A New Method for the Measurement of Solids Holdup in Gas-Liquid- Solid Three-phase Systems

Transcription

1 928 Ind. Eng. Chem. Res. 1996,34, A New Method for the Measurement of Solids Holdup in Gas-Liquid- Solid Three-phase Systems Introduction Fu Wenge, Yusuf Chisti,* and Murray Moo-Young Department of Chemical Engineering, University of Waterloo, Waterloo, Ontario, Canada N2L 3Gl A method for the measurement of gas and solids holdups in gas-liquid-solid multiphase devices is developed and tested. The method depends on measurements of hydrostatic pressures in the three-phase dispersion followed by interruption of gas flow, complete gas disengagement, and a second pressure measurement in the resulting two-phase solid-liquid slurry, over a short period of time (< 30 s). The proposed method is compared with results obtained with physical sampling of the multiphase flow in vertical up- and down-flow in a large airlift reactor (0.243 m diameter, m overall height, 2.44 riser-to-downcomer cross-sectional area ratio). Applicability of the technique to slurries of glass beads in tap water is demonstrated for various sizes and concentrations of beads over a range of gas flow rates ( x m bead diameter, 2500 k ~ msolids - ~ density, m0s-l superficial gas velocity). Gas-liquid-solid multiphase systems are commonly encountered in the chemical process industry, in bioprocessing, and in environmental pollution abatement devices. Slurry bubble columns (Deckwer, 1992), airlift reactors (Chisti and Moo-Young, 19871, fluidized beds (Tang and Fan, 19901, and stirred vessels (MacTaggart et al., 1993) containing suspensions of chemical catalysts, immobilized biocatalysts, and crystals of reactants or products are some examples of multiphase systems. These systems are routinely sampled through a small port on the side wall of the suspending vessel, or conveying pipeline, for the measurement of the concentration of the suspended material (Immich and Onken, 1992). Side wall sampling is known to give erroneous measurements of concentration and particle size distribution for all but the smallest particles having densities close to that of the suspending fluid. Examples of the latter type of systems, where side wall sampling truly reflects the solids contents of the bulk flow, are fermentation broths of bacteria such as Bacillus subtilis and yeasts such as Saccharomyces cereuisiae. For larger and denser particles, the sample may not satisfactorily display the character of the bulk flow. Side wall sampling errors are associated with the inertia of the solid particles. During sampling, the particle must change its direction of flow to move into the sample port. Typically, smaller particles, with lower inertia, are sampled preferentially, and the sample has a greater proportion of the liquid phase than does the bulk flow. Sampling efficiency, the ratio of the concentration of solids in the sample and that in the bulk flow, is affected by such factors as the sampling velocity, the density difference between the solid and the liquid phases, the diameter of the particles, the viscosity of the liquid, and the concentration of solids in the slurry (Nasr-El-Din et al., 1991). The design of the sampler, the diameter of the port and its angle of attachment to the wall, for example, are other factors which affect the efficiency of sampling (Barresi and Baldi, 1987; MacTaggart et al., 1993). Depending on the circumstances, the side wall sampling efficiency may exceed 0.9, or it may be as low as 0.3 or less (Nasr-El-Din et al., 1991). At sufficiently high sampling velocity ratio, that is, the ratio of sampling velocity (USM) and the velocity of the bulk flow * Corresponding author. Fax number: (519) ( UB), the sampling efficiency becomes independent of the sampling velocity (Nasr-El-Din et al., 1991). Under these conditions, the sampling efficiency can be correlated with the properties of the solid-liquid system as follows Equation 1 was determined for upward vertical flow of solid-liquid slurries (no gas) in pipes for USMIUB 1 0.4, but it is expected to apply also to downward flow (Nasr- El-Din et al., 1991). Correlations such as eq 1 provide a means of correcting the measurements, based on a properly withdrawn sample, for calculation of actual concentrations of the solids in the reactor. Other