R.B. Thorpe

Flow patterns in the square cross-section riser of a circulating fluidised bed and the effect of riser exit design

Abstract Solids flow patterns were observed and measured in the square cross-section riser of a laboratory circulating fluidised bed (CFB). Measurements in the 0.14xa0m square riser used a sampling probe, of internal diameter 3.4xa0mm, to measure upwards and downwards solids fluxes throughout the cross-section. Interpolation gave complete solids flux profiles over the entire 0.14×0.14xa0m cross-section. Integration of the solids flux profile gave the external solids circulation rate, in reasonable agreement with measurements external to the riser. Special features of the solids flux profiles are (i) much higher down flux in the corners of the square section and (ii) slightly higher down flux half-way between the corners, near the walls. These features may be due to secondary flow in the square section duct and to enhanced sheltering provided by the two side walls. There is qualitative similarity between these solids flux profiles in the 0.14xa0m square riser and the profiles measured by Werdermann ((1992, Feststoffbewegung und Warmeubergang in zirkulierenden Wirbelschichten von Kohlekraftwerken. Dr-Ingenieur dissertation, Technical University Hamburg-Harburg) for large industrial combustors. But it is clear that there is a scale-up effect: the film, i.e. the cross-sectional area of duct containing the downflow (adjacent to the walls), is a much smaller proportion of the total area in the large units as compared with the laboratory units. The detail design of the riser exit or outlet bend at the top of the riser has a profound effect upon solids flux profiles in the riser and in particular on the reflux ratio defined as k m =(solids downward flow)/(external circulation rate). Measured values of k m varied by a factor of about 20 according to outlet bend design. These measurements were mostly near the top of the riser, but indications are that k m is affected, throughout the riser, by the design of outlet bend, a phenomenon previously observed in a CFB of circular cross-section by Brereton and Grace ((1994). In A. A. Avidan, Circulating Fluidized Bed Technology IV (pp. 137–144). New York: AIChE).

Measurement of bubble size distribution: an acoustic technique

This paper reports the successful correlation of the bubble size distribution in a bubbly two-phase flow with the sound spectrum as measured by a hydrophone and spectrum analyser. Two types of bubbly flow were considered: (i) horizontal two-phase flow in a pipeline and (ii) a two-phase turbulent axisymmetric jet. The scientific basis of this technique of measurement lies in the well-established relationship between the bubble size and the frequency of the sound emitted by a gas bubble when it is suitably stimulated; the frequency of the sound increases as the bubble size diminishes. The development of the simple idea into a potentially useful experimental technique is discussed. The advantages of this technique, as compared to alternative methods, e.g. photographic measurements, include the suitability of the technique for use in existing opaque pipework without requiring major modifications and minimal disturbance of the flow. Results from the acoustic technique are compared with those from a photographic technique; agreement between the two methods is good. The technique was also used to predict successfully the gas-liquid mass transfer coefficient in horizontal pipelines.

The onset of convection caused by buoyancy during transient heat conduction in deep fluids

The onset of convection in a thermal layer generated by transient heat conduction in deep fluid is examined. It is generally accepted that buoyancy driven convection predominates in deep fluids while surface tension driven convection can occur only in very thin layers of liquid. The occurrence of buoyancy convection can be predicted from conventional linear stability analysis for steady-state heat conduction. Its results are summarised in terms of critical Rayleigh numbers. The point of instability in transient heat conduction is, however, less well understood. Its onset in deep fluids is determined by the mode and rate of cooling. In this paper, the judicial application of transient heat conduction equations and a newly defined transient local Ra with the appropriate boundary conditions has allowed the tracking of the time and spatial development of local hydrodynamic equilibrium to the point of instability. The onset of convection can be predicted from the maximum transient Ra whose values are the same as those previously obtained by linear stability analysis for the same boundary conditions. The critical times and critical depths for stable diffusion in fluids (i.e. without convection) can thus be determined accurately. Agreement with observed values from the literature is very good. The mode and rate of heat conduction are confirmed to be the controlling factors in determining the time of onset of convection.

