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WI ‘5 '1 ’IIILLI 5‘55 I“ '5 "L m 5'55 ME? - lu,&¥‘}:\1lifi§“j 5 5:"515.) 5 5“ 91:59“. 5- LI ’1f8959115’9u9grs9‘159'955 ..5 ‘ 4955} 5. .511 5"; “I. ... :1. .5 :5 $15555 “5.9muu 5 . 5 555: 5' 5.5.5:. ”5' .235: 'II .5 555.53 ““5555“: i. :1“ 555:5 553.5%! “HI“! 5;», .55.“ n5- :5..‘ . “.q __ ' . II .flr Lfl 5.551555 55-5 “‘5 II5'I' 5: ”3 .i 5‘ ‘PWI559IIII555W: .5515: .‘L'i5551'51 : "”5 ""‘5‘5355‘5555‘5‘ 5553:”1’9H: 5p ‘15:":‘555FSM “j I: "5: “L“ 55 5"" I 1‘ 5L I" 5 LI . [‘5' "M .5 55'1'55 I55]5.55,5‘ .5 :I '5" I '5 .5 :.'5.,5:I.II.I.55 I 5 III 5'5 'ILILZ: 5 ”55555555 5:. I. 5. 5.5» .. h'5i’.‘ .53: HI .III5, 555.5 .. '95 5,55,}, 1.. 4...... . 5555.555155] 5'5 I .I"5L5 “55:1 : 955555555 i5'55L I5 L 5'". ”15:?" 55559551159H‘555 - 553555555555555' "'5. 555'55 '5 II55 5.15555 555IIII5! 5II'5III.»5MIM 'III ~L5 55.5‘.‘ :IIIII551 5‘5 {HESIS This is to certify that the thesis entitled REVERSE OSMOSIS SEPARATION OF NONELECTROLYTIC SOLUTIONS CONTAINING ETHANOL presented by Thomas L. Troyer has been accepted towards fulfillment of the requirements for M _ 3 - ‘ degree in __C_h§m1_9_&L Engineering ER;¢,C1.9DA~3WUL Major professor Date 30431; \°‘%3 MS U is an Affirmative Action/Equal Opportunity Institution MSU RETURNING MATERIALS: Place in book drop to LIBRARIES remove this checkout from “ your record. FINES will be charged if book is returned after the date stamped below. B ‘1 and. t 4:; REVERSE OSMOSIS SEPARATION OF NONELECTROLYTIC SOLUTIONS CONTAINING ETHANOL By Thomas L. Troyer A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Chemical Engineering 1983 r U /¢1*l£?f‘ ABSTRACT REVERSE OSMOSIS SEPARATION OF NONELECTROLYTIC SOLUTIONS CONTAINING ETHANOL By Thomas L. Troyer The separation of nonelectrolyte solutions composed of organic solutes in an organic solvent has been carried out using commercially available asymmetric cellulose acetate and aromatic polyamide membranes in a differential reverse osmosis membrane cell. Ethanol was the organic solvent and the organic solutes included alcohols, alkenes, alkanes, and saturated aromatics. Membrane selection and flux were re- lated to the applied pressure, feed solute concentration, solute molar volume, and solute chemical function. Neither the porous nor nonporous membrane model repre- sents all the data with meaningful coefficients. Membrane selection was not found to be related to relative diffusi- vities of solute and solvent. Increased membrane selec- tivity with increased solute feed concentration, found for the decalin - ethanol and l-decene - ethanol feed systems, is not predicted by either model. Increases in Thomas L. Troyer membrane selectivity with increased applied pressures were due to mechanical compression of the membrane rather than direct pressure effects on the membrane selection mechan— ism. Design parameters for single and multi-stage counter current reverse osmosis separation units were determined. A calculation scheme to determine the required number of membrane stages to carry out a given separation was devised. For a 5 wt % feed stream and a concentrate stream of 99 wt % solute, fewer than twenty membrane stages were required when the rejection coefficient was greater than 0.5. Power requirements and efficiencies of separation were also calculated using experimental data. Feed streams of 3.5 wt % decalin dissolved in ethanol required 3.A8 watts per gram permeate at 400 psi applied pressure, and 6.97 watts per gram at 800 psi applied pressure. The former separation had an efficiency of 6% while the latter had an efficiency of 3%. To Joyce, My Parents, My Family, and My Friends ii ACKNOWLEDGMENTS I wish to thank the Michigan Agricultural Experiment Station and Michigan State University for providing finan- cial support in the form of research and teaching assistant- ships. I am grateful for the guidance of Dr. Eric A. Grulke without whose help I could hardly have finished this Thesis. I express my thanks to Dr. Frederick Horne for his help- ful criticisms and observations. I wish to thank Desalination Systems, Inc. for the dona- tion of a sample of their aromatic polyamide membrane, and to the Michigan Dynamics division of AMBAC Industries, Inc. for the donation of their porous stainless steel disc. Finally, I am grateful to Joyce Stesiak, my future wife, for her loving support during the completion of this work. iii TABLE OF CONTENTS Chapter Page LIST OF TABLES. . . . . . . . . . . . . . . . . . . . vi LIST OF FIGURES . . . . . . . . . . . . . . . . . . . vii NOMENCLATURE. . . . . . . . . . . . . . . . . . . . . x INTRODUCTION. . . . . . . . . . . . . . . . . . . . . 1 CHAPTER I - THEORIES OF REVERSE OSMOSIS SELECTION AND TRANSPORT . . . . . . . . . A A. A New Approach to an Old Problem. . . . . . . A B. Definitions of Membrane Design Parameters. . . . . . . . . . . . . . . . . 6 l. Membrane Selection. . . . . . . . . . . . 6 2. Membrane Flux ... . . . . . . . . . . . . 7 C. Nonporous Membrane Structure Theory 0 O O O O I I O O 0 O 0 O O O O O O O O 10 D. Porous Membrane Structure Theory 0 O O O O I 0 O O O O O O O O O O 0 O 0 11 E. Relations Between the Permeate Concentration, the Bulk Concentra— tion, and the Component Fluxes. . . . . . . . 13 F. Relationships Between Diffusivity and Selection . . . . . . . . . . . . . . . . 16 CHAPTER II - EXPERIMENTAL RESULTS . . . . . . . . . . 19 A. Experimental Apparatus: Differen- tial RO Membrane. . . . . . . . . . . . . . . 19 B. Experimental Procedures . . . . . . . . . . . 23 C. Solute-Solvent Systems. . . . . . . . . . . . 27 iv Chapter D. Relationship Between Permeate and Solute Concentration. E. Membrane Selection Versus Solute Molar Volume Ratio and Chemical Class F. Membrane Selection and Pressure Effect. CHAPTER III - SINGLE AND MULTI-STAGE REVERSE OSMOSIS SEPARATION SYSTEMS A. Design Parameters B. Single and Multistage Reverse Osmosis Design Options. C. Parallel or Series Multi-Stage Reverse Osmosis Separation Units . D. Optimization of Reverse Osmosis Separation. E. Series Multi-Stage Reverse Osmosis Separation Calculations CHAPTER IV - REVERSE OSMOSIS SEPARATION ENERGY REQUIREMENTS AND EFFICIENTS . A. The Work of Pressurization. B. The Work of Separation and Transport. C. Power Requirements and Efficiencies CHAPTER V - SUMMARY AND CONCLUSIONS REFERENCES. DATA APPENDIX . Page 28 38 All 54 5A 59 59 63 68 73 73 711 76 79 85 87 LIST OF TABLES Table 11-2 List of Materials. . . . . . . . . . . . II-2 Physical Properties of Organic Solutes . . . . . . . . . . . . . . . . . . II-3 Ratios of Alkene Molar Volumes, Selection and the Calculated Exponent n. . . . . . . . . . . . . . . . II-A Ratios of C Molar Volumes, 10 Selections, and the Calculated Exponent n. . . . . . . . . . . . . II-S Ratios of Alkene Molar Volumes, Distribution Coefficients for n = 1/3 . . . . . . . . . . . . . . . . . . II-6 Ratios of C10 Molar Volumes, Distribution Coefficients for n = 1/3 . . . . . . . . . . . . . . . . . . III-l Calculation Scheme for Series Multi-Stage Reverse Osmosis Separation System . . . . . . . . . . . . . IV-l Selected Values of Experimental Re- verse Osmosis Separations vi Page 24 29 39 141 “5 A5 70 78 II-l II—2 II-3 II—A II-5 LIST OF FIGURES Driving Forces of Reverse Osmosis . . . Preferential Sorption-Capillary Flow Rejection Mechanism. . . . . . . Schematic of Experimental Apparatus and Membrane Cell . . . . . . . . . . Upper and Lower Chambers of Membrane Cell with Dimensions. . . . . . . . . . . . Permeate Concentration vs. Concentrate Concentration of l-Hexadecanol in Ethanol. Applied pressure is A00 and 800 psi . . . . . . . . . . . . . . . . . . Permeate Concentration vs. Concentrate Concentration of l—Decanol in Ethanol Using an Aromatic Polyamide Membrane. Applied pressure is 800 psi . . . . . . . . Permeate Concentration vs. Concentrate Concentration of l-Decene in Ethanol and Decalin in Ethanol. Applied Pres- sure is AOO and 800 psi vii Page 12 2O 22 31 33 35 Figure II-6 II-7 11—8 11-9 II-lO II-ll Page Rejection Percentage of Normal Alkenes in Ethanol vs. Applied Pressure. Feed concentrations in wt% are 33.1 for l- decane; 33.0 for l-tetradecene; and 25 for l-hexadecene . . . . . . . . . . . . . A0 Rejection Percentage of C Compounds 10 in Ethanol vs. Applied Pressure. Feed concentrations in wt% are 3A.9 for decalin; 32.7 for decane; 33.1 for l-decene; and 3A.3 for l-decanol. . . . . . . A2 Permeate Concentration and %R vs. Concentrate Concentration of NaCl in Water. Concentrations are expressed in ppm. Applied pressure is A00 psi. . . . . A8 Pure Ethanol Flux Through a Fresh Aromatic Polyamide Membrane vs. Time. Applied pressure is 1000 psi. . . . . . . . . 50 Pure Ethanol Flux Through a Fresh Cellulose Acetate Membrane vs. Time. Applied pressure is 1000 psi. Addi- tional feed was added at times marked with 'r'. . . . . . . . . . . . . . . . . . . 