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ABSTRACT THE EFFECT OF SEPARAN AP-30 ON THE PERFORMANCE OF A 10mm HYDROCYCLONE By Glen Eugene Thomas Present understanding of secondary flow structures within hydrocyclones is insufficient to accurately predict the critical design parameters necessary in many hydrocyclone applications. In this study, an attempt to alter these flow patterns was made by adding small amounts of a high molecular weight polymer to the feed stream of a l0mm hydrocyclone. The resulting effects on the capacity and split ratio were measured. Also, the separation efficiency for kaolinite clay particles (ml micron in size) was examined for different polymer-clay—water suspensions having identical concen- trations. The results showed that the polymer significantly decreased the underflow stream and either increased or decreased the separation efficiency depending on the solution mixing strategy. THE EFFECT OF SEPARAN AP-30 ON THE PERFORMANCE OF A 10mm HYDROCYCLONE By Glen Eugene Thomas A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Chemical Engineering 1982 To my parents -and- To my wife, Barbara ii ACKNOWLEDGMENTS The author gratefully acknowledges the guidance and editorial assistance of Dr. Charles Petty. Funds for this research were provided by the National Science Foundation grant no. 71-1642 and by the Division of Engineering Research, Michigan State University. This assistance is gratefully appreciated. Special appreciation is also expressed to my wife, Barbara, for her encouragement and help in the completion of this thesis. iii TABLE OF CONTENTS Page LIST OF TABLES . . . . . . . . . . . . . . . vi LIST OF FIGURES . . . . . . . . . . . . . . . vii LIST OF NOTATIONS . . . . . . . . . . . . . . x Chapter l. INTRODUCTION . . . . . . . . . . . . . l 2. BACKGROUND . . . . . . . . . . . . . . 3 2.l The Hydrocyclone . . . . . . .. . . . 3 2.l.l Capacity . . . . . . . . . . . 6 2.l.2 Split Ratio . . . . . . . . . . 9 2.1.3 Efficiency . . . . . . . . . . l0 2.2 Polymer . . . . . . . . . . . . . l4 2.3 Clay . . . . . . . . . . . . . . l6 '3. EXPERIMENTAL APPARATUS . . . . . . . . . . 22 ' 3.l Flow Loop . . . . . . . . . . . . . 22 3.2 The Hydrocyclone . . . . . . . . . . 24 4. EXPERIMENTAL PLAN AND PROCEDURE . . . . . . . 29 5. RESULTS AND DISCUSSION . . . . . . . . . . 36 5.l Flow Characteristics Without Polymer Additives . . . . . . . . . . 36 5.2 Flow Characteristics With Polymer Additives . . . . . . . . . . 45 5.3 Separation Characteristics With and Without Polymer Additives . . . . . . 53 iv Chapter 6. CONCLUSIONS AND RECOMMENDATIONS Appendices A. VISCOSITY AND FRICTION FACTOR MEASUREMENTS A.l Apparatus . . ,. . . A.2 Procedure and Results for Viscosity Measurements . . A.3 Procedure and Results for Drag Reduction Measurements A.4 Summary EXPERIMENTAL DATA . Page 62 66 67 67 72 84 85 Table 2.l LIST OF TABLES Values of X for Various Size Hydrocyclones Mixing Strategies Studied Parameters Investigated in This Study The Effect of Back Pressure on the Capacity and Pressure Loss Coefficients . Design Parameters for the Capillary Viscosities Measured Using the Small Capillary Tube . . Experimental Data for Fully DeveIOped Laminar Flow of a Fluid in a Circular Pipe . Experimental Data for Fully Developed Turbulent Flow of a Fluid in a Circular Pipe Experimental Data for Six l0mm Hydrocyclones Performance Data for a l0mm Hydrocyclone vi Page 31 34 47 69 7O 86 87 88 89 Figure 2.l 2.2 5.1 5.2 5.3 5.4 5.5 5.6 LIST OF FIGURES A Typical Hydrocyclone and its Flow Pattern . A Schematic of the Definition of Centrifugal Efficiency Used in this Study . . The Chemical Structure of Separan AP-3O The Structure of Kaolinite Clay . The Mechanism of Adsorption of Two Poly- electrolytes on Kaolinite . . Schematic of Flow Loop . Flow Through A Manifold of Six lOmm Hydrocyclones . . . . . . . Nominal Dimensions of the Doxie 5 Dorrclone . . . . . . . . . Connection of the Dorrclone with the Flow Loop Photographs of the Dorrclone Connections and Cluster Design . . . . . The Effect of Pressure Drop on the Capacity of Six 10mm Hydrocyclones . . . . . The Effect of Reynolds Number on the Pressure Loss Factor for a Single l0mm Hydrocyclone Free Vortex Model for Pressure Loss Coefficient The Effect of Pressure Drop on the Underflow and Overflow Rates of Six 10mm Hydrocyclones . The Effect of Reynolds Number on the Split Ratio The Effect of Back Pressure on the Split Ratio . vii Page 12 15 18 20 23 25 26 27 28 37’ 39 4O 41 43 44 Figure 5.7 The Effect of Polymer on the Capacity of Six l0mm Hydrocyclones The Effect of Polymer on the Pressure Loss Factor for a Single lOmm Hydrocyclone . The Effect of Polymer on the Split Ratio The Effect of Polymer Concentration on the Split Ratio for AP §_50 psi . . . I The Effect of Polymer Concentration on the Split Ratio for AP‘: 50 psi . The Effect of Flow History on the Split Ratio The Effect of Mixing Strategy on the Split Ratio at AP= 40 psi . . . The Effect of Reynolds Number and Polymer 'Concentration on the Centrifugal Efficiency for a lem Hydrocyclone . The Effect of Polymer History on the Centrifugal Efficiency of a l0mm Hydrocyclone . . . . . The Effect of Severe Polymer Degradation on the Centrifugal Efficiency of a l0mm Hydrocyclone . . . . . . . . The Effect of Mixing Strategy II on the Centri- fugal Efficiency of a lem Hydrocyclone Friction Factor for Laminar Flow Friction Factor for Fully Developed Turbulent Pipe Flow . . . . . . . Transient Behavior of Various Polymer Mixtures in Turbulent Pipe Flow The Effect of Clay Concentration on Polymer Degradation in Turbulent Pipe Flow . . The Effect of Shearing Time on Drag Reduction . . . viii Page 46 49 50 SI 52 54 55 57 58 6O 6T 74 75 77 79 BI Figure. Page A.6 The Effect of Clay Concentration on Drag ‘ Reduction . . . . . . . . . 82 A.7 The Effect of Polymer Ageing on Drag Reduction . . . . . . . 83 ix AH AH AHM Kl LIST OF NOTATIONS concentration of the polymer or clay the diameter of the capillary tube used for friction factor measurements in Appendix A the diameter of the hydrocyclone the diameter of the feed (inlet) orifice in the hydrocyclone the diameter of the overflow (vortex) orifice in a hydrocyclone the diameter of the underflow (apex) orifice in the hydrocyclone centrifugal efficiency as defined in Equation_2.l Fanning friction factor used in Appendix A as defined by Equation A.7 the acceleration due to gravity used in Appendix A the pressure loss coefficient as defined by Equation 5.3 the pressure loss coefficient as defined by Equation 5.3 but based on the underflow stream the height differential for a manometer used in Appendix A the height differential for a cc£4 manometer used in Appendix A the height differential for a mercury manometer used in Appendix A a proportionality constant defined by Equation 2.l; also Equation A.2 in Appendix A a proportionality constant related to K AP W W the length of the hydrocyclone; also the distance between the pressure taps in Appendix A a dimensionless group defined by Equation 5.4 based on ReF and hydrocyclone dimensions the difference between the feed PF and overflow Po pressures on the hydrocyclone; also the difference in pressure between the two pressure taps on the capillary tube in Appendix A the feed pressure on the hydrocyclone the overflow pressure on the hydrocyclone the underflow pressure on the hydrocyclone the volumetric flow rate through the capillary tube in Appendix A the volumetric flow rate into the feed of a hydro- cyclone the volumetric flow rate exiting the overflow of a hydrocyclone the volumetric flow rate exiting the underflow of a hydrocyclone the radius of the capillary tube in Appendix A the Reynolds number for the capillary tube in Appendix A the Reynolds number for the feed (inlet) conditions the bulk average velocity of