Hydrodynamic characteristics of 30%TBP/kerosene-HNO₃ solution system in an annular centrifugal contactor

Hydrodynamic characteristics of 30%TBP/kerosene-HNO 3 solution system in an annular centrifugal contactor 1 first-author 1 1 2 corresp Corresponding author. E-mail address: dwh203@mail.tsinghua.edu.cn Corresponding author. E-mail address: dwh203@mail.tsinghua.edu.cn dwh203@mail.tsinghua.edu.cn 1 2 Institute of Nuclear and New Energy Technology, Collaborative Innovation Center of Advanced Nuclear Energy Technology, Tsinghua University, Beijing 100084, China Institute of Nuclear and New Energy Technology, Collaborative Innovation Center of Advanced Nuclear Energy Technology, Tsinghua University, Beijing 100084, China Beijing Key Lab of Radioactive Waste Treatment, Tsinghua University, Beijing 100084, China Beijing Key Lab of Radioactive Waste Treatment, Tsinghua University, Beijing 100084, China Annular centrifugal contactors (ACCs) have many advantages and are recognized as key solvent-extraction equipment for the future reprocessing of spent nuclear fuel (RSNF). To successfully design and operate ACCs for RSNF, it is necessary to understand the hydrodynamic characteristics of the extraction systems in ACCs. The phase ratio ( R = V aq / V org , A/O) and liquid hold-up volume ( V ) of the ACC are important hydrodynamic characteristics. In this study, a liquid-fast-separation method was used to systematically investigate the effects of the operational and structural parameters on the V and R (A/O) of a φ20 ACC by using a 30%TBP/kerosene-HNO 3 solution system. The results showed that the operational and structural parameters had different effects on the V and R (A/O) of the mixing and separating zones of the ACC, respectively. For the most frequently used structural parameters of the φ20 ACC, when the rotor speed was 3500 r/min, the total flow rate was 2.0 L/h, and the flow ratio (A/O) was 1, the liquid hold-up volumes in the mixing zone and rotor were 8.03 and 14.0 mL, respectively, and the phase ratios (A/O) of the mixing zone and separating zone were 0.96 and 1.43, respectively. Annular centrifugal contactor Liquid-fast-separation method Phase ratio (A/O) Liquid hold-up volume Structural parameter Operational parameter 1 Introduction 1 Reprocessing of spent nuclear fuel (RSNF) can recover nuclear resources and reduce nuclear waste and is thus a crucial part of an advanced nuclear fuel cycle for ensuring the sustainable development of nuclear energy. Currently, the plutonium uranium recovery by extraction (PUREX) process employing tri-n-butyl phosphate (TBP) as the extractant and n -dodecane or kerosene as the diluent is the only commercial reprocessing process in the world [ 1 1 ]. An annular centrifugal contactor (ACC) separates the dispersion of two phases by using centrifugal force [ 2 2 ]. As shown in Fig. 1 Fig. 1 , two immiscible liquids in the annular zone are initially mixed intensively by the spinning rotor to form the dispersion. The dispersion then flows into the separating zone of the rotor through the rotor inlet and is separated rapidly owing to the centrifugal force induced by the spinning rotor. After separation, the two phases finally flow through their respective weirs and collectors into their respective collection tanks or adjacent stages. ACCs offer many advantages, including a short residence time and low solvent degradation by irradiation because of their small liquid hold-up volume ( V ), high compactness, high nuclear criticality safety, high mass-transfer efficiency, excellent phase separation, and easy operation [ 3 3 , 4 4 ]. ACCs have been utilized successfully in various demonstration tests of many solvent-extraction processes for RSNF and the partitioning of high-level liquid waste [ 5 5 – 14 14 5–14 ]. Moreover, ACCs are recognized as key solvent-extraction equipment for future nuclear fuel-cycle processes. Hence, many countries engaging in RSNF are investigating ACCs [ 4 4 , 5 5 , 15 15 – 17 17 15–17 ]. The flow in the ACC is three-dimensional, turbulent, transient, and multiphase [ 18 18 , 19 19 ]. Hence, it is difficult to determine the effects of the physical properties, operational parameters, and structural parameters on the hydrodynamic characteristics. The current development of the ACC is recognized as "an art" [ 20 20 ]. To successfully design and operate ACCs for RSNF, detailed hydrodynamic characteristic information, including the phase ratio ( R = V aq / V org , A/O) and liquid hold-up volume ( V ), is