51 Permeate Concentration, Concentrate Concentration, and Membrane Flux Through a Fresh Cellulose Acetate viii Figure Page 11-11 Membrane vs. Time. Solute-solvent system was decalin-ethanol. Applied pressure is 800 psi. Additional feed was added at times marked with a 'r'. . . . . 52 III-l Reverse Osmosis Separation Stage. . . . . . . 55 III-2 Relationship Between the Flow Rate Ratio f and the Concentration Ratio XC/XF . . . . . . . . . . . . . . . . . . . . 58 III-3 Parallel Multi-Stage RO System. . . . . . . . 60 III-A Series Multi-stage R0 System. . . . . . . . . 62 III-5 The Functions g, h, and Z versus the Flow Ratio f. . . . . . . . . . . . . . . 65 III-6 The Function Z vs. f. . . . . . . . . . . . . 67 III-7 f as a Function of X . . . . . . . . . . . 69 max F III-8 N Stages vs. R. . . . . . . . . . . . . . . . 72 xix l. L NOMENCLATURE Symbol - Description, Units (Equation where first used) IM MAX AG MIX area required for one gram per second of permeate to flow, In2 (IV-6). mass fraction of component in region j (I-l). diffusion coefficient of component i, g/(cm s) (I-l2). mass flow rate in region j, g/s (III-2). ratio of permeate flow rate to feed flow rate (III—2). that value of f given the rejection factor and feed concentration for which the concentrate concentra- tion is equal to one (III-5). the value of f which maximizes the optimization function Z (III-1A). mapping operator for component i, g/(cm2 s) (I-7). Gibbs free energy of mixing, joules/g (IV-A). the ratio of the mass flow rate of component a going through the membrane to its mass feed flow rate (III—8). the ratio of mapping operators 02 to G1 (I-lO). mapping operator for component 2 (I-9). rev eq Posm <2 <1) the ratio of the mass flow rate of component b going through the outlet valve to its feed flow rate (III-9). 2 8) mass flux of component i in region j, g/(cm (I-S). total permeate flux, g/(cm2 s) (I-5). distribution coefficient for component i (II-2). a constant defined in Equation (I-l2). power required to perform a given separation, watts (IV-6). power required to perform a given separation re- versibility, watts (IV-7). pressure, dynes/cm2 (IV-l). equilibrium osmotic pressure, psi (I-2). rejection factor, defined in Equation (I-l). 100 R. the gas constant, 1206 (psi—cm3)/(mol-K) (I—2). selection of component i, defined in Equation (1-13)- temperature, K (I-2). partial molar volume of the ith component, cm3/ mole (I-2). molar volume of the component i, cm3/mole (I-l2). specific volume, cm3/g (IV-l). specific volume transported across the membrane, cm3/g (IV-l). xi 2. 3p work of pressurization, joules/g (IV-l). work of separation, joules/g (IV-A). work of transport, joules/g (IV-5). mass fraction of the rejected component of a binary feed stream in region j (III-l). mole fraction of the ith component in the jth region (I—2). the product of g and h, defined in Equation (III-l2). compressibility factor, cmZ/dynes (IV-2). mole fraction based activity coefficient of the ith component in the jth region (I-2). the ratio of the reversible the actual power re- quired to perform a given separation (IV-8). Subscripts - Description (Equation first used) refers to the refers to the cell, refers refers refers refers refers refers refers refers to to to to to to to to (I-l). the the the the the the the the applied pressure (IV—5). bulk solution within the membrane concentrate stream (II-l). feed stream (III-2). membrane phase (II-2). standard state (IV-2). osmotic pressure (I-2). permeate stream (I-l). solvent (I-2). solute (I—l). xii Superscripts - Description (Equation first used) = refers to the high pressure side of the membrane (1-2). = refers to the low pressure side of the membrane (I-2). = refers to the solution next to the face of the membrane (II-A). Sub-subscript - Description (Equation first used) = refers to component a (III-8). = refers to component b (III—9). = refers to the ith stage in a multi—stage separation unit (III-6). xiii INTRODUCTION The production of ethanol from biomass is attractive since it offers a source of fuel and chemical feedstock from renewable resources. Large scale ethanol production is carried out in many parts of the world. Small scale ethanol production units suitable for single farm opera- tion are being marketed. A study (Geiger, 1981) of such small scale units shows their economic feasibility to be dependent on the degree of energy losses incurred during the distillation of the fermentation beer. The degree of energy losses appear to be directly linked to the scale of the distillation process. Small scale units lose energy to a greater degree than large units due to large surface to volume ratios. Because such large ratios are inherent to small scale units, it does not ap- pear reasonable to expect improvement of distillation pro- cesses to lead to significant energy loss reductions. Instead alternative separation techniques such as reverse osmosis need to be explored. The separation of nonelectrolytes such as ethanol and water using reverse osmosis has received little experi— mental attention (Kopecek and Sourirajan, 1970; Nomura E: El. 1978) in comparison to electrolytic separations such as the desalination of brackish water (Merten, 1966; Sourirajan, I970). The vast majority of all commercial separation processes involve nonelectrolytes. If reverse osmosis is to play any significant role in this area of separation technology,new research and development efforts must be made. These efforts must include testing the pres- ently available reverse osmosis membranes for nonelectro- lytic separations; determining the design equations for reverse osmosis separation processes; and devising bases for the evaluation of energy requirements and efficiencies of such separations. The present work represents an initial effort to achieve these goals. Two opposing points of view of the nature of the reverse osmosis membrane were used to structure the experimental approach and evaluate the data; these are the porous and nonporous membrane structure theories. These two opposing View points represent an attempt to categorize the theo- retical reverse osmosis literature into two large groups. At the heart of this division is whether membrane transport is viewed as diffusive or convective, while membrane selec- tion is seen as being based on primary solution component— membrane interactions (£43,, relative mobility of com- ponents within the membrane) or secondary membrane-solvent— solute interactions such as adsorption. Approaching the experimental data with these two theories as models allows the evaluation of the relative importance of the transportation mechanism and selection to the overall separation performance. The design strategy and equations for reverse osmosis separations of nonelectrolytes differ from that for elec- trolytes. Single stage designs for electrolytic separa- tions are sufficient to achieve most design specifications because solute separations of greater than 90% are pos- sible. Nonelectrolytic separations are usually less than 50% per stage. To attain the degree of separation neces- sary in industry, multi-stage designs must be used. The design approach used in multi—stage distillation or absorption units is inappropriate for multi-stage reverse osmosis units. The fraction of material to go on to the next membrane stage or return to the previous membrane stage is controlled by the operator not by the physical properties of the material. The membrane separation can be optimized at each stage rather than overall as is the case for distil- lation and other separation processes. Criteria for opti- mization are proposed in this study. Calculation schemes for achieving the maximum separation using multi-stage reverse osmosis have been devised. Examples worked out in this study include variable feed concentrations and membrane rejections. Finally, the energy requirements and efficiencies for nonelectrolyte separations are calculated from experimental data and tabulated. The area required for a given product flow is also calculated. CHAPTER I THEORIES OF REVERSE OSMOSIS SELECTION AND TRANSPORT A. A New Approach to an Old Problem Reverse osmosis separation techniques are used indus- trially in desalination plants, and some food processing Operations (Fox, 1982). The improvement of these present industrial applications, and the search for new areas to use reverse osmosis techniques is underway in many private and public laboratories. However, this work suffers from a major handicap. Examination of published reverse osmosis membrane literature and private discussions with investigators re- veals that much current research does not attempt to describe the fundamental processes causing the separation. This state of affairs can be said to exist for both historic and philosophic reasons. At the heart of the problem is the inability to make measurements next to, or inside membranes. (Because of this, a strong case can be made that nothing is known about membranes other than they are thin and separate two