A THEORETICAL AND EXPERIMENTAL STUDY OF AIRLIFT PUMPING AND AERATION WITH REFERENCE TO AQUACULTURAL APPLICATIONS. A Thesis

Transcription

1 A THEORETICAL AND EXPERIMENTAL STUDY OF AIRLIFT PUMPING AND AERATION WITH REFERENCE TO AQUACULTURAL APPLICATIONS A Thesis Presented to the Faculty of the Graduate School of Cornell University in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy by Douglas Joseph Reinemann August 1987

2 A Theoretical and Experimental study of Airlift Pumping and Aeration with Reference to Aquacultural Applications Douglas Joseph Reinemann, Ph.D. Cornell University 1987 A theoretical and experimental study was conducted pertaining to the pumping and aeration properties of the airlift pump and its application in intensive aquaculture facilities. The results and discussion of a study of the effects of tube diameter on vertical slug flow, specifically as it relates to 3-25 mm airlift pump performance, are presented in Chapter One: Theory of Small Diameter Airlift Pumps. The theory previously presented by Nicklin (1963) is extended into this range of tube diameters by taking into account the effects of surface tension on bubble rise velocity. Differences are noted between the rise velocity of a single gas slug and a train of gas slugs in small vertical tubes. Comparisons are made between experimental results and theoretical predictions. The results and discussion of a study of the flow dynamics of a 38 mm diameter airlift pump, are presented in Chapter Two: Hydrodynamics of the Airlift Pump in Bubble and BUbbly-Slug Flow. Experimental flow patterns ranged from dispersed bubble flow to bubbly-slug flow.

3 The effects of initial bubble size and water quality on flow dynamics and flow pattern transition are examined. Experimental data are compared with previous two phase flow models and a new prediction equation is developed for the bubbly-slug flow regime. The results of an experimental study of the oxygen transfer properties of a 38 mm diameter airlift pump are presented in Chapter Three: Oxygen Transfer in Airlift Pumping. The effects of varying initial bubble size, flow rate, flow pattern, and water quality on oxygen transfer are examined. A model to predict oxygen transfer in airlift pumping is presented. The results of an energy and cost analysis of salrnonid production in water reuse systems is presented in Chapter Four: Energy and Cost Analysis of Salmonid Production in Water Reuse Systems. Various options to increase system efficiency, including the use of airlifts for pumping and aeration, are considered. The energy inputs for salmonid production in water reuse systems are compared with land based animal protein production, other forms of aquaculture and traditional fishing.

4 Douglas Joseph Reinemann 1987 ALL RIGHTS RESERVED

5 Biographical Sketch Douglas Joseph Reinemann was born on January 25, 1958 in Frankfurt, west Germany, the second of five children to Dr. John M. and Mrs. Joan Hug Reinemann. In 1961 his father finished his tenure with the u.s. Army and the family moved to Milwaukee, Wisconsin for two years and then to Sheboygan, Wisconsin. Douglas graduated from Sheboygan North High School in June of 1976, and enrolled in the University of Wisconsin Madison, where he received a B.S. in Agricultural Engineering in December of He then worked as a volunteer at the st. Francis Mission on the Rosebud sioux Indian reservation for nine months. It was during this time that he gained an understanding of and appreciation for Lakota thought and philosophy. He returned to the University of Wisconsin to complete an M.S. in Agricultural Engineering in august of Upon completion of his M.S. he returned to the Rosebud for a period of one year to continue his studies of Lakota and to work with the Wanekiya Cooperative, a group which was formed during his first visit there. In August of 1984, he was wed to Mary Kay Hauck, of Missoula, Montana, who had been a teacher on the Rosebud Reservation, at the st. Francis Indian School. iii

6 Douglas entered in a Doctoral Program in Agricultural Engineering at Cornell University in September of 1984, where he has studied aquaculture and water management. During his tenure at Cornell, the couples first son, Joseph John, was born. The couple is currently expecting their second child. iv

7 Dedication For my wife, my children, and all my relatives. Mitakuye Oyasin v

8 Acknowledgments I would like to express my appreciation to the members of my committee, M.B. Timmons, J.Y. Parlange, and D. Pimentel. to work with them. It has been an honor and a privilege I would also like to acknowledge the teachers and fellow graduate students at Cornell who have made my time here interesting and enjoyable: especially Rakesh Gupta, Marc Parlange, and Dr. Zelman Warhaft. vi

9 Table of Contents Chapter One Thcnry ~f ~ma]l oiamatqr Airlift Pumps 1 l.nt:icoduul~on 1 Theory Experimental Procedure 11 Results and Discussion 12 Conclusion 17 Chapter Two Hydrodynamics of the Airlift Pump in Bubble and Bubbly-Slug Flow. 27 Introduction Theory Experimental Procedure 35 Results and Discussion. 37 Conclusion Chapter Three Oxygen Transfer in Airlift Pumping 52 Introduction Experimental Procedure Results and Discussion Conclusion Chapter Four Energy and Cost Analysis of Salmonid Production In Water Reuse Systems. 66 Introduction Salmonid Production in Closed Systems. 71 Comparison with Other Forms of Protein Production Conclusion Appendix A Energy and Cost Analysis Details 88 Appendix B Thermal Model Details 91 References. 93 vii

10 List of Tables Table 1.1 Table 2.1 Table 2.3 Table 2.2 Table 3.1 Table 4.1 Table 4.2 Table 4.3 Table 4.4 Table 4.5 Table 4.6 Summary of Airlift Equations 18 Nomenclature and Definitions 43 Summary of Airlift Equations 44 Water Quality Parameters 44 Water Quality Parameters 61 US Fishery Products Supply 84 consumption of Selected Protein Products in the US Energy and Cost Analysis 85 sensitivity Analysis 86 Energy Inputs for Various Protein Production Systems Protein Production and Land Area 83 viii

11 List of Figures Figure 1.1. Typical Airlift Pump. 19 Figure Experimental Apparatus. 20 Figure Velocity Profile Coefficient vs. Reynolds Number. 21 Figure Efficiency vs. Gas Flow, 3.18 mm Tube. 22 Figure Efficiency vs. Gas Flow, 6.35 mm Tube. 23 Figure Efficiency vs. Gas Flow, 9.53 mm Tube. 24 Figure Theoretical Efficiency vs. Gas Flow. 25 Figure optimum Flow Characteristics vs. Tube Diameter.. 26 Figure 2.1. Typical Airlift Pump. 45 Figure Flow Patterns. 46 Figure Local liquid slug gas void ratio, bubble and liquid velocities in bubbly-slug flow. 47 Figure 2.4. Experimental Apparatus. 48 Figure 2.5. Bubble Flow Data. Experimental vs. Predicted Average Gas Velocities. 49 Figure 2.6. Bubbly-Slug Flow Data. Average Gas Velocity vs. Average Mixture Velocity.. 50 Figure mm Diameter Tube Flow Pattern Map. 51 Figure 3.1. Typical Airlift Pump. 62 Figure 3.2. Flow Patterns in Airlift Pump operation. 63 Figure 3. 3 Experimental Apparatus. 64 Figure 3.4. Oxygen Transfer Coefficient vs. Reynolds Number 65 Figure 4.1. Thermal Model Detail. 92 ix

