This contributed volume contains a collection of articles on state-of-the-art developments on the construction of theoretical integral techniques and their application to specific problems in science and engineering. Chapters in this book are based on talks given at the Symposium on the Theory and Applications of Integral Methods in Science and Engineering, held virtually in July 2021, and are written by internationally recognized researchers. This collection will be of interest to researchers in applied mathematics, physics, and mechanical and electrical engineering, as well as graduate students in these disciplines and other professionals for whom integration is an essential tool.

Despite the numerous advantages associated with using compact cylindrical cyclone gas/liquid separators, particularly for upstream production operations, the lack of a full understanding of the complex hydrodynamic process taking place in it and its "unfamiliarity" to oil field personnel has hindered its widespread use. The complexity associated with this technology is attributed to two limiting physical phenomena, liquid carry-over and gas carry-under. While a lot of work has been done to better understand and predict the liquid carry-over operational envelope, little or no information about methods capable of adequately predicting or characterizing the gas carry-under performance of such separators is available. Traditionally, to mitigate the gas carry-under phenomena, the use of complex control algorithms and systems has been employed. These systems make the technology expensive (as opposed to the potential cost reduction it promises) and impractical for realistic use in the oilfield where reliability is of critical importance. A simpler solution, the use of changeable or adjustable inlet-slots that regulate the artificial gravity environment created in the separator, could significantly improve the gas carry-under performance of cylindrical cyclone separators. This research has focused primarily on the use of adjustable inlet-slots. Theoretical analysis and experimental data investigating the benefits of variable inlet geometry have been provided. This work lays the foundation or validation required to perform more tests on a field-scale version to verify the results presented here. A modular design of such a variable inlet-slot inlet-section has the potential of simplifying the design and specifications of cylindrical cyclone gas/liquid separators. From the results of this investigation, it was found that the gas carry-under performance of a cylindrical cyclone gas/liquid separator could be improved considerably over a wider range of operating conditions by adjusting the size of the inlet-slots. This contradicts earlier reports of liquid carry-over improvement in separator performance. Also, for the first time, a simple method for theoretically analyzing the percent improvement in separator gas carry-under performance using the optimum g-force concept is presented. This method could be incorporated into design software for determining the slot-size configuration required for varying separator-operating conditions.