such equations are due to Rushton (19651, Rehakova and Novosad (1971a,b), Torrest and Savage (19751, and Sharma and Das (1980). A review has been presented by MacTaggart et al. (1993). For many practical situations, for example, in stirred tanks and bubble column slurry reactors operating batchwise, the bulk flow velocity for use in eq 1 is not particularly well-defined, making the application of the equation difficult. In addition, physical properties of the system such as the densities of the phases, the size of the particles, the concentration of solids, and the viscosity of the suspending liquid are fixed by the requirements of the process and are not amenable to manipulation to improve the efficiency of sampling. Furthermore, in most practical applications, sampling is a batch operation lasting for brief periods; hence, the sampling velocity increases from zero to some peak value before returning to zero. Attainment and continuous maintenance of a high sampling flow rate is not usually possible. As an additional drawback, eq 1 is not explicit in q&, the desired variable, and an iterative solution is necessary. Because of these problems with sampling of solid-liquid slurries, alternative methods, not relying on physical removal of a sample, are needed for determination of the concentration of suspended solids. This work develops such a technique for complex gasliquid-solid three-phase systems and experimentally illustrates the application of the method to vertical upand down-flows as encountered in pilot scale airlift reactors. Other invasive techniques for the determination of gas and solids holdups in two- and three-phase Q /95I $Q9.QQlQ American Chemical Society

2 Figure 1. The inverted U-tube manometer. systems, for example, the methods based on measurements of electrical conductivity, require complex setups that do not always give accurate measurements (Uribe- Salas et al., 1994; Hills, 1993). Theory The theoretical foundation of the new technique for the determination of solids holdup is detailed here. The proposed method depends on measurements of hydrostatic pressures in the multiphase vessel. The arrangement for manometric measurement of hydrostatic pressure in gas-liquid-solid multiphase systems in vertical up- or down-flow is shown schematically in Figure 1. Such flow situations are encountered in risers and downcomers of airlift reactors, bubble columns, and other three-phase contactors or conveyers. The hydrostatic pressure difference between locations 1 and 2 in Figure 1 is related to the density (@D) of the multiphase dispersion and the vertical distance (2) between points 1 and2. Thus, P, - P, = QDgZ (2) Because the pressures at points 1 and 2 are equal to those in the corresponding legs of the manometer, we have P, = + PM and P2 = g~gh2 + PM (3) is the density of the fluid in the manometer and I'M is the pressure of the enclosed gas space (Figure 1). Further, from Figure 1, z+h,=ah+h2 (4) where Ah is the manometer reading. Validity of eq 4 for systems with flowing fluids has been repeatedly demonstrated in connection with work on manometric measurement of gas holdup (Chisti et al., 1987). Combination of eqs 3 and 4 leads to P2 - P, - Ah) (5) Ind. Eng. Chem. Res., Vol. 34, No. 3, Equation 6 is generally applicable and has been commonly used to determine gas holdup in gas-liquid twophase systems (Nottenkamper et al., 1983; Hills, 19761, or in three-phase dispersions when the solid-liquid slurry can be treated as a pseudo-homogeneous single phase (Chisti, 1989, pp ). This work further develops eq 6 to a form which, in combination with a new experimental procedure, allows for calculation of the gas and solids holdup in gas-liquid-solid threephase systems. This development follows. The density (@D) of the gas-liquid-solid dispersion is related to the densities and fractional holdups of individual phases as Moreover, the sum of the volume fractions of the individual phases is unity; thus, (7) EL + ES + EG = 1 (8) Equations 7 and 8 can be combined to + (@S - (@L G (9) Let us imagine a scenario in which all gas instantaneously escapes from the three-phase dispersion to leave behind a slurry of only the liquid and the suspended solids. For the low density small diameter solids which are of interest, the solids are assumed to not