Viscosity is an important index to evaluate gas flowability. In this paper, a double-porosity model considering the effect of pressure on gas viscosity was established to study shale gas percolation through reservoir pressure, gas velocity, and bottom hole flowing pressure. The experimental results show that when pressure affects gas viscosity, shale gas viscosity decreases, which increases the percolation velocity and pressure drop velocity of the free state shale gas in matrix and fracture systems. And it is conducive to the desorption of adsorbed shale gas and effectively supplemented the bottom hole flowing pressure with the pressure wave propagation range and velocity increasing, so that the rate of pressure drop at the bottom of the well slows down, which makes the time that bottom hole flowing pressure reaches stability shortened. Therefore, the gas viscosity should be fully considered when studying the reservoir gas percolation.
As one of the fast growing activities in the natu ral gas industry, shale gas development is playing an important role in the current energy mix of the world’s growing energy demand [
Shale gas is composed of molecules, and the macroscopic properties of its fluid are essentially determined by the motion of molecules. The characteristic of friction force between fluid molecules in actual fluid flow is called viscosity, and the physical quantity that measures the stickiness of fluid is viscosity, which happens to be one of the migration properties of fluid and affects the fluid percolation velocity [
At present, the percolation law of shale gas is studied mainly from the following aspects. Firstly, the multiscale pore structure of the shale gas reservoir after fracturing is a key factor affecting shale gas percolation. It was found that different gas migration mechanisms exist in different migration channels. Considering the complex structures, such as nanopore, micronanopore, natural fracture, and artificial fracture, the Knudsen number is used to divide the flow among different reservoir scales, so that the shale gas percolation can be described from microscale to macroscale accurately [
In summary, previous studies have mainly focused on the occurrence state of shale gas, multiscale pore structure, percolation patterns and percolation mathematical model, analytical methods, and other properties to study shale gas percolation mainly from two aspects in productivity and reservoir pressure. But few people have interpreted the shale gas percolation law from the perspective of gas molecules, and gas viscosity properties from the molecular level to analyze shale gas percolation were ignored. And most importantly, under high reservoir pressure, the pressure is the main factor affecting the viscosity of the gas. Therefore, a mathematical model of gas percolation, considering the effect of reservoir pressure on gas viscosity in matrix-fracture system-dual media after fracturing, was established based on previous research results. The effect of gas viscosity on shale gas percolation was studied by comparing and analyzing the reservoir pressure, gas percolation velocity, and bottom hole flowing pressure in the near well section in this work.
Hydraulic fracturing technology was adopted in a horizontal well of a shale gas reservoir. According to its symmetry, the reservoir area above the horizontal wellbore was selected for research. Three-stage staged fracturing technology is adopted, and the single-well simulation domain in the reservoir is
Double-porosity physical model.
The following assumptions are put forward based on the double-porosity physical model. Firstly, gas percolation channels in shale reservoirs are mainly matrix and fractures, and fractures are discontinuous and discrete. Secondly, the shale gas reservoir is isotropic, and its fluid only contains compressible single-phase gas. However, the reservoir is slightly compressible, and the compressibility does not change with time. Thirdly, it is isothermal during gas flow. Fourthly, the influence of capillary pressure and gravity is not considered during gas flow. Fifthly, the gas flow in the matrix and fracture systems is in accordance with the Darcy flow. Sixthly, both the free gas and dissolved gas in the initial shale gas reservoir are ignored, and the free gas in the matrix and fractures is from the desorption of adsorbed gas in the matrix system. Seventhly, gas migrated from the distal end reservoir to the fracture zone and finally flows into the wellbore through artificial fractures, ignoring the gas directly flowing into the wellbore from the matrix and natural fractures. Eighthly, the gas well’s imperfection is ignored.
The continuity equation of the matrix system considering adsorbed gas is established as follows:
Substitute the equation of motion
Because both
Let the total compressibility of the matrix system be
The known condition is
When the gas viscosity is related to pressure,
Since the coefficient
Continuity equation of fracture system:
Substitute equation of motion
Because the order of magnitude of
The known condition is
When considering that the gas viscosity is related to pressure,
Since the coefficient
Both the boundary conditions and the initial conditions were constructed to satisfy the discrete fractured reservoir according to the actual production of the gas field and physical model.