regions.) One way to avoid this difficulty, which is used by workers in the membrane field, is to assume how the membrane makes the separation, do experiments and make measurements, and then explain these measurements in terms of the supposition. As more measurements are made the initial supposition is elaborated on, and becomes more and more complex. However, it is not usually directly tested and remains an assumption or axiom. Consequently, there are nearly as many membrane theories as membrane researchers. This has produced a fragmented membrane research effort, and makes the litera- ture difficult to interpret. For real progress to occur in the reverse osmosis field, a more systematic approach must be taken. The first step is to examine what properties of membranes can be measured. The next step is to consider the broadest categories of membrane models and see if the behavior predicted by these models is testable in terms of measur- able membrane properties. Those theories which have no predictive content, or which cannot be tested in terms of the measurables, may be ignored since scientifically, these are not true theories. Examination of the membrane literature shows that a large number of publications may thus be dismissed. Finally, these models which can be tested and are not disproved may be further tested with respect to their in- dividual sets of assumptions and predictions. These tests may include further membrane experimentation. It might be possible to do such work independent of membrane systems where postulated properties and processes could directly be measured. To determine what properties can be measured, the ex- perimental membrane literature is consulted. It is easy to see that for an isothermal reverse osmosis system the measurable properties are membrane selection and membrane flux. These properties are discussed at length in the following sections. B. Definitions of Membrane Design Parameters l. Membrane Selection Membrane selection is defined as the difference in solute concentration of the liquid which flows through the membrane, the permeate stream, to the bulk liquid bathing the upstream face of the membrane. Typically, the mathe- matical definition of selection found in reverse osmosis literature is the rejection factor, R, R = l — (C2p/C2B) I-l where C2 is the concentration of the solute in the per- p meate stream, and 02B is the measured concentration of the solute next to the upstream face of the membrane. The value of the rejection factor may theoretically vary from minus infinity to one. For the case where R is less than zero the solute crosses the membrane in prefer— ence to the solvent. Un-ionized phenol and some other aromatic compounds (Anderson et al., 1972) show such be- havior in aqueous feed streams to organic-based membranes. Much more common is a rejection factor between zero and one. When R is equal to zero the membrane is said to be nonselective since the concentration of the solute is the same in the permeate stream as in the feed stream. When R is equal to one, the membrane is said to be ideally semi-permeable, or totally reflecting to the solute since none is allowed through the membrane. In this study solute-solvent systems with rejection factors approxi- mately mid-way between zero and one will be discussed. 2. Membrane Flux Membrane flux is the permeate flow rate per unit area per unit time (345;, grams per square centimeter per second, or gallons per square foot per day). The flux is driven by the pressure gradient and, for a nonzero rejection factor, the concentration gradient across the membrane. Consider, for example, the case where a solute has a positive rejection factor. When pressure is applied to the upstream solution,a pressure gradient is created so that the pressure decreases moving downstream across the membrane. This is shown schematically in Figure I-l. M Bathing Solution Membrane Permeate Liquid Upstream Pressure Downstream Solvent Concentration Upstream Solvent Concentration ,_Qgggstream,Pressure Figure I-l. Driving Forces of Reverse Osmosis. Since the membrane is selective with respect to the solute, there is a concentration gradient of the solvent such that the solvent concentration increases moving downstream across the membrane. While the pressure gradient tends to move liquid from the upstream side to the downstream side, the concentration gradient tends to move solvent from the downstream side to the upstream side via diffusion. The membrane flux is the net flux due to these two Opposing forces. At equilibrium the difference in pressure and solvent concentration across the membrane are related as follows (Fried at al., 1977), L L eq = RgT [71x1] I-2 P —~— tn —————— osm 'V [ HxH] 1 Yll where ngm is the equilibrium osmotic pressure and is equal to the upstream pressure minus the downstream pressure; R is the gas constant; T is the absolute temperature; 7% is the downstream activity coefficient of the solvent, y? is the corresponding upstream value; x% is the mole fraction of the solvent in the downstream liquid, and x? the corresponding upstream value. 10 C. Nonporous Membrane Structure Theory All reverse osmosis theories can be divided into two categories. These are the nonporous membrane structure theories and the porous membrane structure theories. The nonporous membrane structure theories (Reid and Breton, 1959; Lonsdale et al., 1965) see the membrane as a third phase separating two bulk solutions. On the high pressure side, the molecules of the liquid are driven into the membrane by the imposed pressure. They are pushed through the membrane by exchanging momentum with molecules which have entered the membrane after they did. Membrane transport is thus ac- complished by the diffusion of momentum from the high pres- sure side momentum source to the molecules in the membrane which act as the momentum sink. Membrane selection for the nonporous structure theory is based on the relative ability of different types of mole- cules to enter and move through the membrane. For example, membranes having a somewhat hydrophilic nature might reduce the solubility and flux of hydrophobic molecules, while hydrophilic molecules would tend to move through to the low pressure side more quickly. Thus the membrane system is made up of three types of molecules; solute, solvent, and membrane; and two types of interactions; solute-membrane, and solvent-membrane. Be- cause of this, component fluxes making up the total mem- brane flux are independent of one another. 11 The classic nonporous membrane structure theory is the Solution-Diffusion theory proposed by Lonsdale et a1, 1965. These authors were attempting to explain the salt rejecting capability of asymmetric cellulose acetate mem- branes. D. Porous Membrane Structure Theory The porous membrane structure theory (Matsuuro and Sourirajan, 1981) sees the membrane as a porous barrier between the high and low pressure bulk liquids. The liquid on the high pressure is forced into the membrane pores. It then flows through to the pore to the low pressure side. Membrane transport is thus convective in nature. Membrane selection is determined by the effect of the membrane on the solvent lying next to it. This membrane— solvent effect in turn changes the interactions between the solute and solvent molecules such that solute mole- cules tend to stay away from the solvent next to the mem- brane (R > 0), or move closer to it (R < 0). In the Preferential Sorption—Capillary Flow theory, proposed by Sourirajan to explain the desalination proper- ties of asymmetric cellulose acetate membranes (Sourira- jan, 1963) water molecules are assumed to adsorb to the face of the membrane and form a multilayer structure as shown in Figure I-2. Salt ions are assumed to be unable to adsorb in this fashion and are thus excluded. When l2 Bulk Solution Multi-layer of Adsorpted Solvent._;:> r Tl \ Membrane Surface \V Me b P m rane ore 2 Q A? V V v V \l \r A v \/ if Figure I-2. Preferential Sorption-Capillary Flow Rejec- tion Mechanism. 