the fluid inside the capillary tube in Appendix A the bulk average velbcity of the fluid entering the hydrocyclone mass flow rate of fluid in the capillary tube in Appendix A the mass flow rate entering the hydrocyclone the mass flow rate exiting the overflow of the hydrocyclone . xi * * No ,Hu ,NS* the mass flow rate exiting the underflow of the hydrocyclone hypothetical streams used to define E (see Figure 2.2) eXponent used in Equation 2.l mass fraction of solids in feed stream of a hydro— cyclone mass fraction of solids in the underflow stream of a hydrocyclone maSs fraction of solids in the underflow stream of a hydrocyclone density of water density of carbon tetrachloride density of mercury density of solids shear stress at the wall used in Appendix A to define f viscosity; also microns when discussing particle diameters xii CHAPTER I INTRODUCTION A high molecular weight polymer is added to the feed stream of a hydrocyclone in an attempt to alter internal flow structures- and to develop some additional understanding of those flow patterns which most directly affect the separation efficiency. This research extends the work of Wallace [T980] and of Dabir, et al. [1980] by examining the performance of hydrocyclones for 0.2 wt. % suspensions, which is an order of magnitude smaller than previously investigated. This avoids some of the experimental difficulties encountered earlier. Preliminary results on the effect of a small amountcHiSeparan AP-30 on the separation of kaolinite clays in a 10mm hydrocyclone investigated by Wallace and Dabir in our laboratory showed that for a given pressure drop across the hydrocyclone, the total flow rate is reduced by the presence of the polymer. Presumably, the polymer offers a large resistance to helical flow, similar to the vortex inhibition phenomenon reported by Chiou and Gordon [1976]. A slight increase in the split between the overflow and underflow rates with the addition of polymer was also noticed. Two mixing strategies for the polymer-clay-water suspensions were examined which showed significantly different separation behavior. One strategy "pre-stretched" the polymer before the addition of clay by cycling it through a small capillary tube whereas the other strategy omitted this "pre-stretching" step and added a concentrated polymer solution to a dilute clay suspension. An initial increase in the centrifugal efficiency (E) of 63% occurred for the "pre-stretched" strategy. However, the other formulation, although identical in polymer and clay concentration, showed an initial decrease of 77% in E. After about an hour of operation, the centrifugal efficiency of these two suspensions stabilized above and below the no polymer case. The objective of this research is to examine more carefully the two paradoxical mixing strategies reported earlier by Wallace and Dabir. The effects that these mixing strategies have on the capacity and split ratio are summarized in Section 5.2. Section 5.3 shows the effects of the various mixing strategies on the centri- fugal efficiency of the hydrocyclone. Also, the apparent Viscosities of the suspensions used in this investigation, as well as their drag reducing characteristics for fully developed turbulent pipe flow, were measured and reported in Appendix A. CHAPTER 2 BACKGROUND 2.l The Hydrocyclone The liquid cyclone or hydrocyclone is a processing device that uses pressure to create rotational motion in a body of fluid thus generating a centrifugal force that separates one material from another.. Basically, the hydrocyclone separator is a cylindrical/ conical shell with a tangential feed and two axial exits. A typical hydrocyclone is shown in Figure 2.1. The tangentially injected feed has sufficient velocity to create a vortex action. As the rapidly rotating liquid spins about the axis of the cone it is forced to spiral inward and out through one of the axial exits. The rotation of the fluid causes a centrifugal force field to move solid particles toward the wall. Viscous forces resist this motion and thus particle size and density are both important factors in separation. Larger, heavier particles of solid are thrown outward against the wall and spiral downward to exit at the apex of the cone with the underflow. Smaller particles may remain in the liquid as it spirals inward and upward to be discharged with the overflow. The spiraling pattern can be seen in Figure 2.l. Hydrocyclones are generally used when the particles to be removed are between 5 and 700p. A density differential between the solids and the liquid of 2.7 is also desired but not essential. 3 Q0 overflow (vortex finder) feed QF ; Qu underflow (apex) Figure 2.l. A typical hydrocyclone and its flow pattern The cleaning of pulp stock prior to the making of paper, the separa- tion of coal from shale, the recovery of catalyst from the cracked oil of a fluidized bed cracking unit are a few of the many important industrial applications mentioned by Bradley [l965]. Typically, hydrocyclones are used to recover fine coal particles, less than 0.025", from denser impurities by using water as a separating, medium. Considering that more than half of the coal mined in the United States is beneficiated and approximately 15-20% of this is lost due to inefficient coal preparation methods, a quick and easy way to recover some of the more than 1 billion tons of refuse coal (see Schmidt and Hill, l976) would be to improve the performance of hydrocyclones. I Hydrocyclones used to separate solids from liquids are known as thickeners. The range of particle sizes most common in these applications is 5 to 200 microns. Settling velocities of particles smaller than 2 microns are too low [Bradley, l965] to permit efficient separation even under the high centrifugal forces which exist in small cyclones. The range of values of centrifugal acceleration in the l0mm hydrocyclone are 500 to 30,000 times the acceleration due to gravity and possibly even higher. Because of the magnitude of this centrifugal acceleration, the effect of gravity can easily be neglected and hydrocyclones can be operated in either a horizontal or vertical position. Hydrocyclones can also be used to separate according to particle size, density and shape. This is called classification. Here, the hydrocyclone is not designed to be efficient for all. sizes, shapes or densities of solids. Instead, use of a “cut point"- is made. Particles with densities, sizes or shapes below the cut point are poorly separated. Particles above the cut point are separated with a high degree of efficiency (see Section 2.l.3)- 2.l.l Capacity The capacity of a hydrocyclone is determined by the pressure drop across the unit. The pressure drop is defined as the pressure difference between the feed stream and the overflow stream. This is the most convenient due to the normal predominance of the overflow rate over the underflow rate and the fact that the overflow in many applications remains the process stream. Pressure drop in this case includes entry and exit losses. A number of papers have attempted the theoretical approach of fluid mechanics with the intention of deriving general relation- ships from momentum balances for hydrocyclones. These are unfor- tunately very complex and include, from integration operations, two or three constant coefficients, which have to be determined empirically, despite some simplifying assumptions intended to bypass the mathematical difficulties. Many workers adopted the pragmatic approach of correlation, changing one factor at a time and trying to isolate its effect. Because of the large number of variables and their mutual interaction, this method was limited to narrow ranges of variables and led to inconsistent results (see Dahlstrom, l949;and, Hatschke and Dahlstrom, I958). On a more simplistic view, the total flow rate,(h:.can be arelated to the operating pressure drop, AP, by the following equation: _ X QF — K(AP) (2.1) where K depends on each new design. Although this formula is severely limited to a particular hydrocyclone fluid and solid system, it has one major advantage. By plotting 0F versus AP on a log-log plot, the values of K and X are easily determined. The value of X should be relatively independent of the particular hydrocyclone and thus comparison with other results is meaningful. Table 2.1 gives a list of the exponent values obtained by others. Note the good agreement shown for various size hydro- cyclones. Also, it is interesting to observe that as the hydro- cyclones decrease in size the value of the exponent increases. TABLE 2.1.