The well depth is 2000 m, and the borehole radius is 0.1 m. There are 3 artificial fractures and 9 natural fractures. The reservoir and gas parameters involved in the solution process of the model are partly from the experimental and production data of the shale gas reservoir of the Longmaxi formation in southern Sichuan as shown in Table
Basic parameters of shale reservoir and shale gas [
Symbol | Value | Unit | Description |
---|---|---|---|
333.15 | K | Reservoir temperature | |
400 | m | Length of reservoir | |
480 | m | Width of reservoir | |
38 | m | Thickness of reservoir | |
0.002 | m | Natural fracture width | |
0.005 | m | Artificial fracture width | |
Matrix permeability | |||
Natural fracture permeability | |||
Artificial fracture permeability | |||
MPa-1 | Matrix compressibility | ||
MPa-1 | Natural fracture compressibility | ||
MPa-1 | Artificial fracture compressibility | ||
2 | % | Matrix porosity | |
0.4 | % | Natural fracture porosity | |
0.4 | % | Artificial fracture porosity | |
30 | MPa | Initial reservoir pressure | |
AS | 3 | — | Artificial fracture number |
200 | m | Half length of artificial fracture | |
3000 | m3/d | Half gas flow rate | |
0.717 | kg/m3 | Gas density at standard conditions | |
176.794 | kg/m3 | Gas density at reservoir conditions | |
2 | m3/t | Langmuir volume | |
10 | MPa | Langmuir pressure | |
8.34 | J/(K·mol) | Universal gas constant | |
16 | g/mol | Molecular weight of methane | |
0.76 | m-2 | Shape factor |
Refer to the dimensionless viscosity, corresponding pressure, and temperature chart published by Herning and L. Zipperer [
Viscosity of methane changes over pressure.
According to the fitting curve shown in Figure
Based on the mathematical model of shale gas percolation in dual media and combining with basic reservoir and gas parameters, the reservoir pressure, percolation velocity, and bottom hole flowing pressure under different shale gas viscosities were, respectively, solved by the finite element method. Free triangular mesh (as shown in Figure
Free triangular mesh result.
For shale gas with low viscosity, the velocity of gas percolation and reservoir pressure are greatly affected by viscosity under high reservoir pressure. As shown in Figures
Distribution nephograms of reservoir pressure and velocity field over time under nonconstant gas viscosity.
Distribution nephograms of reservoir pressure and velocity field over time under constant gas viscosity.
By comparing Figures
By comparing Figures
Each curve in Figure
Bottom hole flowing pressure changes with time under different gas viscosities. Stage 1: early stage; Stage 2: middle stage; Stage 3: late stage.
As the production enters the middle stage (Stage 2), the free shale gas in the fracture system gradually decreases, which makes the adsorbed shale gas in the matrix system desorb to supplement the formation pressure gradually and slow down the bottom hole flowing pressure drop rate, but the viscosity differences of shale gas make a significant difference in bottom hole flowing pressure. When pressure affects shale gas viscosity, gas viscosity decreases with reservoir pressure reducing; both the desorption amount of shale gas in the matrix system and the gas percolation velocity are increased to supplement the bottom hole flowing pressure quickly, which slows down the bottom hole flowing pressure drop rate gradually and shortens the gas migration time to the horizontal wellbore. However, when pressure has no effect on shale gas viscosity, gas viscosity remains unchanged with reservoir pressure decreasing; shale gas still flows at a high viscosity, which causes that percolation velocity is relatively slow. But most importantly, it not only is conducive to the desorption of adsorbed gas in the matrix system but also prolongs the gas migration time to the horizontal wellbore. Therefore, the bottom hole flowing pressure is much higher, and the pressure drop range is much larger than that when reservoir pressure has no effect on gas viscosity.
As the production enters the late stage (Stage 3), the adsorption and desorption capacity of shale gas in the matrix system reach a balance. So, when shale gas is extracted at a fixed production capacity, the reservoir pressure remains unchanged, the gas viscosity basically does not change, and the percolation velocity remains unchanged, which makes the bottom hole flowing pressure under different shale gas viscosities tend to be stable.
In conclusion, a double-porosity mathematical model, which is based on unsteady percolation theory of single-phase slightly compressible fluid, was established considering the gas occurrence state and the effect of pressure on gas viscosity, and the role of gas viscosity for shale gas percolation was studied by comparing reservoir pressure, percolation velocity, and bottom hole flowing pressure. The result shows that gas viscosity has significant effect on gas percolation and gas desorption. The following details were drawn: When pressure affects the viscosity of shale gas, the viscosity of shale gas decreased with reservoir pressure decreasing, and it was much smaller than that when pressure did not affect the gas viscosity. Both percolation velocity of free shale gas and the reservoir velocity of pressure drop in the matrix and fracture systems are increased, and the two are the fastest in the fracture system. Meanwhile, the increasing of pressure wave propagation speed and range is conducive to the desorption of adsorbed shale gas at the far end of the horizontal well, and the desorption amount is relatively large When pressure affects the viscosity of shale gas, the viscosity of shale gas decreased, which increased the percolation velocity of shale gas, so that the matrix system pressure decreased relatively fast. This shortens the time for gas migration to the horizontal wellbore and for wellbore pressure to reach stability. With free shale gas in the fracture system being extracted, the free shale gas in the fracture decreased, shale gas in the matrix system comes into play, and the desorption of adsorbed shale gas in the matrix system replenishes formation pressure with the exploitation of free shale gas in the fracture system. And also, the desorption amount of shale gas increased with the increase of pressure difference, which makes the bottom hole flowing pressure decrease slowly, and higher than that pressure has no effect on gas viscosity
This work helps in understanding the mechanism of shale gas percolation with viscosity changing, which will benefit the production of shale gas in unconventional tight shale reservoirs.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that they have no conflicts of interest.
The project was supported by the National Natural Science Foundation of China (Project Nos. 51874239 and 51804254).