(Department of Mechanics and Engineering Science, Liaoning University of Engineering Science, Fuxin 123000)
Author: Wang Qixin, male, born in 1963, Fuxin, Liaoning, Ph.D., mainly engaged in theoretical research on coalbed methane seepage. Email: lbwqx @163.com.
A porous-fractured dual-medium migration model of coalbed methane and water two-phase seepage is established, and the model is solved by finite difference method. The storage and transportation law of coalbed methane reservoirs in Fuxin Basin under different productivity factors is numerically simulated, and the influence of different reservoir factors on coalbed methane reservoir productivity in Fuxin Basin is analyzed. It is pointed out that adsorption time, permeability, gas saturation, original reservoir pressure and supply radius are the key parameters affecting coalbed methane productivity.
Keywords: numerical simulation of productivity sensitivity factors of dual-medium model of coalbed methane pores and fractures
Numerical analysis of coalbed methane productivity sensitivity in Fuxin basin
Wang Qixin, Sun,
(Department of Mechanics and Engineering Science, Liaoning University of Engineering Science, Fuxin 123000)
Abstract: The migration model of pore-fracture dual medium for coalbed methane-water two-phase seepage is established. The model is solved by finite difference method. Using numerical simulation method, the transport law and productivity of Fuxin basin under different influencing factors are analyzed. The results show that adsorption time, permeability, original formation pressure, gas saturation and supply radius are the key factors affecting productivity.
Keywords: coalbed methane; Pore-fracture dual medium model; Production capacity; Sensitive; numerical simulation
introduce
Coalbed methane belongs to unconventional natural gas, and its reservoir productivity is very different from that of conventional natural gas reservoirs. CBM productivity is controlled by CBM desorption, diffusion and seepage parameters [1]. In this paper, the dynamic model of coalbed methane occurrence and migration in Fuxin basin is established, and the model is numerically simulated by finite difference theory, and the sensitivity analysis of many factors affecting coalbed methane reservoir productivity in Fuxin basin is carried out [2] ~ [4].
1 reservoir numerical simulation
1. 1 model establishment
According to the actual geological conditions of coal seam, the migration model of pore-fracture dual medium of coalbed methane-water two-phase seepage is established, and its basic assumptions are as follows: ① The coal seam is regarded as pore-fracture dual medium, the pore medium stores gas, and the fracture medium conducts water and gas. Mass transfer between pores and cracks is realized by pressure difference; (2) The coal seam is incompressible; ③ The fluid flow is isothermal; ④ The fluid flow of water and gas in the fractured system follows Darcy's seepage and Fick's first diffusion law, and the influence of gravity, capillary force and viscous force during seepage is considered; ⑤ The diffusion process of gas in coal matrix is a non-equilibrium quasi-steady process, which obeys Fick's second law.
Because the desorbed coalbed methane enters the fracture from the pore through diffusion, and then enters the wellbore from the fracture, the mathematical model can be established in two processes: pore desorption diffusion process and fracture migration process.
Gas diffusion in micropores of 1. 1. 1
In general, water cannot enter the tiny pores in the matrix block. It is considered that there is only quasi-steady diffusion of single-phase gas in coal matrix block, which obeys Fick's first diffusion law. It is considered that the change rate of total concentration cP with time is proportional to the difference cP-cPx, that is,
Technical progress in exploration, development and utilization of coalbed methane in China: Proceedings of the 2006 symposium on coalbed methane.
Technical progress in exploration, development and utilization of coalbed methane in China: Proceedings of the 2006 symposium on coalbed methane.
Where FS is that shape factor of the matrix block; FG is a geometric factor; DP is the gas diffusion coefficient.
1. 1.2 gas migration in fracture
Technical progress in exploration, development and utilization of coalbed methane in China: Proceedings of the 2006 symposium on coalbed methane.