settle, at least for a brief period of the order of a few seconds. (This assumption is borne out by the experimental data presented later in this work.) Thus, the resulting twophase system is identical to the three-phase dispersion in terms of the absolute quantity of solids held in suspension. The volume fraction (4s) of solids in the resulting two-phase slurry is Dividing the top and the bottom of the right-hand side of eq 10 by VT gives TI (11) where VT is the sum of the volumes of the gas, liquid, and solid phases just prior to the gas escaping from the system. Equations 10 and 11 apply to two-phase systems only. Note that, by definition, and therefore, 'S = 'flt EL = VLWT 12) 13) Comparison of eqs 2 and 5 followed by rearrangement gives (Chisti, 1989, pp ): But, from eq 8, 6~ + 6s = 1 - Q; thefefore, (6) Substitution of eq 15 into eq 9 yields

3 930 Ind. Eng. Chem. Res., Vol. 34, No. 3, + (@S - - EG)& - (@L (16) When only the liquid phase is present in the manometer, = el, comparison of eqs 6 and 16 followed by rearrangement leads to When the gas holdup is zero, eq 17 rearranges - Ah 4% = - (18) (es- QL) * As shown here, eqs 18 and 19 are the basis of the manometric determination of holdups of gas and solid phases in multiphase reactors, such as the airlift reactor, using the following approach: 1. Initially, with no gas flowing into the system, the solids settled to the bottom of the reactor, and the manometer filled with the same liquid as the reactor, the manometer reads zero. 2. Flow of gas is initiated at some preset value. The system is allowed to establish a hydrodynamic steady state (1-2 min), and the manometer reading, Aha, is noted. 3. The gas flow to the reactor is instantaneously interrupted by means of a manual ball valve or a solenoid valve. The manometer reading changes rapidly, over a period of about 20 s, as the gas escapes from the three-phase system until a stable reading, Ahb, is registered in the two-phase system. The reading remains stable for a relatively long period (e.g., 100 seconds), sufficiently long for the measurement, before slowly reverting to zero as the solids settle. 4. The two-phase volume fraction of solids (4s) is calculated from the measured manometer reading, h hb, and the known es, QL, and z, using eq 19. m- SI BAFFLE d cy 3 5. The calculated 4s (step 41, the measured manometer reading, Aha, and the and z are now used to obtain the gas holdup (EG) from eq The three-phase solids holdup (6s) is obtained from the calculated 4s (step 4) and EG (step 5) using eq 15. The following sections demonstrate the foregoing procedure and compare it with data on actual sampling of the multiphase system in up- and down-flow in a large airlift reactor. Experimental Section Measurements were done in a split cylinder airlift reactor depicted in Figure 2. The reactor consisted of a cylindrical plexiglass column, m in diameter, m in overall height, split into a riser and a downcomer by a tightly fitting stainless steel baffle, m wide. This arrangement produced a riser-todowncomer cross-sectional area ratio of The equivalent hydraulic diameters of the riser and the downcomer were 0.19 and m, respectively. The height of the baffle was 2.7 m, and it was located m above the bottom of the reactor except in one set of experiments when a lower baffle location of 0.1 m was used. The static gas-free solid-liquid slurry height was m, giving a clearance of m (or m with the lower location of baffle) between the surface of the liquid and the top of the baffle. The riser was sparged with air at mas-l superficial velocity based on the cross-sectional area of the riser. A perforated pipe, ladder type, sparger, as shown in Figure 2 and previously described by Chisti (1989, pp 94-96), was used for aeration. The sparger had 38 holes, 1.5 x lov3 m diameter, giving a free area of 0.2% of the cross-sectional area of the riser. A circular plastic insert placed at the bottom of the reactor (Figure 2) eliminated stagnant zones and ensured smooth movement of the fluid from the downcomer into the riser. SPARGER DETAILS I A # AIR 0 c1) FILTER/PRESSURE REGULATOR AND PRESSUREGAUGES 7 1 T R S SPARGER DRAIN REACTOR DRAIN Figure 2. The split-cylinder airlir reactor with geometric details of the gas sparger and the bottom zone of the reactor. Dimensions in meters.

