulk modulus (Pa) |

K_{dr}_{0} | Drained modulus when the hydrate saturation is zero (Pa) |

K_{dr}_{1} | Drained modulus when the hydrate saturation is one (Pa) |

${K}_{s}$ | Skeletal grain modulus (Pa) |

${k}_{r}$ | Radial permeability (m^{2}) |

${k}_{r\beta}$ | Relative permeability of phase $\beta $ |

${k}_{v}$ | Vertical permeability (m^{2}) |

$\overline{{k}_{\theta}}$ | Composite thermal conductivity of the medium/fluid ensemble (W∙m^{−1}∙K^{−1}) |

${k}_{\theta d}$ | Formation thermal conductivity under desaturated conditions (W∙m^{−1}∙K^{−1}) |

${k}_{\theta w}$ | Formation thermal conductivity under fully liquid-saturated conditions (W∙m^{−1}∙K^{−1}) |

${k}_{\theta I}$ | Thermal conductivity of ice phase (W∙m^{−1}∙K^{−1}) |

M_{A} | Cumulative mass of aqueous phase |

M_{G} | Cumulative mass of gaseous phase |

M^{θ} | Heat accumulation term |

M^{κ} | Mass accumulation of component κ (kg∙m^{−3}) |

P | Pressure (Pa) |

P_{t} | Average mobile fluid pressure (Pa) |

P_{t}_{,0} | Initial equivalent pore pressure (Pa) |

P_{β} | Pressure of phase $\beta $ (Pa) |

Q_{g} | Volumetric rate of CH_{4} well production |

Q_{w} | Water mass production rate |

q^{κ} | Source/sink term of component κ (kg∙m^{−3}∙s^{−1}) |

r | Radial direction |

R_{wg} | Instantaneous water-to-gas ratio |

R_{wgT} | Cumulative water-to-gas ratio |

${S}_{\beta}$ | Saturation of phase $\beta $ |

T | Temperature (K or °C) |

t | Time (s) |

u_{r} | Radial displacement (m) |

u_{z} | Vertical displacement (m) |

${U}_{\beta}$ | Specific internal energy of phase $\beta $ (J∙kg^{−1}) |

V_{g} | Cumulative volume of CH_{4} produced at the well |

V_{n} | Volume of the subdomain (m^{3}) |

${X}_{\beta}^{\kappa}$ | Mass fraction of component κ in phase $\beta $ |

z | Direction along the z-axis |

$\alpha $ | Biot’s coefficient |

Γ_{n} | Surface of subdomain n (m^{2}) |

γ | Empirical permeability reduction factor |

ε_{v} | Current volumetric strain |

ε_{v,}_{0} | Initial volumetric strain |

${\mu}_{\beta}$ | Viscosity of phase $\beta $ (Pa∙s) |

ν | Poisson’s ratio |

${\rho}_{b}$ | Bulk density (kg∙m^{−3}) |

${\rho}_{f}$ | Fluid density (kg∙m^{−3}) |

${\rho}_{R}$ | Rock density (kg∙m^{−3}) |

${\rho}_{\beta}$ | Density of phase $\beta $ (kg∙m^{−3}) |

$\varphi $ | Reservoir porosity |

${\varphi}_{0}$ | Initial porosity |

${F}^{\kappa}$ | Flux vector of component κ (kg∙m^{−2}∙s^{−1}) |

${F}_{\beta}$ | Flux vector of phase $\beta $ (kg∙m^{−2}∙s^{−1}) |

${F}_{\beta}^{\kappa}$ | Flux vector of component κ in phase $\beta $ (kg∙m^{−2}∙s^{−1}) |

g | Gravitational acceleration vector (m∙s^{−2}) |

k | Absolute permeability tensor (m^{2}) |

u | Displacement vector (m) |

$\epsilon $ | Strain tensor |

$\sigma $ | Total stress tensor (Pa) |

${\sigma}^{\prime}$ | Effective stress tensor (Pa) |

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**Figure 1.**Structural units in the northern South China Sea and the location of SHSC-4 (modified from Li et al. [29]).