--Va1ues of 'X' for Various Size Hydrocyclones Source Size (DC) Exponent (X) Kelsall [1953] 3 inch 0.416 Bradley & Pulling [1959] 3 inch 0.425 Mitzmager & Mizrahi [1964] 3-15cm 0.430 Pilgrim & Ingraham [1962] 3 and 15mm 0.452 Haas, et a1. [1957] 0.50 - 0.16 inch 0.44 Wallace [1980] 10mm ' 0.46 Moder and Dahlstrom [1952] did an extensive study on 3 to 7 inch hydrocyclones. They used a value of 0.5 for X and concluded that K should be broken up into two parts. These parts included a new proportionality factor, K', which was a function of the design variables and the product of the inlet diameter and the overflow diameter to the 0.9 power. Further, it was determined that K' was dependent on the split ratio and the ratio of the inlet to overflow diameters. Another important parameter that affects the capacity of a hydrocyClone is the feed stream viscosity. Even though a viscosity _ term does not enter into the relationship for pressure drop, an increase in viscosity nevertheless causes a decrease in pressure drop for the same flow rate (see Bradley, 1964, p. 142). Therefore, K in Equation (2.1) is also dependent on viscosity. Fontein, et al. [1962] also observed that a rise in viscosity produces a higher capacity at the same pressure drop. They gave the following explana- tion for this phenomenon. The medium is fed tangentially at the circumference of the cyclone and is discharged at a short distance from the center. Besides the rotational flow there is also a radial, inwardly-directed flow which is counteracted by the centrifugal force. At the same feed (tangential) velocity at the wall of the cyclone a rise in the viscosity of the medium reduces the tangen- tial velocity at a radius smaller than the wall which means there is a lower pressure drop. In other words, the tangential velocity profile is flattened. The decrease in pressure can also be shown mathematically if we assume that at least part of the pressure loss is due to a radial pressure gradient in the tangential velocity. 2.1.2 Split Ratio In phase separation applications, such as solid from liquid, or even liquid from liquid, where the object is to obtain the separate phases as free as possible from each other, it is obviously of considerable importance to split the feed into the right volumetric proportions. The term split ratio refers to the overflow rate divided by the underflow rate. Moder and Dahlstrom [1952] developed a relationship for large diameter hydrocyclones that showed a dependence on the under- flow and overflow diameters as well as the volumetric flow rate. The relationship showed an increase in the split with an increase in the flow rate with an exponent value of 0.44. Many other relation- ships for various size hydrocyclones showed no dependence on the flow rate (see Bradley, 1965, pp. 102-104). The dependence was based solely on the ratio of the underflow to overflow diameters. Experimental data from several sources indicate that the split ratio is indeed a weak function of the flow rate. Rietema [1961] has data for a small 3" hydrocyclone with an overflow to underflow diameter ratio of 1 that show a 50% increase in the split for a tenfold increase in the operating pressure. Haas, et al. [1957] have data for 10mm and smaller hydrocyclones that indicate the split is independent of the flow rate.. Kelsall [1953] did 'experiments with a 3 inch hydrocyclone with Do/Du>>1 and saw only 10 a small increase in the split with increasing flow rate. Additionally, Bradley [1965, pp. 103-104] stated that his work with small hydro- cyclones as well as that of others showed conditions where the split decreased, was constant, or increased with an increase in flow rate. Also, the volume split was independent of feed diameter, cyclone diameter, vortex finder external dimensions and wall roughness. Balanced back pressure conditions resulted in the same split as for free discharge. Viscosity of the feed stream also has an effect on the split. Bradley [1965, p. 143] shows that an increase in viscosity causes the split ratio to decrease. This decrease is most dramatic in the range of l-lO cp for feed viscosity. 2.1.3 Efficiency Defining an efficiency for the hydrocyclone is difficult. A single number is not capable of fully describing the results of a separation unless it is ideal. A hydrocyclone not only has to deliver solid as free from liquid as possible in the underflow but also has to remove as much solid from the liquid as possible in the overflow. Van Ebbenhorst Tengbergen and Rietema [1961] do an excellent job of explaining this concept and summarizing the equations found in the literature. The efficiency used in this research is taken from Kelsall [1953] but this definition is a variation of the form recommended by van Ebbenhorst Tengbergen and Rietema [1961]. The centrifugal efficiency is defined as the solids found in the underflow due to the centrifugal separation 11 force divided by the total solids capable of being affected by the centrifugal force. The basic assumption here is that the feed splits into two internal streams when it is introduced into the hydrocyclone. One of these streams accounts for all the liquid found in the under- flow and the other for all the liquid found in the overflow. Both streams have the same solids concentration as the feed. Hypothe- tically, this is the result expected if no centrifugal forces were present in the hydrocyclone. Next, it is assumed that the centri- fugal forces act only on the solids in the "overflow" stream and remove some of them to the "underflow" stream. It should be realized that this definition does not account for any particles that may be driven from the underflow stream to the overflow stream. Also, it does not account for any portion of the overflow that short circuits to the vortex finder and thus is never influenced by the centrifugal forces. Figure 2.1 expresses the foregoing idea schematically. Here WF, W0 and Wu represent the mass flow rates and XF’ X0 and Xu repre- sent the mass fraction of solids in the feed, overflow and underflow streams, respectively. 'W; and N: are the resultant streams when the internal split takes place and contain the same mass fraction of solids as the feed stream, XF' These streams do not actually exist separately within the hydrocyclone but are merely used to illustrate the definition of the centrifugal efficiency, viz., E = W '——1r- XFWo * S . (2.1) 12 hydrocyclone l— ____________ "l 2 : loverflow * l I WO ,XF I No ’Xo I H I l l * Solids removed feed 1 =: 1 WS by centrifugal I F,XFl force I l " I w *,x : u F V lunderflow 1 4,. Figure 2.2. A schematic of the definition of centrifugal efficiency used in this study. 