Two-phase gas and liquid flow is not well established the way the single-phase is established. One can find well-accepted frictional factor correlations for turbulent flow and an analytically derived friction factor correlation for laminar flow. Since both gas and liquid concurrently flow through the pipe and different two-phase flow regimes form in a pipe, the single-phase frictional factors cannot be used directly to predict the pressure drop and design the piping system. One way of dealing with the two-phase gas and liquid flow is to use the single-phase friction factors to determine the frictional pressure drop by considering both gas and liquid are well mixed and flow through the pipe with the same velocity. No relative velocity exists between gas and liquid. The well-mixed gas and liquid become a pseudo-fluid. This fluid has neither the physical properties of gas nor liquid. The physical properties are density, dynamic viscosity, etc. The model that is developed based on the well-mixing of gas and liquid assumption is the Homogeneous Equilibrium Model, HEM. Here, the density and viscosity of a two-phase mixture determination is on the weight basis of the presence of gas and liquid in the two-phase mixture. The developed HEM is the inclusion of frictional pressure drop, accelerational pressure drop, and gravitational pressure drop. The existence of gravitational pressure drop is due to the inclination of the pipe. The homogeneous density of the two-phase mixture and void fraction are the parameters required to determine the gravitational pressure drop. As the gas phase is involved and the piping system is operated at higher pressures, the resulting pressure drop due to the compression of the gas needs to be considered in a two-phase flow. This pressure drop is nothing but an accelerational pressure drop. Coming to the frictional pressure drop, this term contains an important parameter, the ‘two-phase friction factor’. Without knowing this parameter, the determination of a two-phase frictional pressure drop is not possible. As said single-phase friction factor correlations are available and one can take advantage of these friction factor correlations. It is possible when the liquid phase is assumed to flow alone through the pipe with the two-phase mixture flow rate. However, two phases, ‘gas and liquid’ flow through the pipe, to account for the effect of the presence of two phases, a two-phase multiplier is introduced in the model and expressed in known parameters such as mass quality, densities, and viscosities of gas and liquid. Validation of the theoretically predicted two-phase multipliers is presented with the experimental results. This present module covers all these aspects in a lucid form so that learners can appreciate the two-phase phenomena and deal with the two-phase problems with confidence.

The prediction of the two-phase frictional pressure drop and design of the piping system can also be performed by assuming gas and liquid move separately and simultaneously in the pipe. Certain area of the pipe is occupied by the gas and the remaining area of the pipe is occupied by the liquid. The areas occupied by gas and liquid depend on the flow rates of gas and liquid. There is an existence of an interfacial surface between gas and liquid. The single-phase momentum equation is applied to both gas and liquid separately including the interfacial interactions, and added together to obtain the mathematical expression to predict the frictional pressure drop. The developed model through this idealization is known as the “Separated Flow Model”, SFM. In SFM, the gas and liquid velocities are different, i,e., SFM addresses the relative velocity between gas and liquid. To predict the two-phase frictional pressure drop, the derived mathematical expression is manipulated as the product of a single-phase frictional pressure drop term and a two-phase multiplier to take advantage of single-phase friction factor correlations. The challenge is with the two-phase multiplier. Several investigators suggested the graphical and numerical correlations for two-phase multipliers obtained from experiments. These correlations starting from Lockhart-Martinelli to Friedel are provided in this module. Prediction of two-phase frictional pressure drop using SFM is relatively complex when compared with the HEM. Handling of HEM is easier. Further, HEM closely predicts the frictional pressure drops for all two-phase flow regimes. The deviation from the actual pressure drops is mainly due to the no-slip assumption between gas and liquid phases. The inclusion of slip between gas and liquid in the mathematical expression obtained from HEM; further can predict the pressure drops more closely and the prediction can be within the accepted percentage of error. This is what exactly is done in the “Drift Flux Model, DFM”. The void fraction in DFM is expressed in terms of the phase distribution parameter and superficial velocities of gas and two-phase mixture. Several correlations are suggested by the investigators to determine the void fraction as a function of the phase distribution parameter along with other known parameters are provided in this module. Therefore, this module demonstrates SFM, DFM, and all correlations to predict the total static pressure drop of a given two-phase flow, flowing through an inclined pipe and enables the learners to grasp easily the techniques involved in SFM and DFM and brings confidence in them to deal with the two-phase piping design.

This module exclusively covers the two-phase total static pressure drop predictions through individual pipe fittings, piping systems alone, and finally piping networks. Applied the Homogeneous Equilibrium Model and Separated Flow Model together with the Energy Equation to develop the mathematical expressions to determine the total static pressure drop across a sudden enlargement and sudden contraction. This is a good demonstration of applying all the “two-phase models” such as HEM, and SFM to determine the total static pressure drop. While developing the mathematical expression for the total static pressure drop across an orifice, only the Homogeneous Equilibrium Model is used. The methodology is explained for “how to obtain the mathematical expression for total static pressure drop using the Separated Flow Model”. HEM overpredicts the pressure drop across the orifice and hence, suggested corrections in the parameters and methods are included in this module to predict the pressure drop across the orifice more accurately. An orifice is a common device used in the piping systems for both metering and meeting the required pressure drop and hence, accurate prediction is highly expected. Demonstration of pressure drop predictions using all techniques and suggested correlations and methods through solving practical problems is included in this module. Pressure drop predictions across nozzle, venturi, bends with different radius of curvature to diameter ratios, and valves are covered. Two-phase pressure drop in piping networks is complicated and the involvement of pipe fittings further complicate the determination of the two-phase pressure drops in piping networks. A good number of practical problems involving most of the pipe fittings are solved to demonstrate how to predict the two-phase pressure drops. This module is intended to mostly apply all two-phase models, techniques, methods, and suggested correlations to make the learners more conversant with the two-phase phenomena and uplift their confidence levels.