required. The R (A/O) and V depend on the operational parameters, structural parameters, and physical properties of the two phases. However, accurately measuring the V of the ACC and obtaining R (A/O) are difficult because of the unique structure and flow characteristics of the ACC. Zhao used a liquid-discharging method to measure the V of a φ20 ACC by using a kerosene-water system and then to calculate the interface radius ( r i ) of the separating zone and the hold-up volume of the mixing zone [ 21 21 ]. The measurement procedures of this method are shown in Fig. 2 Fig. 2 . Schuur et al. and Ayyappa et al. measured the V of a φ50 ACC using the same method [ 22 22 , 23 23 ]. However, the liquid-discharging method has the following disadvantages. (1) It requires time to discharge the liquids in the mixing zone completely; hence, some liquids in the mixing zone still flow into the rotor. (2) Some liquids in the rotor are thrown into the collectors during liquid discharging. (3) Some liquids cannot be discharged, because they adhere to the inner wall of the housing. Duan et al. developed a liquid-fast-separation method based on an advanced self-made φ20 ACC to measure the liquid hold-up volume [ 24 24 ]. The measurement procedures of this method are shown in Fig. 3 Fig. 3 . In this study, the dimensionless dispersion number ( N Di ) of the 30%TBP/kerosene-HNO 3 solution system was initially determined to evaluate the phase-separation performance of this extraction system. Then, the effects of the operational and structural parameters on the V and R (A/O) of a φ20 ACC were systematically investigated using the liquid-fast-separation method and the 30%TBP/kerosene-HNO 3 solution system. 2 Experimental 1 2.1 Chemicals 2 TBP ( > 98% pure), HNO 3 (analytical purity), and NaOH (analytical purity) were obtained from Beijing Chemical Plant, China. Saturated hydrogenated kerosene was obtained from Jinzhou Refinery Factory, China. The surface tension, density, and viscosity of the TBP were 27.79 mN/m, 973 kg/m 3 , and 3.32 mPa∙s, respectively. The TBP was diluted using kerosene to 30% TBP/kerosene (v/v) without further purification. 2.2 φ20 ACC 2 The φ20 ACC was a self-made solvent-extraction instrument with a rotor inner diameter of 20 mm. It contained two modules—rotor and housing—as shown in Fig. 3 Fig. 3 [ 25 25 ]. The rotor module could be easily lifted up and down by a manipulator or by hand because no screw or nut was used to set the two modules. Therefore, the liquid-fast-separation method could be easily performed using this ACC. 2.3 Determination of dispersion number 2 Leonard proposed the concept of a dimensionless dispersion number ( N Di ) for evaluating the phase-separation performance of an extraction system. Additionally, he developed a standard test for determining N Di [ 26 26 ]. After N Di is determined, the phase-separation performance of the extraction system can be assessed by referring to Table 1 Table 1 . In this study, the N Di of the 30%TBP/kerosene-HNO 3 solution system was determined according to the standard test. 1 1 N Di 1 1 Phase-separation performance 1 1 ≤2 × 10 -4 1 1 Unacceptable 1 1 2 × 10 -4 −4 × 10 -4 1 1 Poor 1 1 4 × 10 -4 −8 × 10 -4 1 1 Fair 1 1 8 × 10 -4 −16 × 10 -4 1 1 Good 1 1 ≥16 × 10 -4 1 1 Excellent The test for determining N Di was conducted at room temperature (23 ± 2 °C) using the 30%TBP/kerosene-HNO 3 solution system. First, two immiscible phases of 50 mL each were placed into a 100-mL graduated glass cylinder with a ground-glass stopper. Then, the total height (Δ z ) of the fluid was measured, and the position of the interface between the two phases was marked. Next, after the graduated cylinder was sealed with the glass stopper, it was shaken vigorously by hand for 20 s, allowed to settle for 10 s, and shaken vigorously again for 20 s. Subsequently, the cylinder was immediately placed on a benchtop, and a stopwatch was used to record the time taken for the dispersion band to break. Finally, after the last droplet disappeared and a clear phase interface appeared, the timer was stopped, and the time was recorded. The experiment was repeated thrice, and the average result was calculated to obtain the phase-separation time ( t B ). N Di is expressed as follows: <math display="block" id="M1"><mrow><msub><mi>N</mi><mrow><mtext>Di</mtext></mrow></msub><mo>=</mo><mfrac><mn>1</mn><mrow><msub><mi>t</mi><mi>B</mi></msub></mrow></mfrac><msqrt><mrow><mfrac><mrow><mi>Δ</mi><mi>z</mi></mrow><mi>g</mi></mfrac></mrow></msqrt><mo>,</mo></mrow></math> where Δ z is the total height of the fluid (m), t B is the time taken for the dispersion band to break (s), and g is the gravitational acceleration (9.8 m/s 2 ) [ 26 26 ]. 