13 Obviously, W3 and w: cannot be observed directly but these parameters can easily be related to measured ones byusing component material balances. A solids balance around control volumes 1 and 3 (see Figure 2.1) gives, respectively, * * xF w0 - xF wF - xF wu (2.2) and w*=xw-x 14*. (2.3) Therefore, Equation (2.1) can be expressed as * vi" T“ 2 iii 3::- <24» F F F u * Now Wu can be determined by a water balance around control volume 3 * inasmuch as all the underflow liquid by assumption comes from Wu. Therefore, with (1 - XF)W = (1 - XU)W u (2.5) u, the centrifugal efficiency, defined by Equation (2.1), can be calculated in terms of measured variables. The efficiency of a hydrocyclone is affected by the fluid viscosity, differences in the solid and fluid densities, the parti- cle's size and shape and, obviously, the centrifugal force generated inside the hydrocyclone. Moreover, because most solids to be 14 separated are not monodisperse, the size distribution is also an important characteristic of the solids. 2.2 Polymer The polymer used in these experiments was Separan AP-30 manufactured by the Dow Chemical Company (Midland, Michigan). It is a high molecular weight polymer (~l-3 million) made by polymeriz- ing acrylamide and carboxyl groups in a 3 to 1 ratio as shown in Figure 2.3.‘ The amide groups are essentially nonionic in solution although a small number (<0.5%) will hydrolyze to form an anionic carboxyl group. The anionic nature of the polymer is determined by the carboxyl group. In neutral or alkaline solution the polymer is classified as an anionic polyelectrolyte. HoweVer, under acidic conditions the ionization is repressed and the electrolyte assumes a nonionic character. Separan AP-30 was chosen for several reasons. It is soluble in water, although care must be taken to avoid clumping, and the polymer is not poisonous. The monomer unit however is highly toxic. Separan is also a known drag reducing agent and is difficult to completely degrade. One drawback, however, is the fact that it is a well-known flocculating agent and thus tends to agglomerate particles in solution. A straight chain Separan AP-30 molecule is ~4.lu in length depending on the molecular weight of that particular chain. Typi- cally, the concentration of clay and polymer are both 100 wppm. 6 This produced a ratio of ~1 x 10 polymer particles per clay parti— cle. This means that there are one million polymer chains to 15 C = 0 NHZ L‘— M M = 3 N = 3000 Figure 2.3.--The Chemical Structure of Separan AP-3O 16 agglomerate each clay particle. Since the clay particles are on the average ~1u in diameter, the clay particles see an endless sea of sticky polymer chains and very few clay particles. The conditions are good for flocculation to occur. -2.3 C1ay The information contained herein on the clay is designed to give the reader some background on the mechanism of flocculation between kaolinite clays and Separan AP-30. Evidence that floccula- tion could occur in this research project is discussed here. This flocculation could have a severe effect on the outcome of this research and needs to be considered carefully because agglomerated particles are larger than the individual clay particles and are easier to separate in the hydrocyclone. The clay used in these experiments was furnished by the Georgia Kaolin Company. It is a kaolinite clay which has a median particle size of ~lu. Typically, a chemical analysis yields 38% Aluminum Oxide, 45% Silicon Dioxide, 14% water and some trace elements. Clays are classified into two main groups, structured and amorphous (see Hillel, 1980). The structured clays are subclassi- fied according to their internal structure into two principal types, 1:1 and 2:1 minerals. The ratio indicates the relative number of tetrahedral to octahedral sheets in the structure. The most 17 common mineral within the 1:1 type is the kaolinite, which is used in this research. The basic layer in the crystal structure, as shown in Figure 2.4A is a pair of silicon-alumina sheets, and these are stacked in alternating fashion and held together by hydrogen bonding in a rigid, multilayered lattice which often forms hexa- gonal platelets. Since water and ions cannot enter between the basic layers, these cannot ordinarily be split. Moreover, since only the outer faces and edges of the platelets are exposed, kaolinite has a. rather low specific surface. This means that the area available for polymer interaction is lower than in other clays. Kaolinite crystals generally range in planar diameter from 0.1 to 2p with a variable thickness of 0.02 - 0.05u. Owing to its relatively large particles and low specific surface, kaolinites exhibit less plasticity, cohesion, and swelling than most other clay minerals. The unit layer formula is A24 Si4 010 (0H)8 and it has a specific gravity of 2.8. When a colloidal clay particle is more or less dry, the neutralizing counterions are attached to its surface as in Figure 2.48. Upon wetting, however, some of the ions dissociate from the surface and enter into solution (see Figure 2.4C). A hydrated clay particle therefore forms a micelle, in which the adsorbed ions are spatially separated, to a greater or lesser degree, from the negatively charged clay particles. The negative charge of the clay particles in solution was confirmed by a simple experiment (see ' Chapter 4). Together, the particle surfaces acting as a multiple 6 O /p\\\ / //\ //D\\\ l/g ’ ' I l + \ 8.4) A Sex 2? 24° \X/"/’ \K/XJK/4M\ <. /\ Rv l L : F R 1 c | 1 Free vortex . . |__.r L11 | l I :,r 2 gflzilig é dr r Pc'Pv _ Rc 2 1 2 ‘ ("R“) ‘1 '2"qu V Figure 5.3. Free vortex model for pressure loss coefficient. Q,GPM 41 I l 1 1 l l I 1 1 1 l l l l l l l l l 10 2O 30 40 50 60 70' 80 90100 Figure 5.4. The effect of pressure drop on the underflow and overflow rates of six 10mm hydrocyclones (water, 25°C). 42 cluster of hydrocyclones studied here, some unexpected features were observed, especially when a small amount of polymer is added to the feed stream (see Section 5.2). Note that Qu suddenly decreases for PF - P0 = 35 psi and then increases again but at a faster rate. For PF - Po < 20 psi, the overflow and underflow streams are very small (trickles) so the desired flow patterns inside the hydrocy- clones may not occur. Figure 5.5 shows the split ratio Qo/Qu as a function of Reynolds number and should be compared with our previous discussion in Section 2.1.2. Dorr-Oliver reports that the "natural" split for this hydrocyclone is 1.5, which is close to the maximum observed in Figure 5.5. Although the overflow and underflow discharge freely, the backpressures within the vortex finder and the apex discharge may not be balanced. This may explain the unusual behavior shown in Figure 5.5. An explanation of the dependence of Qo/Qu on ReF could possibly be developed by using 'thv visualization; however, in what follows we try to develop some additional insight by applying backpressure to the discharge streams. V Figure 5.6 shows how the addition of backpressure to overflow and underflow streams flattens the split ratio curve. ‘The value observed is 0.77 which is significantly lower than the natural split reported by Dorr-Oliver of 1.5. Constricting the overflow and underflow streams may shift the resistance to flow from the internal manifolds (see Figure 3.2) to the external valves. 44 1114— no back pressure 1.3-6 1.14- 3 O’ \ O O’ .9-w P ,P = 10,] a (O u) ( 0) (1817) (26,23) 0 o 0 U ° (“W ~7‘” variable back pressure, constant valve setting .5 l 1 1 i v 0 20 40 60 80 100 PF’ ps1g Figure 5.6. The effect of back pressure on the split ratio ‘ (water, 25°C). 45 Table 5.1 shows various results for the effect of back- pressure on the capacity, split ratio,and pressure loss coefficient for both polymer and water. Unequal backpressure (Po f Pu) is also investigated. Experiments 1, 2 and 10, 11 indicate that the over- flow offers less resistance to flow due to its lower loss coeffi- cient Gu (see Notation). Additionally, the loss coefficient is increased with the addition of polymer (see also, Figure 5.9).