12 Chapter One Theory of Small Diameter Airlift Pumps Abstract: The results and discussion of a study of the effects of tube diameter on vertical slug flow, specifically as it relates to 3-25 mm airlift pump performance are presented. The theory previously presented by Nicklin (1963), is extended into this range of tube diameters by taking into account the effects of surface tension on bubble rise velocity. Differences are noted between the rise velocity of a single gas slug and a train of gas slugs in small vertical tubes. Comparisons are made between experimental observations and theoretical predictions. Introduction A typical airlift pump configuration is illustrated in figure 1.1. A gas, usually air, is injected at the base of a submerged riser tube. As a result of the gas bubbles suspended in the fluid, the average density of the two-phase mixture in the tube is less than that of the surrounding fluid. The resulting buoyant force causes a pumping action. The slug flow regime is most widely encountered in airlift pump operation and is characterized by bubbles large enough to nearly span the riser tube. The length of the bubbles ranges from roughly the diameter of the 1

13 2 tube, to several times this value. The space botwg8n the bubbles is mostly liquid filled and is referred to as a liquid slug (Govier and Aziz, 1972). The large gas bubble is also referred to as a gas slug or Taylor bubble. Extensive experimental and theoretical work has been done on airlift pumps in the slug flow regime (Apazidis, 1985; Clark and Dabolt, 1986; Hjalmars, 1973; Higson, 1960; Husain and Spedding, 1976; Jeelani et al., 1979; Nicklin, 1963; Richardson and Higson, 1962; Sekoguchi et al., 1981; Slotboom, 1957; Stenning and Martin, 1968). These studies have been confined to air/water systems in tubes with diameter greater than 20 mm in which the effects of surface tension are small and have therefore been neglected. As tube diameter is decreased below 20 mm, the effects of surface tension on the dynamics of vertical slug flow become increasingly important (Bendiksen, 1985, Nickens, and Yannitell, 1987; Tung and Parlange, 1976; White and Beardmore, 1962; Zukoski, 1966). It has been speculated that increased efficiency might be obtained by using small diameter tubes at low flow rates (Nicklin, 1963). Neither a satisfactory theory, nor conclusive experimental evidence, however, has as yet been presented for small diameter airlift operation. The objective of this study is to examine the effects of tube diameter on the hydrodynamics of the airlift pump

14 3 in the range of tube diameters in which surface tension effects are significant. Theory In previous work, the rise velocity of a gas slug in a vertical tube relative to a moving liquid slug has been described by (Bendiksen, 1985; Collins et al., 1978; Griffith and Wallis, 1961; Nicklin et al., 1962): [ 1. 1 ] where Vt = rise velocity of Taylor bubble (mjs) Vts = rise velocity of Taylor bubble in still fluid (mjs) Co = liquid slug velocity profile coefficient V m = mean velocity of the liquid slug (mjs) given by: [ 1. 2 ] where QI = volumetric liquid flow rate (m 3 js) Q g = volumetric gas flow rate (m 3 js) A = tube cross sectional area (m 2 ) Following the analysis used by Nicklin (1963), the velocity of the Taylor bubble is set equal to the average linear veioc~~y of the gas in the riser tube: Vt = ~ [1.3] where E = gas void ratio

15 4 It is convenient to express the volumetric liquid and gas flows and bubble velocity in dimensionless form as Froude numbers defined by: Q g Ql' = ----1' Qg' = ----1' Vts' 1 [1. 4 ] A (g D) 2" A (g D) 2" (g D) 2" where Ql' = Dimensionless volumetric liquid flow Qg, = Dimensionless volumetric gas flow Vts, = Dimensionless bubble rise velocity in still fluid D = tube diameter (m) g = acceleration due to gravity (mjs 2) From [l.lj - [1.4J, the gas void fraction in the riser tube can be expressed as: E = Co (Ql I + Qg') + Vts I [1. 5 J The submergence ratio is a parameter commonly found in airlift analysis and is defined as: [1. 6 J where ~ = submergence ratio Zl = lift height (m) (See figure 1.1) Zs = length of tube submerged (m) The submergence ratio is equal to the average pressure gradient along the riser tube which is made up of components due to the weight of the two phase mixture and frictional losses. Performing a static pressure

16 balance on a vertical tube which is submerged in fluid 5 (see figure 1.1), it follows that: [1. 7] where p = fluid density (kgjm 3 ) This assumes that the weight of the gas is negligible relative to the weight of the liquid. If the fluid in the tube is moving, an additional pressure drop due to frictional losses must be added to the right hand side of [1.7]. The single phase frictional pressure drop can be calculated based upon the mean slug velocity as: where P s = f [1. 8] Ps = single phase frictional pressure drop (Njm 2 ) f = friction factor (Giles, 1962) = [1. 9] Re0.25 Re = [1. 10] v v = kinematic fluid viscosity (m 2 js) The single phase frictional loss must then be multiplied by (I-E), the fraction of the tube occupied by the liquid slugs, to obtain the total frictional pressure drop in the riser tube. The frictional effects in the liquid film around the gas bubble have been shown to be

17 small compared to those in the liquid slug and arq 6 therefore neglected (Nakoryakov et al., 1986). Including the frictional effects in the pressure balance results in: Dividing both sides by [p g (Zs+Zl)J and rearranging gives: ex = (I-E) (1 + f/2 (Ql' + Qg') 2) [1. 12 J Thus, for a given tube diameter, imposing the gas flow rate and the submergence ratio, the liquid flow rate may be determined using the system of equations summarized in Table It is usual to define the efficiency of the airlift pump as the net work done in lifting the liquid, divided by the work done by the isothermal expansion of the air (NiCklin, 1963): n = efficiency P a = atmospheric pressure (N/m 2 ) Po = pressure at base of riser tube (N/m 2 ) Nicklin (1963) introduced the concept of point efficiency which is accurate in describing total airlift efficiency to within 1% for submergence lengths of up to 5 meters:

18 7 n = [1. 14 ] Qg' ex:. Two important effects become significant when airlift tube diameter is below about 20 mm. is increased importance of surface tension. The first The second is decreased Reynolds number. The effects of surface tension can be characterized by the inverse E6tvos number or surface tension number, ~, defined as: a ~ = : [1. 15] p 2 g D where ~ = surface tension number a = surface tension (N/m) White and Beardmore (1962) have defined a dimensionless parameter which relates only to the properties of the fluid and expresses the relative importance of viscosity to surface tension: y = -- [1. 16] where Y fluid viscosity/surface tension parameter ~ = fluid viscosity (kg/m s) Experimental results have shown that when this parameter is below 10-8 (which is the case for an air/water system) viscosity does not influence bubble rise velocity in still fluid (White and Beardmore, 1962).

19 Theoretical and experimental analyses of th0 rise 8 velocity of a single gas slug in still fluid have shown that when both surface tension and viscous effects are negligible, the bubble Froude number in still fluid (B) assumes a constant value of about 0.35 (Bendiksen, 1984; Collins et al., 1978; Davies and Taylor, 1950; Higson, 1960; Nakoryakov et al., 1986; Nickens and Yannitell, 1987; Nicklin et al., 1962; White and Beardmore, 1962; Zukoski, 1966). This is the value which has been used in previous airlift analysis (Nicklin, 1963; Clark and Dabolt, 1986). The bubble Froude number in still fluid is influenced by surface tension when the surface tension parameter is above about 0.02 (Bendiksen, 1985; Bendiksen, 1984; Nickens and Yannitell, 1987; Tung and Parlange, 1976; Zukoski, 1966). This corresponds to a tube diameter less than about 20 mm in an air/water system. As the tube diameter is decreased below this value the bubble Froude number decreases. When the surface tension number is above about 0.2 the bubble will not rise in still fluid and the value of the bubble froude number is zero. This corresponds to a tube diameter of about 6 mm in an air/water system. When the effects of viscosity can be neglected, as is the case for an air/water system, the bubble Froude number in still fluid can be expressed as a function of the

