Production logging encompasses profiling of flow velocities, holdup, pressure and temperature along the length of a horizontal well. Its advancement is determined by such factors as mathematical modeling, and development of new tools and software. These activities generalize the understanding of the multiphase flow meter, which requires a proper mathematical tool to calculate the parameters of multiphase flow. The natural water-oil flow always contains surfactants. The substances adsorbed on the surface of oil droplets affect the dynamics of the immiscible fluids; therefore, proper analysis of this effect is particularly important. The paper presents the theory of two-velocity hydrodynamic continuum taking into account the surfactant effect to analyze the flow regimes of a two-phase system and develop the hydrodynamic grounds generalizing the understanding of the multiphase flow meter. Its two-velocity equations are derived only from the main physical laws. The equations are true for an arbitrary class of the state equations. Its difference scheme is based on the control volume method. The effect of a phase interaction force was demonstrated on the two-phase flow regimes, which is essential for accurate holdup measurements in modern hydrodynamic logging. The theory shows that the surface-tension gradient in a two-phase flow produces an additional drag force. The force is significant and can exceed both the viscous and Stokes friction forces. The theory demonstrates that, in a two-velocity medium, in the presence of surfactants, an additional reactive force is observed that is proportional to the gradient of the surfactant dissolved in water. In this case, the hydrodynamic velocity determines the surfactant spatial concentration. The gradient produces the reactive forces in moving subsystems that affect the rate of hydrodynamic transport. The interaction results in a consistent velocity profile of both water and oil. Having slowed the motion of oil, the surfactant increases the velocity of the water. At the relatively low velocities, the surfactant effects on the phase velocities, which is important for determining the holdups of phases in the cross-sections of production wells.
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