2.4 Determination of liquid hold-up volume and phase ratio 2 Fig. 4 Fig. 4 shows the experimental system. A regular direct-current (DC) power supply was used to control the rotor speed. Two peristaltic pumps were used to feed the two phases into the φ20 ACC. The rotor included the separating and weir zones, and the mixing zone was composed of the zone under the rotor and the annular zone between the outer wall of the rotor and the inner wall of the housing. The liquid-fast-separation method was used to measure the liquid hold-up volumes of the mixing and separating zones. First, the pumps were shut down when the operation of the ACC reached a steady state. Then, the rotor module was manually lifted up and simultaneously moved above a beaker within 2 s. Next, the rotor operation was stopped, and the liquids of the rotor flowed into the beaker and were then transferred into a measuring cylinder. Thus, the liquid hold-up volume of the rotor ( V r ) was determined. Finally, the liquids in the mixing zone were transferred into a measuring cylinder through a pipette. Hence, the liquid hold-up volume of the mixing zone ( V m ) was determined. The sum of the two liquid hold-up volumes was the total liquid hold-up volume ( V t ) of the ACC. The volume of each phase was determined after the separation of the two phases in each measuring cylinder. Thus, the phase ratios (A/O) in the separating and mixing zones were obtained. The liquid hold-up volume of the separating zone ( V s ) was obtained as follows: <math display="block" id="M2"><mrow><msub><mi>V</mi><mtext>s</mtext></msub><mo>=</mo><msub><mi>V</mi><mtext>r</mtext></msub><mo>–</mo><msub><mi>V</mi><mtext>w</mtext></msub><msub><mo>,</mo><mrow/></msub></mrow></math> where V s is the liquid hold-up volume of the separating zone (mL), V r is the liquid hold-up volume of the rotor (mL), and V w is the liquid hold-up volume of the weir zone (mL). In this study, the organic phase was 30%TBP/kerosene, and the heavy phase was an HNO 3 solution. The effects of the operational and structural parameters shown in Table 2 Table 2 on V and R (A/O) were investigated. When to investigate the effect of one parameter on the V and R (A/O), the values of the other parameters are bold in Table 2 Table 2 . In each experiment, < 0.5% of the other phase entrainment in either out effluent was required. 1 1 Parameter types 1 1 Parameters 5 1 Values 1 1 Operational parameters 1 1 Rotor speed ( ω , r/min) 1 1 3000 1 1 3500 1 1 4000 1 1 4500 1 1 5000 1 1 1 1 Total flow rate ( Q , L/h) 1 1 0.5 1 1 1.0 1 1 2.0 1 1 4.0 1 1 6.0 1 1 1 1 Flow ratio ( F , A/O) 1 1 0.25 1 1 0.5 1 1 1 1 1 2 1 1 4 1 1 Structural parameters of housing 1 1 Width of annular ( W , mm) 1 1 2.5 1 1 3.5 1 1 4.0 1 1 4.5 1 1 5.5 1 1 1 1 Number of radial vanes ( N r ) 1 1 0 1 1 2 1 1 4 1 1 6 1 1 8 1 1 1 1 Height of clearance ( H c , mm) 1 1 2.0 1 1 3.0 1 1 3.5 1 1 4.0 1 1 5.0 1 1 Structural parameters of rotor 1 1 Length of separating zone ( L , mm) 1 1 30.0 1 1 40.0 1 1 45.0 1 1 50.0 1 1 60.0 1 1 1 1 Diameter of heavy-phase weir ( D A *, mm) 1 1 10.0 1 1 10.5 1 1 11.0 1 1 11.5 1 1 12.0 1 1 1 1 Diameter of light-phase weir ( D O *, mm) 1 1 6 1 1 7 1 1 8 1 1 9 1 1 10 1 1 1 1 Height of underflow ( H u , mm) 1 1 1 1 1 3 1 1 5 1 1 7 1 1 9 1 1 1 1 Diameter of rotor inlet ( D m , mm) 1 1 3 1 1 4 1 1 5 1 1 6 1 1 7 1 1 1 1 Number of axial vanes ( N a ) 1 1 0 1 1 2 1 1 4 1 1   1 1   3 Results and Discussion 1 3.1 Dispersion number N Di 2 Fig. 5 Fig. 5 shows the effects of the HNO 3 concentrations on the N Di of the 30%TBP/kerosene-HNO 3 solution system. As shown, the N Di increased with the HNO 3 concentrations and was > 14 × 10 -4 when the HNO 3 concentration was > 0 mol/L. According to Table 1 Table 1 , good phase-separation performance of an extraction system in the ACC is expected when N Di > 8 × 10 -4 . Hence, the 30%TBP/kerosene-HNO 3 solution system was expected to exhibit good phase-separation performance in the ACC. 3.2 Liquid hold-up volume 2 3.2.1 Effects of operational parameters 3 Fig. 6 Fig. 6 shows the effects of the operational parameters, such as the flow ratio ( F , A/O), total flow rate of the two phases ( Q ), and rotor speed ( ω ), on the liquid hold-up volume ( V ). The liquid hold-up volume of the rotor ( V r , approximately 14.0 mL) hardly changed with respect to F (A/O), Q , and ω . The liquid hold-up volume of the mixing zone ( V m ) initially increased with the increase in F (A/O) and Q and then remained almost constant; however, with the increase in ω , it initially decreased and then remained almost constant. Thus, the effects of the operational parameters on the total liquid hold-up volume ( V t ) and V m were identical. When the ACC is operated, the relative pressure at the rotor inlet becomes slightly negative [ 19 19 , 27 27 ]. Moreover, a higher ω yields a greater absolute value of the negative pressure. To maintain the balance of the pressure, the annular liquid height ( ALH ) is decreased with the increase in ω . Hence, V m is also decreased with the increase in ω . Wardle investigated the effects of F (A/O) and Q on the ALH and reported that the ALH increased with an increase in Q and a decrease in F (A/O) [ 18 18 ]. Our results for the effect of Q agree with those of Wardle. However, our results for the effect of F (A/O) disagree with those of Wardle. All our results for the effects of the operational parameters on V agree with those of Duan et al. and Zhao [ 21 21 , 24 24 ]. 3.2.2 Effects of structural parameters of housing 3 Fig. 7 Fig. 7 shows the effects of the structural parameters of the housing, including the height of the clearance ( H c ), width of the annular ( W ), and number of radial vanes ( N r ), on V . The structural parameters of the housing had almost no effect on V r , because they hardly influenced the geometric volume of the rotor. V m increased with H c and W but decreased with the increase in N r . Thus, the effects of the structural parameters of the housing on V t and V m were the same. When H c and W increased, the geometric volume of the mixing zone obviously increased; hence, V m increased. Wardle investigated the effects of N r on the ALH and reported that with the increase in N r , the ALH decreased, resulting in the decrease in V m [ 18 18 ]. Therefore, our results for the effect of N r on V m agree with those of Wardle. We also performed the experiment without radial vanes, i.e., with N r = 0. The results showed that the ACC could not operate normally without radial vanes, because the liquids in the mixing zone could not be absorbed into the rotor. 3.2.3 Effects of structural parameters of rotor 3 Fig. 8 Fig. 8 shows the effects of the structural parameters of the rotor, including the diameter of the heavy-phase weir ( D A *), diameter of the light-phase weir ( D O *), length of the separating zone ( L ), height of the underflow ( H u ), and diameter of the rotor inlet ( D i ), on V . V r hardly changed (approximately 14.0 mL) with respect to D A * and H u but increased with L and decreased with the increase in D O *. The structural parameters of the rotor had almost no effect on V m , because they hardly influenced the geometric volume and flow of the mixing zone. Accordingly, the effects of the structural parameters of the rotor on V t and V r were the same. In the φ20 ACC, when D A * was 12 mm, an organic-phase entrainment occurred in the aqueous-phase outlet under the experimental conditions. Variations in D A *, H u , and D i hardly affected the geometric volume of the rotor, thus hardly influencing V r . The geometric volume of the separating zone increased with the increase in L and the decrease in D O *. Table 3 Table 3 shows the effects of the number of axial vanes ( N a ) on V for the ACC. N a hardly affected V m , because it hardly influenced the geometric volume and flow of the mixing zone. V r increased slightly with the increase in N a . Accordingly, the V t of the φ20 ACC increased slightly with the increase in N a The axial vanes were used to accelerate the dispersion in the separating zone to ω . During the experiment, when the rotor module was lifted, some liquids in the separating zone flowed into the mixing zone. Reducing the rotation speed of the liquids in the separating zone caused the liquids to flow out easily. Therefore, the number of axial vanes had almost no effect on V m and V r during the operation of the φ20 ACC. 1 1 N a 1 1 V m (mL) 1 1 V r (mL) 1 1 V t (mL) 1 1 R m (A/O) 1 1 R s (A/O) 1 1 0 1 1 8.25 1 1 12.75 1 1 21.0 1 1 0.92 1 1 2.19 1 1 2 1 1 7.97 1 1 13.4 1 1 21.37 1 1 0.99 1 1 1.71 1 1 4 1 1 8.03 1 1 14.0 1 1 22.03 1 1 0.96 1 1 1.43 3.3 Phase ratio (A/O) 2 3.3.1 Effects of operational parameters 3 Fig. 9 Fig. 9 shows the effects of the operational parameters— F (A/O), Q , and ω —on R (A/O). The phase ratio of the mixing zone ( R m , A/O) decreased with the increase in Q and increased with the increase in ω and F (A/O). The phase ratio of the separating zone ( R s , A/O) decreased with the increase in ω and increased with the increase in Q and F (A/O). When ω was 3500–4000 r/min, R m (A/O) was close to F (A/O). However, when Q was large or ω was low, R m (A/O) was lower than F (A/O). When Q was small or ω was high, R m (A/O) was higher than F (A/O). The density of the aqueous phase ( ρ A ) was higher than that of the organic phase; thus, the upper and lower sections of the mixing zone were organic- and aqueous-rich regions, respectively. Via computational fluid dynamics simulations and experiments, Wardle showed that the center region between the radial vanes at the bottom of the housing contained an aqueous-rich region [ 28 28 ]. When ω was low and Q was large, V m was large, as shown in Fig. 6 Fig. 6 , Therefore, the organic-rich region accounted for the majority of the fluids in the mixing zone; accordingly, R m (A/O) was lower than F (A/O). When ω was high or Q was small, V m was small, as shown in Fig. 6 Fig. 6 . Thus, the aqueous-rich region accounted for the majority of the fluids in the mixing zone, and R m (A/O) was higher than F (A/O). In the ACC, the interface radius ( r i ) of the two phases in the separating zone ( Fig. 1 Fig. 1 ) is determined as follows [ 13 13 ]: <math display="block" id="M3"><mrow><msub><mi>r</mi><mtext>i</mtext></msub><mo>=</mo><msub><mi>r</mi><mtext>A</mtext></msub><msqrt><mrow><mfrac><mrow><mn>1</mn><mo>−</mo><mfrac><mrow><msub><mi>ρ</mi><mtext>O</mtext></msub><msubsup><mi>r</mi><mtext>O</mtext><mn>2</mn></msubsup></mrow><mrow><msub><mi>ρ</mi><mtext>A</mtext></msub><msubsup><mi>r</mi><mtext>A</mtext><mn>2</mn></msubsup></mrow></mfrac></mrow><mrow><mn>1</mn><mo>−</mo><mfrac><mrow><msub><mi>ρ</mi><mtext>O</mtext></msub></mrow><mrow><msub><mi>ρ</mi><mtext>A</mtext></msub></mrow></mfrac></mrow></mfrac></mrow></msqrt><mo>,</mo></mrow></math> where r i is the interface radius (mm), ρ O is the density of the light phase (kg/m 3 ), ρ A is the density of the heavy phase (kg/m 3 ), r O is the actual liquid radius at the light-phase weir (mm), and r A is the actual liquid radius at the heavy-phase weir (mm). However, determining r i using Equation (3) is difficult because both r A and r O are challenging to obtain. However, Eq.(3) can be used to analyze r i qualitatively. Duan et al. and Zhao qualitatively analyzed the effects of the operational parameters on r i by using Eq. (3) [ 21 21 , 24 24 ]. The results showed that r i decreased with the increase in F (A/O) and Q and increased with the increase in ω , which was verified experimentally. The changes in R s (A/O) are the same as the changes in r i with the changes in F (A/O), Q , and ω . When R s (A/O) is 1.5, the interface position between the two phases in the separating zone is in the middle of the inner wall of the underflow and the light-phase weir. A higher R s (A/O) yields easier aqueous-phase entrainment in the organic-phase outlet, and a lower R s (A/O) yields easier organic-phase entrainment in the aqueous-phase outlet. 3.3.2 Effects of structural parameters of housing 3 Fig. 10 Fig. 10 shows the effects of the structural parameters of the housing— H c , W , and N r —on R (A/O). R s (A/O) hardly changed with respect to the structural parameters of the housing, because these parameters hardly affected the flow in the separating zone. R m (A/O) decreased with the increase in W and increased with the increase in H c and N r . Moreover, R m (A/O) was inconsistent with F (A/O). This is mainly because the organic- and aqueous-rich regions appeared in the upper and lower sections of the mixing zone, respectively. V m increased with W , as shown in Fig. 7 Fig. 7 . Hence, R m (A/O) decreased with the increase in W . When H c increased, the liquids of the organic-rich region in the upper section of the mixing zone were initially absorbed in the rotor. The aqueous-rich region accounted for the majority of the fluids in the mixing zone. Thus, R m (A/O) increased with H c . When N r increased, although V m (and the ALH ) increased, the aqueous-rich region also increased, because of the increase in the number of chambers between the radial vanes. Moreover, the aqueous-rich region accounted for the majority of the fluids in the mixing zone. Thus, R m (A/O) increased with N r . 