- Table 5.2 shows how an increase in viscosity (due to a decrease in temperature) decreases the loss factor Go and decreases the split ratio. This is an important result and it agrees with the literature results discussed in Section 2.1.2. Additionally, it helps support the fact that the polymer is affect- ing flow structures inside the hydrocyclone in a manner not associated with the viscosity changes. 5.2 Flow Characteristics With Polymer Additives The flow characteristics of the 10mm hydrocyclone can be altered significantly by the addition of only 100 wppm polymer. These changes cannot be accounted for by the change in viscosity alone. Thus the polymer is affecting the mechanisms inside the hydrocyclone in an unknown manner. Figure 5.7 shows the reduction in total capacity associated with the addition of polymer. Others (see Section 2.1.1) have reported that the hydrocyclone capacity increases with viscosity. Because the addition of polymer increases the viscosity and correspondingly decreases the capacity, the polymer QF,GPM 46 10-1- ] I l l l l l I J l l T I l I 1 1 I 1 10 ' 20 30 40 50 60 70 30 90100 PF - P09 pSi Figure 5.7. The effect of polymer on the capacity of six 10mm hydrocyclones (AP-30, 25°C). 47 TABLE 5.1.--The Effect of Backpressure on the Capacity and Pressure Loss Coefficients,(Water, 1-11; 100 wppm AP-30,,12-16). Exp Pressure, psig -4 G G Qo/Qu PF Po Pu ReF x 10 o u l 70 - 3.32 10.96 - m 2 70 - O 3.16 - 12.07 0 3 70 0 0 3.50 9.87 9.87 1.264 4 70 10 0 3.35 9.22 10.76 0.22 5 7O 0 10 3.24 11.54 9.89 4.03 6 25 0 0 2.20 8.90 8.90 0.967 7 35 10 10 2.14 9.39 9.39 0.766 8 25 2.5 0 2.21 7.95 8.83 0.40 9 25 0 1 2.19 8.65 8.30 3.27 10 25 0 - 2.22 8.73 - w 11 25 - 0 2.13 — 9 48 0 12 70 0 - 3.01 13.31 - m 13 70 - 0 3.09 - 12.63 0 14 70 0 0 2.89 11.73 11.73 1.65 15 70 10 0 2.82 10.58 12.34 0.23 16 70 0 10 2.73 13.11 11.24 6.79 TABLE 5.2.--The Effect of Viscosity on the Capacity and Loss Coeffi- cient (water). 4 T°C u, cp PF - P0, psi ReF x 10- Go QO/Qu 16.5 1.105 10 1.30 6.79 0.757 25 0.900 10 1.59 6.84 0.760 16.5 1.105 40 2.24 9.16 1.19 25 0.900 40 2.68 9.63 1.46 16.5 1.105 90 3.21 10.02 1.13 25 0.900 90 3.92 10.11 1.16 16.5 1.105 60 2.71 9.37 1.17 25 0.900 60 3.26 9.75 1.35 48 is suspected of altering the tangential velocity fields found in the hydrocyclone. Furthermore, if the solution viscosity is increased by merely lowering the water temperature,a resultant increase in capacity is observed. The addition of polymer also increases the pressure loss factor G0 as seen in Figure 5.8. This indicates that the polymer solution requires a higher pressure drop to obtain the same kinetic energy in the feed stream. Additionally, the polymer solution is also closer to the free vortex value for Go. Figure 5.9 shows the increase in the split ratio curve due to the polymer. This is consistent with results obtained by Wallace [1980] but inconsistent with the results of others dis- cussed in Section 2.1.2. Primarily, the increase in the split ratio was due to a corresponding decrease in the underflow rate. The change in mechanism observed for the water case at a feed pressure of ~35 psig is enhanced by the polymer. Chiou and Gordon [1976] have observed that the tangential and axial velocities in a draining tank are reduced by the addition of a small amount of polymer. Since the qualitative velocity profiles in a hydro- cyclone are similar to those in a draining tank, this may be a possible explanation for the decrease in the underflow rate. Figures 5.10 and 5.11 show the alteration in the split ratio for two polymer concentrations at a constant feed pressure. The results for 100 and 200 wppm are almost identical except at the feed pressure closest to the change in mechanism observed in Figure 5.9. Go 49 16¢:- 15-~ -—— ——--—— -—- ——--—— ——- ——;}r- -—--—- -—--—- -—--—— -—--—— l4-r' free vortex 13-- polymer 100 wppm ‘2-_ 11.0— io-e 10 O to A 2 u...— 0 \l on Figure 5.8. The effect of polymer on the pressure loss factor for a single 10mm hydrocyclone (100 wppm AP-30, 25°C). 50 2.18- 1.9‘1- polymer 1.7 ‘- P 1.5'fi” 3 CD’ \ O O 1.3-9— 1-1‘” water .9 T- 7 1 4 4 1 0 l 2 3 4 ReF Figure 5.9. The effect of polymer on the split ratio (100 wppm AP-30, 25°C). 00/0u 51 2.0 ‘1’" a AP=50 psi L5 ‘- 30 psi LO-— 10 psi fl_fl_—fl_fl'__JL____—————'”"““"flflfifl’flflflflFfl‘ 4»——’——r* , P0 = Pu - 0,ps1g .5 1 1' 0 100 200 ‘ c,wppm Figure 5.10. The effect of polymer concentration on the split ratio for AP :_50 psi. nee;- 00/0u 52 mm" .5 1 I o . 100 200 c,wppm Figure 5.11. The effect of polymer concentration on the split ratio for AP.: 50 psi. 53 Figure 5.12 shows the effect of flow history on the split ratio.. The arrows indicate the direction in which data were recorded by starting with fresh polymer solutions. Because it takes approximately 20 minutes to record data for a complete run, the % drag reduction differs for the two curves at the ends but not in the middle. It is believed that this accounts for the differences in the observed split ratio values. Differences in the split ratio for water were not observed when the order of recording the data was reversed. Thetransient behavior of the split ratio due to the polymer is observed in Figure 5.13. The result for mixing strategy I and II and the no clay case are qualitatively the same, except the clay case has a higher asymptote. Note that none of the solutions obtain a value of 2.0 observed in Figure 5.9. The critical time frame is the first 5 minutes after the polymer is added. During this time not only is the split ratio changing very rapidly but, as shown in the next section, the highest values of centrifugal efficiency are observed. 5.3 Separation Characteristics With and Without Polymer Additives Another way to indirectly measure changes in the internal flow structures of a hydrocyclone due to polymer addition is to observe the effects it has on centrifugal separation efficiency (see Equation 2.1). While specific changes in the flow structure cannot be identified, changes can be inferred if no other effects are present. 00/0u 2.1'51- 1.9__ 1.7- 1.5% 1£3~ 1.1'1 Figure 5.12. 54 OD 0 - 20 min. (+) ‘— ‘ L I 1 I 40 60 80 100 PF-P0 psi The effect of flow history on the split ratio (100 wppm AP-30, 25°C). 00/0u 55 AP = 40 psi Lo-«- 1.9‘1" a 1.8-- ‘4 1.7-- "2 = L6-- 1% 1.5-.. 1’ y 100 wppm, 0.2% clay 1.4--' / o 1* 1.3-, II 11* Al no clay 1.2- *(see Table 4.1) 1.1."— L0 1 1 1 i i O 10 2O 30 40 50 Time, min Figure 5.13. The effect of mixing strategy on the split ratio at AP = 40 psi (25°C). 56 Figure 5.14 shows the effect of polymer concentration and Reynolds number on the centrifugal efficiency for mixing strategy I. The increase in the efficiency is probably due to two different 'mechanisms. First, the polymer reduces the swirl velocity, as mentioned in Section 5.2, and thus the centrifugal force felt by the clay particles. Second, the effective particle diameter is increased due to flocculation of the polymer and clay as discussed in Section 2.2. These 'flocsfl however, are easily destroyed and thus the change in diameter is small - possibly only 4 or 5 clay particles combined. Additionally, the time frame of the transient observed is 5-10 minutes which corresponds to the transients observed for the split ratio in Section 5.2 and the drag reduction 1 in Appendix A. A 200 wppm solution yields a separation efficiency which is below the 100 wppm solution because it further reduces the ' swirl velocity but has little effect on the flocculation. It should be noted that no flocculation was observed during any of the runs by visual inspection. However, changing the effective [diameter from lu to 5p is not an effect that would be apparent. The Reynolds number also has an effect on the centrifugal efficiency. For both the polymer cases and the no polymer case an increase in the Reynolds number produced a corresponding increase in the efficiency. This is consistent with results reported by Haas, et al. [1957] and others in the literature (see Section 2.1.3). Figure 5.15 shows that the transient behavior observed (A) can be eliminated by altering the polymer mixing strategy. By 57 __ a 0‘ 1 15 minutes 100 wppm no polymer 3'15 [111". (+) L Mixing Strategy I (see Table 4.1) ‘— ~ I 1 1.5 21) 2.5 31) 3.5 4 ‘- ReF x 10 Figure 5.14. The effect of Reynolds number and polymer concentra- tion on the centrifugal efficiency for a 10mm hydrocyclone (0.2 wt% clay, 25°C). 