20 9 surface tension parameter alone (Nickens and YannitQll, 1987; White and Beardmore, 1962): Vts' = ( ~ ~2) [1.17J Correction can also be made on B for other gas/liquid systems when viscous effects are significant (Nickens and Yannitell, 1987; White and Beardmore, 1962). Theoretical analyses of bubble rise velocity have applied potential flow theory at the bubble tip, expressing the stream function of the flow in terms of a Bessel function series of the first kind and first order (Bendiksen, 1985; Nickens and Yannitell, 1987; Tung and Parlange, 1976). This treatment of the hydrodynamics only at the bubble tip has been justified by several experimental studies in which air/water bubble dynamics have been shown to be independent of bubble length (Nicklin et al., 1962; Griffith and Wallis, 1961). The effects of surface tension are accounted for in the application of the boundary condition of constant gas pressure along the bubble surface. As the radius of curvature of the bubble is reduced, surface tension acts to increase the pressure at the gas/liquid interface. This changes the flow dynamics at the bubble surface and hence the bubble rise velocity. Nicklin et ai, (1962), have shown that a value of 1.2 for Co is suitable when the liquid slug Reynolds number is above For airlift pumps with diameter greater than 20 mm, the Reynolds number is usually above

21 The Reynolds number can be considerably less than 8000 when airlift diameter is less than 20 mm, however. An increase in the velocity profile coefficient has been observed for Reynolds numbers below 8000 (Bendiksen, 1985; Nicklin et al., 1962). The limiting value of the velocity profile coefficient has been found to be about 2 for Reynolds numbers approaching zero. This rise in Co has also been predicted theoretically when a laminar velocity profile was imposed in the liquid ahead of the gas slug (Bendiksen, 1985, Collins et al., 1978). Bubble rise velocity as expressed in [1.1J can thus be interpreted as its rise velocity in still fluid plus the velocity of the fluid encountered at its tip. The velocity profile coefficient is then the ratio of the liquid velocity at the tube axis to the average velocity of the liquid slug. The limiting values of Co (1.2 for high Reynolds numbers and 2.0 for low Reynolds numbers) reflect either turbulent or laminar velocity profiles in the liquid slug. Neglecting frictional effects, the efficiency of the airlift from [1.5J, [1.10J and [1.12J is: n = Co (Ql '+ Qg') + Vts' - Qg' [1. 18 J Decreasing tube diameter in the range where surface tension effects are significant will decrease the value of the bubble froude number, Vts'. This will increase

22 11 efficiency. Previous experimental work has shown that 3 reduction in the liquid slug Reynolds number will increase Co if the transition to a laminar velocity profile occurs in the liquid slugs. This will reduce efficiency. Thus, two opposing effects are predicted. An experiment was performed to determine the relative importance of the two effects. Experimental Procedure The test apparatus is illustrated in figure 1.2. The reservoir and return sections were glass tube with a 38 mm inside diameter. The riser tubes were 1.80 m in length and ranged in inside diameter from 3.18 mm to 19.1 mm. Volumetric air and water flow rates, bubble rise velocity, submergence, and lift height were measured after the flow stabilized for each trial. Air and water flows were determined by means of pressure drop measurements across calibrated orifices. Bubble rise velocities in both still and moving liquid were determined by timing a bubble over a known travel distance. The flow was allowed to develop for a distance of 0.8 meters before bubble velocity measurements were started. Slug flow developed within 1 to 5 diameters of the entrance for all of the riser tubes and flow rates tested. The static head at the pressure tap immediately before the riser tube was used as a reference level in determining lift height and submergence (see figure

23 12 1.2). This same pressure was used as the air inlot pressure. By using this pressure as a reference, all losses in the water return line, air supply line and across the orifices were separated from the riser tube measurements. The resulting experimentally measured flow variables are therefore as close as possible to measuring the conditions of the riser tube alone. Submergence ratios were varied by changing the amount of fluid in the reservoir. Air was injected into the system by means of a small diaphragm type compressor. Air flow rate was controlled by a valve between the compressor and the air flow measurement orifice. The velocity profile coefficient was determined using [l.lj, and [1.2J with measured flow rates and bubble rise velocities. The experimental efficiency was determined using [1.12J with measured values of liquid flow, gas flow and submergence ratio. Results and Discussion For all of the tube sizes tested, the bubble rise velocity in still fluid corresponded very closely to the prediction equation used and results reported by previous workers (White and Beardmore, 1962; 1976; Zukoski, 1966). Experimental results for tubes with 3.18, 6.35, and 9.53 mm diameters, showed the velocity profile coefficient scattered closely about 1.2 with no increasing trend for Reynolds number decreasing to as low as 500 (See figure 1.3). This differs from earlier

24 13 results in which the velocity profile coefficient increased for Reynolds numbers below 8000 (Bendiksen, 1984; Nicklin et al., 1962). The experiment was repeated using a 19.1 mm diameter tube to determine whether surface tension effects influenced this phenomenon. For this tube size surface tension effects were negligible as in previous studies. The results again showed no increasing trend in the velocity profile coefficient for low Reynolds numbers. There are two major differences noted between the previous experiments (Bendiksen, 1984; Nicklin et al., 1962)and the present one: 1. In the previous experiments the motion of a single gas slug moving through a moving stream of liquid was studied. In the present experiment the gas was introduced continuously resulting in a series of gas slugs moving through a series of liquid slugs. 2. The previous experiments used a pump to regulate the liquid flow whereas in the present experiment, liquid motion was the result solely of buoyancy. When a single gas slug is placed in a stream of liquid whose motion is pump driven, the velocity profile in the liquid ahead of the gas slug is a result of single phase pipe flow. When a series of gas and liquid slugs rise concurrently, the velocity profile in the

25 14 liquid slugs is a result of two phase slug flow dynamics. The results of the present experiment show that the liquid slugs have a turbulent velocity profile for Reynolds numbers as low as 500. Observation of the motion of very small gas bubbles suspended in the liquid slug showed erratic behavior further confirming the presence of turbulence in the liquid slug at low Reynolds numbers. A laminar velocity profile in the liquid ahead of the gas slug was observed at low Reynolds numbers in previous experiments (Bendiksen, 1985; Nicklin et al., 1962). It is believed that this difference is the result of vorticity generated in the liquid film surrounding the gas slugs and in their wake when a series of gas slugs rise concurrently with a series of liquid slugs. A value of 1.2 was used for the velocity profile coefficient in all subsequent theoretical airlift calculations since a turbulent velocity profile was observed in the liquid slug for the range of flow conditions tested. The experimentally determined efficiencies versus submergence ratio and gas flow are shown in figures 1.4 through 1.6. Theoretical efficiencies for lines of constant submergence are also shown. The agreement between theory and experiment is good except when the gas flow rate is low and the submergence ratio is below 0.7. This region signifies the approach of flow

26 15 oscillations which are not considered in the theoretical model. other workers have observed flow oscillations in large diameter airlift operation (Apazidis, 1985; Higson, 1960; Hjalmars, 1973; Sekoguchi et al., 1981; Wallis and Heasley, 1961;). Oscillations have been reported to both decrease air-lift efficiency, (Higson, 1960; Richardson and Higson, 1962) and increase efficiency (Sekoguchi et al., 1981). Measurements taken in the present study, in the region approaching oscillatory behavior show efficiencies higher than those predicted by theory for the tube sizes tested in this regime. It is instructive to examine the situation in which no frictional losses are included in theoretical predictions. This is an excellent approximation to actual performance at low flow rates when frictional losses are small. Efficiencies will drop increasingly below the frictionless case as flow rates increase, (see figure 1.7). For small tubes (less than 6 mm diameter) the bubble froude number in still fluid (Vts) is zero and the efficiency is constant with respect to gas flow and increases with increasing submergence ratio in the frictionless case. For large tubes (greater than 20 mm diameter), The bubble Froude number is equal to 0.35, its upper limit, and frictionless efficiency depends on both submergence