The transport of particles at low loading in near-horizontal pipes by intermittent flow

The transport of sand particles at low concentration in horizontal and near horizontal pipes in air/water slug flow has been studied. Low concentration means less than 1 in 1000 by volume, a level of concentration of interest in the transport of sand by oil and gas in subsea flowlines (Stevenson & Thorpe, Proceedings of the Ninth International Conference on Multiphase Flow, Cannes, France, 1999) but much lower than the range of interest in all previous work on hydraulic conveying which may be thought to be a related field of study. The velocity of sands of sieving diameter of 1.1 and 0.51mm have been measured for various gas and liquid flowrates and in liquids of viscosity in the range 1.0–7.1mPas in two 12m long pipes of internal diameter 40 and 70mm. Video recordings have been analysed to determine the mechanisms involved in transport of particles in slug flow and are used to explain the observed decrease in particle propagation velocity with increased liquid viscosity. There being no totally satisfactory mechanistic model for intermittent flow in the literature, a semi-theoretical model for sand transport is not currently facilitated. Therefore the approach taken is that of dimensional analysis. Particle velocity, VP, is successfully correlated using dimensionless groups which include liquid viscosity, particle size and liquid and gas flow rates. The preferred correlation for sand in liquids of viscosity less than about 5mPas is nVPjf=0.951+jgjf−1.38jgjf+0.88FrfRefFrfdD1.5−0.180. nAll the parameters, except gravitational acceleration, have been varied in the experimental programme. It is found that particle velocity, VP is independent of pipe inclination in slug flow for pipe inclinations of up to three degrees. The above correlation is used to produce an equation that predicts the point of incipient-sand deposition. This equation can be used to estimate the maximum turndown of two-phase offshore oil production from satellite wells before sand will begin to deposit at the bottom of the pipe.

Dimensionless groups for practicable similarity of circulating fluidised beds

Abstract Sets of dimensionless groups from the literature used for scaling are classified according to the number of groups in a set. At least five dimensionless groups are required for full hydrodynamic scaling of a Circulating Fluidised Bed (CFB). Sets of four groups, given by Glicksman, Hyre and Woloshun (1993, Powder Technology, 77, 177–199) and Horio, Ishii, Kobukai and Yamanishi (1989, Journal of Chemical Engineering of Japan, 22(6), 587–592) and sets of three groups given by Glicksman (1988, Chemical Engineering Science, 43, 1419–1421) and Horio et al. (1989) are in both cases shown to give essentially equivalent scaling. A survey concludes that most experimental results reported in the literature scale up better to catalytic cracking CFBs than to CFB combustors.

Gas diffusion into viscous and non-Newtonian liquids

Abstract A quiescent technique has been developed to detemine the diffusion coefficients of carbon dioxide in water and viscous and non-Newtonian liquids. The rate of gas absorption was measured accurately as the pressure change of a fixed volume of gas by a micromanometer. Gas penetration analysis suggests that a plot of gas absorption rate against the square root of contact time should be linear. The plot revealed a distinct initial phase of molecular diffusion lasting for about 100 seconds when water was instantaneously exposed to carbon dioxide. This was followed by non-linear behaviour in which natural convection is driven by density gradients. The diffusion coefficient of carbon dioxide in water was found to agree well with the values reported in the literature. Mass transfer coefficients, k L , were determined for the interface in the convective regime. Diffusion without natural convection of CO 2 into viscous and pseudoplastic aqueous solutions appeared to be prolonged and proceeded at a slower rate. The onset of convection was suppressed considerably depending on the (apparent) viscosity of the solutions. A critical Rayleigh number was computed to characterise the onset of linear instability leading to natural convection. The critical times for stable diffusion were predicted from this critical Rayleigh number. Agreement with observed values is fair.

The onset of convection driven by buoyancy effects caused by various modes of transient heat conduction: Part I. Transient Rayleigh numbers

The onset of convection induced by transient heat conduction in deep fluid is examined for two boundary conditions, namely: fixed surface temperature (FST) and linear rate of change of surface temperature with respect to time (LTR). Transient Rayleigh numbers (Ra) for these boundary conditions are defined for each of the respective modes of heat transport. It is found that the onset of convection can be predicted from a maximum transient Ra if its corresponding Biot number (Bi) is known. Hence the critical times and critical depths for stable heat conduction in fluids are obtained. However, the Biot number for an interface in an unsteady-state experiment is diƒcult to determine. A transient Biot number is defined to allow the evaluation of Bi between Bi0 and R. The onset of convection for a FST boundary has yet to be verified experimentally, although it has been shown to be valid in analogous gas absorption experiments. The LTR model is found to have no distinct value of Biot number, which could lie between those of CHF (constant heat flux) and FST. The purported LTR experiments were diƒcult to verify because surface temperature profiles were generally non-linear and the Biot numbers for the system under study could not be determined with certainty. In all cases the critical magnitude of the maximum Rayleigh number for each mode of heat conduction is unique and is independent of the critical time and the depth of the fluid. ( 1998 Elsevier Science Ltd. All rights reserved.