4 Ind. Eng. Chem. Res., Vol. 34, No. 3, RISER + DOWNCOMER h Figure 3. The syringe samplers and sampling arrangements in the riser and the downcomer of the airlift reactor. Table 1. Particle Size Distribution sieve size Tap water at 25 "C was the liquid phase in all experiments. Three grades of glass beads, BT-9, BT- 11, and BT-13 (Flex-0-Lite, St. Thomas, Ontario), were the solid phase. The beads had a density of 2500 kgm-3. Mean particle diameters were 150, 100, and 70 pm, respectively, for the three grades. The size distributions were narrow, and the shape of the particles was essentially spherical (80-95% sphericity). Details are given in Table 1 which is based on data supplied by the manufacturer. Tests were done with 5.05%, 5.14%, and 7.7% (v/v) initial solids in the solid-liquid slurry in the reactor. The volume of the slurry was about 0.14 m3. Batch operation was employed with respect to the solids and the liquid. The actual amount of solids in suspension depended on the flow rate of the gas. Manometric measurements were done in the riser, where the upward direction of multiphase flow was against the direction of gravitational settling of solids, as well as in the downcomer, where the slurry flowed downward. The vertical distances between the manometric taps in the riser and the downcomer were equal at 1.58 m; in both cases, the lower taps were located 0.92 m above the bottom of the reactor. Location with respect to the baffle was opposite the flat faces of the baffle in the riser and the downcomer. At any preset gas flow rate, after a hydrodynamic steady state had been attained, the manometer readings were noted and, as explained later in this section, samples of the slurry were withdrawn for direct determination of concentrations for comparison with the manometric data. The flow of the gas to the reactor was now terminated instantaneously by a manually operated quarter-turn ball valve. As soon as the gas had escaped from the reactor (determined visually), the new stable manometer readings were noted. These data were used to calculate the gas holdups and volume fractions of solids in the riser and the downcomer as explained in a previous section. The overall gas holdup in the reactor was determined from the increase in level of the threephase dispersion upon introduction of the gas into the I" TIME, t (s) Figure 4. The riser and the downcomer manometric readings as functions of time. The data are for glass beads BT-13 at 5.05% (vh) total concentration in water. system; thus, where hd is the height of the three-phase dispersion and hl is the level of gas-free liquid-solid system in the reactor. The solid-liquid slurry was sampled approximately midway between the manometric taps in the riser and the downcomer using the samplers shown in Figure 3. Samples were taken with the needle inserted, perpendicular to the baffle, up to the half-way point between the baffle and the wall of the reactor. At 2 x lop3 m, the internal diameter of the sampler needle was more than 10-fold that of the largest particle being sampled. Suction applied to the graduated sample tube by means of the syringe (Figure 3) caused the slurry to flow into the tube to the desired level. The total volume of the settled solids was read directly on the graduated tube. This data was converted to volume fraction of solids using the knowledge that for uniformly shaped solids of a given size, the ratio of the packed, or settled, volume (Vp) and the true volume (VS) is a constant; that is, The experimentally determined k-value for the BT-9, BT-11, and BT-13 glass beads was with a standard deviation (population) of Thus, for a solidliquid slurry sample of total volume VSL, producing a settled solids volume Vp, the volume fraction of solids (4s) could be calculated with the equation 9s = kvpsl (21) This approach, using constant k-factors and measured settled volumes of solids for calculation of the volume fraction, was successfully employed in earlier studies (Yuan and Gu, 1990) with three-phase airlift reactors. Note that the experimentally obtained k-values were close to the expected value of 0.6 for a bed of perfect spheres. Results and Discussion The manometer readings, as functions of time before and after the instant of interruption of the gas supply (time = 0) to the riser of the airlift reactor, are shown in Figure 4. The figure is for BT-13 glass beads suspended in the reactor at a total volume fraction, +s, of 5.05% (v/v). Data for the riser (up-flow) and the downcomer (down-flow) are shown (Figure 4). The behavior depicted in Figure 4 is typical: Stable manometer readings are observed for t < 0 because, with stable flow of gas in the riser, a hydrodynamic steady