27 and flow rate. Negative values of efficiency occur at 16 low flow rates, indicating a situation in which work is done by the expanding gas and no useful work is being performed pumping the fluid. For tubes in the intermediate size range (6 mm to 20 mm), the bubble Froude number falls between its upper and lower limits. Efficiencies fall between the positive values encountered with small tubes and the negative values for large tubes as flow rate decreases. Frictional losses are negligible at low gas flow rates. Frictional losses increase faster for higher submergence ratios as gas flow increases. This causes the characteristic crossing of the constant submergence ratio efficiency curves (see figure 1.7). A summary of the optimal flow characteristics of the airlift pump versus tube diameter is presented in figure 1.8. Nicklin (1963) concluded that optimal pump efficiency and submergence ratio were insensitive to tube diameter. This is indeed the case for air/water systems when tube diameters are above 20 mm and surface tension effects are negligible. As tube diameters are decreased below this value, the effects of surface tension act to increase optimal airlift efficiency and submergence ratio confirming Nicklin's (1963) speculations. The maximum attainable theoretical airlift efficiency is 83% and occurs for tube with

28 17 diameter less than 6 mm in the limit of zero gas flow and 100% submergence. Conclusion A difference has been observed between single bubble and bubble train slug flow in air-water systems at low Reynolds numbers. When a single gas slug rises in a moving liquid stream the velocity profile coefficient approaches a value of 2.0 for low Reynolds number flow in air/water systems. This indicates a laminar velocity profile in the liquid ahead of the gas slug. When a series of gas slugs rise concurrently with a series of liquid slugs, the velocity profile coefficient remains at a value of 1.2 for Reynolds numbers as low as 500. This indicates turbulent flow in the liquid slugs. It is believed that this difference is the result of vorticity generated in the liquid film surrounding the gas slugs and in their wake. It has been shown that including this effect and the effects of surface tension on bubble rise velocity allows the airlift pump theory previously described by Nicklin (1963) to be extended to lower tube diameters of from 3 mm to 20 mm. It has also been shown that airlift efficiency and optimal submergence ratio increase in this range of tube diameters. The theory described here can be used with confidence to design small diameter airlift pumps.

29 18 Summary Table 1.1 of Airlift Equations E = Q g, 1.2(Ql'+Qg')+Vts' ex = (I-E) (1+f/2 (Ql '+Qg') 2) Q1' f Q1 Qg ZS = Qg, = ex = 1 1 A (g D) "2 A (g D) "2 Zl + Zs Vts, = ( : : 2 ) D(Q1 + Qg ) a = Re = 2: = ReO. 25 l/ A p g D2

30 19...-AIR INPUT Figure 1.1. Typical Airlift Pump.

31 LIQUID PRESSURE TAPS /"" LIFT, ~ I AIR FLOW ORIFICE ~ LIQUID FLOW ORIFICE MANOMETER. COMPRESSOR Figure 1.2. Experimental Apparatus.

32 21 '"' 0 0 'V l- z w 0 ii: 11. w * #.,," o *... #,* w t.j ii: 0 0:: a. ~ J t ott I:,1 ti ", TO Q t 0 0, + #! # I 'i 4 0 oro q. + t t t + to 4 J.. + t * D = 3.18 mm.j + D = 6.35 mm w > o D = 9.53 mm D = 19.1 mm 0.8 I T r T I I r -T, (Thousands) REYNOLDS NUMBER Figure 1.3. Velocity Profile Coefficient vs. Reynolds Number.

33 mm TUBE NUMBERS ON GRAPH BODY INDICATE PERCENT SUBMERGENCE OF EXPERIMENTAL POINTS. SOUD UNES INDICATE THEORETICAL UNES OF CONSTANT SUBMERGENCE. > t) Z w 0 Ii: IL w ~ THEORY sr. THEORY + t 71r. THEORY DIMENSIONLESS GAS FLOW (Qg') Figure 1.4. Efficiency vs. Gas Flow, 3.18 mm Tube.

34 mm TUBE r. THEORY 0.7 t-~ r. THEOR~ " > z 81 III 0 il 93 IL III NUUBERS ON GRAPH BODY INDICATE PERCENT 0.2 SUBMERGENCE OF EXPERIMENTAL POINTS. SOLID LINES INDICATE THEORETICAL 0.1 UNES OF CONSTANT SUBMERGENCE. 90r. THEORY """'T""" r , j DIUENSIONLESS GAS FLOW (09') Figure 1.5. Efficiency vs. Gas Flow, 6.35 mm Tube.

35 NUMBERS ON GRAPH BODY INDICATE PERCENT mm TUBE SUBMERGENCE OF EXPERIMENTAl.. POINTS. SOUD UNES INDICATE THEORETICAL 0.8 UNES OF CONSTANT SUBMERGENCE THEORY 48 > 0.. z 71 w il ll w DIMENSIONLESS GAS FLOW (Og') Figure 1.6. Efficiency vs. Gas Flow, 9.53 mm Tube.

36 25 Figure 1.7. Theoretical Efficiency vs. Gas Flow.

37 SUBMERGENCE RAno (0) : w W 0.7 DIMENSIONLESS UQUID FLOW (QI') 0.6 ~ ( 0: ( 0.5 tl EFFICIENCY (n) 0.2 DIMENSIONLESS GAS FLOW (09') DIAMETER (mm) Figure 1.8. optimum Flow Characteristics vs. Tube Diameter.

38 Chapter Two Hydrodynamics of the Airlift Pump in Bubble and Bubbly-Slug Flow Abstract: The results and discussion of a study of the flow dynamics of a 38 mm diameter airlift pump are presented. Flow patterns ranged from dispersed bubble flow to bubbly-slug flow. The effects of initial bubble size and water quality on flow dynamics and flow pattern transition are examined. Experimental data are compared with previous two phase flow models and a new prediction equation is presented for the bubbly-slug flow regime. Introduction A typical airlift pump configuration is illustrated in figure 2.1. A gas, usually air, is injected at the base of a submerged riser tube. As a result of the gas bubbles suspended in the fluid, the average density of the two-phase mixture in the tube is less than that of the surrounding fluid. The resulting buoyant force causes a pumping action. Extensive experimental and theoretical work has been done on the airlift pump (Castro et al., 1975; Clark and Dabolt, 1986; Kouremenos and Staicos, 1985; Murray, 1980; Nicklin, 1963; Reinemann et al., 1987; Richardson and Higson, 1962; Slotboom, 1957; Stenning, 27

39 28 and Martin, 1968; Todoroki et al., 1973). These studies have been confined, however, to the slug flow regime. In slug flow, the gas phase is contained in large bubbles which nearly span the tube and range in length from the tube diameter to several times this value. These are referred to as gas slugs or Taylor bubbles. The liquid filling the space between the Taylor bubbles is referred to as the liquid slug. The liquid between the Taylor bubbles and the tube wall is referred to as the liquid film (see figure 2.2). Other flow patterns are possible in vertical gas/liquid flow. In bubble flow, the bubble diameter is much smaller than the tube diameter and the bubbles are distributed over the pipe cross section. Bubbles remain close to their initial size, and there is little interaction between bubbles (see figure 2.2). The bubble flow pattern has been largely neglected in the studies of the airlift pump because it has been assumed to be absent in the useful operating regime. Clark et ale (1985) presented a theoretical treatment of the airlift in the bubble flow regime but offers no experimental verification and does not clearly define the bubble flow operating regime. An intermediate regime referred to as bubbly-slug flow has been observed in several studies (Akagawa and Sakaguchi, 1966; Fernandes et al., 1983; Mao and Duckler, 1985; Nakoryakov and Kashinsky, 1981;

