P.J. Hamersma

Correlations predicting frictional pressure drop and liquid holdup during horizontal gas-liquid pipe flow with a small liquid holdup

Experimental data and correlations available in the literature for the liquid holdup ϵL and the pressure gradient ΔPTP/L for gas-liquid pipe flow, generally, do not cover the domain 0 < ϵL < 0.06. Reliable pressure-drop correlations for this holdup range are important for calculating flow rates of natural gas, containing traces of condensate. In the present paper attention is focused on reliable measurements of ϵL and ΔPTPIL values and on the development of a phenomenological model for the liquid-holdup range 0 < ϵL < 0.06. This model is called the “apparent rough surface” model and is referred to as the ARS model. The experimental results presented in this paper refer to air-water and air-water + ethyleneglycol systems with varying transport properties in horizontal straight smooth glass tubes under steady-state conditions. The holdup and pressure gradient values predicted with the ARS model agree satisfactorily with both our experimental results and data obtained from the literature referring to small liquid-holdup values 0 < ϵL < 0.06. Further, it has been shown that in the domain 38 < α < 72 mPa m the interfacial tension of the gas-liquid system has no significant effect on the liquid holdup. The pressure gradient, however, increases slightly with decreasing surface tension values.

A pressure drop correlation for gas/liquid pipe flow with a small liquid holdup

During the transport of natural gas through pipelines small amounts of liquid are present as a result of condensate formation. These small amounts of liquid corresponding to a volume flow rate fraction ζL < 2 × 10−3 may result in a liquid holdup eL < 0.04 and a relatively large increase in the pressure drop. In the present paper a model is introduced which describes the liquid holdup and the axial pressure gradient in co-current gas/liquid flow in horizontal tubes with a small liquid holdup (eL s

Enhancement of the gas-absorption rate in agitated slurry reactors by gas-adsorbing particles adhering to gas bubbles

0.04), mainly covering the stratified-wavy and annular flow regimes. A good agreement was found between the measured values of the liquid holdup and pressure drop of gas/liquid pipe flow and those obtained from the correlations introduced in this paper. Further, the experimental results were also compared with values calculated with correlations obtained from literature.

Single- and two-phase flow through helically coiled tubes

Abstract In this paper, it is shown that the rate of hydrogen absorption into an aqueous solution is considerably enhanced by the presence of small particles, provided that (a) particle-to-bubble adhesion occurs, so that, during the absorption, a sufficiently large part of the gas—liquid interface is covered by adhering particles; (b) at equilibrium, the hydrogen concentration in the particles is much higher than that in the surrounding liquid. A model is derived to calculate the relationship between the enhancement factor E 0 of the initial gas-absorption rate, the fraction ζ of the gas-liquid interface covered by adhering particles, and the concentration γ s of the catalyst particles in the slurry. The model is verified by flotation experiments and gas-absorption measurements, performed with hydrogen and aqueous suspensions containing different concentrations of small carbon-supported or alumina-supported catalyst particles.

Adhesion of small catalyst particles to gas bubbles: determination of small effective solid—liquid—gas contact angles

A tube friction chart is introduced for single-phase fluid flow through curved tubes. This chart covers both laminar flow (0 Recrit). In constructing this chart use is made of a correlation between friction factor and Dean number, which is introduced in the present paper and which covers the whole laminar flow domain 0 <Re <Recrit with Recrit = 2100[1 + 12(d/D)12]. Moreover, experimental results are reported concerning the pressure gradient of gas-liquid flow with a small liquid holdup (ϵL ⩽ 0.03) through a helically coiled tube (vertical coil axis, helix angle 3.7°). Models have been presented and experimentally verified for gas-liquid flow through helically coiled tubes to describe the liquid holdup as a function of the ratios of the superficial velocities and transport properties of the fluids, and to predict film inversion occurring in curved pipes.