58 1.1 B .3-- no polymer 3-15 minutes ( + ) .2 1 1 i 1 1.5 2.0 2.5 3.0 3.5 ' -4 ReF x 10 Figure 5.15. The effect of polymer history on the centrifugal efficiency of a 10mm hydrocyclone (0.2 wt% clay, 100 ppm AP-30, 25°C; A: Flow loop mixing of polymer; B: Gentle turbine mixing of polymer; C: Hand mixing of polymer, clay added wet). .59 gently shearing the polymer with a turbine on a low speed setting (8) or hand mixing (C) the transients are greatly reduced. The efficiency for B has a higher asymptote than the flow loop mixing for A. Polymer degradation can also reduce transient behavior as shown in Figure 5.16. Preparation 8 has been degraded for 30 minutes by the pumps yet it yields the highest efficiency data reported and has no transient behavior. The addition of 100 wppm polymer to 8 brings it below the no polymer case as shown by C. Presumably, this additional polymer slows the swirl velocity yet does not help flocculate the clay. Figure 5.17 compares the results for mixing strategies I and II. When the polomer is added first (I), the centrifugal effi- ciency shows a significant increase over the no polymer and clay first (II) cases. The 200 wppm cases are both below their corre- sponding 100 wppm cases which supports the lowering of the swirl velocity argument in Section 5.2. This anomolous effect was first observed by Wallace [1980]. .4-— 60 0.2 wt% clay __Z5fC ,_fl[flwre,yfl, no polymer 3'15 111111. (+) single runs I I i 1 . 1 1.5 2.0 2.5 3.0 3.5 -4 ReF x 10 Figure-5.16. The effect of severe polymer degradation on the centrifugal efficiency of a 10mm hydrocyclone (A: 100 wppm polymer, 0.2 wt% clay, flow loop mixing, 65% initial drag reduction; 8: 100 wppm polymer, flow loop mixing for 30 minutes, 25% initial drag reduction; C: 200 wppm polymer prepared by adding dry polymer to B). 61 Mixing Strategy I 100 wppm no polymer 100 wppm Mixing Strategy II 3-15 min. (+) -1 " 200 wppm I 1 l 1.5 24) 2.5 3.0 3.5 4 ‘— ‘ ReF x 10' Figure 5.17. The effect of mixing strategy 11 on the centrifugal effiniency of a 10mm hydrocyclone (0.2 wt% clay, 25°C . CHAPTER 6 CONCLUSIONS AND RECOMMENDATIONS The addition of Separan AP-30 to the feed stream of a 10mm hydrocyclone seems to have altered some important internal flow structures. In particular, one of the flow structures which con- trols the underflow stream has been weakened. The reduction in the underflow stream can be observed in Figure 5.9. This data possibly suggests a decrease in the swirl velocity and, more importantly, the centrifugal forces similar to that observed by Chiou and Gordon [1976]. This reduction hypothesis is consistent with the results obtained for the separation experiments portrayed in Figure 5.17. Although the addition of polymer to the solution increases the viscosity slightly, this has an opposite effect on hydrocyclone performance than simply increasing the viscosity by lowering the temperature, This conclusion follows by comparing the pressure loss coefficient, Go’ for the polymer solution (see Table 5.1) and water at 25°C and 16°C (see Table 5.2). Thus, the polymer alters flow structures within the hydrocyclone which are unaffected by comparable changes in viscosity. The mixing strategy paradox (see Chapter 1) was determined to be dependent on the order in which the polymer-clay-water suspen- sion was mixed and not to any "pre-stretching" of the polymer (cf. 62 63 Wallace, 1980). The differences in efficiency for mixing strategies I and II were believed to be due to polymer-clay flocculation (see Section 2.3), although no evidence of this flocculation was observed directly. However, the amount of flocculation required for the observed changes in efficiency would be minimal and quite possibly unobservable. The reason why mixing strategy I should promote flocculation relative to II remains unclear. It is noteworthy that both mixing strategies yield polymer-clay-water suspensions which exhibit similar drag reducing characteristics for fully developed pipe flow (see Figure A.3). Moreover, the two different mixing strategies showed no important differences in the capacity and the split ratio of the hydrocyclone, although these differed significantly from the no polymer studies. Thus our main conclusion based on a set of indirect observations is that, in the absence of flocculation, the addition of Separan AP-30 to the feed stream reduces the centrifugal efficiency (lower curve in Figure 5.17). For clay suspension this adverse effect can be compensated by particle flocculation, provided the clay and polymer are mixed according to strategy I (see Table 4.1). This yields the upper curve in Figure 5.17. Obviously, further research in this area should include an inveStigation into the flocculating capabilities of Separan AP-30 with kaolinite clay. Other high molecular weight polymers, which have a greater or lesser tendency to flocculate with clay, should be investigated. Two excellent choices would be the copolymers which make up Separan AP-30, polyacrylamide and polyacrylate. 64 It is already known that they affect flow structures in turbulent pipe flow (Virk, 1975) and thus are good candidates to affect flow structures in hydrocyclones. Flow visualization should also be considered in order to determine exactly which flow fields are being altered by the polymer. This may lead to a better under- standing of how hydrocyclones operate and thus improve and expand their applications. APPENDICES 65 APPENDIX A VISCOSITY AND FRICTION FACTOR MEASUREMENTS 66 APPENDIX A VISCOSITY AND FRICTION FACTOR MEASUREMENTS A.l Apparatus The flow characteristics of the various mixtures used in the hydrocyclone experiments (see Table 4.1) were determined for a straight capillary tube in parallel with the Doxie 5 Dorrclone (see Figure 3.1). The Specific design parameters for the capillary are listed in Table A.l. The inside diameter of the tube was measured by inserting a drill bit into the cut ends of the tube and measuring its diameter with a micrometer. Visual inspection of the tube ends showed no crimping. The design gave an entrance length of 250 D so 1a fully developed profile in the test section would occur. Both monometers produced steady readings for all the measurements reported. Accurate low Reynolds number measurements were difficult for clay suspensions with more than 0.2 wt % solids. A.2 Procedure and Results for Viscositngeasurements Apparent Viscosities of the polymer-water-clay suspensions used in the hydrocyclone studies were measured by applying the HagenePoiseuille equation for fully developed laminar flow of a Newtonian fluid in a circular tube. By measuring the volumetric 67 us“. ». r. . J‘r T 68 flow rate Q and the pressure drop AP (>0), the viscosity was calculated as follows u = 45:. 4;. (4.1) where R and L represent, respectively, the radius and length of the tube (see Table A.l). Flow rates were measured by timing and weighing the fluid exiting the capillary tube; the pressure drop was measured manometrically. The hydrostatic equation for the manometer and Equation (A.l) can be combined to give a final working equation for the viScosity in terms of the mass flow rate W and the change in height of the manometer fluid AH. The result is u = K 4&1 (A.2) where K e 4%:- 029 (——5££--1). (A.3) With the units of u in cp, AHC in inches of CCRI, and W in tbm/sec, Equation (A.2) becomes 4 AH u = 6.767 x 10‘ c . (A.4) All of the mixtures used in this study (see Table 4. ) showed the behavior I 14 cc AHc (A.5) 69 for low flow rates. Therefore, Equation (A.4) was used to define the Viscosities experimentally. A typical set of experimental data is shown in Appendix B and the final results for the Viscosities are tabulated in Table A.2. The pH of each solution was measured using pH paper but only varied from 7.0 to 7.3 for all the systems studied. TABLE A.1.