40 Nakoryakov et a1., 19B6~ 29 serizawa et a1., 1975; Shiplay, 1984). In bubbly-slug flow, small bubbles are found in the liquid slug (see figure 2.2). The presence of these bubbles is due to the region of extreme turbulence encountered at the tail of the Taylor bubble. Small bubbles are broken off of the Taylor bubble and dispersed in the liquid slug. In previous studies of bubble and bubbly-slug flow dynamics, liquid motion has been pump driven (Akagawa and Sakaguchi, 1966; Clark and Flemmer, 1985; Fernandes et al., 1983). In airlift operation the sole driving force is that developed by buoyancy. As a result of this difference, many of the previous two phase flow studies have been conducted at flow velocities much higher than those encountered in airlift operation. The objective of this study is to determine the hydrodynamics of bubble and bubbly slug flow in the range of gas concentrations and liquid velocities generally encountered in airlift pump operation. Theory Bubble Flow: The drift flux model developed from the kinetic theory of gasses by Zuber and Findlay (1965) is widely used to describe two phase flows. The velocity of the gas phase at a point is taken relative to the volumetric flux density of the two phase mixture at that point: v ' = _J' + V [2.1] -g -gj.1

41 The nomenclature and definitions used in this paper are 30 listed in table 2.1. The volumetric flux density does not, in general, correspond to the velocity of either phase but is used to represent the average velocity of the two phase mixture. The average velocity of the gas phase is obtained by taking a weighted average of [2.1J over the tube cross section: <s. Yg '> <s.!:i'> <s. Ygj'> Vg ' = E = [2.2J E E Average gas velocity in bubble flow is generally expressed in the following form: [2.3J with the distribution parameter, Cb, defined as: <E J'> Cb = --=""'""=-:- E <!:II> [2.4 J The distribution parameter takes into account the variation across the tube diameter of both the volumetric flux density and the gas concentration. If the gas concentration is higher than its average in regions of higher than average flux the parameter will be greater than one. Conversely if the gas concentration is higher than its average in regions of lower than average flux the parameter will be less than one. The value of the distribution parameter (Cb), has been found to range between 0.9 and 1.6 (Clark and Flemmer, 1985: Govier and Aziz, 1972; Nicklin, 1962: Zuber and Findlay, 1965). Values of Cb less than 1 have been found when

42 flow velocities are less than about 1 m/s. Cb is 31 generally above 1 when flow velocities are above 1 m/s. The last term on the right hand side of [2.2J is generally expressed as the rise velocity of a bubble in still fluid (Vbs'), multiplied by a correction term, (1 - ~ E), to account for reduced bubble velocity due to the presence of other bubbles (Zuber and Findlay, 1965). When average flow velocities are above about 1 meter per second, this effect is often neglected (~ = 0). For flow velocities less than 1 meter per second the value of ~ has been found to fall between 0 and 2 (Govier and Aziz, 1972; Nicklin, 1962; Zuber and Findlay, 1965). Slug Flow: In slug flow, the average velocity of the liquid in the liquid slug region can be shown to be equal to the average volumetric flux density by continuity considerations (see figure 2 2) The rise velocity of a Taylor bubble is taken as the rise velocity of a Taylor bubble in still liquid plus the velocity of the liquid encountered at the bubble tip and is set equal to the average gas velocity (Nicklin et al., 1962): Vg ' = Cs <~'> + Vts' [2.5 J The distribution parameter for slug flow, Cs, represents the ratio of the liquid centerline velocity to the average liquid velocity in the slug. Several workers have found that the distribution parameter assumes a value of about 1.2 when the Reynolds number is

43 32 above about 8000 (Bendiksen, 1985; Govipr nnct ~~i~_ 1972; Nicklin et al., 1962). This is approximately equal to the theoretical ratio of centerline to average velocity in turbulent pipe flow. Bubbly-Slug Flow: The results of detailed local gas concentration and liquid and bubble velocity measurements in bubbly slug flow are summarized in figure 2.3 (Akagawa, 1964); Akagawa and Sakaguchi, 1966; Nakoryakov and Kashinsky, 1981; Nakoryakov et al., 1986; Serizawa et al., 1975). The maximum gas concentration has been found to occur at a distance of 3 to 5 mm from the tube wall for tube diameters of 15 to 80 mm. This corresponds approximately to the average diameter of the small bubbles in the liquid slug. The velocity of the small bubbles in the liquid slug at the tube center is slightly higher than the velocity of the Taylor bubble. The region just ahead of the tip of the Taylor bubble can, therefore, be expected to be essentially free of small bubbles. The small bubbles near the tube wall move with a velocity equal to or slightly less than that of the Taylor bubbles. These bubbles either migrate into the liquid slug and rejoin the preceding Taylor bubble, or stay near the tube wall and combine with the following Taylor bubble. Because of the small bubbles in the liquid slug, the effective tube area available for liquid flow is less than the total tube cross section. The velocity of

44 the liquid at the tip of the Taylor bubbles in bubblyslug flow is, therefore, different from that found in a 33 slug flow free of small bubbles. The drift flux model can be used to take into account the effect of the small bubbles on the average liquid velocity in the liquid slug. Equating the volumetric fluxes entering and leaving the control volume abcd yields (see figure 2.2): [2.6J Retaining the physical interpretation that the rise velocity of a Taylor bubble is equal to the velocity of the liquid encountered at its tip plus its rise velocity in still liquid, the velocity of the Taylor bubble can be expressed as: <JI> - <Ygs' ~s>j Vt' = Cbs [ + Vts' [ 2 7 J 1-E s The coefficient Cbs corresponds to the ratio of the liquid centerline velocity to its average value in the liquid slug. Assuming that the average velocity of the gas in the liquid slug is approximately equal to the velocity of the Taylor bubble, the average gas velocity in bubbly-slug flow can be expressed as: V g ' = Cbs<J'> + Vts' (1-Es) 1 + (Cbs-1)Es [2.8J In the experimental work of Fernandes et al. (1983), it was found that the average gas concentration in the liquid slug, ES' in bubbly-slug flow was about 0.27 and did not vary significantly when flow parameters were

45 34 changed. The liquid velocity profile in bubbly-slug flow is similar to those found in turbulent single phase flows. The distribution parameter can therefore be expected to be about 1.2. The denominator of [2.8] is then expected to be about The submergence ratio is a parameter commonly found in airlift analysis and is defined as: Q = [2.9] The submergence ratio is equal to the average pressure gradient along the riser tube which is made up of components due to the weight of the two phase mixture and frictional losses. In bubble flow, the frictional loss is generally taken as the product of the single phase frictional losses based upon the mean liquid velocity and a two phase correction factor. Clark (1985) suggests ( E) for the two phase correction factor. In slug flow the frictional effects in the film around the gas slug are generally neglected and the single phase frictional component is multiplied by the fraction of the tube filled with liquid (I-E). In bubbly slug flow, the single phase frictional loss must also be multiplied by the two phase correction factor, ( Es), due to the bubbles in the liquid slug. Assuming that the average gas concentration in the liquid slug is about 0.27, the correction factor is equal to about 1.5.

