Yehuda Taitel

On the parabolic, hyperbolic and discrete formulation of the heat conduction equation

NOMENCLATURE mean speed of a molecule : function defined by equation (8): spatial increment. of the order oft he mean free path : spatial index : modified Bessel Function. 1 st order: time index : wall thickness : integer: Laplace variable : J(P2 + 2p): time : temperature: unit step function. u(t x) = 1 for t > Y: = 0 for t < x: speed of heat propagation : Cartesian coordinate : thermal diffusivity: transformed temperature : mean free path : propagation time increment = h/u. also dummy variable.

Two-Phase Slug Flow

Publisher Summary Slug flow is a highly complex type of flow with an unsteady nature. The prediction of pressure drop, heat, and mass transfer for such flow is often considered a difficult task. The chapter deals with steady slug flow. The chapter introduces several options of modeling the hydrodynamic parameters and pressure drop using a unified approach that is applicable for the vertical, horizontal, and inclined cases. The chapter also reviews transient phenomena in slug flow by illustrating an example of severe slugging in a pipeline-riser system. It is noted that heat transfer in slug flow is of major importance for practical applications. The treatment of the two-phase flow is usually considered as a two-phase mixture. The severe slugging that consists of one riser and one pipeline is one of the simplest example of slug flow under nonsteady conditions. The Boe criterion differentiates between steady and cyclic operations with two exceptions. At high liquid flow rates, a steady flow can also exist within the severe slugging region predicted by the Boe criterion. There is a region outside the Boe criterion that is in an unsteady state and leads to unsteady oscillations.

Flow pattern transition for gas-liquid flow in horizontal and inclined pipes. Comparison of experimental data with theory

Abstract Experimental measurements of flow patterns for gas-liquid flow in inclined pipes are reported. The results compare well with a recently published theory for the prediction of flow patterns in horizontal and inclined pipes (Taitel & Dukler 1976).

Flow pattern transition for vertical downward two phase flow

Abstract Experiments of flow pattern for vertical downward gas—liquid flow are reported. In addition theoretically based transition criteria for the flow pattern are presented. The experimental results compare resonably well with the theoretical model for the prediction of flow pattern in vertical downward flow.

Flow pattern transition for downward inclined two phase flow; horizontal to vertical

Abstract Data on the flow pattern transition for gas liquid flow in pipes for downward 0–90° inclination was collected. Mathematical models were developed to predict the flow pattern in the whole range of downward inclination.

A model for slug length distribution in gas-liquid slug flow

Abstract Intermittent, or slug flow, is a very common occurrence in gas—liquid two-phase pipe flow. Usually slug flow is an undesirable flow pattern since the existence of long lumps of liquid slugs that move at high speed is unfavorable to gas—liquid transportation. Considerable efforts have been devoted to the prediction of the slug hydrodynamic characteristics, primarily by considering an average slug length and calculating average parameters. This approach is useful, and in many cases it is adequate for many engineering calculations. There are, however, cases where this information is not sufficient and much more detailed information concerning the slug length distribution, the mean slug length and the maximum possible slug length is essential. This work presents a model that is able to calculate the slug length distribution at any desired position along the pipe. The model assumes a random distribution at the inlet of the pipe and it calculates the increase or decrease in each individual slug length, including the disappearance of the short slugs, as they move downstream. The results of the calculation show that for the fully developed slug flow the mean slug length is about 1.5 times the minimum stable slug length and the maximum length is about 3 times the minimum stable slug length.

A model for slug frequency during gas-liquid flow in horizontal and near horizontal pipes

Abstract Slug formation is an entry region phenomena. Waves form on a growing stratified film eventually blocking the gas to form a slug. The liquid level drops when the slug is swept away and the waves disappear. Then the film rebuilds its level in a time equal to the inverse frequency. The process is modelled and the results shown to be in agreement with experiment.

STABILITY OF SEVERE SLUGGING

For a constant flow rate of liquid and gas in a pipe one expects the conditions along the pipe to be of a steady state nature. However, for a pipe in a hilly terrain or in an offshore pipeline-riser system, a steady state operation is often not possible, and conditions of severe or terrain slugging develop. This causes the system to operate in an undesired cyclic fashion in which alternate long liquid slugs are followed by the production of high gas flow rate. The present work deals with the condition under which steady state operation is possible. It shows theoretically that it is possible to stablize the flow by increasing the back pressure of the separator or by employing a controlled choking at the pipe exit.

Kelvin-Helmholtz stability criteria for stratified flow: viscous versus non-viscous (inviscid) approaches

Abstract The neutral stability lines obtained from the viscous Kelvin-Helmholtz analysis and the inviscid analysis are quite different for the case of low liquid viscosities, whereas they are quite similar for high viscosity, contrary to what one would expect. This puzzling result is considered in this work. It is shown that the stability behavior regarding the amplification rate is actually almost the same for the two analyses for a wide range of liquid viscosities and for various pipe inclinations. The results obtained in the present work also support Barneas interpretation of the viscous and inviscid analyses as a means for predicting various transitions from stratified flow.

Two-phase flow splitting in a tee junction—experiment and modelling

Abstract A model is presented for the prediction of two-phase flow splitting in a horizontal pipe tee for the stratified wavy and annular flow patterns. The model is based on a splitting mechanism which suggests that the preferential liquid flow is controlled by competing inertial and centripetal forces acting on the liquid phase at the tee junction. The model is compared with experimental data and gives reasoanble agreement.