--Design Parameters for Capillary Tube. Material: drawn steel (carbon) Inside diameter: 0.146" (3.708 mm) Length between pressure taps: 89" (2.26m) Entrance length: 36" (0.9l4m) Pressure taps: Branch welded U-tube manometers: chL4 for low Re Hg for high Re Although the Viscosities listed in Table A.2 are not signi- ficantly different from the solvent (H20), these values were used whenever a characteristic Reynolds number was calculated (see, for example, the results presented in Section 5.3). Earlier Wallace [1980] assumed that the viscosity of the dilute polymer solutions at high shear rates would be equal to the solvent viscosity. This idea was not tested in this study and should be investigated further. It is noteworthy, however, that the maximum strain rate in the 3 capillary tube at Re = 10 is approximately 800 seE1 for water. Therefore, the apparent shear Viscosities for the dilute polymer 70 lgggg_A.2.--Viscosities Measured Using the Small Capillary Tube. T 0c Concentration wppm Mixing strategy 1 c ’ Polymer Clay (see Table 4. ) L’ p 25 0 0 0.909(.8904)* + 100 _ 1.001 200 1.001 300 1.201 25 0 100 _ 0.895 T l 2000 0.981 25 100 100 I 1.024 - 200 1.149 1 300 1 I 1.260 25 100 2000 I 1.004 + 1 1 II 1.0045 15° 0 0 - .1.158(l.139)* + 100 0 - 1.195 100 100 I 1.200 *CRC, 1981 solutions listed in Table A.2.may be appropriate for correlating data obtained in the hydrocyclone experiments. Applications of Equation (A.l) assumes that the fluid is effec- tively Newtonian and that the Reynolds number, defined by 334.. (A.6) nRu Re is less than 2100. Obviously, the mass flow rate W, the radius of the tube R, and the viscosity u all have consistent units in (A.6). Pressure drop-flow rate data for fully developed flows are often correlated in terms of a friction factor and a Reynolds number given by Equation (A.6). The Fanning friction factor, defined by 71 f a Tw/%pug , (A.7) is used here to correlate the flow data in the laminar and turbulent regimes. In Equation (A.7),T is the average wall shear stress and w ub is the bulk average velocity. Because both ends of the capillary tube are at the same height, an overall force balance on the fluid in the tube is 2 211RLTw = nR AP. (A.8) Equation (A.8) holds for all Reynolds numbers (laminar or turbulent flows) and for all fluids (Newtonian and non-Newtonian). Eliminating Tw between (A.7) and (A.8) gives an expression for f in terms of the observable pressure drop and flow rate, viz., 11 AP f =-—— (A.9) 2L 1”20‘12 b Introducing the mass flow rate, R = 2 - pubnR , (A.10) and the hydrostatic equation for the manometer into Equation (A.9) given f = ( m2R509(6me6) ) Afl_. (A.11) L N2 The densities of the mixtures studied were assumed to be the same and equal to 62.31 2bm/ft3. Thus, a final working equation for the friction factor used in this work is 72 1.476 x 10 fflm_, mercury 142 f = (A.12) '8 AH . 6.969 x 10 c ,carbontetrachlor1de w2 In Equation (A.12), W has units of tbm/sec whereas AHm and AHC have units of inches of mercuryenulcarbon tetrachloride, respectively. For laminar flow, Equation (A.l) is equivalent to f = l6/Re (A.l3) where f and Re are given by Equations (A.11) and (A.6), respectively. The working equation (A.12) gives f in terms of the measured parameters AHC and W. Figure A.l shows how f depends on Re for some of the mixtures used in this research. Because u was determined by Equation (A.4), which is really a rearrangement of Equation (A.l3), it should not be surprising that all the data correlate with Equation (A.l3); the relevant experimental observation is contained in expression (A.5). A.3 Procedure and Results for the Drag Reduction Experiment Drag reduction information was recorded for the following concentrations of clay and polymer: - No clay with 0, 100, 200 wppm AP-30 - 100 wppm AP-30 with O, 100, 400, 20,000 wppm clay. Most of the data were taken at 25°C although some were taken as low as 15°C. The amount of time that the polymer was mechanically ‘degraded inside the pumps before data was recorded was also an 73 10“» [I no polymer 10'» o 100 wppm AP-3O . 100 wppm AP-30 sheared for 1 hour . 100 wppm AP-3O 100 wppm clay 10" i i . 102 '03 10 R e Figure A.l. Friction factor for laminar flow (25°C). 74 important parameter. This degradation time ranged from 0 to 60 minutes and is shown on each graph in minutes. If no time is men- tioned, the shear time is zero and data were taken innmdiately after mixing the suspension. The order in which the clay and polymer were added to solution was recorded for each run (see Table 4.1). The effect of ageing on the suspension was investigated by allowing a suspension to sit overnight before drag reduction experiments were performed. To determine the amount of drag reduction present at various polymer and clay concentrations, pressure drop and flow rate data were obtained. The pressure drop across the capillary tube was measured with a water over mercury manometer. The flow rate was measured by allowing the water to flow from the capillary tube into a container where it was weighed and the time was recorded. A typical sample weighed 4.06 Abm and took 37.7 seconds. The pressure 4 drop was 45.16 inches of Hg for a Reynolds number of 1.65 x 10 and a friction factor of 6.20 x 10'3 (see Equation (A.12)). Standard friction factor versus Reynolds number curves for turbulent flow in a pipe were reproduced by measuring pressure drops at various flow rates. A typical set of data is shown in Appendix B. This information was converted to friction factors and Reynolds numbers using Equations (A.6) and (A.12). Viscosity data are recorded in Table A.l.n Figure A.2 shows the results for water at 25°C. Although the data fall below the classical Blasius correlation, they are very reproducible. Equation (A.11) shows that the friction factor is very sensitive to the radius of the capillary (f a R5). 75 10"-- 10’» . _ .25 Bla51us f — 0.079l/Re lo 13 two separate runs - 1 1 10 1 ‘ '5 103 1° 10 Re Figure A.2. Friction factor for fully developed turbulent Pipe flow (water, 25°C). r-O- - ’. J.“ '0‘.) l -. ‘5‘ 'I. 76 An increase of only 1 or 2% in R would move the experimental data onto the Blasius correlation. Also, because Re « l/u, small errors in the viscosity (see Table A.l) would shift the data in Figure A.2 in the right direction. Because the polymer seems to degrade significantly during the first hour after preparation, a constant pressure drop experiment was performed to determine the transient behavior of the friction factor for various polymer solutions. Figure A.3, which shows how the mass flow rate changes at constant AP, summarizes the main observations made. All of the mixtures tested fell within the hatched area. Within this region small differences between the various runs were observed, but the quantitative significance of this remains unclear. The transient behavior of Mixture E (see legend in Figure A.3) was the largest in magnitude whenever Mixture B was the smallest. Figure A.3 shows that an initial surge immediately followed the addition of polymer to the system which often made it difficult to stabilize the pressure drop for the first minute or two. Following this initial period, the flow rates dropped from some maximum value, often 50% higher than the flow rate of plain tap water, to a flow rate slightly above that of tap water. Thus, the drag reducing quali- ties are not completely lost and a residual lO-20% drag reduction effect remains for several hours. The addition of clay to the suspension has no noticeable effect. Wallace, et al. [1979] and Dabir, et a1. [1980] suspected that a small amount of clay might help to stabilize the drag w, lbm/sec .132 .128 .124 .120 .116 .112 .108 .104 .100 .096 77 Conc. wppm Mix AP-30 Clay Prep 9- A 100 0 -- B 100 100 I " C 100 100 II ./ D 100 100 I* 7' / E 100 400 II *Degraded 10 minutes Water R€_: ___________ 1 1 1 1 1 o 10 2o 30 40 50 Time, min Figure A.3. Transient behavior of various polymer mixtures in turbulent pipe flow (AP = 41.63", 25°C). 