3.3.3 Effects of structural parameters of rotor 3 Fig. 11 Fig. 11 shows the effects of the structural parameters of the rotor— D A *, D O *, L , H u , and D i —on R (A/O). R m (A/O) hardly changed with respect to the structural parameters of the rotor and was nearly equal to F (A/O), because the parameters of the rotor hardly affected the flow in the mixing zone. R s (A/O) increased with D O * and L but decreased with the increase in D A *, because r i increased with D A *. However, r i decreased with the increase in D O *, according to Equation (3). According to the equations for r A and r O proposed in [ 29 29 ], with the increase in L , r O increases, but r A remains unchanged. Thus, in accordance with Eq. (3), r i decreased, and R s (A/O) increased. H u and D i hardly affected R s (A/O), because they hardly influenced r i according to Eq. (3). The effects of N a on R (A/O) are presented in Table 3 Table 3 . N a hardly affected R m (A/O), because it hardly influenced the geometric volume and flow of the mixing zone. R s (A/O) decreased with the increase in N a . According to the equations for r A and r O in [ 29 29 ], with the increase in N a , r O decreases, but r A remains unchanged. Hence, in accordance with Equation (3), r i increased, and R S (A/O) decreased. 4 Conclusion 1 For successfully designing and operating ACCs for RSNF, the effect of the HNO 3 concentration on N Di for a 30%TBP/kerosene-HNO 3 solution system was investigated. Then, the effects of the operational and structural parameters on V and R (A/O) in both the mixing and separating zones of the φ20 ACC were systematically investigated using the liquid-fast-separation method and the 30%TBP/kerosene-HNO 3 solution system. The N Di of the 30%TBP/kerosene-HNO 3 solution system was > 14 × 10 -4 ; hence, the 30%TBP/kerosene-HNO 3 solution system should exhibit good phase-separation performance in the ACC. V r hardly changed with respect to the operational parameters, the structural parameters of the housing, D A *, and H u but increased with L and N r and decreased with the increase in D O *. V m hardly changed with respect to the structural parameters of the rotor but increased with F (A/O), Q , H c , and W and decreased with the increase in ω and N r . R m (A/O) hardly changed with respect to the structural parameters of the rotor and N a but decreased with the increase in Q and W and increased with ω , F (A/O), H c , and N r . R s (A/O) hardly changed with respect to the structural parameters of the housing but decreased with the increase in ω , W , and D A * and increased with Q , F (A/O), H c , N r , D O *, L , and N a . Additionally, R (A/O) was inconsistent with F (A/O), except in the case of suitable operational and structural parameters. These results are useful for understanding the flow characteristics and optimizing structure of ACCs. References S.T. Xiao , L. Li , G.A. Ye et al ., An improvement in APOR process I-uranium/plutonium separation process . Nucl. Sci. Tech . 26 , 040605 ( 2015 ). doi: 10.13538/j.1001-8042/nst.26.040605 http://doi.org/10.13538/j.1001-8042/nst.26.040605 An improvement in APOR process I-uranium/plutonium separation process R.A. Leonard , G.J. Bernstein , A.A. Ziegler et al ., Annular centrifugal contactors for solvent extraction . Sep. Sci. Technol . 15 , 925 - 943 ( 1980 ). doi: 10.1080/01496398008076278 http://doi.org/10.1080/01496398008076278 Annular centrifugal contactors for solvent extraction R.A. Leonard , D.B. Chamberlain , C. Conner , Centrifugal contactors for laboratory-scale solvent extraction tests . Sep. Sci. Technol . 32 , 193 - 210 ( 1997 ). doi: 10.1080/01496399708003194 http://doi.org/10.1080/01496399708003194 Centrifugal contactors for laboratory-scale solvent extraction tests W.H. Duan , T.X. Sun , J.C. Wang , An industrial-scale annular centrifugal extractor for the TRPO Process . Nucl. Sci. Tech . 29 , 46 ( 2018 ). doi: 10.1007/s41365-018-0395-z http://doi.org/10.1007/s41365-018-0395-z An industrial-scale annular centrifugal extractor for the TRPO Process W.H. Duan , M.M. Zhao , C.Q. Wang et al ., Recent advances in the development and application of annular centrifugal contactors in the nuclear industry . Solvent Extr. Ion Exch . 32 , 1 - 26 ( 2014 ). doi: 10.1080/07366299.2013.833741 http://doi.org/10.1080/07366299.2013.833741 Recent advances in the development and application of annular centrifugal contactors in the nuclear industry R.J. Taylor , C.R. Gregson , M.J. Carrott et al , Progress towards the full recovery of neptunium in an advanced PUREX process . Solvent Extr. Ion Exch . 