The production performances of a well with a shale gas reservoir displaying a complex fracture network are simulated. In particular, a micro-seismic cloud diagram is used to describe the fracture network, and accordingly, a production model is introduced based on a multi-scale flow mechanism. A finite volume method is then exploited for the integration of the model equations. The effects of apparent permeability, conductivity, Langmuir volume, and bottom hole pressure on gas well production are studied accordingly. The simulation results show that ignoring the micro-scale flow mechanism of the shale gas leads to underestimating the well gas production. It is shown that after ten years of production, the cumulative gas production difference between the two scenarios with and without considering the micro-scale flow mechanisms is 19.5%. The greater the fracture conductivity, the higher the initial gas production of the gas well and the cumulative gas production. The larger the Langmuir volume, the higher the gas production rate and the cumulative gas production. With the reduction of the bottom hole pressure, the cumulative gas production increases, but the growth rate gradually decreases.

Shale gas reservoirs with rich reserves, as an important supplement to the energy supply, have become a focus of global development in recent years [

Fractures in shale have various types and scales, including micro-scale natural fractures and large-scale hydraulic fractures. Fractures can serve as both storage space and transport channels for free gas in shale, and they provide effective flow channels, increasing the effective porosity and permeability of the reservoir. Therefore, reservoir characterization and geological modeling of shale gas reservoirs require the fine portrayal and modeling of fractures. When predicting the production performance of fractured horizontal wells in shale gas reservoirs, the characterization of the complex fracture network is the key to obtaining the most accurate results [

In recent years, researchers have studied the production performance of post-fracturing horizontal wells from three aspects, i.e., analytical models [

To overcome these problems, a series of numerical models have been developed by researchers. Composite reservoir models based on continuum media have been proposed to numerically predict the flow mechanisms in shale gas reservoirs, but they are only appropriate for reservoirs with small-scale fractures [

In addition, in the above numerical models, the fracture network is characterized by random simulation, which makes it difficult to guarantee the correctness of the predicted production of the gas wells. When using numerical simulation or commercial software to deal with the fracture system, the grid around the fracture needs to be refined, which increases the number of calculations in the numerical simulation and increases the calculation time. The embedded discrete fracture model embeds the fracture attributes into the matrix grid, divides the calculation area using a structural grid, reduces the number of grids, and does not need to refine the fractures [

In summary, in this study, a micro-seismic cloud map was used to characterize the actual shapes of hydraulic fractures. By considering the comprehensive flow mechanisms of shale gas, including the flow through micro-scale pores, isothermal adsorption, and desorption characteristic, as well as the stress sensitivity of the fractures, a mathematical model of gas reservoir seepage was established based on the embedded discrete fracture model. A numerical solution model was established using a structured grid and the finite volume method. Using on-site data, the production performance of horizontal wells after fracturing was simulated and predicted, and the factors affecting the gas well production and stimulation effect were analyzed.

After fracturing, shale reservoirs form complex fracture network zones, including fracture systems with multi-scale characteristics [

Through on-site microseismic monitoring, it was found that there are dense signal response points around a fractured horizontal well. Through interpretation and processing of the fracturing monitoring data, an embedded discrete fracture model based on microseismic data for multi-stage fractured horizontal wells in shale reservoirs was constructed.

The main steps for constructing a discrete fracture model based on microseismic monitoring data are as follows:

Step 1: Interpret and process the microseismic data collected during the fracturing process, and record the important parameters, including the number of fracturing segments, fracturing construction time, spatial location, and signal amplitude.

Step 2: Combine the geological and geophysical data, pre-process the relevant parameters, and eliminate unreasonable microseismic points generated during monitoring of surface or shallow wells.

Step 3: Combine the borehole trajectory and shot hole data and reconstruct the fracture network system using an iterative algorithm for each level of the fractured section.

Step 4: Superimpose the fracture networks of the fractured sections at each level in turn to form the overall fracture network of the fractured horizontal wells and establish a discrete fracture network model.

Step 5: Match the historical production data to the numerical simulation prediction results obtained using the discrete fracture network model to modify the fracture property parameters and fracture distribution.

The following assumptions were made in the physical model (

Shale reservoirs have a complex pore structure, and the gas seepage in shale reservoirs has multiple flow mechanisms such as Knudsen diffusion, surface adsorption diffusion, slip flow, and viscous flow (

The molar mass flux of Knudsen diffusion is as follows:

where _{g} is the molar mass of the gas (kg/mol);

The molar mass flux of surface adsorption diffusion is as follows:

where _{s} is the surface diffusion coefficient (m^{2}/s); _{u} is the concentration of the adsorbed gas (mol/m^{3}).

The molar mass flux of viscous flow is as follows:

where

The molar mass flux of slip flow is as follows:

where _{n} is the Knudsen diffusion constant;

For Knudsen diffusion and slip flow, a weighting factor is introduced to characterize their contributions to the total gas flow [

where _{H} is the weighting factor of the slip flow; _{K} is the weighting factor of the Knudsen diffusion; _{std} is the volume of gas in the standard state (m^{3}/mol); and _{L} is the Langmuir volume (m^{3}/kg).

Based on the expression of the molar mass flux of Darcy seepage, the apparent permeability of the gas shale, considering the microscopic seepage mechanism, can be obtained from

Taking into account the reduction of the nanopore size due to the gas adsorption effect, the effective pore size is as follows:

where _{c} is the molecular diameter of the gas (m); and _{L} is the Langmuir pressure (MPa).

The apparent permeability of the shale considering the pore tortuosity can be obtained by combining

The continuity equation for the gas flow in the reservoir is

where _{g} is the density of the gas (kg/m^{3}).

The equations of motion for gas are

where _{gsc} is the density of the gas under standard conditions (kg/m^{3}).

