This paper presents a rigorous, mechanistic model for simulating a gas kick, that uses the thermodynamic approach to account for gas solubility. This thermodynamic solubility model uses the pressure and temperature data from the kick simulations and estimates the mole fraction of various gas components in the liquid phase. We validated these gas solubility results using Aspen HYSYS, a commercial chemical process simulation software.
The thermodynamic solubility model presented in this paper assumes a pure-methane kick and applies the concepts of phase-equilibrium and fugacity to estimate the amount of dissolved gas in the drilling fluid. Application of fugacity equilibrium between the gas and liquid phases, in conjunction with the Peng-Robinson equation, gives the liquid phase mole fraction of methane. The analytical kick model uses the Hasan-Kabir two-phase flow modeling approach to describes the changes in pressure during kick migration, at various points in the annulus. Since the expansion of the gas bubbles depends on the variation in pressure, these studies also lead to pit gain estimates.
A comparison between our model results and HYSYS values for methane liquid-phase mole fraction showed a maximum 8% deviation with complete agreement on bubble point (Pb) pressure and location estimates. Similarly, our model calculated the solution gas-oil ratio (Rs), with a maximum divergence of 3% from HYSYS estimates. From the comparison studies with other empirical Bo & Rs correlations, we note that the estimates of our model agreed best with those of O’Bryan’s (O'Bryan 1988) correlations.
Many numerical kick simulators exist today, but they are notoriously time-consuming, limiting their on-field utility. Our kick simulator’s simplicity makes it potentially useful for on-field well control decisions. Most of these existing numerical simulators ignore the effects of kick solubility in synthetic-based muds. In the few models that do not ignore solubility, the approach to accounting for gas solubility and mud swelling is empirical, limiting their usage under conditions beyond the range of the source data used in developing these correlations. The mud swelling calculation approach we developed does not have these pressure and temperature range limitations.