Where: qP is the mass source, kg/m3 s; Qg and qw are dissolved coalbed methane and water quantity; Vfg and Vfw are the velocities of gas and water; The subscripts f, g and w represent the correlation coefficients of cracks, gas phase and water phase respectively.
The water phase mass equation of 1. 1.3 in the fracture.
Technical progress in exploration, development and utilization of coalbed methane in China: Proceedings of the 2006 symposium on coalbed methane.
1. 1.4 boundary conditions
(1) Internal boundary conditions:
cP(t)=cPy t=0
cP(t)= cPx t≥0°c∈г(5)
(2) External boundary conditions: usually constant flow boundary, also known as impermeable boundary,
Technical progress in exploration, development and utilization of coalbed methane in China: Proceedings of the 2006 symposium on coalbed methane.
1. 1.5 initial conditions
(l) initial saturation value:
Sfw∣t=0= 1Sfg∣t=0=0(7)
(2) Initial pressure value: Assuming that the top of coal reservoir is taken as the reference point, the initial pressure value of water is,
Pw0=Pd+γwd (8)
Where Pw0 is the initial value of water phase pressure, MPa；; Pd is the hydrostatic column pressure at the reference point, MPa；; γw is the specific gravity of water, MPa/m; D is the distance above or below the reference point, m.
Equations (1) ~ (4) constitute the pore-fracture dual-medium migration model of coalbed methane and water two-phase seepage.
Numerical simulation of 1.2 model
The mathematical differential equations (3) and (4) of methane gas migration in coal seam are discretized in space and time, and the difference equations are obtained as follows:
Technical progress in exploration, development and utilization of coalbed methane in China: Proceedings of the 2006 symposium on coalbed methane.
Technical progress in exploration, development and utilization of coalbed methane in China: Proceedings of the 2006 symposium on coalbed methane.
Through the numerical discretization of the mathematical model, the numerical model of coalbed methane migration in coal seam is obtained, and the numerical model is solved by Newton iteration method [5].
2 Sensitivity factor analysis
The productivity of coalbed methane is affected by many factors, such as adsorption time, initial water saturation, reservoir thickness, permeability, porosity, original reservoir pressure, gas saturation and supply radius. Among many factors affecting coalbed methane productivity, adsorption time, permeability, original reservoir pressure, gas saturation and supply radius have great influence on Fuxin Basin. Using the drainage parameters of LJ- 1 CBM well in Liujia District, the productivity affected by the above factors was numerically simulated [6] and [7].
2. Effect of1adsorption time
Adsorption time reflects the time required for coalbed methane to desorb and diffuse from coal matrix and enter cleavage system, which directly affects the gas production of coalbed methane wells in different production periods. Figure 1 shows the influence of adsorption time on gas production of LJ- 1 coalbed methane well in Fuxin basin. As can be seen from the figure, the shorter the adsorption time, the higher the early yield.
Fig. 1 Effect of adsorption time on gas production of LJ- 1 well
Fig. 2 Effect of adsorption time on cumulative gas production of LJ- 1 well.
The production of coalbed methane wells in Fuxin basin with adsorption time of 1 d, 30 d and 80 d is predicted. The results show that the shorter the adsorption time, the earlier the peak value of gas production and the higher the peak value. When the adsorption time is 80 d, the peak value of gas production appears at the latest and is low. The comparison of cumulative gas production curves of coalbed methane wells (Figure 2) shows that the shorter the adsorption time, the better the production of coalbed methane wells.
2.2 Influence of permeability
Permeability is the main factor that determines the flow of gas and water in coal seam. The permeability of coal seam is good, and the decompression of shaft drainage can effectively spread to a wider range, thus controlling a larger area of coal seam, desorbing more coalbed methane and obtaining higher output. High permeability, not only high early yield, but also high cumulative yield.
