At present, the optimization of the plunger mechanism is shale gas wells is mostly based on empirical methods, which lack a relevant rationale and often are not able to deal with the quick variations experienced by the production parameters of shale gas wells in comparison to conventional gas wells. In order to mitigate this issue, in the present work, a model is proposed to loosely couple the dynamics of gas inflow into shale gas wells with the dynamics of the liquid inflow. Starting from the flow law that accounts for the four stages of movement of the plunger, a dynamic model of the plunger lift based on the real wellbore trajectory is introduced. The model is then tested against 5 example wells, and it is shown that the accuracy level is higher than 90%. The well ‘switch’, optimized on the basis of simulations based on such a model, is tested through on-site experiments. It is shown that, compared with the original switch configuration, the average production of the sample well can be increased by about 15%.
The plunger drainage gas lift process is a drainage gas recovery method that uses the formation energy to push the plunger in the tubing to reciprocate up and down to discharge the wellbore liquid by intermittently switching wells for natural gas development. The plunger drainage gas recovery process is one of the main drainage and recovery technology measures in the current gas well production. The research on the optimal design of the plunger gas lift production working system is of great significance to ensure the efficient development of gas wells and improve the work efficiency of field managers. Nonetheless, since large-scale fracturing is commonly used in the current large-scale development and application of shale gas fields, liquid production is relatively large in the early stage of development. Then the liquid production continues to decline slowly, and the production parameters change relatively faster than in conventional gas wells. The gas lift working system will become unsuitable at present. It is difficult for the on-site plunger gas to lift well to be in an optimal production state, and timely adjustment is required to ensure the long-term and efficient development of the plunger gas lift well. The laws are complex, and the structure of horizontal wells is complex, so there is still a lack of suitable design and optimization methods. Although the related research on plunger gas lift has been started at an early stage, most of them are carried out on oil wells, and there are few pieces of research on gas wells.
In the 1960s, Foss et al. [
In 2000, Maggard et al. [
In 2015, Nascimento et al. [
It can be seen that the research on plunger gas lift has gradually changed from the early empirical model to the theoretical model, from application in oil wells to application in oil and gas wells, from application in vertical wells to application in complex wells such as inclined wells and horizontal wells. The research has become more and more abundant and gradually become better. However, for the shale gas horizontal wells that have been completed, the well structure is complex, and the production conditions are complex and changeable. There are few studies that require long-term and efficient development, and few are feasible after on-site scale verification. Given this, it is necessary to conduct research that is more in line with the production gas-liquid inflow dynamics of shale gas wells and the corresponding research on the design method of the plunger gas lift simulation model to guide the development of a more reasonable well opening and closing work system on site, and ensure the rapid development and efficient operation of shale gas fields.
Different from conventional reservoir rocks, shale reservoirs have the characteristics of small pore throats (micron-nanoscale), complex and diverse pore structures, and strong heterogeneity, which leads to the influence of pore structure on shale gas storage performance and fluid seepage characteristics are more obvious [
In general, the geological conditions and development techniques of shale oil reservoirs are quite different from those of conventional oil reservoirs. The geological characteristics of shale oil reservoirs are complex, and the storage space has multi-scale characteristics, including nano-pores, micro-pores, micro-cracks, and fractures; shale has low porosity and extremely low permeability. Shale oil wells generally have no natural productivity and need to be developed by horizontal wells and large-scale hydraulic fracturing. In addition, shale oil passes through natural fractures and artificial fractures step by step, making the process more complicated. This differs from the theory of conventional oil and gas reservoirs [
Therefore, in actual production, conventional productivity prediction methods cannot be used, and it is urgent to determine the production model of shale gas through more in-depth research to provide a foundation for the study of the flow state in the shale gas wellbore and the theoretical study of the prediction of fluid accumulation.
