J.M.H. Fortuin

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.

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

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.

Gas-liquid flow in slightly inclined pipes

Abstract The modified apparent rough surface (MARS) model is presented, which facilitates prediction of liquid holdup and pressure gradient in gas-liquid flow through horizontal and slightly sloping pipes. The model is based on two steady-state, one-dimensional momentum balance equations, which include the superficial velocities and transport properties of gas and liquid, the diameter of the pipe and its angle from the horizontal. Separate correlations are proposed for the interfacial friction factor f i , the liquid-to-wall friction factor f L , the interfacial perimeter S i and the wetted perimeter S L . Predicted values of liquid holdup and pressure gradient are verified against results of 2400 carefully performed, laboratory experiments in horizontal and sloping glass pipes (−3 ≤ β ≤ +6°) of 15, 26 and 51 mm diameter. The liquid holdup ϵ L ranges from 0 to 0.42, and the superficial liquid velocity u LS from 0 to 0.06 m s −1 and the superficial gas velocity u GS from 1.8 to 34 m s −1 . The gas-liquid systems used are air/water and air/tetradecane ( n -C 14 H 30 ) at atmospheric pressure and room temperature. Significant effects of small inclination angles were found at low gas flow rates, leading to an eightfold increase in liquid holdup and more than a fourfold increase in pressure gradient compared to horizontal flow. Nevertheless, the average relative error in the prediction of liquid holdup and pressure gradient is less than 10%.

The use of adhesion of catalyst particles to gas bubbles to achieve enhancement of gas absorption in slurry reactors—II. Determination of the enhancement in a bubble-containing slurry reactor

The rate of hydrogen absorption into an aqueous hydroxylaminephosphate solution is measured as a function of the concentration of catalyst particles in the liquid phase using a bubbles-containing slurry reactor. It is found that the gas absorption rate is enhanced considerably when small (dP ⩽ 20 μm) Pd/C catalyst particles are used, while no enhancement is observed when Pd/Al2O3 catalyst particles are used for catalyst particles concentrations up to 1.2 kg m−3. The measured enhancement factors can be described by a model, based on the film theory, in which it is assumed that the relation between the concentration of catalyst particles in the liquid film at the gas-liquid interface and in the bulk of the liquid is similar to a Freundlich-type adsorption isotherm with an exponent n &>1. From a combination of this model and the experimentally determined enhancement factors it can be concluded that the difference in behaviour between the Pd/C and Pd/Al2O3 catalysts is mainly due to a difference in adhesion between the catalyst particles and the surface of the hydrogen bubbles as was found in Part I of this study.

The diffusion coefficients of helium, hydrogen, oxygen and nitrogen in water determined from the permeability of a stagnant liquid layer in the quasi-s

Abstract At temperatures between 10 and 60°C the diffusion coefficients of helium, hydrogen, oxygen and nitrogen in water have been determined from the permeability of a stagnant liquid layer in the quasi-steady state (SLL method). With this method we actually measure the difference in diffusive flow between two gases through a horizontal stagnant liquid layer between gas-permeable membranes. If oxygen is one of the gases, we are able to determine the diffusion coefficient of oxygen with a maximum experimental error of 3.5% and that of the other gases within 5%. Results are given and compared with experimental values stated in the literature.

Axial dispersion in single-phase flow in pulsed packed columns

Abstract Axial dispersion in single-phase flow through a pulsed packed column (length 4 m; Raschig-ring packing) has been investigated using an imperfect pulse method. It has been shown that under certain conditions axial dispersion can be reduced by means of pulsation. A three-parameter model based on the Taylor-Aris dispersion equation for tube flow has been developed. This model, which has been verified experimentally, describes the relation between the axial dispersion coefficient and the interstitial and pulsation velocities.

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

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.

The use of adhesion of catalyst particles to gas bubbles to achieve enhancement of gas absorption in slurry reactors—I. Investigation of particle-to-bubble adhesion using the bubble pick-up method

Abstract The adhesion between small catalyst particles (Pd/C, Pd/Al 2 O 3 and activated carbon) and hydrogen bubbles, situated in aqueous electrolyte solutions or in ethanol/water mixtures, has been investigated with the Bubble Pick-up method. It was found that the adhesion between catalyst particles and hydrogen bubbles strongly depends on the properties of both catalyst particles and liquid. For solid particles adhering to a gas bubble rising in a liquid a model has been derived to estimate the fraction of the gas bubble surface area which is covered by solid particles. This model is based on a balance of forces exerted on a solid particle adhering to a gas bubble and has been applied for a bubble in a stagnant liquid, as used in the BPU method, and for a bubble rising in a liquid as occurs in slurry reactors. Considering the systems investigated, this model and the experimental results obtained with the BPU method lead to the conclusion that only Pd/C catalyst particles in an aqueous electrolyte solution show an adhesion to hydrogen bubbles which is so large that in a slurry reactor containing this system, gas bubbles will be covered partly by adhering catalyst particles. This phenomenon can result in an enhancement of the gas absorption rate and can consequently lead to a remarkable reduction of concentration and costs of expensive noble metal containing catalysts in slurry reactors.

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

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.

Enhancement of absorption of a gas into a stagnant liquid in which a heterogeneously catalysed chemical reaction occurs

Abstract The CBS method[1, 2] is applied to measure the enhancement factor for the absorption of pure hydrogen from a gas bubble of constant size into a sta