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A semi-analytical model to simulate the behavior of a gas kick in an annulus was developed utilizing various concepts, including gas solubility in oil-based drilling fluids. This simulator examines critical kick indicators such as Pit Gain and Wellhead Pressure with time. It models the gas behavior using a drift-flux approach with bubble rise velocity appropriate for flow through an annulus. It also uses the Peng-Robison equation of state, van der Waals mixing rules, along with binary interaction coefficients appropriate for drilling fluids, to account for gas solubility in oil-based mud. The simulation results predict that a five-barrel (bbl) gas kick, would reach the wellhead of a 10,000 ft deep, non-circulating, vertical well in approximately 78 minutes. But it would only take 35 minutes to traverse the same well, if the well is circulating at 702 gallons per minute. The simulations also predict that if there is a constant kick influx of 1 scf/sec, the first gas bubbles would reach the wellhead of the same, non-circulating well in 4.45 hours. But only take 52 minutes when it is circulating. Incorporating gas solubility into these simulations revealed that the choice of drilling fluid volume factor (Bo) correlation affects the results significantly. It also showed that some of the existing Bo correlations fail, for drilling fluid swelling calculations, at higher pressures and temperatures. Finally, the results indicate that a gas kick would take longer to reach the wellhead when it is soluble in the mud than when it is not, regardless of the choice of Bo correlation. Most of the existing kick simulators either partially or entirely overlook the effects of solubility on gas migration. This model accounts for the gas kick's solubility in Oil-based drilling fluids, an issue that is critical for off-shore drilling. Applicability of empirical two-phase flow correlations developed for flow in cylindrical conduits, to a gas kick situation is questionable. This simulator addresses this issue by using a semi-analytical approach for modeling two-phase flow in an annulus.

Gas kick is an ever-present hazard whose importance is magnified for offshore drilling situations. Modeling gas kick is a complex problem that requires an understanding of the relevant fluid dynamics as well as the solubility of natural gas in oil-based muds (OBM). Drilling fluid swelling due to natural gas solubility in OBM significantly affects the extent of pit gain — one of the primary indicators of a kick in progress. This paper specifically addresses the issue of drilling fluid swelling from gas dissolution in OBM. Drilling fluid swelling due to gas dissolution is generally expressed the same way as oil swelling due to dissolved gas, by the volume factor, Bo. Many correlations for estimating Bo as a function of temperatures and pressures are available. We have developed a rigorous thermodynamic approach for estimating Bo. Our approach uses the Peng-Robison (1976) equation of state (EOS), van der Waals mixing rules, and binary interaction coefficients appropriate for drilling fluids to account for gas solubility. Solving the cubic form of the Peng-Robinson EOS yields a z-factor for the liquid phase of the mixture. The model uses this z-factor to estimate the liquid-phase volume of dissolved methane and, consequently, Bo. This paper validates the results of estimated Bo from this method with volume factor calculations obtained from Aspen HYSYS. Finally, this paper also presents a section where the methane mole fraction data at different P&T conditions, obtained from HYSYS simulations, is used to validate the solubility model previously developed by Manikonda et al. (2019).

This paper presents a simple mechanistic model to describe a gas kick in a drilling riser with water-based mud (WBM) and synthetic-based mud (SBM). This model can estimate key kick parameters such as the change in the wellhead pressure, kick ascent time, and pit gain. In addition, this model also predicts the solubility of the gas kick in SBM at various depths in the annulus. We used the commercial chemical process simulation software, HYSYS, to validate the results of this solubility model. This paper also presents the gas kick experimental results from a 20-ft. tall vertical flow loop at Texas A&M University, Qatar. The base case investigates a gas kick in a vertical 10,000 ft. deep, 12.415 in. drilling riser with WBM. Our analytical model uses the Hasan-Kabir two-phase flow model and develops a set of equations that describe the pressure variation in the annulus. This computed pressure change allows estimates of pit-gain. Our experimental data comes from a 20-ft. tall flow loop with a 2.5 in. steel tube, inside a 4.5 in. Acrylic pipe, that simulates a riser. For these gas kick experiments, we injected specific amounts of gas at the bottom of the setup and recorded the bubble's expansion and migration. The mechanistic model predicted explosive unloading of the riser near the wellhead. 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 (Patrick Leon O'Bryan, 1988) correlations. Numerical kick simulators that exist today are notoriously time and power-intensive, limiting their on-field utility. Our mechanistic model minimizes computation time through its simple, analytical form to describe kick migration. Our model offers another layer of novelty through the analytical, thermodynamic solubility modeling as opposed to empirical modeling sused by most of the current gas kick simulators.