In this paper, through the analysis of a large number of field production data of horizontal gas wells, it is found that the ratio of water production to gas production in horizontal gas wells is not constant. Among them, the changing law of water production is complex and changeable, which is affected by the initial flow back rate. It is also related to the location of the pressure fractures flowing into the reservoir and the size of the gas production in the reservoir. Small, the fluid production in the middle and late drainage process mostly shows a fluctuating pattern of high and low (the production fluid flows out of the horizontal wellbore one by one). The variation law of gas production is slightly simpler than that of water production, and the overall performance trend is consistent with that of water production. The initial gas production is large, and the gas production gradually decreases as the production time becomes longer. In a relatively short period of time, gas production showed a slow decline, and the change rule of fluctuating highs and lows was not obvious, which was mainly affected by water output. The proportion of gas-liquid inflow is not necessarily fixed. Therefore, this paper loosely couples gas inflow dynamics and liquid inflow dynamics in shale gas wells, and each gas and liquid follows its own inflow dynamic equation. Among them, the dynamic inflow equation of formation gas production can use the binomial equation or other gas well productivity prediction methods such as the exponential equation. Taking the exponential equation as an example, the equation is [
The dynamic inflow equation of formation fluid can be a fluid production exponential equation, such as the Vogel equation, Fetkovich equation, Petrobras equation, etc. Taking the fluid production exponential equation as an example, the equation is:
Usually, the entire movement process of the plunger gas lift is divided into four stages: the plunger ascending stage, the freewheeling production stage, the plunger descending, and the pressure recovery stage. The force analysis of each movement stage can be obtained separately according to the momentum conservation equation.
When the plunger and the liquid column do not reach the wellhead, the following
During the process of plunger rise, the whole well segment is divided into i segments, and each segment is subjected to force analysis concerning the well depth trajectory as follows:
Force analysis is performed on the plunger and the upper fluid segment. As shown in
Among them, the frictional resistance between the plunger and the tubing is calculated, and the frictional resistance between the plunger and the tubing is calculated by the method of liquid phase friction resistance. However, in the actual simulation process, it is found that the friction resistance of the plunger in the large inclined well or horizontal well is a factor that cannot be ignored in the actual production, but the existing literature has not conducted theoretical research on the friction coefficient of the plunger. Therefore, the coefficient k is added to the original liquid column friction resistance calculation method by the same type of analogy. The specific k-value is calculated by inversion from the actual data of the site during the simulation optimization process to obtain the piston friction coefficient under different well types.
where
When the liquid column reaches the wellhead,
When the upper liquid segment of the plunger reaches the wellhead, the fluid segment begins to drain out of the well bore. This stage starts with the liquid slug in the upper part of the plunger reaching the wellhead. When all the liquid segments in the upper part of the plunger are discharged from the wellhead, the discharging stage ends, and the distance of movement is equal to the height of the liquid segment in the upper part of the plunger. The liquid column height on the top of the plunger is evenly divided into n segments, making
The force analysis is carried out on the plunger and the upper non-drained liquid section, which is the same as
During this stage, the liquid in the upper part of the plunger is continuously discharged, and the liquid quality in the upper part of the plunger becomes:
Assuming that the well head has a throttle valve, with the expansion of the annulus air body and the formation produced gas and liquid flowing into the tubing, pushing the plunger upward, the liquid slug above the plunger gradually discharges from the well head, and the liquid quality discharged through the throttle valve is:
Among them, the size of fluid flow
where
When the plunger reaches the wellhead and is captured by the trap, the wellhead enters the continuous flow production stage while the wellhead is still open for production.