13 the radius of the membrane pore is of the same length as the thickness of the multilayer structure, only the material in this structure passes through the membrane pore. Under these conditions the bulk liquid cannot pass through the pore. For the porous membrane structure theory the three different types of molecules interact but differently from the nonporous membrane structure case. Because the solute interacts with only the solvent, the solute flux is dependent on the solvent flux. The solvent flux in turn is dependent on the solvent membrane interactions. E. Relations Between the Permeate Concentration, the Bulk Concentration, and the Component Fluxes Six measurable quantities are present in a reverse osmosis separation of a binary mixture under steady state conditions of constant applied pressure and temperature. These are the solute flux, sz, and the solvent flux, le; the bulk solute fraction, C2B’ the permeate solute fraction, C2p, the bulk solvent fraction, ClB’ and the permeate solvent fraction, Clp‘ There are four indepen- dent mass balance relationships between these six vari— ables, i.e., 1B 2B - 1A Clp + 02p = 1 I-A J c = —39 I—5 2p J P J c = _£B I-6 lp J 9 Two additional equations must be specified to uniquely fix all six variables. Of these six, only the bulk con- centration is experimentally manipulable for the isothermal, isobaric, binary component steady state case. There are only three possible independent relationships which can be written between the bulk concentration and the permeate concentration and fluxes. These are, le = GlclB 1—7 J2p = G2 C2B I-8 where GI’ 02, and H2 are operators or functions which map the bulk concentration on to the observed permeate flux or 15 concentration. The explicit form of these operators may be derived from theoretical considerations or from graphs of experimental data. In the context of comparing experimental results to the predictions of the porous and nonporous membrane struc- ture theories, an important observation can be made without such detailed knowledge of the operators. Namely, a linear relationship between the bulk and permeate concen— tration of the solute ous theory. This may (1-7), and (I-8) into 2p cannot hold in general for the nonpor- be shown bv substituting Equations Equation (I-6), i.e., where g2 is equal to 02/01. Comparing Equation (I-10) to Equation (I-9) it can be seen that the operator H2 can be expressed as a J2p = G2 025 Jp GlClB + G20213 8 Cg 2 B 1-10) nonlinear function of g2, and C2B’ g 2 1-11 16 Only for the cases where g2 is approximately equal to one (ttgt, R = 0), or where g2 is very small with respect to one (tggt, R 2 1), will the experimental relationship between the permeate and bulk concentrations appear linear. For data where the rejection factor is immediate be- tween 0, and 1, and the data is best fit by a linear curve though out of the range of C2B values used, a porous mem- brane model is the best model to represent the data. When the data is best fit by a nonlinear curve, either the porous or nonporous model can be used. F. Relationships Between Diffusivity and Selection A second test of the nonporous membrane structure theory can be based on its assumed mechanism of selection. Recall that selection is based on the relative ability of the com- ponents of a binary feed solution to move through the mem- brane. The valuecfi‘the diffusion coefficient of a solute in a solvent is a direct measurement of the solute's mobility. While the exact value of a solute's diffusion coefficient is difficult to predict, it can be shown theo- retically and from experiment that it is inversely prOpor— tional to the solute's molar volume raised to some power (Reid gt gl., 1977). It follows that the ratio of diffusion coefficients of two solutes under identical conditions should be equal to the reciprocal of the ratio of their molar volumes raised 17 to some power, i.e., The Strokes-Einstein theory of diffusion coefficients (Bird gt gt., 1960) predicts that n is equal to one-third (ttgt, the diffusivity of a solute is inversely propor- tional to its molecular radius). Other authors have used other values. For example, the Wilke-Chang correlation uses 0.6 (Reid gt gt., 1977). If the nonporous membrane structure theory is correct, the ratio of one solute's selection to another solute's selection, where selection is defined as, S1 = Cip/Cic I-l3 should be equal to the ratio of their diffusion coefficients and inversely proportional to their molar volumes raised to some power, D V r1 S _l = (.2) = _l_ 1.11; D V S2 2 where n should be some constant for the particular solvent 18 membrane system used. This prediction can be tested by using solutes with different molar volumes, or approxi- mately the same molar volume but from different chemical classes. CHAPTER II EXPERIMENTAL RESULTS A. Experimental Apparatus: Differential RO Membrane A schematic of the experimental apparatus used to col- lect reverse osmosis data is shown in Figure 11-1. A cylinder of nitrogen gas is connected by copper tubing to a pressure vessel containing the feed solution. A high pres- sure gas regulator allows pressures from zero up to a max- imum of 2000 psig to be used. The pressurized feed solution is forced into a copper tube which connects the pressure vessel to the membrane cell. The membrane cell is shown in greater detail below the apparatus schematic. The membrane cell was manufactured from stock aluminum plate and consists of two sections, each one inch thick, and six inches in diameter. Each section is machined so that an interior chamber is formed when they are bolted to- gether. The membrane is placed between the two sections and divides the interior chamber into a lower and upper chamber. The feed stream is introduced into the lower chamber of the cell. A portion of this solution passes through the 19 2O (HE :HfiSQfiE: IflMBmmm CYLINDER VESSEL CELL Heating Channels -.I) MHflmEME CEUL Figure II-l. Schematic of Experimental Apparatus and Mem- brane Cell. 21 membrane and forms the permeate stream. The remainder passes out of the lower chamber and forms the concentrate stream. A needle valve is used to control the volumetric flow of the concentrate stream. A magnetic stir bar is used to keep the solution in the lower chamber well stirred so that the solute concentration in the concentrate stream is equal to the solute concentration in the lower chamber. In the upper chamber of the membrane cell the membrane is backed by a piece of filter paper and both are supported by a porous stainless steel disc as shown in Figure 11-2. The filter paper prevents the membrane from being perforated by the disc. These items completely fill the upper chamber. The permeate stream leaves the upper chamber through a cen- trally located opening. Each section of the cell has two heating channels through which water from a water bath may circulate. The membranes used in this study were asymmetric cel- lulose acetate and a composite membrane having a poly- sulfone support. The cellulose acetate membranes were pur- chased from Osmonics, Inc. and are specified to have a 9A-97% NaCl rejection. The pure water flux is 10-15 gallons per square foot per day at A00 psig. The composite membranes were donated by Desalination Systems, Inc. The membranes consist of a polysulfone sheet with a thin coating of material on one side. This coating is responsible for the selection characteristics of the 22 S. S. Screen (0.02257) S. S. Porous Plate (0.052.) ilter Paper (0.006‘) M embrane (O .005 7) g 7 Upper Chamber 1 I 0.081% 1 Lower Chamber Port Y \ “ ‘ Feed 1.980 s 0323’ 0355* Entrance A Figure 11-2. Upper and Lower Chambers of Membrane Cell with Dimensions. 23 membrane. The material is derived from aromatic polyamide polymer whose exact nature is proprietary. The membrane is specified to reject approximately 80% NaCl and has a pure water flux of 3-5 x 10-5 grams per square centimeter per second per atmosphere. (See Table II-l for list of mater- ials.) B. Experimental Procedures Material balances were needed to determine membrane re— jection coefficients and net fluxes through the membrane. Feed solutions were made up either by volume or weight. Samples were taken from the feed, permeate, and concentrate streams in clean one or two dram vials. When the membrane flux was to be determined the permeate stream was collected in pre-weighed vials during measures time intervals. The filled vials were then re-weighed. The difference in weight was divided by the total membrane area and collection time to yield the membrane flux. The solute concentration in the collected samples was determined by measuring the samples refractive index using a sodium lamp and comparing the result to a previously con- structed standard curve. The standards used to construct the standard curve were made using an analytical balance and their solute weight percentages were determined to a hundredth of a weight percent. The standard's refractive index was measured and plotted 2A Table II-l. List of Materials. —Chemicals— Chemical Grade Source Decalin 97% Fisher Scientific n-Decane 98% Matheson, Coleman & Bell l-Decanol 99% Aldrich l-Decene 96% Aldrich Ethanol 200 Proof AAPER Alcohol & Chemical l-Hexadecanol 96% Aldrich l-Hexadecene 9A% Aldrich 1-Tetradecene 95% Aldrich Water Distilled, 1x —Membranes- Class Type %RNaCl Product Rate Aromatic Polyamide G5 80 3-5 x 10’5 S/(cm2 5 atm) Asymmetric Cellulose SEPA 97 9A—97 10—15 gfd at Acetate A00 psig -Membrane Cell- Manufactured in the MSU Engineering Machine Shop 25 against the standard's concentration. The measurements were made on a thermostated (25°C) Abbe-type refractometer with a precision of 0.0005 refractive index units. A least squares fit to the plotted standard's concentra- tion versus refractive index was used to construct a linear equation. For example, for l-hexadecanol dissolved in ethanol, the equation was determined to be, Wt% Hexadecanol = 1,212.7 * refractive index + 1,6A6.0 The error in the calculated solute concentration was set equal to the largest difference between any of the known standard concentrations and the concentration calculated using the measured refractive index. The average error was 1.1A weight percent, and the largest error was 1.5 weight percent. A fresh membrane was used for each solute-solvent system to insure that each system was tested under identi- cal membrane conditions. The membranes compacted when initially subjected to a constant applied pressure. Mem- brane fluxes showed initial rapid decreases which leveled off with time. The effect on measured solute concentration in the permeate and concentrate streams was less than ex- perimental error after approximately 20 minutes. The membrane system was considered to have reached steady state conditions at this point. 