46 The single phase frictional pressure gradi8nt can be written as: 35 F = f/2 <J:,>2 [2.10J Where the friction factor, f, is obtained from (Giles, 1962): f = ReO. 25 [2.11J Thus for bubble flow: cr = (1 - E) + ( E)F [2.12J and for bubbly slug flow: cr = (I-E) (1+1.5F) [2.13J For a given tube diameter, imposing the gas flow rate and the submergence ratio, the liquid flow rate may be determined using the system of equations summarized in table 2.2. Experimental Procedure The experimental apparatus consisted of a circular loop of glass tubing (38 mm ID) with a 34 liter reservoir (See figure 2.4). The riser tube was 2.35 m in length. Volumetric air and water flow rates, submergence, and lift height were measured after the flow stabilized for each trial. Calibrated orifices were used to measure air and water flow rates. The gas concentration in the riser tube was determined from the measured gas and liquid flows, and submergence ratio and equation [2.12J or [2.13J, depending on the flow pattern.

47 Air was injected into the system by a rotary vanq 36 type compressor. Air flow rate was controlled by a valve between the compressor and the air flow measurement orifice. Two different diffusers were used; 1) An aquarium air-stone which generated bubbles of 1 to 3 mm diameter, and 2) a 6 mm diameter tube which generated bubbles of 10 to 15 mm diameter. The airstone produced the bubble flow pattern when the gas concentration was low and the bubbly slug pattern when the gas concentration was above some critical value, which depended on the water type. The 6 mm tube produced the bubbly slug pattern for both water types and at all gas concentrations. Note that it was not possible to produce the slug flow pattern, i.e., without small bubbles, for any of the test conditions. The static head at the pressure tap immediately before the riser tube was used as a reference level in determining lift height and submergence (See figure 2.4). By using this pressure as a reference, frictional losses in the liquid return lines and across the flow measurement orifice were separated from the riser-tube flow measurements. Tap water and waste water from an aquaculture facility were the liquids used. Water quality parameters were determined by standard analytic procedures at the Cornell University Agronomy lab (see table 2.3).

48 37 Results and Discussion Regression analysis of both the bubble and bubblyslug flow data showed no significant difference in flow dynamics between the two gas diffusers or the two water types. Differences were noted, however, in the critical gas void ratio for transition from bubble to bubbly-slug flow for the two water types, as discussed below. Regression of the combined bubble flow data yielded the following equation (see figure 2.5): Vg ' = 0.62 <J'> (1-1.4E) [2.14] (coefficient of correlation, R 2 = 0.57) in agreement with the theoretical form of [2.3]. The results of the bubble flow data regression are significantly different than those suggested by Clark et al., (1985) (Cb = 1.2, ~ = 0). Regression of the bubble flow data in the form suggested by Clark et al., (1985), with no dependence on the gas concentration resulted in considerably reduced accuracy (Cb = 0.32, ~ = 0, R 2 = 0.21). Thus, including the correction on Vbs due to the presence of other bubbles as suggested by Nicklin et al., (1962), considerably improves the accuracy of prediction. The prediction equation used by Clark et al., (1985) was obtained from bubble flow data in which the liquid motion was forced by a pump. He considered flow velocities in the range of 1 to 5 m/s. In airlift pump operation, buoyancy is the sole driving force. In order

49 38 to increase the buoyant driving force the gas concentration of the two phase mixture must be increased. If the gas concentration is increased beyond a certain point, however, slugging occurs and flow dynamics change. Thus, flow velocities are limited in the airlift pump in the bubble flow regime. In the present study average flow velocities ranged from 0.1 to 0.3 mls in the bubble flow regime. When flow velocities are high, the rise velocity of the bubble in still liquid, (Vbs), becomes negligible in relation to the average flow velocity. The accuracy of the bubble flow model is therefore very insensitive to the value chosen for the bubble rise velocity (Vbs), and depends mainly on the choice of the distribution parameter Cb. When flow velocities are reduced, however, the bubble rise velocity in still liquid becomes significant and prediction accuracy depends upon the proper choice of this value. The distribution parameter found in this study is considerably lower than that recommended by Clark et al., (1985). It has been observed by several workers, that in low velocity vertical bubble flow, the maximum concentration of bubbles occurs near the tube wall (Akagawa, 1964; Akagawa and Sakaguchi, 1966; Nakoryakov and Kashinsky, 1981; Nakoryakov et al.,1986; Serizawa et al., 1975). This is also a region of lower than average flow velocity. It is therefore expected that the

50 distribution parameter (Co) should assume a value less 39 than one. As flow velocities increase the bubble concentration profile assumes a parabolic shape with its maximum at the pipe center. Thus for high speed flows Co would be expected to be above 1, as observed by Clark et al. (1985). When the slug flow model is applied to bubbly slug flow data, it predicts average gas velocities consistently higher than the experimental values (see figure 2.6). Regression analysis of the bubbly-slug data showed no significant difference in flow dynamics between water or diffuser types. Regression of the combined bubbly-slug flow data yielded the following equation: v' g = 1.1 <J'> Vts' [2.15] (R 2 = 0.90) which follows the form of [2.8]. The results of the bubbly-slug flow data regression agree well with the model presented above for the bubbly-slug flow pattern. The bubbly slug model is also very close to the empirical relationship used by Hills (1976), for average gas velocity in buoyancy driven bubbly-slug flow in a 150 mm diameter tube 10.5 meters long. Thus, the equation presented here is valid for tube of larger diameter and greater length. It has been shown (Reinemann et al., 1987) that the slug flow model works well for describing airlift pump

51 40 performance when the riser tube diameter is less than 20 mm and a correction is made for the effects of surface tension on the rise velocity of the Taylor bubble in still liquid (Vts). Increased surface tension also acts to suppress bubble breakup for tubes in this size range. Small bubbles are less easily shed from the Taylor bubbles and true slug flow results. When the tube diameter is greater than 20 mm, small bubbles are more easily shed from the tail of the Taylor bubbles and bubbly-slug low results. It has been speculated by Nicklin (1963), that for long airlifts, the bubble and bubbly-slug flow patterns are encountered only in the developing flow region. Based on the results of this study and other vertical air/water slug flow studies, it is doubtful that true slug flow will ever exist in the airlift pump with the exception of small diameter (D < 20 mm) riser tubes. Previous studies of the airlift pump have concluded that slug flow would develop regardless of the method of introducing the gas. It has been demonstrated in this study that a region of stable bubble flow exists for airlift pumps. The first requirement for bubble flow to exist is that the gas is introduced as bubbles much smaller than the riser tube diameter. The second requirement is that the gas concentration is below some critical value. Above this critical gas concentration, bubble collision and coalescence occurs. If the bubbles

52 41 increase in size to form Taylor bubbles the transition from bubbly to bubbly slug flow occurs. Flow pattern maps are commonly presented to predict two phase flow behavior. In most two phase flow applications the air and liquid flows can be independently determined. In airlift pump operation, however, for a given air flow volume and submergence ratio, the liquid flow is fixed. The possible operational regime of the airlift pump is, therefore, a subset of the conventional flow pattern map (see figure 2.7) The upper limit of the airlift operational regime has been determined for a 38 mm diameter airlift with 100% submergence. No useful pumping work is being performed in this configuration since there is no lift provided. There are some practical applications, however, such as the mixing or aeration of liquids. The right hand boundary of the bubble flow regime is defined by the critical gas concentration for the transition form bubble to bubbly-slug flow. When tap water was used, a transitional gas concentration of 0.25 provided an accurate criteria for transition for bubble to slug flow. When the waste water was used the transitional gas concentration increased to Small amounts of surface contaminants have been shown to affect the stability of bubble surfaces (Keitel and Onken, 1982). The following effects indicative of

53 42 surface contamination were observed when the waste water was used: 1) The stable bubble size in the flow was slightly lower than that in tap water. 2) The bubbles were more spherical in shape than those in tap water. 3) The transitional gas concentration was higher than in tap water. These surface effects could explain the large variation of transitional gas concentrations found in the literature. Conclusion Equations have been presented to describe operation of the airlift pump in bubble and bubbly-slug flow. The effect of small bubbles dispersed in the liquid slug on the average gas velocity in bubbly-slug flow has been accurately predicted. The stable operating regimes for bubble and bubbly-slug flow have been identified. The transition from bubble flow to bubbly-slug flow was found to be sensitive to gas/liquid surface contamination. Surface contamination did not however significantly influence flow dynamics. Due to bubble breakup and dispersal in the liquid slug, it is doubtful that true slug flow will ever exist in the normal operating regime of airlifts with the exception of narrow diameter tubes (D < 20 mm, for air/water systems).