**Figure 4.**System geometry and configuration of the single vertical well with a radius of 0.05 m, which is perforated from 201 mbsf to 268 mbsf as shown in the checkboard pattern, produced from a cylindrical section at well SHSC-4.

**Figure 8.**Evolution of (

**a**) the volumetric rate of the total CH4 production (Q

_{g}) and (

**b**) the cumulative volumes of CH

_{4}produced at the well (V

_{g}) in the base case.

**Figure 9.**Evolution of (

**a**) the instantaneous water-to-gas ratio at the well (R

_{wg}) and (

**b**) the cumulative water-to-gas ratio at the well (R

_{wgT}) in the base case.

**Figure 11.**Evolution of the spatial distributions of pressure (MPa) in the reservoir of the base case. (

**a**) 1-day production, (

**b**) 3-day production, (

**c**) 10-day production, (

**d**) 20-day production, (

**e**) 30-day production, (

**f**) 60-day production, (

**g**) 90-day production, and (

**h**) 120-day production.

**Figure 12.**Evolution of the spatial distributions of temperature (°C) in the reservoir of the base case. (

**a**) 1-day production, (

**b**) 3-day production, (

**c**) 10-day production, (

**d**) 20-day production, (

**e**) 30-day production, (

**f**) 60-day production, (

**g**) 90-day production, and (

**h**) 120-day production.

**Figure 13.**Evolution of the spatial distributions of hydrate saturation in the reservoir of the base case. (

**a**) 1-day production, (

**b**) 3-day production, (

**c**) 10-day production, (

**d**) 20-day production, (

**e**) 30-day production, (

**f**) 60-day production, (

**g**) 90-day production, and (

**h**) 120-day production.

**Figure 14.**Evolution of the spatial distributions of gas saturation in the reservoir of the base case. (

**a**) 1-day production, (

**b**) 3-day production, (

**c**) 10-day production, (

**d**) 20-day production, (

**e**) 30-day production, (

**f**) 60-day production, (

**g**) 90-day production, and (

**h**) 120-day production.

**Figure 15.**The spatial distributions of pressure (MPa) in the reservoir with permeability enhancement in FGL after 120-day production. (

**a**) (k

_{f}, r

_{s}) = (2, 0.3 m), (

**b**) (k

_{f}, r

_{s}) = (2, 0.5 m), (

**c**) (k

_{f}, r

_{s}) = (2, 1.0 m), (

**d**) (k

_{f}, r

_{s}) = (2, 2.0 m), (

**e**) (k

_{f}, r

_{s}) = (4, 0.3 m), (

**f**) (k

_{f}, r

_{s}) = (4, 0.5 m), (

**g**) (k

_{f}, r

_{s}) = (4, 1.0 m), (

**h**) (k

_{f}, r

_{s}) = (4, 2.0 m), (

**i**) (k

_{f}, r

_{s}) = (8, 0.3 m), (

**j**) (k

_{f}, r

_{s}) = (8, 0.5 m), (

**k**) (k

_{f}, r

_{s}) = (8, 1.0 m), and (

**l**) (k

_{f}, r

_{s}) = (8, 2.0 m).

**Figure 16.**The spatial distributions of temperature (°C) in the reservoir with permeability enhancement in FGL after 120-day production. (

**a**) (k

_{f}, r

_{s}) = (2, 0.3 m), (

**b**) (k

_{f}, r

_{s}) = (2, 0.5 m), (

**c**) (k

_{f}, r

_{s}) = (2, 1.0 m), (

**d**) (k

_{f}, r

_{s}) = (2, 2.0 m), (

**e**) (k

_{f}, r

_{s}) = (4, 0.3 m), (

**f**) (k

_{f}, r

_{s}) = (4, 0.5 m), (

**g**) (k

_{f}, r

_{s}) = (4, 1.0 m), (

**h**) (k

_{f}, r

_{s}) = (4, 2.0 m), (

**i**) (k

_{f}, r

_{s}) = (8, 0.3 m), (

**j**) (k

_{f}, r

_{s}) = (8, 0.5 m), (

**k**) (k

_{f}, r

_{s}) = (8, 1.0 m), and (

**l**) (k

_{f}, r

_{s}) = (8, 2.0 m).