Coalescence of freely moving bubbles in water by the action of suspended hydrophobic particles

Abstract The adhesion of small particles to a gas bubble in water is studied with the aid of a modified bubble pick-up (BPU) method. The particle-to-bubble adhesion is revealed in the angle α max by which the gas-bubble surface is covered by adhering particles under static conditions. The value of α max depends on the particle and bubble sizes and on the physical properties of the three phases involved, especially on the effective contact angle θ E . A “particles-to-bubble adhesion” (PBA) model, based on a balance of forces under static conditions, is developed to calculate the value of θ E from the measured values of α max . The value of θ E measured according to the BPU method reflects the particle-to-bubble adhesion encountered during flotation processes and in slurry reactors. Experiments carried out under static conditions with air bubbles in water and commercially available catalyst particles showed that θ E is smaller than the contact angle θ which occurs at “flat” solid and liquid surfaces. In accordance with the extended Young—Dupre equation, the value of θ can be obtained by extrapolation of measured θ E values to a value where the curvatures of the surfaces are zero. The particle-to-bubble adhesion for the hydrogen—water—Pd/C system is much larger than that for the air—water—Pd/C system. For the hydrogen—water—Pd/AI 2 O 3 and the hydrogen—water—Pd/BaSO 4 systems, the particle-to-particle cohesion dominates the particle-to-bubble adhesion resulting in hardly any attachment of the catalyst particles to the hydrogen bubbles.

A model for predicting liquid route preference during gas—liquid flow through horizontal branched pipelines☆

The presence of (catalyst) particles in slurry columns may induce significant changes in the overall column hydrodynamics. This is commonly attributed to changes in the apparent viscosity and density of the slurry phase as a result of the presence of particles. However, in case of solids demonstrating a strong repulsive S-L interaction, other factors come into play. Presently, we address the behaviour of hydrophobic particles in aqueous slurry bubble columns, using an air-water-carbon model system. Hydrophobic particles, as most carbons, tend to segregate from an aqueous phase, thus giving rise to particle-particle cohesion in the liquid phase and to particle-bubble adhesion. Cohesion or agglomeration is important, for instance in relation to the filtration behaviour of catalysts. In this study, however, the focus is particle-to-bubble adhesion. From antifoaming studies it is known that particles adhering to bubbles may promote bubble coalescence. Whereas in foams particles are forced in the G-L interlayer and bubbles are stagnant, in slurry bubble columns both the solid phase and the bubbles move freely. As is currently demonstrated, adhering particles do nevertheless promote bubble coalescence also under flow conditions. By consequence the bubble-size distribution is markedly shifted to larger bubbles. As these latter govern the overall flow pattern and back-mixing behaviour of a bubble column, this is crucial to practical operation.

Correlations predicting liquid hold-up and pressure gradient in steady-state (nearly) horizontal co-current gas-liquid pipe flow

A model has been developed for the calculation of liquid route preference during separated gas—liquid flow with small liquid holdup values of eL < 0.06, through horizontal tubes with a horizontal branch. This so-called Double Stream Model (DSM) has been derived from the steady-state macroscopic mechanical energy balance (extended Bernoulli equation), applied to the “inlet-to-run” stream and the “inlet-to-branch” stream of both the gas phase and the liquid phase. According to the DSM, whose application is given in Appendix A, the branch liquid mass intake fraction λL is a function of: (1) the branch gas mass intake fraction λG, (2) the geometry of the junction, and (3) the ratio κ of the kinetic energy per unit volume of the inlet gas flow and that of the inlet liquid flow. The value of κ depends on the densities, mass flow rates, holdup values and velocity profiles of gas and liquid in the inlet. The DSM has been verified with experimental data from three institutes obtained with gas-liquid systems with different values of transport properties and three types of dividing junctions, namely sharp-edged regular, radiused regular and radiused reduced tees.

Pressure-induced phase separation of polymer-solvent systems with dissipative particle dynamics

The liquid hold-up ɛL and pressure gradient (– dP/dx)TP occurring during steady-state (nearly) horizontal co-current gas-liquid pipe flow have been calculated using the general momentum balances for both phases, two different models for the wall shear stresses and 22 different correlations for the interfacial friction factor. The calculated results are compared with an experimental database of the University of Amsterdam, consisting of 3981 measurements of gas-liquid pipe flow in three flow regimes, i.e. stratified, wavy and annular flow, and the following process conditions: pipe diameters 0.0127

Axial dispersion in single-phase flow in a pulsed packed column containing structured packing

An important problem in the polymer-processing industryis the separation of solvents and impurities, like unreactedmonomer, from the polymer. In the polymer industry,devolatilising the solvent from the solution by steamstripping can be very energy-intensive as the solvent canamount to 95 wt.-% of the solution. In certain solutionpolymerisation processes, such as the production ofethene-propene copolymers, the cost of this separationcould be up to 10% of the final product cost (Gutowski etal.