5 932 Ind. Eng. Chem. Res., Vol. 34, No. 3, 1995 state exists in the reactor. For the same vertical separation between the manometer taps in the riser and the downcomer, the two manometer readings are different (phase I, Figure 4). The higher reading in the riser reflects a higher gas holdup (eq 17) in this zone in comparison with that in the downcomer. This difference in gas holdup between the riser and the downcomer is well-known to exist in airlift reactors (Chisti, 1989, pp 33, 70-72; Chisti and Moo-Young, 1987) where it provides the driving force for circulation of the liquid or slurry. At t = 0, the gas supply to the reactor was instantly cut off, and the manometer readings changed abruptly as the gas escaped from the three-phase dispersion (phase 11, Figure 4). The readings passed through zero and attained new steady states (phase 111, Figure 4). The time for complete disengagement of the gas was approximately 20 s (Figure 41, which corresponded to a very reasonable mean bubble rise velocity of 0.14 ms-' between the bottom of the reactor and the upper pressure tap of the manometer. After disengagement of the gas, the manometer readings were stable for a sufficiently long period, approximately 100 s in Figure 4, for accurate measurements. The new stable readings were indicative of the solids holdup (4s) in the gas-free system (eq 18). As the solids gradually settled, over a period of minutes, the manometer readings approached zero. The durations of phases 11,111, and IV depended on the concentration of solids and the diameter of the particles; however, in all cases examined in this work, phase I1 was sufficiently short and phase I11 sufficiently long for accurate measurements to be made. In other applications, the lengths of phases 11, 111, and IV in Figure 4 are expected to depend on the density of solids, the viscosity and density of the suspending liquid, and the particle size and concentration; but these dependencies do not affect the manometric measurements so long as phase I1 is sufficiently short, that is, gas disengages rapidly, and phase I11 is of adequate duration. Use of fast-response pressure transducers, instead of manometers, can improve the accuracy and the reproducibility of the proposed method while further reducing the requirement on the stable length of phase 111. The worst-case potential for measurement of lower than actual solids concentration because of sedimentation of solids out of the measurement zone between the taps of the manometer can be estimated quantitatively. Thus, for the largest particles (dp = 150 x m) used in this work the sedimentation velocity was estimated with the well-established Richardson and Zaki (1954) equation, where the recommended a-value for supermicron particles is 4.65 (Barnes and Holbrook, 1993). For a 4svalue of 0.05, the terminal sedimentation velocity was calculated to be ms-l. The mean bubble rise velocity was experimentally estimated to be 0.14 ms-'. The uppermost tap of the manometer was located m above the gas sparger; hence, the time taken by the gas to clear the manometer measurement zone was 16.8 s. During this period, solid particles at or below a height of 0.24 m above the lower tap of the manometer could settle out, leading to a measured solids volume fraction that is up to 15% lower than the actual value. In practice, over a short time scale, not only is sedimenta EDUD OM.IX), n M I E :I:, :::: v 8 M-Is 5.fO X* I QS (MANOMETER) (-) Figure 5. Comparison of the solids holdups (4s) measured by the sampler with the corresponding holdups measured by the manometric technique. The data shown are for three-phase up-flow in the riser es (MANOMETER) (-) Figure 6. Comparison of the solids holdups (4s): Data from the syringe sampler versus that from the manometer for three-phase down-flow in the downcomer. tion small but the few particles settling out of the measurement zone of the manometer are replaced by an equivalent amount settling into the measurement zone from the section of the riser that is above the upper tap of the manometer. The stable manometer reading in zone I11 of Figure 4 supports this point. As a result, possible errors due to sedimentation are negligible. Figures 5 and 6 compare the manometrically measured volume fractions (&) of solids with the values determined by sampling in the riser and the downcomer, respectively. The diagonals in these figures represent exact agreement of the two methods of measurement. The figures confirm that, for up-flow as well as downflow, there is a direct correlation between the two measurement techniques; however, the holdups based on sampling of the multiphase dispersion were consistently low compared with the manometrically measured data. This was expected because the efficiency of sampling is always less than unity. When the data shown in Figure 5 were corrected for sampling efficiency using eq 1, the two measurement methods agreed to within &20% of each other as shown in Figure 7. The correction factors ranged over The true volume fraction of solids in the bulk flow, required for the calculation (eq 11, was assumed to be that obtained with the manometer. The velocity of the bulk flow in the riser was measured with the acid tracer technique described elsewhere (Chisti, 1989, p 116). The criterion that USMIUB L 0.4 was assumed to hold, even though the sampling velocity was neither measured nor steady. Equation 1, developed for side wall sampling, was assumed to apply also to the needle samplers as used in this work. These factors, combined with inherent