**Figure 17.**The spatial distributions of hydrate saturation in the reservoir with permeability enhancement in FGL after 120-day production. (

**a**) (k

_{f}, r

_{s}) = (2, 0.3 m), (

**b**) (k

_{f}, r

_{s}) = (2, 0.5 m), (

**c**) (k

_{f}, r

_{s}) = (2, 1.0 m), (

**d**) (k

_{f}, r

_{s}) = (2, 2.0 m), (

**e**) (k

_{f}, r

_{s}) = (4, 0.3 m), (

**f**) (k

_{f}, r

_{s}) = (4, 0.5 m), (

**g**) (k

_{f}, r

_{s}) = (4, 1.0 m), (

**h**) (k

_{f}, r

_{s}) = (4, 2.0 m), (

**i**) (k

_{f}, r

_{s}) = (8, 0.3 m), (

**j**) (k

_{f}, r

_{s}) = (8, 0.5 m), (

**k**) (k

_{f}, r

_{s}) = (8, 1.0 m), and (

**l**) (k

_{f}, r

_{s}) = (8, 2.0 m).

**Figure 18.**The spatial distributions of gas saturation in the reservoir with permeability enhancement in FGL after 120-day production. (

**a**) (k

_{f}, r

_{s}) = (2, 0.3 m), (

**b**) (k

_{f}, r

_{s}) = (2, 0.5 m), (

**c**) (k

_{f}, r

_{s}) = (2, 1.0 m), (

**d**) (k

_{f}, r

_{s}) = (2, 2.0 m), (

**e**) (k

_{f}, r

_{s}) = (4, 0.3 m), (

**f**) (k

_{f}, r

_{s}) = (4, 0.5 m), (

**g**) (k

_{f}, r

_{s}) = (4, 1.0 m), (

**h**) (k

_{f}, r

_{s}) = (4, 2.0 m), (

**i**) (k

_{f}, r

_{s}) = (8, 0.3 m), (

**j**) (k

_{f}, r

_{s}) = (8, 0.5 m), (

**k**) (k

_{f}, r

_{s}) = (8, 1.0 m), and (

**l**) (k

_{f}, r

_{s}) = (8, 2.0 m).

Properties, Conditions, Models | Values |
---|---|

Initial pressure at the bottom of TPL | 14.93 MPa |

Initial temperature at the bottom of TPL | 14.82 °C |

Gas composition | 100% CH_{4} |

Initial saturation of HBL | S_{H} = 0.34 |

Intrinsic permeabilities of HBL | k_{h} = 2.86 × 10^{−15} m^{2} = 2.9 mD; k_{z} = k_{h} |

$\mathrm{Porosity}\varphi $ of HBL | 0.35 |

Initial saturation of TPL | S_{H} = 0.31, S_{G} = 0.078 |

Intrinsic permeabilities of TPL | k_{h} = 1.48 × 10^{−15} m^{2} = 1.5 mD; k_{z} = k_{h} |

$\mathrm{Porosity}\varphi $ of TPL | 0.33 |

Initial saturation of FGL | S_{G} = 0.078 |

Intrinsic permeabilities of FGL | k_{h} = 7.30 × 10^{−15} m^{2} = 7.4 mD; k_{z} = k_{h} |

$\mathrm{Porosity}\varphi $ of FGL | 0.32 |

Intrinsic permeabilities of OB | k_{h} = 9.87 × 10^{−18} m^{2} = 0.01 mD; k_{z} = k_{h} |

$\mathrm{Porosity}\varphi $ of OB | 0.10 |

Intrinsic permeabilities of UB | k_{h} = 9.87 × 10^{−18} m^{2} = 0.01 mD; k_{z} = k_{h} |