The onset of convection induced by buoyancy during gas diffusion in deep fluids

Abstract The onset of convection induced by buoyancy caused by interfacial gas diffusion in deep fluids is analysed. It was found, as in heat transfer, that transient convection during mass diffusion is dependent on a Biot number. A transient diffusive Biot number ( Bi D ) was defined such that Bi D =0 and ∞ correspond to constant mass flux (CMF) and fixed surface concentration (FSC) boundaries, which have theoretical critical Rayleigh numbers of 669 and 1100, respectively. Transient Rayleigh numbers were derived for both boundary conditions. Experiments of soluble and sparingly soluble gases diffusing in water were found to agree very well with the theory advanced in this paper for the onset of convection in accordance with CMF and FSC models. The stable diffusion times were also predicted accurately for both gases. They also represent the theoretical time limits for the gas penetration theory, which relies on Fick’s law that assumes no convection. The horizontal dimension of the plunging plumes was also predicted with reasonable accuracy. Monolayer formed by surfactant was found to produce an FSC boundary for a soluble solute and to render the liquid surface rigid and prolonged the onset of convection.

Evaporation of water from air-fluidized porous particles

Abstract The drying rate of wetted porous silica–alumina particles, FCC catalyst, was measured in a 15 cm diameter air-fluidized bed with a cloth distributor, containing about 1.5 kg catalyst. The particles tolerated the addition of remarkably large quantities of liquid water, up to 50% of the dry weight, without upsetting the fluidization characteristics: evidently the water was accommodated within the porous particle structure. The drying rate was measured in two ways: (1) by mounting the whole fluidized bed on a balance and (2) by measuring the inlet and outlet air humidities by wet and dry bulb thermometers and measuring also the air flow rate. The change in weight from method (1) agreed well with results from (2) using a material balance. Tests with two methods of injecting the water, locally and evenly distributed, gave the same drying rate after an initial transient, showing that water readily distributes itself amongst the catalyst particles. The wet catalyst exhibited a constant drying rate followed by a falling rate. At the transition between these rate laws, the water content is consistent with the N2 BET area of the catalyst being covered by a monolayer of water; this could be of practical value to designers and operators of dryers. During the constant-rate period, the exit air had a relative humidity which was constant at 60–70%. Calculations show that there is excellent air–solids contact, so the exit air appears to be in equilibrium with the wet catalyst. During the falling-rate period, it appears that the area of the monolayer diminishes, as also does its equilibrium vapour pressure. These characteristics make FCC catalyst an admirable material for a hospital fluidized bed to support a patient with certain injuries, e.g., serious burns, for which dry conditions and an ability to absorb liquid are important.

Gas–solids flow in the diffuser of a circulating fluidised bed riser

Abstract Measurements of particle flux are reported for air/particle flow in and near a diffuser in the riser of a circulating fluidised bed. A diffuser is here defined as a duct of tapered cross-section, the larger cross-section at the top; the top and bottom are each connected to a vertical duct of uniform cross-section. In the present work, the top and bottom sections were square: the top section was 0.14×0.14 m; the bottom section was 0.11×0.11 m; the diffuser connecting the two sections was slab-sided, each side being inclined at 6.8° to the vertical; the total duct height, comprising the diffuser and the two parallel sections, was 5.1 m. Co-current upflow of air and cracking catalyst, mean diameter 60 μm, was studied. The conditions were chosen to give similarity with a large industrial circulating fluidised bed (CFB): the air velocity was 1.3–2.1 m/s and the flux net particle flux 2.3–3.8 kg/m 2 /s. Upward and downward particle flux profiles, across sections in the parallel ducts and at the top and bottom of the diffuser, were measured with a sampling probe 3.4 mm in diameter. Interpolation algorithms gave flux profiles across each section, showing core-annulus flow. Integration of these profiles across the duct gave the net particle flow, in good agreement with external measurements using a slot flow meter. While single phase (air only) flow in the duct showed unseparated motion in the diffuser, the flux profiles for solids suggest a strong recirculation of solids and probably air also, in the diffuser. Adjacent to the wall is the usual region of solids downflow; the mean thickness of this region in the diffuser is about twice as much as in the parallel sections remote from the diffuser. Likewise the reflux ratio=(Particle downflow at a section)/(External particle circulation rate) is 2–3 times as much in the diffuser as compared with the parallel sections. For any industrial CFB including a diffuser, the results imply increased particle mixing in the diffuser, but the higher solids downflow, especially in the corners of a square section diffuser, may increase wall erosion.