Pipe fractional flow through branched conduits

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Stewart, Jeffrey Robert

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In the field of multiphase flow, the so-called phase splitting problem is a recurrent topic of discussion. In a branching conduit, it is of practical importance to know a priori how the phases split. Over the years, a variety of models have been developed to predict this and describe the physics involved. Despite this wealth of knowledge, little connection has been made between this question and fluid flow in networks. How phases split is determined by the system of equations solved, and no physics is incorporated to determine the phase split. To address this issue, a novel formulation of a multiphase network has been devised and validated against data and existing solutions, as well as compared to existing software. Additionally, current phase-splitting models have been discussed and compared. A new phase-splitting model based on a conservation-of-momentum approach is discussed and compared to branched-flow data. In building and validating this new model, a database of branched-flow experiments containing over 5000 data points from multiple laboratories has been gathered and systematized. This model has been incorporated into the existing network model to serve as additional equations when boundary conditions are unknown, and also to validate solutions found by the solver to ensure it is feasible. From this study, it was found that some current network solvers commercially available can arrive at inaccurate solutions. Moreover, such solvers can use an unorthodox approach to solve network problems and does not explicitly solve for Kirchhoff's laws. This issue is compounded by solution non-uniqueness--especially in networks with a high degree of looping. It is shown here that convergence is largely dependent on the initial guess. The phase splitting equation developed shows the degree of phase splitting at a junction varies primarily with branch configuration, pressure, void fraction, and flow rate. Current phase-splitting equations tend to exaggerate the phase split at a branch. In order to obtain the most exaggerated phase split, a vertical side-branch orientation should be used with a high mass takeoff.



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