26 For the percentage rejection versus applied pressure experiments solute concentration measurements were col- lected over time at each applied pressure. The system was considered to have reached steady state conditions and data were taken when the measured concentrations showed less than experimentally significant changes between measurements. Experiments exploring the effect of feed solute concen- tration on permeate solute concentration were done at two different applied pressures for each solute-solvent system tested. Solute concentration measurements were taken over time at each applied pressure to insure steady state con- ditions had been reached before data were taken. The pres- sure was then changed to the second applied pressure holding the feed solute concentration fixed. Again solute concen- tration measurements were taken over time to insure steady state conditions. After data were taken at the second pres- sure, the pressure was returned to the first pressure and a new feed solute concentration was tested, etc. To minimize any compaction effects due to cycling between the two pres— sures, the membranes used in this study were pre—conditioned with pure solvent at 1000 psi for at least four hours and then immediately used. The membrane cell sat upon a Sargent magnetic stirrer. This stirrer rotated a magnetic stir bar within the lower chamber of the membrane cell at 30-60 rpm. This stirring 27 was done to keep the solution well mixed and decrease con— centration polarization effects. In Operation, the magnetic stirrer generated enough heat to raise the temperature of the solution and membrane within the membrane cell. It is known that changes in temperature affect membrane performance (Sourirajan, 1970). To ensure isothermal conditions Of 25°C, heating channels were bored through the body of the membrane cell and thermostatted water was pumped from a Haake water bath. C. Solute-Solvent Systems It is desirable to select as broad a class of solute- solvent systems as possible for reverse osmosis experi- mentation so that the effect of molecular weight (or molar volume), chemical class, pressure gradient, and feed concentration can be studied. However, not all solute- solvent systems can be utilized. The study of the ethanol-water system was attempted using a cellulose acetate membrane. The measured differences between the permeate and concentrate solute concentrations were less than the error of measurement (1 wt%) at all ap- plied pressures (from 200 to 800 psi in 200 psi intervals) and two feed concentrations (8.72, 21.52 wt% ethanol). The membrane was next conditioned by being exposed to a 800 psi applied pressure for 5 hours and then exposed to 28 feed concentrations Of 96.5, A.56, and 8.72 weight percent ethanol. No difference in solute concentration between the permeate and concentrate streams could be detected. The membrane flux measured during the pressure conditioning A g/(cm2 s) indicated the membrane was not (12.51 x 10- leaky. It was concluded that the ethanol—water system was not a suitable system for study since the separation of the solute was too low to be measured using the available equipment. Solute-solvent systems which did show significant selec- tion and reproducibility were found. These systems consisted of ethanol as the solvent, and various organic liquids and solids as solutes. These solutes are listed in Table II-2. They were chosen on the basis of coming from the same chemical class but differing in molar volume, or having approximately the same molar volume but coming from different chemical class. As a rule, the percentage rejection coefficient was intermediate to that of ethanol-water (0.%) and sodium chloride-water (90.%). D. Relationship Between Permeate and Solute Concentration In the previous chapter it was shown that the non- porous membrane structure theory predicted a nonlinear relationship between the permeate and bulk solute concen- tration while the porous membrane structure theory could model either linear or nonlinear data. Experiments were 29 Table II-2. Physical Properties Of Organic Solutes. Molar Vol. Compound Density (g/Cm3) Mole Wt. (cm3/mole) Decalin 0.8695 138.25 159.00 Decane 0.7300 1A2.29 19A.92 l-Decanol 0.8297 158.29 190.78 l-Decene 0.7408 1A0.27 189.35 Ethanol 0.7893 A6.07 58.37 l-Hexadecanol 0.8176 2A2.A5 296.5A l-Hexadecene 0.7811 22A.AA 287.3A l-Tetradecene 0.77A5 196.38 253.56 Molar Volume = Molecular Weight/Density performed to test the linearity of C vs. C for organic 2p 2C solute-ethanol solvent separations over a range of concentra- tions and pressures. The dependence Of the solute permeate concentration, C2p’ on the solute concentrate concentration, C20, was experimentally found for several solute-solvent systems by varying the feed concentration of the solute while holding the applied pressure constant. Some systems showed linearity and supported the porous model; some could be equally well modeled by either a linear or nonlinear curve (nonporous model) and some showed behavior which was not predicted by either the porous or nonporous model. This 30 behavior could however be rationalized in terms of the physical assumptions of both theories. The solution within the lower chamber of the membrane cell was stirred with a magnetic stir bar at 30 to 60 rpm. It is assumed in the following discussion that this stirring was complete enough that the solute concentration in the concentrate stream was equal to the solute concentration in the membrane cell. Under these conditions C2C is equal to the bulk concentration C2B discussed in the preceding chap- ter. The results for the hexadecanol-ethanol system using a cellulose acetate membrane are shown in Figure 11-3. Data were taken at A00 and 800 psi applied pressure. Little difference can be seen between the two data sets. The data were fit to a linear model using the least squares method, with the result expressed in weight per— centage, C2p = 0.5339 C2C - 0.2AOA II-l Since the solute concentration could be determined to within 1.1 wt % the calculated nonzero y—intercept value is not significant. The linear fit is drawn as the solid line in Figure 11-3. The data were also fit to the nonlinear case as pre- dicted from the nonporous model (Equation I-lO) using the 31 30 C / 2P - . / Nonlinear Casea,t ,/ // X ’/ lO 1’ 1’ 6‘ _- l’ zj:>”’ / / " .I o = A00 psi '- /§“ Linear Case /' X==BUmei *0 41 11_ J I 1 I J O 10 20 30 2C Figure 11-3. Permeate Concentration vs. Concentrate Con— centration of l-Hexadecanol in Ethanol. Applied pressure is A00 and 800 psi. 32 initial slope of the data for the value of g2. The non- linear fit is drawn with the dashed line in the figure. The difference between the two drawn curves increases with increasing C2C values and is greater than experi- mental uncertainty for C2C values greater than 10 weight percent. The linear curve (porous membrane model) can be seen to fit the data better than the nonlinear curve (nonporous membrane model) throughout the range of 020. The results for the decanol—ethanol system using an aromatic polyamine membrane are shown in Figure II-A. In this case both the nonlinear and linear models fit the data to within experimental uncertainty and would serve equally well to explain the results. Data were collected at 800 psi applied pressure and is accurate to one weight percent. Only one high pressure was used since at low pressures the membrane flux was too low to be of practical use. The same procedure as before was used to fit the data. Based on the above two cases, it can be stated that the porous membrane structure theory better fits the case of a large solute - small solvent - low density membrane (l—hexadecanol - ethanol - cellulose acetate) better than the nonporous membrane structure theory. But that for a medium sized solute - small solvent - dense membrane (1- decanol - ethanol - aromatic polyamide) no such conclusion can be reached. It is possible that as the density of the membrane is increased, the membrane structure becomes 33 A0 .