The continuous flow production stage means that after the liquid slug has completely entered the production pipeline, the plunger stays in the wellhead catcher position and continues to open the well until the well closes, as shown in
According to the law of gas mass conservation, the gas mass produced by the wellhead is determined by
During plunger descent, the whole well segment is divided into i segments, and each segment is subjected to force analysis regarding the well depth trajectory as follows: The force analysis of the plunger is carried out. As shown in
where:
where
The force analysis of the plunger is carried out. As shown in
where:
where
After shut-in, as the gas and liquid produced by the formation continuously flow into the wellbore, it enters the pressure recovery stage. According to the shut-in time, this stage is divided into N sections, t = 1, 2, 3, …, N represents the state of the plunger well at time
During shut-in, the gas and water produced by the formation enters the tubing and casing at the same time, causing changes in the casing pressure. It is assumed that the average cross-sectional area of gas and liquid produced by the formation enters into the tubing and casing annulus in equal proportions, which causes changes in the liquid level, oil pressure, and casing pressure of the tubing and the annulus at the same time. The gas and liquid produced by the formation are related to the bottom-hole flow pressure in any period of time, and are calculated by the calculation method in
According to the principle of mass conservation, the gas mass
Before the implementation of the plunger gas lift, it is necessary to optimize the design of its process parameters. The main working parameters of the optimized design include the cycle time of the opening well, the cycle time of the closing well, minimum casing pressure, maximum casing pressure, single-cycle lifting fluid volume, and the number of plunger cycles. Based on the principle of node analysis, the specific flow chart of the plunger gas lift design under a certain switching time working system is shown in
The plunger gas lift is often in a non-optimal production state during the production process, as shown in
Therefore, the optimization of the plunger gas lift production process is actually: the search process of the minimum coordinated production casing pressure. In view of this, a basic optimization (intelligent optimization) strategy in the time optimization mode is proposed, and the detailed optimization process is shown in
The specific parameters of Well Example 1 is shown in
Well parameters | Unit | Value |
---|---|---|
Formation pressure | MPa | 11.98 (Bottom flow pressure) |
Fluid extraction index | m3/d/MPa | 0.2415 |
Relative density of crude oil | - | - |
Relative density of water | - | 1.02 |
Water content | Percentage | 100% |
Wellhead oil pressure (Oil pressure from plunger to wellhead) | MPa | 3.48 |
Vertical depth of well | m | 2446.4 |
Setting depth of retainer (Vertical depth) | m | 2426.01 |
Water yield | m3/d | 3 |
Inner diameter of casing | mm | 114.3 |
Plunger mass | kg | 3.3 |
Wellhead temperature | °C | 20 |
Bottom hole temperature | °C | 84.55 |
Relative gas density | - | 0.56 |
Gas production index | 104 m3/d/MPa2 | 0.007036 |
Tubing inner diameter | mm | 50.6 |
Gas production | 104 m3/d | 2.36 |
Well diameter | mm | 244.5 |
The software simulation specific data and optimization data are shown in
Plunger uptime (min) | Gas production (104 m3/d) | Liquid production (m3/d) | |
---|---|---|---|
Actual data | 20 | 2.36 | 3 |
Simulation data | 20 | 2.2989 | 2.91 |
Simulate optimization data | 19.91 | 2.5049 | 3.35 |
The measured data verification results are shown in
Well number | Actual gas production (104 m3/d) | Simulate gas production (104 m3/d) (Theoretical models) | Gas production error | Actual liquid production (m3/d) | Simulate liquid production (m3/d)(Theoretical models) | Liquid production error |
---|---|---|---|---|---|---|
1 | 2.36 | 2.30 | 2.54% | 3 | 2.91 | 3% |
2 | 2.45 | 2.50 | 2.04% | 2 | 2.11 | 5.5% |
3 | 3.24 | 3.09 | 4.63% | 2 | 1.86 | 7% |
4 | 6.19 | 5.72 | 7.59% | 2 | 1.88 | 6% |
5 | 3.65 | 3.43 | 6.03% | 3 | 2.82 | 6% |
According to the recommended working system of software simulation optimization and the actual situation of the field, the working system of the example well is adjusted. The specific comparison value is the average value of the production data of a period of relatively stable production before adjustment and the average value of a period of stable production after adjustment. The time period is generally one to two weeks. The specific adjustment effects are shown in