6 Ind. Eng. Chem. Res., Vol. 34, No. 3, Y t H 0 0.0: (MANOMETER) (-) Figure 7. Solids holdup (9s) in the riser: The holdup data shown in Figure 5, calculated from the withdrawn samples, were corrected for sampling efficiency (eq 1) and plotted against the manometrically measured solids holdup. Dashed lines represent f20% of exact agreement RISER GAS VELOCITY (mas-') Figure 9. Manometrically measured gas holdups in the riser and the downcomer and the total gas holdup determined by volume expansion are plotted as functions of superficial gas velocity in the riser. The data are for BT-13 glass beads at a total concentration of 5.05% (v/v). v 0.14 h p 0.12 W (L SOCK) CON. x x n-o + n-ll a h I W e" h I W e" 0 RISER 0 MI*NCCUER I I I I I RISER GAS VELOCITY (m.s-') 0.02c : I 0 RISER 0 DOYNCOYCR RISER GAS VELOCITY (m.s-') Figure 8. Manometrically measured solids holdup versus the superficial air velocity in the riser and downcomer. The data for BT-9 and BT-13 solids at 5.05% (v/v) total concentration are shown. errors associated with physical sampling of multiphase flow, contributed to the scatter in Figure 7. The manometric measurements were reproducible to within f10% of mean values. The direction of the multiphase flow, whether up or down, did not seem to affect the agreement between the two methods (Figures 5 and 6); nor could any trend be discerned between the level of agreement and the diameter or the concentration of the solid particles. The manometrically measured volume fractions of solids are plotted in Figure 8 as functions of the superficial gas velocity in the riser. As shown for BT-9 and BT-13 glass beads, although the initial amount of solids were the same at 5.05% (v/v), the amount of solids in suspension depended on the flow rate of the gas. In general, below a certain low gas flow rate, no solids were suspended (Figure 8). As the gas velocity increased, the corresponding liquid flow rate was sufficient to suspend solids having a given diameter. The steps in the holdup curves in Figure 8 were due to larger diameter solids (within a batch of a given mean particle size) coming into suspension. For all solids tested, the volume fractions in suspension in the riser and downcomer were nearly identical, unlike predictions made by Livingston and Zhang (1993). Once the solids holdup (4s) had been obtained using eq 18, it was used in equation (17) to calculate the gas holdups in the riser (E&) and the downcomer (EGd). I 5, GAS HOLDUP (CALCULATED) (-) Figure 10. The overall gas holdup calculated using eq 23 is plotted against the overall holdup measured by the volume expansion method. These holdups are shown in Figure 9 plotted against the superficial gas velocity in the riser. As expected, for any gas flow rate, the gas holdup in the downcomer was lower than that in the riser. The holdups in both zones and the overall holdup increased with gas velocity. The overall or total gas holdup shown in Figure 9 was determined, independently of manometers, by the volume expansion technique. For the split-cylinder type of internal-loop airlift reactors, Chisti (1989, p 284) has demonstrated that the total gas holdup and the holdups in the riser and the downcomer are related by the analytical equation (23) where A, and Ad are the cross-sectional areas of the riser and the downcomer, respectively. Equation 23 can be used to calculate a total gas holdup using the manometrically measured holdups in the riser (E&) and the downcomer (EGd). Comparison of this calculated total holdup (eq 23) with that actually measured by the volume expansion technique is shown in Figure 10 which is based on the data presented in Figure 9. The excellent agreement of the calculated and the measured data in Figure 10 is further strong evidence in support of the accuracy of the proposed method of measuring solids holdups because, for three-phase systems, eq 17 can yield correct gas holdup only if the correct values of solids holdup (4s) from eq 18 are used in it. For the solid-liquid system and the manometer arrangement used, d&jd(hh) was 0.422; thus, a reasonably accurately measurable 1 x 10-3 m change in the manometer reading corresponded to a 0.04% (v/v) change in C#JS, which is an indication of the sensitivity of the measurements.