- 3O __ 20___ 2p Linear Case 0% 1", 10 __ 2/ O’ / I’a’ . I / / Nonlinear Case // O 10 20 30 C20 Figure II-A. Permeate Concentration vs. Concentrate Con- centration of l-Decanol in Ethanol Using an Aromatic Polyamide Membrane. Applied pressure is 800 psi. 3A less porous and better represented by a nonporous struc- tural theory. In Figure 11-5 the data for the l-decene-ethanol, and decalin-ethanol systems using cellulose acetate membranes is presented. Data was collected at A00 and 800 psi for both solute types and is accurate to 1.00 wt %. For both systems the pressure data show higher selection against the solute. There are two major differences between these two solute-solvent systems and the previous cases. Firstly, as the concentrate concentration, C20, increases so does the permeate concentration, C2p’ but at a decreasing rate. This type of behavior is predicted neither by the nonporous nor porous models. Secondly, there appears to be a minimum value of C20 for each solute type below which no separation takes place. That is, the difference in solute concentra- tion between the permeate and concentrate streams decreases as the concentrate stream concentration decreases. At the lowest measured CC values, the difference is less than or equal to the error in determining the solute concentration (1.26 wt% for 1-decene and 0.6 wt% for decalin). To inter- pret such results it is necessary to look at the under- lying physical picture Of both theories. The structure of the membrane is made up of both the membrane polymer and solvent - that is, some solvent mole- cules are associated with the polymer such that they are 35 .Hmo oow osm oo: wH madmmoaq OOHHQQ¢ .Hocmnpm CH CHHOOOQ osm Hosmnum CH ocooomua no coapmppcoocoo opmnpcoocoo .m> :oapmhpcoocoo oumoEpom .mIHH opswfim Tl co 3 on om ca q _ a _ \ 0 Hum oow u hadron l Ga 03 n m4... ll OH 9 O f x\\\\\ .. 8mm ... « \u.. l 8 J 36 stationary with respect to the membrane flux. This is especially true of membranes made from cellulose acetate. This type of membrane must always be kept wet with solvent to prevent drying and permanent loss of permeability. In terms of the porous structure membrane theory, the membrane pore size distribution will be affected by the amount of solvent associated with the membrane polymer. Within this distribution there will be pores so large that they allow the bulk solution to pass through and pores so small that they allow only a minimal amount of solute to pass. When the solute concentration is increased in the bulk solution and proportionally more solute is moving through the membrane pore, there will be a competition be- tween the membrane polymer and the solute molecule as to which will be solvated by the 'structural' solvent. As solvent is stripped from the membrane pore, the individual polymer segments will tend to move closer together and the pore radius shrink. Conversely, as the solute bulk con- centration is decreased more solvent will be available to solvate the membrane, the polymer segments will be pushed further apart, and the pore radius expand. From this picture, both of the non-predicted phenomenon of Figure 11-5 can be rationalized. First, as C2C is in- creased, the average pore size Of the membrane decreases. This brings with it an increase in selection against the solute. Therefore C2p should increase at a slower rate 37 than C This is the behavior shown by the data. As 2C‘ C2C decreases the selection against the solute should de- crease as the average pore size increases. At some low value of C2C the selection will go to zero. This behavior is shown by the data where the minimal C2C value for the l-decene-ethanol system is 5 wt% and 2.5 wt% for the decalin-ethanol system. Note that these minimal values appear to be pressure insensitive. For the nonporous membrane structure theory, a case similar to the above can be made. Instead of the polymer and structural solvent forming the pores of the membrane, they form a third phase through which both mobile solvent molecules and solute molecules diffuse. As the solute concentration increases structural solvent is again stripped causing the membrane to become denser. This increase in density has the effect Of slowing the solute molecule re- latively more than the solvent molecule. This would ac- count for the increased selection at high C2C values. At low 0 values the membrane is less dense and the relative 2C differences in mobility between the solute and solvent mole- cule disappear. Since the two types of molecules move through the membrane equally fast no selection would be seen below some C2C value. These structural solvent effects are not seen in the l-hexadecanol-ethanol-cellulose acetate membrane system, or the l-decano1—ethanOl-aromatic polyamide membrane system. 38 Large solutes such as 1-hexadecanol (see Table II-2 for solute molar volumes) may be less sensitive to membrane 'drying' since they will only move through the largest pores. These large pores will be less sensitive to the removal of structural solvent than smaller pores since pro- portionally more solvent must be stripped from them to significantly change their radius. Aromatic polyamide mem- branes require no solvent to keep their porous (ttgt, they may be stored dry). Since their pure solvent flux is less than 25% of the cellulose acetate membrane, they may be considered denser. As a consequence, they will be less likely to depend on the presence of solvent within the membrane to maintain their internal structure, and so be less sensitive to changes in solvent concentration. E. Membrane Selection versus Solute Molar Volume Ratio and Chemical Class The nonporous membrane structure theory predicts that membrane selection follows Equation I—lA, I m I ll <2 H lm ll H l l-" .t: This prediction was tested in two ways. First, a series of solutes of the same chemical class but of different molar 39 volume were tested under the same applied pressures and ap- proximately the same concentration. The solutes were 1- decene, l-tetradecene, and l-hexadecene. The solvent was in all cases ethanol. The results of these experiments are shown in Figure 11-6. The results are in qualitative agreement with the pre- diction since as the solute molar volume increases the solute selection decreases and the percentage rejection increases (see Table 11—2 for molar volumes). The data were also fit to Equation I-lA and the exponent n calcu- lated. The results are shown in Table II-3. Using l-decene as a basis, it can be seen that the cal- culated values of n are greater than one. While no one‘ Table II-3. Ratios of Alkene Molar Volumes, Selection and the Calculated Exponent n. ” 7* a * Compound V/V S /S200 r1200 S /8800 n800 l-Decene* 1.00 1.00 1.00 1.00 1.00 1-Tetradecene 1.3A 1.93 2.25 2.31 2.86 l-Hexadecene 1.52 2.Al 2.10 A.A3 3.56 value of n is universally accepted, no commonly used theory or correlation has n greater than one. Also, if exponents greater than one were acceptable, it would be expected that 1&37— (l— T 80 _. HEHUECME} % R TEHMDEHEE 60 L— t I40 1 mama y. 20 .. .4 l l l l o 200 A00 600 800 A P (Ps1) —-’ Figure 11—6. Rejection Percentage Of Normal Alkenes in Ethanol vs. Applied Pressure. Feed concentra- tions in wt% are 33.1 for 1-decane; 33.0 for l-tetradecene; and 25 for l-hexadecene. L11 n should remain constant. This is not observed here. The value of n changes significantly between different solute pairs and pressures. In short, the results in no way can be said to support the nonporous membrane structure theory. The second test of the nonporous theory used a series of compounds of approximately the same molar volume but of different chemical classes. Again each type of solute was tested under the same conditions. The results of these experiments are shown in Figure 11-7. It is apparent that the nonporous prediction is not supported since only two of the solutes have similar rejection percentages and more- over of the four solutes used these two solutes have the largest difference in molar volumes. When the data is fit into Equation I—lA (see Table II- A) as before a much wider range of values for the exponent Table II-A. Ratios of C10 the Calculated Exponent n. Molar Volumes, Selections, and ~ ~* * * Compound V/V S /8200 n200 S /S800 “800 Decalin* 1.00 1.00 1.00 1.00 1.00 l-Decene 1.19 0.809 -1.21 0.510 -3.85 l-Decanol 1.20 0.727 -l.75 0.337 -5.97 n-Decane 1.23 1.08 0.370 0.979 -0.10 A2 80 (- 6O _ / :t’4i~imnANE A0 ... ' ' IEDENE (II- 20 r— ' ./ DEGANOL k I J I I 1 J J i o 200 A00 600 800 AP (PSI) —-> Figure II-7. Rejection Percentage of C10 Compounds in Ethanol vs. Applied Pressure. Feed concentra- tions in wt% are 3A.9 for decalin; 32.7 for decane; 33.1 for l-decene; and 3A.3 for l- decanol. A3 n is found than previously (i.e., -5.97 - 0.36) with the majority of values less than zero. A negative exponent indicates that the larger solute is passing through the membrane faster than the smaller. This is Opposite to the nonporous membrane structure theory's prediction. Again, the value of n changes significantly between different solute pairs and pressures. On the basis of these results, it would appear a further assumption must be made if the nonporous theory is used to explain these results. An assumption made by Merten (Mer- ten, 1966) and which appears consistent with the rest of the nonporous theory is that there exists a distribution co- efficient for each solution component between the bulk solution and the membrane, i.e., K = ——— II-2 where K1 is the distribution coefficient for component i, and C is the concentration of component i in the membrane. 