In this seminal work, we reveal for the first time an extensively field-tested, demonstrably accurate and simple analytical equation for the calculation of the critical gas velocity limit (or onset of liquid flow reversal) in horizontal wells as an explicit and direct function of diameter, inclination and fluid properties. For the independently verifiable and first-of-its-kind multi-play field validation study, we carefully assimilate a very large database of actual horizontal gassy oil and gas liquid loading wells from several unconventional U.S. shale plays with different bubble point and dew point fluid systems and varying gas-to-liquid ratios and varying water cuts. The shale plays in our validation database include the Eagle Ford, Woodford, Cleveland Sands, Haynesville, Cotton Valley, Fayetteville, Marcellus and Barnett formations within their associated Western Gulf, South Texas, Arkoma, Western Anadarko, East Texas, Appalachian and Permian basins. Then, after summarizing our comprehensive field testing results, practical production optimization applications of the new analytical equation and advanced use cases of interest are further highlighted in various liquid loading prediction and prevention scenarios.
As opposed to prior critical gas velocity calculation methods (droplet reversal-based, film reversal-based, flow structure stability/energy), video observations both in the lab and the field clearly show continuously-evolving, co-existing and competing flow structures even with simple fluids without mass exchanges. Therefore, this work avoids skewed assumptions on demarcating the prevailing or dominant flow structure. Instead, the new analytical equation developed is based on an analysis of the major forces in the flow field, namely the axial buoyancy vector, the convective inertial and the interfacial tension forces, in combination with an assumption of the onset of liquid flow reversal based on flow field bridging (Taylor instability). Since the new analytical equation was formulated using these minimalist assumptions, this unique characteristic results in the highest predictability obtainable for the critical gas velocity calculation because there is the least amount of uncertainties (fudge factors). The consistent accuracy of the equation against our extensive horizontal well liquids loading database verifies this fact. Moreover, the simplicity of form of the equation makes it easy to use in that every practicing engineer in practice can perform fast hand or spreadsheet calculations. In effect, this equates to having a model as simple as the Turner model but now with additional direct functions of diameter and inclination. Also, the results clearly invalidate the need for artificial variables (such as interfacial friction factor) that cannot be directly measured in any experiment. In terms of usage, the new model is used in liquid loading prevention scenarios such as end-of-tubing (EOT) landing optimization and tubing-casing selection. Evidently, this work proves that no complex, computer-only procedure is necessary for accurate critical gas velocity calculation. This finding has significant speed and improved answer-reliability implications in strong favor of the presented simple equation for use in artificial lift, production optimization and digital oilfield software in industry, in addition to being ideally suited for ‘physics-guided data analytics’ applications in real-time production operations environments.