31 , 442 - 462 ( 2013 ). doi: 10.1080/07366299.2013.800438 http://doi.org/10.1080/07366299.2013.800438 Progress towards the full recovery of neptunium in an advanced PUREX process T.S. Rudisill , M.C. Thompson , Demonstration of the use of formohydroxamic acid in the UREX process . Sep. Sci. Technol . 50 , 2823 - 2831 ( 2015 ). doi: 10.1080/01496395.2015.1085413 http://doi.org/10.1080/01496395.2015.1085413 Demonstration of the use of formohydroxamic acid in the UREX process M. Carrott , K. Bell , J. Brown et al , Development of a new flowsheet for co-separating the transuranic actinides: the “EURO-GANEX” process . Solvent Extr. Ion Exch . 32 , 447 - 467 ( 2014 ). doi: 10.1080/07366299.2014.896580 http://doi.org/10.1080/07366299.2014.896580 Development of a new flowsheet for co-separating the transuranic actinides: the “EURO-GANEX” process J.D. Law , T.G. Garn , D.H. Meikrantz et al ., Pilot-scale TRUEX flowsheet testing for separation of actinides and lanthanides from used nuclear fuel . Sep. Sci. Technol . 45 , 1769 - 1775 ( 2010 ). doi: 10.1080/01496395.2010.493832 http://doi.org/10.1080/01496395.2010.493832 Pilot-scale TRUEX flowsheet testing for separation of actinides and lanthanides from used nuclear fuel R. Malmbeck , O. Courson , G. Pagliosa et al ., Partitioning of minor actinides from HLLW using the DIAMEX process. Part 2-"hot" continuous counter-current experiment . Radiochim. Acta 88 , 865 - 871 ( 2000 ). doi: 10.1524/ract.2000.88.12.865 http://doi.org/10.1524/ract.2000.88.12.865 Partitioning of minor actinides from HLLW using the DIAMEX process. Part 2-"hot" continuous counter-current experiment G. Modolo , H. Asp , H. Vijgen et al ., Demonstration of a TODGA-based continuous counter-current extraction process for the partitioning of actinides from a simulated PUREX raffinate, part II: centrifugal contactor runs . Solvent Extr. Ion Exch . 26 , 62 - 76 ( 2008 ). doi: 10.1080/07366290701784175 http://doi.org/10.1080/07366290701784175 Demonstration of a TODGA-based continuous counter-current extraction process for the partitioning of actinides from a simulated PUREX raffinate, part II: centrifugal contactor runs Y. Morita , M. Kubota , J.P. Glatz et al ., Actinide partitioning from HLW in a continuous DIDPA extraction process by means of centrifugal extractors . Solvent Extr. Ion Exch . 14 , 385 - 400 ( 1996 ). doi: 10.1080/07366299608918346 http://doi.org/10.1080/07366299608918346 Actinide partitioning from HLW in a continuous DIDPA extraction process by means of centrifugal extractors X.M. He , Y.S. Yan , Q.R. Zhang et al . Recent advances of annular centrifugal extractor for hot test of nuclear waste partitioning process . Nucl. Sci. Tech . 9 ( 3 ), 157 - 162 ( 1998 ). Recent advances of annular centrifugal extractor for hot test of nuclear waste partitioning process W.H. Duan , J. Chen , J.C. Wang et al ., Application of annular centrifugal contactors in the hot test of the improved total partitioning process for high level liquid waste . J. Hazard. Mater . 278 , 566 - 571 ( 2014 ). doi: 10.1016/j.jhazmat.2014.06.049 http://doi.org/10.1016/j.jhazmat.2014.06.049 Application of annular centrifugal contactors in the hot test of the improved total partitioning process for high level liquid waste D.H. Meikrantz , T.G. Garn , J.D. Law et al ., A centrifugal contactor design to facilitate remote replacement . Nucl. Technol . 173 , 289 - 299 ( 2011 ). doi: 10.13182/NT11-A11662 http://doi.org/10.13182/NT11-A11662 A centrifugal contactor design to facilitate remote replacement K. Mandal , S. Kumar , V. Vijayakumar et al ., Hydrodynamic and mass transfer studies of 125 mm centrifugal extractor with 30% TBP/nitric acid system . Prog. Nucl. Energ . 85 , 1 - 10 ( 2015 ). doi: 10.1016/j.pnucene.2015.05.005 http://doi.org/10.1016/j.pnucene.2015.05.005 Hydrodynamic and mass transfer studies of 125 mm centrifugal extractor with 30% TBP/nitric acid system W.H. Duan , C.L. Song , Q.L. Wu et al ., Development and performance of a new annular centrifugal contactor for semi-industrial scale . Sep. Sci. Technol . 40 , 1871 - 1883 ( 2005 ). doi: 10.1081/SS-200064531 http://doi.org/10.1081/SS-200064531 Development and performance of a new annular centrifugal contactor for semi-industrial scale K.E. Wardle , Liquid–liquid mixing studies in annular centrifugal contactors comparing stationary mixing vane options . Solvent Extr. Ion Exch . 33 , 671 - 690 ( 2015 ). doi: 10.1080/07366299.2015.1082835 http://doi.org/10.1080/07366299.2015.1082835 Liquid–liquid mixing studies in annular centrifugal contactors comparing stationary mixing vane options S.W. Li , W.H. Duan , J. Chen et al ., CFD simulation of gas−liquid−liquid three-phase flow in an annular centrifugal contactor . Ind. Eng. Chem. Res . 