1M Equation I-lA is modified to, Dl Kl _ K1 V2 n _ 51 D K " it" '~_' ‘ s— “'3 2 2 2 V1 2 When n is taken to be one third, the ratio of the dis- tribution coefficients needed to produce the equality of AA Equation II-3 may be calculated. This has been done for the previously considered alkene and C cases and the 10 results are shown in Tables II-5 and 11-6. The most striking aspect of the tabulated results is that in almost all cases the effect of the distribution co- efficient is seen to be greater than that of the diffusion coefficients. Since the porous membrane structure theory assumes that selection is due to the solute distributing itself between the bulk solution and the solution next to the membrane, a distribution coefficient for the solute can be written, i.e., Ci K2 = E- II-A 2B where G; is the solute concentration next to the membrane. It can be concluded that whether the nonporous or porous membrane structure theory is used, both require that the important part of selection occurs at the face of the mem- brane. And, as a corollary, while transport mechanisms might contribute to the selection process, other processes appear more important. F. Membrane Selection and Pressure Effect As shown in Figures 11-5, 6, and 7, as the applied pressure is increased the percentage rejection also increased. This type of pressure effect has been reported in membrane A5 Table 11-5. Ratios of Alkene Molar Volumes, Distribution Coefficients for n = 1/3. Compound (V/V’*)]‘/3 K*/K K*/K 200 800 l-Decene* 1.00 1.00 1.00 l-Tetradecene 1.10 1.76 2.10 l-Hexadecene 1.15 2.10 3.85 Table II—6. Ratios of C10 Molar Volumes, Distribution CO- efficients for n = 1/3. Compound (V/V*)l/3 K*/K K*/K 200 800 Decalin* 1.00 1.00 1.00 l-Decene 1.06 0.763 0.A81 1-Decanol 1.06 0.686 0.318 n-Decane 1.07 1.01 0.915 A6 literature for a wide variety of membrane systems besides cellulose acetate. These include membranes made from cel- lophane (Michelsen and Harriot, 1970), aromatic polyamide (Dickson gt gt., 1976), and polyvinyl alcohol polymers (Reid and Spenser, 1960) as well as membranes composed Of porous clay plugs (Jocazio gt gt., 1972) and sheets of graphic oxide (Flowers gt gt., 1970). The underlying causes Of this effect can be explained in terms Of the nonporous membrane structure theory. In Section D the increases in rejection with increasing C2B values for l-decene and decalin were rationalized as being due to density changes in the membrane. These changes were thought to be caused by 'structural' solvent moving into or out of the membrane. The increase in rejection of the solute was assumed to be due to the solute being slowed relatively more than the solvent in moving through the membrane. If the solute is relatively more sensitive to density changes than the solvent, it is consistent for the solute to be less sensitive to pressure changes than the solvent (ttgt, the solute molecule is transferring relatively more momentum to the membrane than the solvent molecule under git conditions). As the applied pressure is increased, solvent molecules flow through the membrane relatively faster than solute molecules and the permeate stream has relatively more solvent than before the pres- sure was increased. The result is the observed increase A7 in rejection of the solute with increasing pressure. It is not so clear how this pressure effect can be ex- plained in terms of the porous membrane structure theory. Selection is assumed to be due to the distribution of the solute between the bulk solution and the solution next to the membrane surface. The region of transition between these two solutions is probably much less than 1000 A in width (Derjaguin and Churaea, 1969). It is unlikely that a significant pressure gradient would be seen over such a small distance. In addition, increases in the scalar pres- sure are known to have little effect on equilibrium constants such as distribution coefficients. In sum, it appears im- probable that the pressure effect can be explained in terms of chemical, hydrostatic, or hydrodynamic effects modifying the selection process directly. It is possible that the pressure effect is mechanical in origin. That is, as the applied pressure increases the membrane is compressed. This compression would be greatest in extent where the membrane is less dense. This would be the spongy sub-layer and any parts Of the dense layer which were relatively less dense than the material sur- rounding them. Such low density areas in the surface layer might be responsible for leaks which allow bulk solution to pass through the membrane. In Figure II-8 data are presented for the separation of sodium chloride from water using a cellulose acetate membrane. I 300 T 220 c p 1A0 60 , it I l J o 0 RX) .MXD IRX> 00 —-s Figure 11—8. Permeate Concentration and %R vs. Concentrate Concentration of NaCl in Water. Concentra- tions are expressed in ppm. Applied pres- sure is AOO psi. A9 As shown, the extrapolated salt concentration in the per- meate stream and the concentrate stream become equal at a concentration of 32 ppm. This minimum level for observ- ing separation differs from the previously discussed 1- decene and decalin cases since the data show no decrease in the slope of C2p with respect to C2C (l;2;2 the membrane appears not to be changing in density). This implies that the minimum level of selection is due to a permanent leak rather than changes in the average pore radius. The effect of such a leak is swamped out as C2C increases and may be- come undetectable at high C2C values in the presence of other effects such as concentration polarization. Membrane compression effects are most easily seen in fresh membranes which have not previously been exposed to high pressures. Figure II-9 andlI)are graphs of pure ethanol flux through fresh aromatic polyamide and cellulose acetate membranes versus time. In both experiments fresh membranes were subjected to applied pressures of 1000 psi using pure ethanol and the flux measured at approximately 20 minute intervals. Both studies show decreases in flux over time. The cellulose acetate membrane can be considered less dense than the aromatic polyamide membrane because Of its' higher flux and greater decrease in flux over time. Evidence of the link between compression and selection is shown in Figure II-ll. Here a fresh membrane has been used in a reverse osmosis separation of decalin from 50 5— 6) 32+_ 0] 8 E :r . S ‘\\t7~43_—13—__—C¥_ ‘“{}———-<}—r ‘3 11c}. N 3.. E rt. 2 J J l l o 1 2 3 A Figure 11-9. Pure Ethanol Flux Through a Fresh Aromatic Polyamide Membrane vs. Time. Applied pres- sure is 1000 psi. 51 32'— 30__ 28_ \. I 26- 08 2A.. \ 3’ \ :3 22- \ >4 V. E? \. El 20+- \K .\.\ 18- r r r J, I l. l J l J o 1 2 3 A TDIE(HR)—’ Figure II-10. Pure Ethanol Flux Through a Fresh Cellulose Acetate Membrane vs. Time. Applied pres- sure is 1000 psi. Additional feed was added at times marked with 'r'. 52 15 h—- c c ..16 1, __ “l I Q E? I __14 5m tn 91)) V a 1“ >< a s 8 12 7 cl: ._ «P C X ti 9_. p '3 3 N _10 r r 1 l 11 l 11 l o 10 20 30 A0 50 TIME:(MIN.) ——. Figure II-ll. Permeate Concentration, Concentrate Concen- tration, and Membrane Flux Through a Fresh Cellulose Acetate Membrane vs. Time. Solute- solvent system was decalin-ethanol. Applied pressure is 800 psi. Additional feed was added at times marked with a 'r'. 