The use of the acoustic well sounding (AWS) technique to determine bottomhole pressure (BHP) requires an estimate of the gas-void fraction (fg) in the liquid column of a pumping well annulus. Three correlations relating the annular superficial gas velocity to fg are available for saturated oil columns. These correlations were developed by Godbey and Dimon,1 Podio et al.,2 and Gilbert as reported by Gipson and Swaim.3 Use of these correlations for determining the BHP, either flowing or shut in, involves a stepwise numerical integration often performed by a computer.
This work addresses three aspects of estimating the BHP from AWS data: (1) estimation of the superficial gas velocity, (2) development of analytical solutions for a single-step BHP calculation, and (3) comparison and interpretation of the predicted BHP's by use of the three correlations for the field examples.
A mathematical model, based on the principle of mass balance of the annular, gas phase, is used to determine the superficial gas velocity. This model rigorously accounts for the time-dependent pressure, volume, and the gas deviation factor in the liquid-free annulus.
Analytical solutions are obtained for both the Godbey-Dimon and Podio et al. correlations to calculate the BHP in a single step. These analytical solutions provide a significant improvement over the numerical stepwise integration technique, because a hand-held calculator can be used for the BHP calculations.
The field examples studied indicate that both the pumping liquid column height and the superficial gas velocity play a key role in estimating the gas void fraction—an essential element in calculating the BHP. We observe that only the early-time shut-in pressures are affected by the presence of gas bubbles in the liquid column. Because the bottomhole flowing pressure (BHFP) is dependent on the correlation used to predict the fg, both skin and productivity index calculations are affected. Estimation of the permeability/thickness product and the static reservoir pressure, however, are independent of the fg correlation used.