Existence, uniqueness and monotonic behavior of the solution of classical flow distribution problem for hydraulic networks with pressure-dependent closure relations

Abstract

Existence, uniqueness and monotonic behavior of the solution of classical flow distribution problem for hydraulic networks with pressure-dependent closure relations was proved. The closure relation can have very general form, restricted only by continuity and monotonicity conditions necessary for providing existence, uniqueness and continuity of flow distribution problem for each branch. It is shown that network as a whole “inherits” monotonicity and continuity of its branches behavior, and this provides existence and uniqueness of solution.

Analysis of Horizontal Gas-liquid Intermittent Flow Sub-Regimes Transitions: Physical Mechanisms and Flow Maps

“…Given the recent progress made in mapping the horizontal ow pattern by Osundare et al (2022) and Korelstein and Pereyra (2023), the results obtained raises the idea of using a separate coordinate system for the different ow transition for this pipe con guration, as suggested by Taitel and Dukler (1976). Future work, using larger pipe diameters, is strongly encouraged to con rm/correct the proposed subregimes transitions.…”

“…Liquid super cial velocity (V SL ) vs gas super cial velocity (V SG ) (Mandhane et al, 1974 ;Kong and Kim, 2017;Kong et al, 2018a); Liquid mass ux (G L ) vs gas mass ux (G G ) (Govier and Omer, 1962); Gas mass ux (G G ) vs gas-to-liquid mass ux (G G /G L ) (Baker, 1953); Liquid mass ow rate (M L ) vs gas mass ow rate (M G ) (Ghajar, 2020); Input gas fraction (λ G ) vs mixture velocity (V M ) (Kostrein, 1949); Liquid Reynolds number (Re SL ) vs gas Reynolds number (Re SG ) (Thaker and Banerjee, 2015); Liquid Froude number (Fr M ) vs gas Froude number (Fr SG ) (Shell, 2007;Korelstein and Pereyra, 2023); Mixture Froude number (Fr M ) or square mixture Froude number vs input liquid fraction (λ L ) (Beggs and Brill, 1973); Mixture Froude number (Fr M ) vs gas-to-liquid super cial velocity (V SG /V SL ) or liquid-to-gas super cial velocity (V SL /V SG ) (Spedding and Nguyen, 1980); F vs X (Breber et al, 1980 ;Lamari, 2001).…”

Analysis of Horizontal Gas-liquid Intermittent Flow Sub-Regimes Transitions: Physical Mechanisms and Flow Maps

“…As Korelstein and Pereyra (2023) pointed out, the mechanistic ow pattern models such as that of Taitel and Dukler (1976), are seldom used. This is can be explained by the fact that these kinds of models are based on idealized assumptions that limit their quantitative agreement with the experiments.…”

Analysis of Horizontal Gas-liquid Intermittent Flow Sub-Regimes Transitions: Physical Mechanisms and Flow Maps

“…As Korelstein and Pereyra (2023) pointed out, the mechanistic flow pattern models, such as that of Taitel and Dukler (1976), are seldom used. This is can be explained by the fact that these types of models are based on idealized assumptions that limit their quantitative agreement with experiments.…”

“…-Liquid superficial velocity (VSL) vs gas superficial velocity (VSG) (Mandhane et al, 1974 ;Kong and Kim, 2017;Kong et al, 2018a); -Liquid mass flux (GL) vs gas mass flux (GG) (Govier and Omer, 1962); -Gas mass flux (GG) vs gas-to-liquid mass flux (GG/GL) (Baker, 1953); -Liquid mass flow rate (ML) vs gas mass flow rate (MG) (Ghajar, 2020); -Input gas fraction (λG) vs mixture velocity (VM) (Kostrein, 1949); -Liquid Reynolds number (ReSL) vs gas Reynolds number (ReSG) (Thaker and Banerjee, 2015); -Liquid Froude number (FrM) vs gas Froude number (FrSG) (Shell, 2007;Korelstein and Pereyra, 2023); -Mixture Froude number (FrM) or square mixture Froude number vs input liquid fraction (λL) (Beggs and Brill, 1973); -Mixture Froude number (FrM) vs gas-to-liquid superficial velocity (VSG/VSL) or liquid-to-gas superficial velocity (VSL/VSG) (Spedding and Nguyen, 1980); -F vs X (Breber et al, 1980 ;Lamari, 2001).…”