A Full-Stage Productivity Equation for Constant-Volume Gas Reservoirs and Its Application
Abstract
:1. Introduction
2. Mathematical Model
2.1. Darcy Equation
2.2. Material Balance Equation
2.3. Full-Stage Productivity Equation
2.4. Pressure-Conversion Skin Factor
2.5. Open-Flow Capacity
3. Model Validation
4. Application
5. Conclusions
- (1)
- For a fixed-volume gas reservoir, a full-stage productivity equation has been created; continuous production and pressure are not required during the derivation process. Except for adding the pressure-conversion skin, the relevant stage was expanded from the stable production stage to the full gas reservoir development stage, compared to the quasi-steady-state production equation. The full-stage production-capacity equation was solved by building approximative and independent solutions for the pressure-conversion skin without influencing the addition of non-Darcy terms and the wellbore pressure drop skin.
- (2)
- The approximate solution and independent approximate solution of the pressure-conversion skin are the only sources of error in the full-stage productivity equation. The validation of the model reveals that the approximate and independent solutions of the average formation pressure consistently exhibited good accuracy under varying production systems and fundamental factors. In contrast, the approximate and independent solutions of the absolute open-flow rate nearly overlap. The application results show that the full-stage productivity equation also has relatively reliable accuracy compared to the corrected isochronous well testing. The comprehensive model validation and application results indicate that the full-stage productivity equation is not affected by production systems, and this applies to the entire stage of gas reservoir development.
- (3)
- The precision of the approximation answer is marginally greater overall, and the effect of various pressure-conversion skins on the entire stage production-capacity equation varies. The independent approximation solution eliminates the effect of the venting radius. It is advised to utilize the approximate pressure-conversion skin solution for computing parameters like the average formation pressure. It is advised to utilize the independent approximation solution of the pressure-conversion skin to determine the absolute open-flow rate.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Number | Set-Up | ε(t)max of (t) | ε(t)avg of (t) | ||||
---|---|---|---|---|---|---|---|
Approximate Solution | Independent Approximate Solution | The Quasi-Steady-State Productivity Equation Solution | Approximate Solution | Independent Approximate Solution | The Quasi-Steady-State Productivity Equation Solution | ||
Model 1 | Fix production before fixing pressure | 1.95% | 3.27% | 6.46% | 0.72% | 1.48% | 2.71% |
Model 2 | Reduce production before increasing it | 3.56% | 0.77% | 5.50% | 0.23% | 0.15% | 0.51% |
Model 3 | Sgi = 80% | 1.93% | 3.18% | 7.77% | 0.73% | 1.21% | 2.54% |
Model 4 | K = 10 × 10−3 μm2 | 2.04% | 1.73% | 2.73% | 0.32% | 0.27% | 0.49% |
Model 5 | pi = 30 MPa | 1.78% | 7.11% | 7.65% | 0.59% | 2.22% | 2.39% |
Model 6 | h = 15 m | 1.54% | 4.38% | 5.77% | 0.66% | 1.35% | 1.82% |
Model 7 | φ = 8% | 2.22% | 6.14% | 7.12% | 0.97% | 2.27% | 2.61% |
Model 8 | re = 900 m | 1.73% | 4.36% | 6.60% | 0.94% | 2.10% | 2.80% |
Parameter | Well A | Well B | Parameter | Well A | Well B |
---|---|---|---|---|---|
rw/m | 0.108 | 0.108 | re/m | 23.74 | 483.93 |
μi/mPa.s | 0.02059 | 0.02161 | pwf(1)/MPa | 23.736 | 23.323 |
Zi | 0.96540 | 0.97202 | qsc(1)/(m3/d) | 8864 | 50,450 |
pi/MPa | 27.233 | 27.551 | t/d | 26 | 637 |
T/K | 376.59 | 360.06 | pwf(t)/MPa | 22.859 | 17.780 |
K/10−3 μm2 | 0.357 | 1.15 | μwf(t)/mPa.s | 0.02059 | 0.01776 |
h/m | 5.6 | 6.7 | Zwf(t) | 0.96406 | 0.92752 |
φ | 4.07% | 8.20% | S | −0.09 | −2.85 |
Sgi | 73.01% | 75.90% | qsc(t)/(m3/d) | 10,079 | 46,154 |
Parameter | Solution Method | Well A | Relative Error | Well B | Relative Error |
---|---|---|---|---|---|
/MPa | Test result | 27.005 | / | 22.260 | / |
Approximate solution | 27.960 | 3.54% | 21.777 | −2.17% | |
Independent approximate solution | 27.951 | 3.50% | 21.386 | −3.92% | |
the quasi-steady-state productivity equation solution | 29.737 | 10.11% | 23.422 | 5.22% | |
qAOF(t)/(m3/d) | Test result | 33,585.27 | / | 175,495.43 | / |
Approximate solution | 36,054.94 | 7.35% | 163,799.28 | −6.66% | |
Independent approximate solution | 36,125.61 | 7.56% | 183,294.24 | 4.44% | |
the quasi-steady-state productivity equation solution | 25,844.08 | −23.05% | 112,304.79 | −36.01% |
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Zhang, L.; Cheng, S.; Wu, K.; Xin, C.; Song, J.; Zhang, T.; Xie, X.; Zhao, Z. A Full-Stage Productivity Equation for Constant-Volume Gas Reservoirs and Its Application. Processes 2024, 12, 1855. https://doi.org/10.3390/pr12091855
Zhang L, Cheng S, Wu K, Xin C, Song J, Zhang T, Xie X, Zhao Z. A Full-Stage Productivity Equation for Constant-Volume Gas Reservoirs and Its Application. Processes. 2024; 12(9):1855. https://doi.org/10.3390/pr12091855
Chicago/Turabian StyleZhang, Lei, Shiying Cheng, Keliu Wu, Cuiping Xin, Jiaxuan Song, Tao Zhang, Xiaofei Xie, and Zidan Zhao. 2024. "A Full-Stage Productivity Equation for Constant-Volume Gas Reservoirs and Its Application" Processes 12, no. 9: 1855. https://doi.org/10.3390/pr12091855