7 934 Ind. Eng. Chem. Res., Vol. 34, No. 3, 1995 Unlike the side wall sampling method, which is influenced by the local heterogeneities in the concentration of solids arising from movement of particles away from walls and concentration profiling perpendicular to the direction of flow, the manometric technique developed in this work provides the mean bulk solids concentration in a large zone between the two ports of the manometer. The proposed measurement technique applies to laminar as well as turbulent flows because it does not require a homogeneous distribution of solids across the cross-section of the reactor. If axial profiles of solids concentration are expected, these can be determined by using multiple manometers with closely spaced pressure taps located vertically along the column. The manometric method is unaffected by the density of the solids, the size of the particles, the viscosity of the liquid, and the concentration of solids so long as suecient spacing of manometer taps can be maintained to ensure sensitivity and the time for gas disengagement can be kept short in comparison with solids settling times. Conclusions A new method for measurement of gas and solids holdups in gas-liquid-solid multiphase systems was proposed for use in airlift reactors and other similar devices. The method relied upon measurements of hydrostatic pressures in the gassed and gas-free states of the system over periods so short that no significant sedimentation of the solid phase occurred. For a range of sizes and concentrations of solids, in either vertical up- or down-flow, the method gave accurate measurements of gas and solids holdups. In contrast, solids holdups determined by withdrawal of samples of the multiphase dispersion were consistently lower than actual values in the bulk fluid. The manometrically determined holdups were checked with independent measurements, confirming the reliability of the proposed technique. Manometric measurement of the solids holdup was simple and accurate and did away with the uncertainties of sampling. The method is capable of being automated with differential pressure cells providing accurate digital pressure readouts. Nomenclature A, = cross-sectional area of the riser (m2) Ad = cross-sectional area of the downcomer (m2) dp = mean diameter of particles (m) ds = internal diameter of sample port (m) g = gravitational acceleration (m.~-~) hl = height of the liquid leg 1 in Figure 1 (m) hz = height of the liquid leg 2 in Figure 1 (m) Ah = manometer reading (m) Aha = manometer reading in gas-liquid-solid system (m) Ahb = manometer reading in gas-free liquid-solid slurry (m) h~ = height of gas-liquid-solid dispersion in reactor (m) h~ = height of gas-free liquid-solid slurry in reactor (m) k = constant defined by eq 20 PM = pressure of the air space in manometer (Pa) PI = hydrostatic pressure at location 1 (Pa) Pz = hydrostatic pressure at location 2 (Pa) t = time (s) UB = velocity of bulk flow (m-s-l) US = terminal settling velocity of particles (m-s-l) USM = sampling velocity (m-s-1) VL = volume of liquid (m3) VP = apparent volume of packed bed of solids (m3) VS = volume of solids (m3) VSL = volume of solid-liquid slurry sample (m3) VT = total volume of gas-liquid-solid dispersion (m3) z = vertical distance between measuring points 1 and 2 (m) Greek Symbols EG = volume fraction of gas in gas-liquid-solid dispersion 6Gd = volume fraction of gas in the downcomer EG~ = volume fraction of gas in the riser EL = volume fraction of liquid in gas-liquid-solid dispersion ES = volume fraction of solids in gas-liquid-solid dispersion p~ = viscosity of the liquid = density of gas-liquid-solid dispersion = density of gas = density of liquid = density of the manometric fluid (kgm-3) es = density of solids (kgm-3) 4s = volume fraction of solids in liquid-solid two-phase slurry &M = volume fraction of solids in sample Literature Cited Barnes, H. 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