$\mathrm{Porosity}\varphi $ of UB | 0.10 |

Dry thermal conductivity | k_{θd} = 1 W∙m^{−1}∙K^{−1} |

Specific heat C_{R} | 1000 J kg^{−1}∙K^{−1} |

Grain density ρ_{R} | 2650 kg∙m^{−3} |

Composite thermal conductivity model [40] | $\begin{array}{c}\overline{{k}_{\theta}}={k}_{\theta d}+\left(\sqrt{{S}_{A}}+\sqrt{{S}_{H}}\right)\left({k}_{\theta w}-{k}_{\theta d}\right)\\ \hspace{1em}+\varphi {S}_{I}{k}_{\theta I}\hfill \end{array}$ |

Relative permeability model EPM#2 [40] | ${k}_{rA}=\mathrm{max}\left\{0,\mathrm{min}\left\{{\left[\frac{{S}_{A}-{S}_{irA}}{1-{S}_{irA}}\right]}^{n},1\right\}\right\}$; ${k}_{rG}=\mathrm{max}\left\{0,\mathrm{min}\left\{{\left[\frac{{S}_{G}-{S}_{irG}}{1-{S}_{irA}}\right]}^{{n}_{G}},1\right\}\right\}$; ${k}_{rH}=0$ |

S_{irA}, S_{irG}, n, n_{G} [69] | 0.65; 0.03; 3.50; 2.50 |

Capillary pressure model [70] | ${P}_{cap}=-{P}_{0}{\left[{\left({S}^{*}\right)}^{-\frac{1}{\lambda}}-1\right]}^{1-\lambda}$ ${S}^{*}=\frac{{S}_{A}-{S}_{irA}}{{S}_{mxA}-{S}_{irA}}$ |

λ, P_{0}, S_{irA}, S_{mxA} of HBLs | 0.45; 10^{4} Pa; 0.65; 1.0 |

Porosity–permeability relationship [71] | $\frac{k}{{k}_{0}}=\mathrm{exp}\left[\gamma \left(\frac{\varphi}{{\varphi}_{0}}-1\right)\right]$ |

Empirical permeability reduction factor γ [71] | 29.0 |

Properties | Values |
---|---|

Young’s modulus of HBL | E = 200 MPa at S_{H} = 0;E = 1.4 GPa at S _{H} = 1 |

Young’s modulus of TPL | E = 200 MPa at S_{H} = 0;E = 1.4 GPa at S _{H} = 1 |

Young’s modulus of FGL | E = 200 MPa |

Young’s modulus of OB | E = 70 MPa |

Young’s modulus of UB | E = 200 MPa |

Poisson’s ratio of HBL | ν = 0.15 |

Poisson’s ratio of TPL | ν = 0.15 |

Poisson’s ratio of FGL | ν = 0.45 |

Poisson’s ratio of OB | ν = 0.45 |

Poisson’s ratio of UB | ν = 0.45 |

Biot’s coefficient | α = 0.99 |

**Table 3.**The cumulative gas production with permeability enhancement (V

_{g}) after 120-day production.

Cumulative Gas Production (ST m^{3}) | ||||||
---|---|---|---|---|---|---|

r_{s} (m) | ||||||

0.3 | 0.5 | 1 | 2 | |||

k_{f} | HBL | 2 | 631,851 | 637,193 | 642,373 | 645,883 |

4 | 639,688 | 648,514 | 661,047 | 679,954 | ||

8 | 646,531 | 657,912 | 677,975 | 711,590 | ||

TPL | 2 | 641,762 | 648,207 | 657,112 | 667,160 | |

4 | 654,888 | 667,240 | 685,330 | 702,448 | ||

8 | 660,201 | 676,255 | 698,987 | 706,541 | ||

FGL | 2 | 687,226 | 696,737 | 714,312 | 731,513 | |

4 | 712,884 | 740,743 | 811,315 | 855,335 | ||

8 | 758,690 | 788,555 | 924,427 | 1,160,649 |

**Table 4.**The ratios of cumulative gas production with permeability enhancement (V

_{g}) to that in the base case (V

_{g,}

_{0}) after 120-day production.

