Rate Transient Analysis for Multi-Fractured Wells in Tight Gas Reservoirs Considering Multiple Nonlinear Flow Mechanisms
Abstract
:1. Introduction
2. Mathematical Model
2.1. Physical Model
2.2. Characterization of the Nonlinear Flow Mechanisms
2.3. Solution for Flow in the Fractured Tight Formation
2.4. Rate Transient Analysis Method
2.4.1. Production Data Processing
2.4.2. Linear/Bilinear Flow Regime Analysis
2.4.3. Type Curve Fitting
3. Results and Discussion
3.1. Flow Regimes of Gas and Water Phase
3.2. The Effects of Nonlinear Flow Mechanisms
3.2.1. Stress-Dependent Permeability
3.2.2. Gas Slippage
3.2.3. Low-Velocity Non-Darcy Flow
3.2.4. Gas–Water Two-Phase Flow
3.3. The Effects of Fracture and Formation Parameters
3.3.1. Half-Length of the Fractures
3.3.2. Fracture Number
3.3.3. Fracture Conductivity
3.3.4. Formation Permeability
4. Field Case
5. Conclusions
- The flow regimes of fractured tight gas wells can be recognized using the log-log plots of normalized production rate against material balance time. According to the slopes of the type curves, six flow regimes can be observed, including linear flow dominated by the fractures (I), bilinear flow dominated by both the fractures and inner reservoir (II), linear flow dominated by the inner reservoir (III), transition flow dominated by the inner and outer reservoirs (IV), linear flow dominated by the outer reservoir (V), and boundary dominated flow (VI).
- The nonlinear flow mechanisms, and formation and fracture properties can have significant influences on the rate transient responses of fractured tight gas wells. Fracture number, fracture conductivity, and half-length mainly influence the early and medium flow regimes. Low-velocity non-Darcy flow mainly influences the late flow regimes. Stress-dependent permeability, gas-water two-phase flow, and formation permeability can have a significant influence on almost all the flow regimes.
- The RTA method for fractured tight gas wells should consider the effects of nonlinear flow mechanisms, especially gas-water two-phase flow in the formation. The nonlinear flow mechanisms should be considered in the mathematical model for RTA to obtain a reasonable theoretical solution. In addition, gas and water production data can be processed and analyzed separately with the techniques of the material balance method.
- In making field applications, reasonable history-matching results can be obtained using either gas or water production data of tight gas wells, and the parameter inversion results can be averaged in analysis. In addition, the typical square root of time and log-log plots can be incorporated into the RTA method for uncertainty reduction.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
References
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Variables | Definition | Variables | Definition |
---|---|---|---|
Dimensionless length-X direction | Dimensionless pseudo-pressure (gas) | ||
Dimensionless length-Y direction | Dimensionless pseudo-time (gas) | ||
Dimensionless length-Z direction | Dimensionless production rate (gas) | ||
Dimensionless permeability | Dimensionless pseudo-pressure (water) | ||
Dimensionless threshold gradient pressure | Dimensionless pseudo-time (water) | ||
Dimensionless pseudo-threshold gradient pressure | Dimensionless production rate (water) |
Model Parameter | Value | Units |
---|---|---|
Initial formation pressure | 23.4 | MPa |
Formation temperature | 345 | K |
Formation thickness | 10 | m |
Well length | 1100 | m |
Number of fractures | 11 | Dimensionless |
Fracture conductivity | 20 | D·cm |
Half-length of the fracture | 100 | m |
Well space | 600 | m |
Rock compressibility | 5 × 10−5 | MPa−1 |
Porosity of the hydraulic fracture | 0.3 | Dimensionless |
Bottom hole pressure of the wellbore | 5 | MPa |
The permeability of the matrix | 0.01 | mD |
The porosity of the matrix | 0.1 | Dimensionless |
kI/kO | 2 | Dimensionless |
Viscosity of water | 0.3 | mPa·s |
Water compressibility | 5 × 10−4 | MPa−1 |
Initial water saturation | 0.5 | Dimensionless |
PTPG | 1 × 10−3 | MPa/m |
Permeability modulus | 0.01 | MPa−1 |
Slippage factor | 1 | MPa |
Model Parameter | Value | Units |
---|---|---|
Initial formation pressure | 23.4 | MPa |
Formation temperature | 345 | K |
Formation thickness | 10 | m |
Well length | 1215 | m |
Well space | 600 | m |
Rock compressibility | 5 × 10−5 | MPa−1 |
Porosity of the hydraulic fracture | 0.3 | Dimensionless |
Bottom hole pressure of the wellbore | 5 | MPa |
The porosity of the matrix | 0.1 | Dimensionless |
Initial water saturation | 0.65 | Dimensionless |
Viscosity of water | 0.3 | mPa·s |
Water compressibility | 5 × 10−4 | MPa−1 |
PTPG | 5 × 10−4 | MPa/m |
Permeability modulus | 0.01 | MPa−1 |
* kI/kO | 1 | Dimensionless |
* Fracture space | 35.7 | m |
* Number of fractures | 17 | Dimensionless |
* Fracture conductivity | 1.3 | D.cm |
* Half-length of the fracture | 100 | m |
* The permeability of the matrix | 0.07 | mD |
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Wu, Y.; Mi, L.; Ma, L.; Zheng, R.; Feng, X. Rate Transient Analysis for Multi-Fractured Wells in Tight Gas Reservoirs Considering Multiple Nonlinear Flow Mechanisms. Water 2024, 16, 1866. https://doi.org/10.3390/w16131866
Wu Y, Mi L, Ma L, Zheng R, Feng X. Rate Transient Analysis for Multi-Fractured Wells in Tight Gas Reservoirs Considering Multiple Nonlinear Flow Mechanisms. Water. 2024; 16(13):1866. https://doi.org/10.3390/w16131866
Chicago/Turabian StyleWu, Yonghui, Lidong Mi, Liqiang Ma, Rongchen Zheng, and Xiujuan Feng. 2024. "Rate Transient Analysis for Multi-Fractured Wells in Tight Gas Reservoirs Considering Multiple Nonlinear Flow Mechanisms" Water 16, no. 13: 1866. https://doi.org/10.3390/w16131866