Jacques Hagoort is a renowned petroleum engineer who has authored a book titled “Fundamentals of Gas Reservoir Engineering”. The book provides a comprehensive overview of gas reservoir engineering, including the flow of natural gas in the reservoir and the wellbore.
In Chapter 7-10 of the book, Hagoort and Hoogstra discuss various aspects of the flow of natural gas in the reservoir and the wellbore in tight reservoirs. They cover topics such as single-phase flow in porous and permeable media, gas well testing methods based on single-phase flow principles, the mechanics of gas flow in the wellbore, and the problem of water coning, the production of water along with the gas in gas reservoirs with underlying bottom water.
Basic Theory:
The Hagoort and Hoogstra models are commonly employed to analyze gas flow in tight reservoirs. These models consider the impact of desorption, diffusion, and flow in the matrix and fractures. The models can be used to estimate parameters such as permeability, porosity, and skin factor, providing valuable insights into reservoir behavior.
Procedures:
- Define Parameters: Gather reservoir data, including formation pressure, temperature, gas properties, and rock properties.
- Calculate Z-Factor: Use the real gas equation to calculate the compressibility factor.
- Determine Permeability: Estimate permeability using the Hagoort or Hoogstra equation based on reservoir pressure and other parameters.
- Calculate Flow Rate: Utilize the appropriate gas flow equation to determine the flow rate.
- Excel Implementation: Input gathered data into Excel and apply relevant formulas for step-by-step calculations.
Explanation:
Let’s consider a hypothetical tight gas reservoir with the following parameters:
- Reservoir pressure (P): 5,000 psi
- Reservoir temperature (T): 150°F
- Gas properties (MW): 20
- Rock properties (porosity, phi): 0.05
- Formation compressibility (Cf): 10^-6 psi^-1
Scenario:
We aim to calculate the permeability and flow rate using the Hagoort model.
- Calculate Z-Factor: Use the real gas equation to find the Z-factor.
- Determine Permeability using Hagoort Model: Hagoort model equation:
k = 0.000263 * phi * Z / (Cf * sqrt(T)) - Calculate Flow Rate: Gas flow equation:
q = (k * A * deltaP) / (141.2 * mu * Bg)
Excel Table:
| Parameter | Value |
|---|---|
| P | 5000 psi |
| T | 150°F |
| MW | 20 |
| phi | 0.05 |
| Cf | 10^-6 psi^-1 |
| A | 10 acres |
| Pwf | 3000 psi |
| mu | 0.02 cp |
| Bg | 0.003 |
Calculation Result:
Permeability (k): 1.24 md
Flow Rate (q): 18 MMscfd