Figure 3 shows the influence of permeability on gas production of coalbed methane wells in Fuxin Basin. When K= 1mD, the gas production is only 250 ~ 350m3/d, and there is no gas production peak in the production period of 15. When the permeability K=5mD, the peak gas production began to appear after 450d of production, and the highest gas production reached1836m3/d. When the permeability k = 65438+ 100md, the gas production reached its peak after 200d, and the highest gas production reached 3628m3/d. Figure 4 shows the influence of permeability on Fuxin. It can be seen that with the increase of permeability, the peak gas production of coalbed methane wells is advanced, and the gas production and cumulative gas production are increased. However, it should be noted that in the later stage of production, due to insufficient gas supply and high permeability, gas production decreased rapidly.
Fig. 3 Influence of permeability on gas production of coalbed methane wells in Fuxin Basin
Fig. 4 Influence of permeability on cumulative gas production of coalbed methane wells in Fuxin Basin
2.3 Influence of original reservoir pressure
The influence of original reservoir pressure on reservoir productivity involves the ratio of original reservoir pressure to desorption pressure. It is ideal that the ratio of original reservoir pressure to critical desorption pressure is close to 1. If the critical desorption pressure is much lower than the original reservoir pressure, it is bound to need long-term drainage and depressurization to produce gas. Fig. 5 shows the influence of original reservoir pressure on gas production rate and water production of coalbed methane wells in Fuxin basin, showing the gas production of coal seam under 20% overpressure, 20% normal pressure and 20% negative pressure. It can be seen that when the gas saturation of coal seam is determined, that is, its critical desorption pressure is fixed, the original reservoir pressure only affects the initial gas production time of coalbed methane wells. When overpressure occurs, the gas production starts late; Undervoltage can be discharged earlier. But it has little effect on the peak gas production and cumulative gas production of coalbed methane wells.
Fig. 5 Influence of original formation pressure on gas production of coalbed methane wells in Fuxin Basin (K=5mD)
2.4 the influence of gas saturation
The gas saturation of coal seam determines its critical desorption pressure. The higher the critical desorption pressure, the smaller the range of drainage and depressurization of coalbed methane wells, and the earlier the gas production starts, the greater the methane gas quantity that can be desorbed from the coal seam. Fig. 6 shows the influence of gas saturation on gas production of coalbed methane wells in Fuxin basin. The higher the gas saturation, the greater the gas production of coalbed methane wells, and the earlier the gas production peak appears.
Fig. 6 Effect of gas saturation on gas production of coalbed methane wells in Fuxin Basin (k = 65438+ 100md)
2.5 Influence of supply radius
Because permeability has a great influence on coal seam pressure relief, small well spacing is usually used to improve coal seam pressure relief effect and increase coalbed methane production for low permeability coal seams. Therefore, the supply area of coalbed methane wells, that is, well pattern density, is a major problem of coalbed methane wells. See Figure 7 and Figure 8 for the influence of supply area on gas well productivity. As can be seen from the figure, the supply area has a great influence on gas production and cumulative gas production. The larger the supply radius, the greater the cumulative gas production, but the later the peak gas production comes, the longer the development life of coalbed methane wells. Therefore, from an economic point of view, there should be an optimal well pattern density. For coalbed methane wells in Fuxin Basin, when the permeability k = 65438+1000 MD, the gas supply area of 800 mu is later than that of 600 mu and 400 mu (Figure 7), but its cumulative gas production 15 is much higher than that of them (Figure 8).
Fig. 7 Influence of recharge area on gas production of coalbed methane wells in Fuxin Basin (k = 65438+ 100md)
Fig. 8 Effect of recharge area on cumulative gas production of coalbed methane wells in Fuxin Basin (k = 65438+ 100md)
3 Conclusion
By establishing the pore-fracture dual-medium migration model of coalbed methane and water two-phase seepage, the model is solved by finite difference method, and the drainage and production of LJ- 1 coalbed methane well in Liujia District of Fuxin are numerically simulated. The results show that adsorption time, permeability, original formation pressure, gas saturation and recharge radius are the key parameters affecting the productivity of coalbed methane reservoir in Fuxin Basin.
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