By combining

The form of

The form of

where

The conductivity between the fracture and matrix is

For both the matrix and fracture systems, the conductivity satisfies the following relationship:

where

The connection pair between the matrix and fracture is as follows:

where _{ij,k} is the harmonic average of the permeability of matrix grid _{ij,k} is the contact area between matrix grid _{ij,k} is the average distance from a point within matrix grid

The conductivity between two fractures is

The connection pair between the two fractures is as follows:

where _{fi} is the fracture permeability; _{fi} is the fracture aperture; _{fi} is the distance from the center of the fracture segment to the fracture intersection line; and _{int} is the length of the intersection line.

According to Gauss’s theorem and the finite volume method,

where Δ_{x} and Δ_{y} are the surface areas of the structured grid in the

Similarly, according to Gauss’s theorem and the finite volume method,

where Δ_{f} is the discrete length of the fracture segment; and Δ_{f} is the fracture aperture.

The outer boundary of the shale reservoir is closed, and the inner boundary is set for constant bottom-hole pressure production. The Gauss-Seidel iteration method is used to solve

Jiang et al. [^{−5} mD. The hydraulic fracture permeability was 500 mD, and the fracture width was 0.003 m. The complex fracture model of the horizontal well is shown in

After 3000 days of production, the pressure drop around the hydraulic fractures was greater, and the range of the pressure drop in the reservoir was closely related to the fracture distribution characteristics. Regarding the total gas production, the results obtained using our model match Jiang’s model well (

For a fractured horizontal well with a complex fracture network in a shale gas reservoir block in Southern Sichuan (

Parameters | Value | Parameters | Value |
---|---|---|---|

Initial reservoir pressure, _{i} (MPa) |
45 | Matrix nanopore radius, _{e} (nm) |
2 |

Reservoir thickness, |
50 | Stress sensitivity coefficient, _{f} (MPa^{−1}) |
0.1 |

Horizontal well section length, |
1650 | Reservoir temperature, |
368 |

Bottom hole pressure, _{bh} (MPa) |
15 | Relative gas specific gravity, _{g} |
0.55 |

Langmuir pressure, _{L} (MPa) |
15 | Langmuir volume, _{L} (m^{3}/kg) |
0.01 |

Hydraulic fracture permeability, _{f} (mD) |
0.1 | Secondary fracture permeability, _{sf} (mD) |
0.05 |

Matrix permeability, _{m} (mD) |
0.001 | Matrix porosity, _{m} |
0.03 |

^{8} m^{3}, while the cumulative gas production considering the mechanisms is 1.47 × 10^{8} m^{3}. The difference between these two scenarios is 19.5%. If the mechanisms are not considered, the gas production capacity of the gas wells will be underestimated, especially in the later stage of production, which is characterized by prominent adsorption and desorption contributions.

_{FD} is set to 0.1, 0.5, and 1.0 D·cm, the cumulative gas production after ten years is 0.91 × 10^{8} m^{3}, 1.34 × 10^{8} m^{3}, and 1.71 × 10^{8} m^{3}, respectively. Therefore, in hydraulic fracturing in shale gas reservoirs, the conductivity of the hydraulic fractures should be improved as much as possible, thereby increasing production.

_{L} on gas production. It can be seen from _{L} is, the larger the daily gas production and cumulative gas production of the gas well are, the slower the rate of decrease of the gas well production is, and the longer it takes for the gas well to reach the stable production stage. As the gas well production progresses, the free gas from the fracture system is preferentially produced. The continuous reduction of the reservoir pressure causes the gas adsorbed on the surfaces of the organic matter to begin to desorb and enter the fracture system as a supplementary gas source in the reservoir, delaying the decrease in the gas well production. When the Langmuir volume _{L} is set to 0.01, 0.02, and 0.04 m^{3}/kg, the cumulative gas production after ten years of depletion production is 1.01 × 10^{8} m^{3}, 1.35 × 10^{8} m^{3}, and 1.59 × 10^{8} m^{3}, respectively. Adsorption and desorption are important seepage mechanisms that distinguish shale gas reservoirs from conventional gas reservoirs. As production progresses, the reservoir pressure decreases and a large amount of adsorbed gas is desorbed, which helps stabilize the production of the fractured horizontal wells in shale gas reservoirs.

^{8} m^{3} to 1.66 × 10^{8} m^{3} and then to 1.81×10^{8} m^{3}. Therefore, reasonable bottom-hole flow pressure should be selected to achieve better production from a fractured well.

(1)A micro-seismic cloud map was used to characterize the hydraulic fracture networks, which can more accurately describe the effective stimulation region after the fracturing of horizontal wells in shale gas reservoirs. Consequently, a more accurate simulation of the production performance of the fractured horizontal wells in shale gas reservoirs can be achieved.

(2)The sensitivity analysis of the parameters revealed that ignoring the microscopic seepage mechanisms will lead to underestimation of the production of the horizontal well. The hydraulic fracture conductivity has a significant impact on the early production of fractured horizontal wells. The larger the Langmuir volume is, the higher the daily and cumulative production are. The lower the bottom hole pressure is, the greater the initial daily gas production is, but the increment of the cumulative gas production gradually decreases as the bottom hole pressure decreases.

(3)For fractured horizontal wells in shale gas reservoirs, the shape of the fracture network significantly affects the pressure drop characteristics. The pressure drop in the reservoir mainly occurs around the hydraulic fractures. it is difficult for the pressure drop to propagate into the reservoir matrix area that is far away from the fractured wells. This is one of the main reasons for the rapid reduction in shale gas well production. Therefore, it is necessary to enlarge the volume of the stimulated reservoir to obtain higher production.

This work was supported by the

The authors declare that they have no conflicts of interest to report regarding the present study.

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