54 43 D = pipe diameter [LJ Table 2.1 Nomenclature and Definitions 7f D 2 2 A = pipe cross sectional area = -4- [L J X Point Quantity * <x> = average over tube cross section = l/a f X da Qg = volumetric flow rate of gas [L 3 /TJ ** Ql = volumetric flow rate of liquid [L 3 /TJ ~ = volumetric flux density of the mixture [L/TJ <~> = average volumetric flux density of the mixture Ql + Q g = [L/TJ A ~ = point volumetric gas concentration [OJ E = average gas concentration in riser tube [OJ ~s point gas concentration in liquid slug [OJ ES = average gas concentration in liquid slug [OJ Yg = point velocity of gas [L/TJ *** Q g V g = average gas velocity in riser tube =-- [L/TJ A E Ygj = velocity of gas relative to volumetric flux density [L/TJ Ygs = velocity of gas bubbles in liquid slug [L/TJ Yls = velocity of liquid in liquid slug [L/TJ Vt = Velocity of Taylor bubble [L/TJ Vts = Velocity of Taylor bubble in still fluid [L/TJ z 0.35 (g D)1/2 for tube diameters greater than 20mm Vbs = rise velocity of small gas bubbles in still fluid [L/TJ z 0.25 mls in air water systems considered Re = Reynolds number = <J> D v v [OJ = kinematic viscosity of liquid [L 2 /TJ ~ = submergence ratio [oj Zl lift height [LJ Zs submergence [LJ

55 F = frictional head loss gradient expressed in meters of fluid (pressure) per meter of pipe length [OJ f = friction factor [OJ g = acceleration due to gravity [L/T 2 J Cb, Cs, Cbs = distribution parameter for bubble flow, slug flow, and bubbly-slug flow [OJ * Underlined quantities depend on position. ** Dimensionless volumetric flow rates are obtained by dividing flow rate by A (g 0)1/2 [L3/TJ, and are primed (e.g. Ql', Qg'). *** Dimensionless velocities are obtained by dividing velocity by (g 0)1/2 [L/TJ, and are primed (e.g. Vts'). Table 2.2 Summary of Airlift Equations Bubble Vg, = 0.6 <~'> + Vbs' (1-1.4E) Flow ex = (I-E) + (1+1. 8E) F Bubbly- V g, = 1.1 <~'> Vts, Slug Flow ex = (l-e) (1+1. SF) For all Flow patterns 44 Qg + Ql f <~,> <~'> = F = f = A(g D)' 2 Re 0.25 (Ql + Qg)D Zs 0.25 m/s Re, = ex = Vbs'= Vts = 0.35 A v Zl+Zs (g D)! (0 > 0.02 m) Table 2.3 Water Quality Parameters Tap Water Waste Water ph BOD (mg/l) Suspended Solids conductivity (~mho/cm) chloride (mq/l)

56 45 +-AIR INPUT Figure 2.1. Typical Airlift Pump.

57 b e f i=i-u::= l.i::::i-i d c h g OJ 01 OJ 01 BUBBLE FLOW BUBBLY SLUG FLOW SLUG FLOW Figure 2.2. Flow Patterns.

58 ~ local BUBBlE VElOCITY IN UQU/D SlU~ It: w I W ~ 0.5 4: It: 4: ll LOCAl.. UQUID VELOCITY IN UQUID SlUG (\IIs')" ~ LOCAl.. GAS CONCENTRATION IN UQUID SLUG (Es) " RADIAL POSITON (r/r) Figure 2.3. Local liquid slug gas void ratio, bubble and liquid velocities in bubbly-slug flow.

59 48 LIQUID PRESSURE TAPS /"-. LIFT, ZL RISER TUBE AIR FLOW ORIFICE L LIQUID FLOW ORIFICE MANOMETER COMPRESSOR Figure 2.4. Experimental Apparatus.

60 49 --, b B BUBBLE FLOW, TAP WATER b b B / 0.6 / 0.5 b BUBBLE FLOW, WASTE WATER b..j ~ z w 0.4 ~ B Il Vg' = 1.1 <J') + 0.4!b rp B w Il. X w 0.3 (JI > Vg' =0.62 <J') t 0.44 (1-1.4E) B f r---...,-----r------r ~ Vg' PREDICTED Figure 2.5. Bubble Flow Data. Experimental vs. predicted Average Gas Velocities.

61 ljl > BUBBLY SLUG UOOEL Vrf = 1.1 <JI) Vts' S' so S = SLUG FLOW, TAP WATER s = SLUG FLOW, WASTE WATER = SLUG FLOW, TAP WATER, NO DIFFUSER <J') Figure 2.6. Bubbly-Slug Flow Data. Average Gas Velocity vs. Average Mixture Velocity.

62 ~ mm rube ~ o -' II. o J o J III III W -' Z o III Z W Z Q '; SUBMERGENCE d. I.;. 00 ~ ' E = ~ E = 0.3 o BUBBLE FLOW + 0 BUBBLY-SLUG FLOW o o o 0.1 O , ~ r,.. r.-., r DIMENSIONLESS GAS FLOW (Og') Figure mm Diameter Tube Flow Pattern Map.

63 Chapter Three Oxygen Transfer in Airlift Pumping Abstract: The results of an experimental study of the oxygen transfer properties of a 38 mm diameter airlift pump are presented. The effects of varying initial bubble size, flow rate, flow pattern, and water quality on oxygen transfer are examined. A model to predict oxygen transfer in airlift pumping is presented. Introduction The airlift pump has been of practical use as a pumping device for many decades (see figure 3.1). It has been reported that the famous Roman water distribution system used airlifts 2000 years ago. Airlifts also found application in removing water from mines in the late 1800's. The first recorded pumping studies were performed at that time and have continued to the present. Airlifts have become popular in the aquaculture industry and in waste water treatment plants where large volumes of water must be both circulated and aerated. Several studies have been done on the aeration properties of the airlift (Nagy, 1979; Zielinski et al., 1978) but no theory or predictive equation for oxygen transfer rates were given. 52

64 53 The flow dynamics of the airlift pump have been described previously (Reinemann et al., 1987). Complicating the prediction of the hydrodynamics of the airlift is the fact that there are two flow patterns possible in airlifts when tube diameters are greater than about 20 mm. When the initial bubble size is much smaller than the tube diameter and the gas void ratio is low, the bubble flow pattern results. Small bubbles are distributed over the pipe cross section. Bubbles remain close to their initial size, and there is little interaction between bubbles (see figure 3.2). If the gas void fraction is above some critical value, coalescence occurs and bubble size increases. Bubbles with average diameter greater than about 0.7 times the riser tube diameter are referred to as gas slugs or Taylor bubbles. The presence of Taylor bubbles only is referred to as the slug flow regime. The slug flow regime has been found to occur only when the riser tube diameter is below 20 mm (Reinemann et al., 1987). In the bubbly-slug flow regime, small bubbles are found suspended in the liquid slug between the Taylor bubbles. The presence of these bubbles is due to the region of extreme turbulence encountered at the tail of the Taylor bubble. Small bubbles are broken off of the tail of the Taylor bubble and dispersed in the liquid slug. Experiments were performed in both the bubble flow and bubbly slug flow regimes to determine if any