51 , 11245 - 11253 ( 2012 ). doi: 10.1021/ie300821t http://doi.org/10.1021/ie300821t CFD simulation of gas−liquid−liquid three-phase flow in an annular centrifugal contactor S. Vedantam , K.E. Wardle , T.V. Tamhane et al ., CFD simulation of annular centrifugal extractors . Int. J. Chem. Eng. Volume 2012 , 759397 (2012) . doi: 10.1155/2012/759397 http://doi.org/10.1155/2012/759397 CFD simulation of annular centrifugal extractors B.R. Zhao , A study on the interface radius and hold-up in an annular centrifugal extractor, M.D diss ., Tsinghua University, P.R China , ( 1996 ). (in Chinese) A study on the interface radius and hold-up in an annular centrifugal extractor, M.D diss B. Schuur , G.N. Kraai , J.G.M. Winkelman et al ., Hydrodynamic features of centrifugal contactor separators: experimental studies on liquid hold-up, residence time distribution, phase behavior and drop size distributions . Chem. Eng. Process . 55 , 8 - 19 ( 2012 ). doi: 10.1016/j.cep.2012.02.008 http://doi.org/10.1016/j.cep.2012.02.008 Hydrodynamic features of centrifugal contactor separators: experimental studies on liquid hold-up, residence time distribution, phase behavior and drop size distributions S.V.N. Ayyappa , M. Balamurugan , S. Kumar et al ., Mass transfer and hydrodynamic studies in a 50 mm diameter centrifugal extractor . Chem. Eng. Process . 105 , 30 - 37 ( 2016 ). doi: 10.1016/j.cep.2016.04.005 http://doi.org/10.1016/j.cep.2016.04.005 Mass transfer and hydrodynamic studies in a 50 mm diameter centrifugal extractor W.H. Duan , S. Cao , Determination of the liquid hold-up volume and the interface radius of an annular centrifugal contactor using the liquid-fast-separation method . Chem. Eng. Commun . 203 , 548 - 556 ( 2016 ). doi: 10.1080/00986445.2015.1048802 http://doi.org/10.1080/00986445.2015.1048802 Determination of the liquid hold-up volume and the interface radius of an annular centrifugal contactor using the liquid-fast-separation method W.H. Duan , Q. Cheng , X.Z. Zhou et al ., Development of a φ20 mm annular centrifugal contactor for the hot test of the total TRPO process . Prog. Nucl. Energ . 51 , 313 - 318 ( 2009 ). doi: 10.1016/j.pnucene.2008.08.002 http://doi.org/10.1016/j.pnucene.2008.08.002 Development of a φ20 mm annular centrifugal contactor for the hot test of the total TRPO process R.A. Leonard , Solvent characterization using the dispersion number . Sep. Sci. Technol . 30 ( 7-9 ), 1103 - 1122 ( 1995 ). doi: 10.1080/01496399508010335 http://doi.org/10.1080/01496399508010335 Solvent characterization using the dispersion number K.E. Wardle , T.R. Allen , M.H. Anderson , Experimental study of the hydraulic operation of an annular centrifugal contactor with various mixing vane geometries . AIChE J . 56 ( 8 ), 1960 - 1974 ( 2010 ). doi: 10.1002/aic http://doi.org/10.1002/aic Experimental study of the hydraulic operation of an annular centrifugal contactor with various mixing vane geometries K.E. Wardle , Summary Report on liquid-liquid contactor scoping experiments and validation test case definition, ANL-LTR-CERT-12-001 , Argonne National Laboratory , USA , 2012 . Summary Report on liquid-liquid contactor scoping experiments and validation test case definition, ANL-LTR-CERT-12-001 G.J. Bernstein , D.E. Grosvenor , J.F. Lenc et al ., Development and performance of a high-speed, long-rotor centrifugal contactor for application to reprocessing LMFBR Fuels. ANL-7968 , Argonne National Laboratory , USA , 1973 . Development and performance of a high-speed, long-rotor centrifugal contactor for application to reprocessing LMFBR Fuels. ANL-7968 10.1007/s41365-019-0615-1 This work was supported by the Program for Changjiang Scholars and Innovative Research Team in University of Ministry of Education of China (No. IRT13026), and the National 863 Program for Nuclear Fuel Cycling and Nuclear Safety Technology Project (No. 2009AA050703). 2018-09-28 2018-11-19 2019-02-23 2019-05-14 2019-06-01 2021-04-10 © China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, ChineseNuclear Society and Springer Nature Singapore Pte Ltd. 2019 This is a post-peer-review, pre-copyedit version of an article published in Nuclear Science and Techniques. The final authenticated version is available online at: http://dx.doi.org/10.1007/s41365-019-0615-1 http://dx.doi.org/10.1007/s41365-019-0615-1 . 2019 Nuclear Science and Techniques 06 30