Pipe fractional flow theory : principles and applications




Nagoo, Anand Subhash

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The contribution of this research is a simple, analytical mathematical modeling framework that connects multiphase pipe flow phenomena and satisfactorily reproduces key multiphase pipe flow experimental findings and field observations, from older classic data to modern ones. The proposed unified formulation presents, for the first time, a reliably accurate analytical solution for averaged (1D) multiphase pipe flow over a wide range of applications. The two new fundamental insights provided by this research are that: (a) macroscopic single-phase pipe flow fluid mechanics concepts can be generalized to multiphase pipe flow, and (b): viewing and analyzing multiphase pipe flow in general terms of averaged relative flow (or fractional flow) can lead to a unified understanding of its resultant (global) behavior. The first insight stems from our finding that the universal relationship that exists between pressure and velocity in single-phase flow can also be found equivalently between pressure and relative velocity in multiphase flow. This eliminates the need for a-priori flow pattern determination in calculating multiphase flow pressure gradients. The second insight signifies that, in general, averaged multiphase flow problems can be sufficiently modeled by knowing only the averaged volume fractions. This proves that flow patterns are merely the visual, spatial manifestations of the in-situ velocity and volume fraction distributions (the quantities that govern the transport processes of the flow), which are neatly captured in the averaged sense as different fractional flow paths in our proposed fractional flow graphs. Due to their simplicity, these new insights provide for a deeper understanding of flow phenomena and a broader capability to produce quantitative answers in response to what-if questions. Since these insights do not draw from any precedent in the prior literature, a science-oriented, comprehensive validation of our core analytical principles was performed. Model validation was performed against a diverse range of vapor-liquid, liquid-liquid, fluid-solid and vapor-liquid-liquid applications (over 74,000 experimental measurements from over 110 different labs and over 6,000 field measurements). Additionally, our analytical theory was benchmarked against other modeling methods and current industry codes with identical (unbiased), named published data. The validation and benchmarking results affirm the central finding of this research – that simple, suitably-averaged analytical models can yield an improved understanding and significantly better accuracy than that obtained with extremely complex, tunable models. It is proven that the numerous, continuously interacting (local) flow microphysics effects in a multiphase flow can be (implicitly) accounted for by just a few properly validated (global) closure models that capture their net (resultant) behavior. In essence, it is the claim of this research that there is an underlying simplicity and connectedness in this subject if looking at the resultant macroscopic (averaged) behaviors of the flow. The observed coherencies of the macroscopic, self-organizing physical structures that define the subject are equivalently present in the macroscopic mathematical descriptions of these systems, i.e., the flow-pattern-implicit, averaged-equations mixture models that describe the collective behavior of the flowing mixture.


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