65 54 significant difference existed between the gas transfer properties in these two regimes. The equation most commonly used to describe gas transfer in gas/liquid dispersions is (Barnhart, 1969: Clark, 1985: Colt and Tchobanoglous, 1981: Nagel et al., 1977) : e - KIa t [3.1] where Ci = initial gas concentration (mg/l) Cs saturation gas concentration (mg/l) C = gas concentration at time t (mg/l) KIa = gas transfer coefficient (s-l) t = gas/liquid contact time (s) The gas transfer coefficient is a function of the rate of molecular diffusion of gas in the liquid, the gas/liquid surface area per liquid volume and the degree of turbulence in the flow. The gas transfer coefficient is commonly given as a function of the pipe Reynolds number for two phase flow (Clark, 1985; Kubota et al., 1978: Lin et al., 1976: Nagel et al., 1977: Shilimkan and stepanek, 1977). The Reynolds number is a measure of the degree of turbulence encountered in the flow. The degree of turbulence influences both the gas/liquid surface area and the transfer rate across the surface.

66 The Reynolds number for gag/liquid pipo flow ig 55 calculated as (Govier and Aziz, 1972): where Re=~ [ 3 2 ] v Vm = average velocity of two phase mixture given by: [ 3 3 ] Ql = volumetric liquid flow rate (m 3 /s) Qg volumetric gas flow rate (m 3 /s) A = pipe cross sectional area (m 2 ) D = pipe diameter (m) v = kinematic viscosity of liquid (m 2 /s) studies have been done on mass transfer in two phase gas/liquid pipe flow (Clark, 1985; Kubota et al., 1978; Shilimkan and stepanek, 1977;). These studies do not directly apply to airlift operation, since the flow speeds encountered in airlifts (Vm < 1 m/s), are much lower than those encountered in these studies (1 to 10 m/s). It has been shown that the results of high speed two phase flow studies cannot always be extrapolated into the slower flow regimes of the airlift (Reinemann et al., 1987). The hydrodynamics and gas/liquid surface area of two phase flow can change considerably as flow speed increases. Both of these factors influence the gas transfer coefficient. The objective of this study is to determine oxygen transfer coefficients for the

67 flow patterns and flow velocities encountered in airlift pump operation. 56 ~xperlmental ~rocedure The test apparatus consisted of a circular loop of 38 mm glass tubing with a liquid reservoir (See figure 3.3). The total volume of the system was approximately 34 liters. The circuit was closed to the atmosphere except for a gas outlet at the top of the riser tube. Air was injected at the base of the riser tube. An aquarium air stone was used to produce bubbles from 1 to 3 mm in diameter. This is the bubble size associated with commercial fine bubble aerators. The diffuser produced the bubble flow pattern at low gas flow rates, and bubbly-slug flow at higher gas flow rates. A single 6 mm glass tube was used to produce large gas bubbles and the resulting bubbly-slug flow pattern at all gas flow rates. Air and water flows were determined by means of pressure drop measurements across calibrated sharp edged orifices. Tap water and waste water from an intensive water reuse aquaculture system were the liquids used to examine the effects of contaminants in the liquid. Water quality parameters were determined by standard analytic techniques at the Cornell University Agronomy lab (see table 3.1). Sodium sulfite with a cobalt catalyst was used to remove all oxygen from the tap water. The aquaculture

68 waste water was allowed to stand for 5 day9 in a clo9gd container to allow the resident BOD to reduce the 57 dissolved oxygen level. The pump/reservoir system was filled with a measured quantity of deoxygenated water and the pump was started. Dissolved oxygen measurements were taken with a YSI meter at 30 second intervals beginning from the initiation of a run until saturation was reached. Liquid temperature was also recorded for each run. A typical raw data set is shown in figure 3.4. The system gas transfer coefficient was determined by regressing the left hand side of [3.4] vs. time: In l~: = ~j = - KIa' t [3.4] where Kla'= system oxygen transfer coefficient (s-l) The system gas transfer coefficient relates to the gas/liquid contact area per total system liquid volume. The oxygen transfer coefficient for the airlift pump alone relates to the gas/liquid contact area per liquid volume in the airlift pump riser tube. The airlift pump gas transfer coefficient is therefore determined as follows: KIa = KIa' ~ [3.5] V r

69 58 where V s total liquid volume in the system Vr = liquid volume in the riser tube (see figure 3.5) correction was also made to adjust all Kla values to standard temperature conditions (20 C). The temperature correction used was (Barnhart, 1969); where Kla (T) Kla(20) = (j (T-20) [3.6] T = temperature (OC) Kla(T) = gas transfer coefficient at temperature T Kla(20) = gas transfer coefficient at standard temperature (20 C) (j = Results and Discussion Regression analysis of the gas transfer coefficient as a function of the pipe Reynolds number showed no significant difference between water type, flow pattern or diffuser type (See figure 3.6). The data was therefore pooled. Regression of the entire data set yielded the following empirical correlation for the oxygen transfer coefficient (R 2 = 0.92, std. err. of estimate = 0.009) : Kla(20) = 6.5xIO- 6 Re [3.7] The gas/liquid surface area in the bubbly-slug regime is less than that in the bubble flow regime.

70 59 This tends to reduce the gas transfer rate. The increased turbulence at the gas slug tail, however, tends to increase gas transfer. These two effects thus compensate for one another and the gas transfer rate remains unchanged for the two flow regimes. While the degree of surface active substances present in the waste water produced an observable change in the flow characteristics, the gas transfer rate was not significantly reduced. contaminants on the gas/liquid surface tend to reduce the gas transfer rate. The bubble size is slightly reduced, however, increasing the gas/liquid surface area. These two effects combined to yield no significant change in the gas transfer rate between waste water and tap water. When tap water was used, the bubbles in the developed region were elliptical with mean diameter of 2-3 mm. Coalescence was observed for gas void fraction above about When the waste water was used the bubbles were spherical with average diameter of 1-2 mm. Coalescence was not observed for waste water until the gas void fraction was over This effect has been documented previously and is caused by surface active agents attaching to and stabilizing the bubble surface (Keitel and Onken, 1982). The oxygen transfer for the airlift pump operating in bubble and bubbly-slug flow can be described by [3.1J, [3.6J and [3.7J. The gas/liquid contact time can

71 be expressed as the average liquid velocity divided by the length of the riser tube: [ 3 8 J where Z = length of riser tube (m) VI = average liquid velocity (m/s) given by: 60 VI = QI I A (I-E) [3.9J QI = liquid volumetric flow rate (m 3 /s) A = pump cross sectional area (m 2 ) E = gas volumetric void ratio Conclusion Oxygen transfer was not significantly affected by flow pattern, initial bubble size, or the wastes present in the water studied. Wastes in the water did however influence the transition from bubble to slug flow. An empirical correlation is presented relating the oxygen transfer coefficient (Kla(20)), to the two phase pipe Reynolds number. It is not advantageous to use a small pore gas diffuser to increase gas transfer in airlift pumps. Reducing the orifice size increases the pressure drop across the diffuser and the gas transfer rate will not increase.

72 61 Table 3.1 Water Quality Parameters Tap Water Waste Water ph BOD (mgjl) Suspended Solids(mgjl) conductivity(~mhojcm) chloride (mgjl)

73 62.-AIR INPUT Figure 3.1. Typical Airlift Pump.