In the petroleum industry, multiphase flow dynamics within the tubing string have gained significant attention due to associated challenges. Accurately predicting pressure drops and wellbore pressures is crucial for the effective modeling of vertical lift performance (VLP). This study focuses on predicting the multiphase flow behavior in four wells located in the Faihaa oil field in southern Iraq, utilizing PIPESIM software. The process of selecting the most appropriate multiphase correlation was performed by utilizing production test data to construct a comprehensive survey data catalog. Subsequently, the results were compared with the correlations available within the PIPESIM software. The outcomes reveal that the Hagedorn and Brown (HB) correlation provides the most accurate correlation for calculating pressure in FH-1 and FH-3 while the Beggs and Brill original (BBO) correlation proves to be the optimal fit for wells FH-2 and Gomez mechanistic model for FH-4. These correlations show the lowest root mean square (RMS) values of 11.5, 7.56, 8.889, and 6.622 for the four wells, respectively, accompanied by the lowest error ratios of 0.00692%, 0.00033%, 0.00787%, and 0.0011%, respectively. Conversely, Beggs and Brill original (BBO) correlation yields less accurate results in predicting pressure drop for FH-1 compared with other correlations. Similarly, correlations, such as Orkiszewski for FH-2, Duns and Ros for FH-3, and ANSARI for FH-4, also display less accuracy level. Notably, the study also identifies that single-phase flow dominates within the tubing string until a depth of 6000 feet in most wells, beyond which slug flow emerges, introducing significant production challenges. As a result, the study recommends carefully selecting optimal operational conditions encompassing variables such as wellhead pressure, tubing dimensions, and other pertinent parameters. This approach is crucial to prevent the onset of slug flow regime and thus mitigate associated production challenges.
In this paper, we introduce new definitions of the - spaces namely the - spaces Here, and are natural numbers that are not necessarily equal, such that . The space refers to the n-dimensional Euclidean space, refers to the quaternions set and refers to the N-dimensional quaternionic space. Furthermore, we establish and prove some properties of their elements. These elements are quaternion-valued N-vector functions defined on , and the spaces have never been introduced in this way before.