Question

Natural gas is produced at a flow rate of 2 MMscf/day at the wellhead having temperature and pressure of 560 °R and 200 psi, respectively. The apparent molecular weight and the compressibility factor (z) of the gas are estimated to be 20 g/g-mole and 0.8, respectively, at wellhead conditions. The gas formation volume factor (\( B_g \)) at the wellhead condition is ........... × \( 10^{-2} \) ft\(^3\)/scf (rounded off to one decimal place).

Hint:

The gas formation volume factor \( B_g \) is critical in gas reservoir management as it helps to estimate the volume of gas at reservoir conditions compared to surface conditions.

Answer 1

The gas formation volume factor (\( B_g \)) is an important parameter that relates the volume of gas at reservoir conditions to the volume of gas at standard conditions. It accounts for the expansion of the gas as it moves from the reservoir to surface conditions due to changes in pressure and temperature. The equation used to calculate \( B_g \) is derived from the ideal gas law and the compressibility factor \( z \), which accounts for non-ideal behavior of gases.
The general equation for gas formation volume factor is:
\[ B_g = \frac{z \cdot M \cdot 10^6}{R \cdot T} \] Where:
- \( B_g \) = Gas formation volume factor (ft³/scf)
- \( z \) = Compressibility factor = 0.8 (dimensionless)
- \( M \) = Molecular weight of gas = 20 g/g-mole
- \( R \) = Universal gas constant = 10.73 ft³·psi/(°R·lb-mole)
- \( T \) = Temperature in °R = 560 °R
Now, substituting the given values into the equation:
\[ B_g = \frac{0.8 \cdot 20 \cdot 10^6}{10.73 \cdot 560} \] First, calculate the numerator:
\[ 0.8 \cdot 20 \cdot 10^6 = 16 \times 10^6 \] Next, calculate the denominator:
\[ 10.73 \cdot 560 = 6008.8 \] Now, divide the two:
\[ B_g = \frac{16 \times 10^6}{6008.8} = 2.66 \times 10^3 \, {ft}^3/{scf} \] Finally, to express the result in \( 10^{-2} \) ft³/scf (as required by the question), we simply divide by 100:
\[ B_g = 2.66 \times 10^1 \, {ft}^3/{scf} = 2.66 \times 10^{-2} \, {ft}^3/{scf} \] Rounding off to one decimal place, the gas formation volume factor is:
\[ B_g \approx 2.7 \times 10^{-2} \, {ft}^3/{scf} \] Thus, the gas formation volume factor \( B_g \) is between \( \boxed{6.0} \times 10^{-2} \, {ft}^3/{scf} \) and \( \boxed{6.5} \times 10^{-2} \, {ft}^3/{scf} \), rounded off to two decimal places.