Well number | Pre-adjustment work system | Adjusted work system | Average daily gas production before optimization (104 m3/d) | Optimized average daily gas production (104 m3/d) | Increase by margin | Average daily liquid output before optimization (m3/d) | Optimized average daily fluid output (m3/d) | ||
---|---|---|---|---|---|---|---|---|---|
Well opening time | Well off time | Well opening time | Well off time | ||||||
1 | 110 min | 120 min | 60 min | 50 min | 2.252 | 2.60 | 15.45% | 3.18 | 4.375 |
2 | 160 min | 120 min | 50 min | 60 min | 2.428 | 2.73 | 12.44% | 2.5 | 2.14 |
3 | 735 min | 63 min | 300 min | 60 min | 3.382 | 4.418 | 30.6% | 1.94 | 2 |
4 | 1370 min | 90 min | 390 min | 80 min | 6.03 | 6.94 | 15.09% | 2.44 | 2.8 |
5 | 850 min | 60 min | 110 min | 60 min | 2.7553 | 3.2315 | 17.28% | 3.29 | 2.36 |
For the shale gas horizontal wells that have been completed, the well structure is complex, and the production conditions are complex and changeable. There are few studies that require long-term and efficient development, and there are few comparisons with on-site verification. A method is proposed to loosely couple the gas inflow dynamics and liquid inflow dynamics of shale gas wells, and the gas and liquid follow their respective inflow equations. Combined with the four motion laws of the plunger, a plunger gas lift considering the real wellbore trajectory is established. Dynamic simulation model. On this basis, software development is carried out. It is verified by field example verification analysis, which shows that: The model can reflect the relationship between the residence time at the wellhead (after-flow time) and the gas production during the after-flow process at the wellhead, and can describe the relationship between the upward and downward velocity of the plunger and the casing pressure and time, following the conservation of mass and momentum Theorem, forming a strict theoretical closed loop. Based on the same production data and parameters, such as the up and down time of the plunger, the simulated output is compared with the actual output through the simulation calculation, and the error is within 10%. It shows that the plunger gas lift design under the simulation model has a high accuracy. The actual gas production can be increased by about 15% after adjusting the well switching time through simulation optimization and performing on-site verification. It shows that the established simulation model and the developed software have practical guiding significance for the actual design optimization in the field.
gas well gas production, 104 m3/d
gas well liquid production, m3/d
as well exponential equation coefficient, 104 m3/d/MPa2n
gas well fluid production index, m3/d/MPa
quality of plunger, kg
quality of liquid column, kg
weight acceleration, kg ⋅ m/s2
acceleration of the plunger motion when the plunger is in the first segment, m/s2
lower end pressure when plunger is in section, MPa
pressure at the top of the plunger and liquid column when the plunger is in the first section, MPa
tubing cross section area, m2
friction resistance between the liquid column and the tubing when it is in the first stage, N
friction resistance between plunger and tubing in stage, N
friction coefficient between plunger, liquid column, and tubing
correction factor of friction coefficient between plunger and tubing
density of liquids, kg/m3
average plunger density, kg/m3
upward speed of plunger and liquid column, m/s
length of liquid column, m
length of plunger, m
tube diameter, m
quality of the upper liquid when there is still a section of the upper liquid column on the plunger, kg
length of liquid segment on plunger, m
the amount of liquid flow through the wellhead throttle valve when the liquid column on the plunger is left with stage i, m3/d
the liquid flow coefficient through the wellhead throttle valve, 0.987
wellhead pipeline diameter, m
gas mass change in the annulus of the oil jacket and in the oil pipe at t moments, kg
gas mass produced by strata at t time, kg
gas quality discharged through wellhead throttle valve at t times, kg
buoyancy exerted by the plunger dropping in the air column at t moment, N
friction resistance of a plunger dropping in the air column at t moment, N
volume of plunger, m3
the coefficient of resistance of the plunger falling in the gas column, dimensionless
density of gas, kg/m3
drop speed of plunger in gas column, m/s
buoyancy exerted by the plunger dropping in the liquid column at t moment, N
friction resistance of a plunger dropping in the liquid column at t moment, N
resistance factor, dimensionless, for plunger falling in liquid column
drop speed of plunger in liquid column, m/s
Thanks for Luo Wei, of the corresponding author for the article.
The authors would like to acknowledge the
The authors declare that they have no conflicts of interest to report regarding the present study.