V_{g}/V_{g,0} | ||||||
---|---|---|---|---|---|---|

r_{s} (m) | ||||||

0.3 | 0.5 | 1 | 2 | |||

k_{f} | HBL | 2 | 1.019 | 1.028 | 1.036 | 1.042 |

4 | 1.032 | 1.046 | 1.066 | 1.097 | ||

8 | 1.043 | 1.061 | 1.094 | 1.148 | ||

TPL | 2 | 1.035 | 1.046 | 1.060 | 1.076 | |

4 | 1.056 | 1.076 | 1.106 | 1.133 | ||

8 | 1.065 | 1.091 | 1.128 | 1.140 | ||

FGL | 2 | 1.109 | 1.124 | 1.152 | 1.180 | |

4 | 1.150 | 1.195 | 1.309 | 1.380 | ||

8 | 1.224 | 1.272 | 1.491 | 1.872 |

**Table 5.**The cumulative water-to-gas ratio with permeability enhancement (R

_{wg}) after 120-day production.

Cumulative Water-to-Gas Ratio (kg H_{2}O/m^{3} CH_{4}) | ||||||
---|---|---|---|---|---|---|

r_{s} (m) | ||||||

0.3 | 0.5 | 1 | 2 | |||

k_{f} | HBL | 2 | 3.599 | 3.624 | 3.676 | 3.760 |

4 | 3.683 | 3.739 | 3.834 | 3.939 | ||

8 | 3.725 | 3.800 | 3.920 | 4.029 | ||

TPL | 2 | 3.373 | 3.349 | 3.318 | 3.282 | |

4 | 3.325 | 3.283 | 3.226 | 3.172 | ||

8 | 3.308 | 3.256 | 3.192 | 3.173 | ||

FGL | 2 | 3.308 | 3.307 | 3.289 | 3.221 | |

4 | 3.294 | 3.268 | 3.159 | 2.969 | ||

8 | 3.234 | 3.236 | 3.066 | 2.406 |

**Table 6.**The ratios of cumulative water-to-gas ratio with permeability enhancement (R

_{wgT}) to that in the base case (R

_{wgT,}

_{0}) after 120-day production.

R_{wgT}/R_{wgT}_{,0} | ||||||
---|---|---|---|---|---|---|

r_{s} (m) | ||||||

0.3 | 0.5 | 1 | 2 | |||

k_{f} | HBL | 2 | 1.268 | 1.277 | 1.296 | 1.325 |

4 | 1.298 | 1.318 | 1.351 | 1.388 | ||

8 | 1.313 | 1.339 | 1.382 | 1.420 | ||

TPL | 2 | 1.189 | 1.180 | 1.169 | 1.157 | |

4 | 1.172 | 1.157 | 1.137 | 1.118 | ||

8 | 1.166 | 1.148 | 1.125 | 1.118 | ||

FGL | 2 | 1.166 | 1.165 | 1.159 | 1.135 | |

4 | 1.161 | 1.152 | 1.113 | 1.046 | ||

8 | 1.140 | 1.140 | 1.080 | 0.848 |

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## Share and Cite

**MDPI and ACS Style**

Wang, R.; Zhang, J.; Wang, T.; Lu, H.
Numerical Simulation of Improved Gas Production from Oceanic Gas Hydrate Accumulation by Permeability Enhancement Associated with Geomechanical Response. *J. Mar. Sci. Eng.* **2023**, *11*, 1468.
https://doi.org/10.3390/jmse11071468

**AMA Style**

Wang R, Zhang J, Wang T, Lu H.
Numerical Simulation of Improved Gas Production from Oceanic Gas Hydrate Accumulation by Permeability Enhancement Associated with Geomechanical Response. *Journal of Marine Science and Engineering*. 2023; 11(7):1468.
https://doi.org/10.3390/jmse11071468

**Chicago/Turabian Style**

Wang, Rui, Jiecheng Zhang, Tianju Wang, and Hailong Lu.
2023. "Numerical Simulation of Improved Gas Production from Oceanic Gas Hydrate Accumulation by Permeability Enhancement Associated with Geomechanical Response" *Journal of Marine Science and Engineering* 11, no. 7: 1468.
https://doi.org/10.3390/jmse11071468