Water Coning Calculation for Gas Well (Trimble & DeRose Method)

Steps to Solve

1. Calculate Effective Gas Permeability ($k_g$)

Given the effective gas permeability $k_g = 44.20 , md$, this is a parameter required for further calculations.

2. Identify Required Values for Gas Flow Rate ($q_g$)

Using the formula for gas flow rate: $$ q_g = 3.067 \cdot P \cdot v_g \cdot A / (T \cdot z) $$

You need:

• $P$ (Reservoir Pressure): 1556.00 psia
• $v_g$ (Gas velocity): Calculated in the next step
• $A$ (Wellbore cross-sectional area): This may need to be calculated based on well radius $r_w = 0.09 , ft$.
• $T$ (Temperature): Obtain as necessary
• $z$ (Gas compressibility factor): 0.667

3. Calculate Gas Velocity ($v_g$)

Using the formula: $$ v_g = 1.593 \cdot \sigma^{0.25} \cdot \left(\frac{\rho_L - \rho_g}{\rho_g^{0.5}}\right) $$

Here:

• $\sigma$ (interfacial tension), $\rho_L$ (density of liquid), and $\rho_g$ (density of gas) are needed parameters.

4. Calculate Areas and Further Constants

Calculate the wellbore cross-sectional area $A$ using: $$ A = \pi \cdot r_w^2 $$

Substituting $r_w = 0.09 , ft$: $$ A = \pi \cdot (0.09,ft)^2 $$

5. Substitute Values and Calculate $q_g$

Insert the calculated values of $A$, $v_g$, and the known parameters into the gas flow rate equation to find $q_g$.

6. Adjust with Corrected Critical Gas Rate

Once $q_g$ is calculated, reference the corrected critical gas rate for additional context: $$ Qg_{corrected} = 37,137.72 , Mcfd $$