78 reducing qualities of the suspension by either retarding polymer degradation or by increasing the residual drag reduction left after mechanical degradation due to the pumps. However, the set of experi- ments summarized by Figure A.3 does not seem to support this hypo- thesis. The transient behavior of five different mixtures fall within the hatched region (If Figure A.3. Mixture C is identical in composition to Mixture B but the preparation strategy was reversed (see Table 4.1). No significant differences were noted between Mixtures B and C. Mixture D was cycled through the pumps for 10 minutes before adding clay. The clay was added to see if this would stop or slow the mechanical degradation. Although the transient decay after the addition of clay remained within the hatched region shown in Figure A.3, there seemed to be a slight reduction in the rate of decay. As mentioned earlier, Mixture E has the highest clay concen- tration and its transient behavior remained within the hatched region, but was above all the other studies. Higher concentrations of clay have a dampening effect on the drag reduction. This is shown in Figure A.4 where two different suspensions are compared. Both suspensions contain 100 wppm AP-30 but the clay content of one is 400 wppm whereas the clay concentra- tion of the other is 2%. The 2% clay suspension exhibits drag reduction qualities that are greatly reduced when compared to the 400 wppm suspension. The initial surge that usually accompanies the addition of polymer was very small. Both these suspensions had 79 I 100 wppm AP-3O 2 wt % clay ~13?" ‘ 100 wppm AP-30 400 wppm clay 128—4- 0 100 wppm AP-30 .124~~ 0.4 J20~~ U (I) (I) E? .1169— I .Q 3" ,1124— P I A . 108 -1— I A I O I I I .1044- ‘ A I o ‘ ‘ . A . O 100 ~- 1 1 1 .096 1 A1 1 1 1 Time, min Figure A.4. The effect of clay concentration on polymer degrndation in turbulent pipe flow (AP = 41.63", 25°C . 80 the clay added before the polymer. As mentioned in the procedure section, a 2 wt. % solution is difficult to work with due to settling of the clay. This may have caused some problems here due to surging in the capillary tubes and inaccurate flow rate measurements. The effect of Reynolds number on the drag reduction character- istics of the polymer—clay suspensions used in the hydrocyclone experi- f3 ments was also determined. Data were recorded from high Reynolds I “1 numbers to low Reynolds numbers and took between 1 and 2 hours to l complete each run. The amount of time each polymer suspension 1 1 recycled through the pumps before the experiment started is listed PA with the graphical results which follow. In Figure A.5 the first and third cases contain the same polymer concentration but differ in the amount of shearing action. After 30 minutes of recycling through the pumps the 100 wppm AP-3O solution shows little drag reduction. Comparing this to the friction factor data for tap water, only about 10% drag reduction is present. The middle curve is a 200 wppm solution and has been sheared for 60 minutes before taking data. This higher concentration greatly resists the degradation induced by the pumps. The effect of clay on the drag reducing qualities can be observed in Figure A.6. Here, as before, the data were recorded from high to low Reynolds numbers. In these two runs the exact pressure drops were reproduced so the data could be compared easily. The data show no effect of clay on drag reduction. The effects of ageing the polymer suspension overnight can I be seen in Figure A.7. Both suspensions contain 100 wppm of clay and 81 Shearing AP-30 Time Data Temp. °C wppm Min [1 20 100 30 ‘0 7’ o 19 200 60 21 15 100 0 10' -_ 10 I 1 10° 10 Re cub 10‘ Figure A.5. The effect of shearing time on drag reduction. eixfmm 2‘22.- E- 82 Shear Temp wppm Time Data °C AP-3O Clay Min 4 15 100 O 0 101—- l 16 100 100 0 10 I I 3 4 10 10 Re u-lh- 10 Figure A.6. The effect of clay concentration of drag reduction. 83 . Shear Temp Time Data °C AP-30 Clay Min. Age 0 16 100 100 10 fresh 10”__ [I 25 100 100 20 1 day 10‘ 3 10 I T 110’ Figure A.7. The effect of polymerageingcnudrag reduction. 84 polymer. The solution that sat overnight was sheared for 20 minutes. The only observable effect is a decrease in the drag reduction (an increase in the friction factor) which is more than likely due to the longer shearing time. A.4 Summary Drag reduction is definitely present in a solution containing Separan AP-30. The presence of clay, in small concentrations, and the mixing strategies have no significant effects on these properties. However, high concentrations of clay (2%) tend to dampen this effect. The drag reduction is transient in behavior. Its largest effect is noticeable when the polymer is first added to solution and quickly degrades as it is constantly recycled by the pumps. Complete degradation of the polymer is difficult. A residual amount of drag reduction remains after an hour of operation when further degradation has subsided. APPENDIX 8 EXPERIMENTAL DATA 85 86 TABLE B-l.--Experimental Data for Fully Developed Laminar Flow of a Fluid in a gircular Pipe. (D=0.l46 in., L=89 in., p= 62.4 lbm/ft , c = 100 wppm AP-30) T . AHC W p 3 (°C) (1n. CC14) (lbm/sec) (cp) Re fxlO 25.0 22.0 0.01385 1.075 2149 7.99 23.5 19.9 0.01288 1.046 1998 8.36 23.5 18.2 0.01209 1.019 1876 8.68 24.3 15.8 0.0184 0.986 1682 9.37 25.0 13.8 0.00959 0.974 1488 10.46 25.0 11.8 0.00821 0.973 1274 12.20 25.0 9.8 0.00680 0.975 1055 14.77 25.2 7.8 0.00537 0.983 833 18.85 24.9 6.05 0.00415 0.987 644 24.48 24.8 3.70 0.00253 0.990 393 40.28 87 TABLE B-2.--Experimental Data for Fully Developed Turbulent Flow of a Fluid in a Circular Pipe. (D=O.l46 in., L=89, p=62.4 lbm/ft3, u=l.024 cp, c=100 wppm AP-30, 100 wppm clay) 1 411m . w -4 3 (°C) (1n. Hg) (lbm/sec) RexlO fxlO 25.0 56.25 0.1349 2.046 4.557 24.9 51.88 0.1271 1.928 4.734 24.4 47.88 0.1194 1.811 4.952 24.8 44.38 0.1131 1.715 5.114 24.8 39.94 0.1054 1.598 5.317 24.9 35.69 0.0982 1.489 5.457 24.9 31.69 0.0901 1.366 5.755 25.0 28.06 0.0833 1.263 5.937 24.9 23.25 0.0738 1.119 6.295 24.7 19.25 0.0651 0.987 6.697 24.5 15.50 0.0568 0.861 7.085 24.6 9.50 0.0438 0.664 7.301 24.8 5.50 0.0308 0.467 8.541 25.0 1.50 0.0162 0.246 8.431 -. . In- fish? 1 88 TABLE B-3.--Experimenta1 Data for Six 10mm Hydrocyclones (T=25°C, c=100 wppm AP-30, Po=Pu=0 psig) PE Q0 Qu QF ReF x 10‘4 Split Ratio (9519) (GPM) (6PM) (6PM) (GO/QU) 98 3.54 2.36 5.90 3.28 1.500 90 3.41 2.24 5.65 3.14 1.522 80 3.35 2.09 5.44 3.03 1.603 70 3.23 1.96 5.19 2.89 1.648 60 3.09 1.77 4.86 2.70 1.746 50 2.86 1.59 4.45 2.48 1.799 40' 2.72 1.36 4.08 2.27 2.000 35 2.56 1.33 3.89 2.17 1.925 30' 2.36 1.28 3.64 2.03 1.844 25 2.10 1.32 3.42 1.90 1.591 20 1.71 1.45 3.16 1.76 1.179 10 1.09 1.35 2.44 1.36 0.809 5 0.88 1.23 2.11 1.17 0.715 89 NNNm.o mmom.o mmmw.o wm~.o omcm.o P¢P.o mmm¢.o mm.m ow Nmmm.o u mmwn.o omN.o mmom.o m¢~.o mm~¢.o mm.m om ponm.o com.o momm.o mmN.o o¢m~.o omp.o mmom.o m¢.N o¢ owmm.o wo~.o anm¢.o omm.o momm.o w¢p.o o~o~.o mn.p om A&.ezv Aeem\sn_v Aa.gzv Auem\eAPV Ax.yzv Aeem\eAPv .¢-op x Ampmav m xmpou u: xmpuu =3 Awpou o3 gem ma vow; zopmgwuc: 3opmgm>o .Ampmg on:muoa.om1m< oz .oemmuhv wcopuauogu»: seep a com mung wucmecomgmmnu.vum m4m