53 ethanol. The permeate flux has also been measured. As the flux drops so does the solute concentration in the permeate stream; the rejection percentage increases. A possible explanation Of this data would be that the com- pression of the membrane reduces or eliminates leaks. This could occur by compressing the leaky area of the mem- brane surface or by pushing the spongy membrane material beneath the dense layer into the leaks. The effects discussed above are in part irreversible in nature. Once a membrane has been exposed to high pres- sures it does not regain its initial permeability after a rest period. It is possible however that besides the ir- reversible effect there exists a reversible effect which is not so pronounced. This reversible effect may be the basis of the Observed pressure effect. Such an effect would also be consistent with the nonporous membrane structure theory if the compression at only the spongy layer was responsible for the increase in the rejection percentage. CHAPTER III SINGLE AND MULTI-STAGE REVERSE OSMOSIS SEPARATION SYSTEMS A. Design Parameters Schematically, a single reverse osmosis separation stage consists of a chamber into which is introduced a pres- surized feed stream, FF, with solute concentration, XF. This is shown in Figure III-l. One wall of the chamber is a membrane. The flow leaving the chamber through the mem- brane is referred to as the permeate flow, FP’ with solute concentration XP' The remainder of the original feed stream is the concentrate stream FC, with solute concentration XC. This stream leaves the chamber through an outlet valve. It will be assumed that the fluid in the chamber is well stirred and the solute concentration in the chamber is equal to the concentrate stream concentration XC. To be of practical use, the permeate stream concentra- tion XP must differ from the concentrate stream concentra- tion XC. The measure of the difference between these two concentrations is the rejection factor R. This parameter is defined as, R = 1 - (XP/XC) III-1 5A 55 A Figure III-l. \\\ \\ OUNIE'WMWE Reverse Osmosis Separation Stage. 56 It will be assumed in the subsequent discussion that the rejection factor is a function only of pressure. The rejection factor, R, may in general take any value from minus infinite to plus one depending on the solute- solvent-membrane system and the pressure. However, in the subsequent discussion, R will be assumed to lie between zero and one. This may be done with no loss of generality for any solute-solvent system by calculating R for the com- ponent whose permeate stream concentration is less than its concentrate stream concentration. The other parameter of practical importance is the ratio of the permeate stream flow to the feed stream flow, f, i.e., f = —— III-2 This f factor is nearly unique to reverse osmosis unit separation. In other separation techniques such as distil- lation or absorption the f factor can not be adjusted for each stage by the operator; Only overall reflux ratios can be manipulated. In reverse osmosis any value of f can be attained by opening or closing the concentrate stream valve. As the valve is closed restricting the concentrate stream, the solute concentration in the chamber increases. The size of this increase depends on both the R and f 57 factors as can be shown from the solute material balance equation, X F = X F + X F III-3 Dividing Equation III-3 by F and substituting into the F resulting equation, Equations 111-1 and III—2,yie1ds, O [.1 r— : I_-_R_f 111‘” Since XC cannot be greater than one, there is a maximum value for f for any given value of R and XF' This maximum f value, fLIM’ is, f =-———-—— III-5 The response of XC/XF to changes in f are shown in Figure III-2. From this graph it can be seen that as the solute concentration increases in the concentration stream, the volume of that stream decreases. As an example, con- sider the case where R is equal to 0.A. If the f factor is increased from 0.3 to 0.5 the concentrate concentration in- creases by 20%. Clearly there will always be a trade off between outlet concentrations and volumetric flow rates. 58 2.2 fLIM(XP‘=O ° 5) 2.0.— 1.8._ 113105506) 1.0 _ l J l I 0.0 0.2 0.1+ 0.6 0.8 f Figure III-2. Relationship Between the Flow Rate Ratio f and the Concentration Ratio XC/XF. 59 B. Single and Multistgge Reverse Osmosis Design Options Whether a single or multiple reverse osmosis separation is used depends on whether a single stage separation can meet or surpass the specified outlet conditions X F P’ P’ X0, and FC, given the inlet conditions XF, FF’ and the re- jection factor R. The value of R will be assumed fixed by the specified operating pressure. Using the specified value of XP’ the value of XC can be calculated from Equation III-l. The required f factor is found from Equation III-A using the calculated or speci- fied value of XC and the specified value of X The value F' of F and F is then found from Equation III-2. P C If the calculated concentrations and flow rates are considered satisfactory given the design specifications, then the design process may be considered finished. If the single stage cannot meet the required values, a multi- stage reverse osmosis separation scheme is indicated. C. Parallel Or Series Multi-Stage Reverse Osmosis Separa- tion Units Extensive variables such as flow rates may be adjusted to the designer's satisfaction without pressure changes by increasing the volume of the single stage or by running a number of stages in parallel as shown in Figure III—3. Parallel multi-stage systems may be reduced diagramically 60 Figure III-3. l \\ \\ l\\ Parallel Multi-Stage RO System. 61 to a single large reverse osmosis unit and so no new design equations are necessary. Single stage or parallel multi—stage systems may be found unsatisfactory if the separation attained is smaller than required. This would be the case where the product is too dilute or, for expensive solutes, where there is too much wastage. Series multi-stage reverse osmosis designs may be used to improve separation performance. An example of such a design is shown in Figure III-A. Series reverse osmosis systems are more complex to design than single or parallel systems since the number of independent equations needed to be solved increases by three for each additional stage re- quired, i.e., x = (1 - R) x III-6 Pi Ci x = x r + x (1-r ) = (1 - R f ) x III-7 Fi P1 1 0i i i ci FPi r =-——— III-8 i F Fi Only intensive variables need to be considered since the size of the individual stages can be adjusted to produce the re- quired flow rates. Because of this, a new equation can be written for the f factor in terms of the variables XP and i 62 PA PA l //7‘ XE," FFL‘ x , F p // XF’FF x,F p2 p2 Figure III-A. F I xFl’ FFl Series Multi-stage RO System. 63 XC . There will result a system of equations which may be i solved for each stage. This third equation can be derived from requiring the separation at each stage to be optimized. D. Optimization of Reverse Osmosis Separation The separation for each component of a binary feed stream can be expressed as, Pa g = F—-— III-8 Fa FCb h = F—— III-9 F b where the subscripts a and b stand for components a and b. Component b is the component whose rejection factor R is greater than zero. The term FPa is the permeate flow of component a, Fcb is the concentrate flow Of component b, and FFa and FFb are respectively the feed flow rates of com— ponent a and b. These functions may be rewritten in terms of the rejec- tion factor, R, the f factor, and the feed concentration of component b, XF’ as follows, 6A 1 ‘ (l-R)XF f 93: 1‘73?) ((l-Rf)) 111’” _ 1-1‘ h - (1 _ R I.) III-ll The rejection factor R is fixed by the solute-solvent-mem- brane system and the Operating pressure. The solute feed concentration X is determined by the streams coming into F the stage from different stages. This leaves the f factor as the only manipulable variable in Equations III-10 and 11. The separation is maximized when the fraction of com- ponent a that passes through the membrane and the fraction of component b rejected from the membrane are maximized. Various optimization functions can be constructed using these fractions. The product of g and h was selec- ted since the resultant function is defined and bounded between f equal to zero and one. Also the product has a well-defined maximum in this interval. This product will be defined as the optimization function Z, i.e., Z = g h III-l2 The variation Of g, h, and Z to different values of f is shown in Figure III—5 for XF equal to 0.2 and R equal to 0.2 and 0.8. The function g monotonically increases with 1,0 0.8 0.6 0.A 0.2 0.0 0.8 0.6 0.1+ 0.2 0.0 Figure III-5. 65 __ L. L. L. X? 0.2 f 0.53 1 MAX 1 I The Functions g, h, and Z versus the Flow Ratio f. 66 increasing values of f while the function h monotonically decreases. Thus the function Z always has a maximum for some value of f between zero and one. It is this value of f, call it f that is desired. MAX’ The analytical solution for fMAX is found by taking the derivative of Z with respect to f at constant R and XF and setting it equal to zero. This procedure results in the following expression, 2 2 [2 xF — 2 — (3 xF + 1) R + XFR R2 [1 — (1 - R) XF] - 2 III-13 R Since the resultant equation is a cubic expression, the function Z has at most three maximum and/or minimum. The general form of Z for f ranging from plus to minus infinity is shown in Figure III-6. As shown, Z has three real roots. These occur at f equal to zero, one and f equal to (l/R) - (XF/R)(l-R). There is an asymptote at f equal to (l/R). Finally, there are two local minimum and one local maximum. This last local maximum is fMAX' For a cubic equation with three unequal real roots the only practical analytical solution is the trigonometric 67 S. o I . Z U g —- 68 solution (Perry and Chilton, 1973). This yields a solu- tion for fMAX of, \ _ 1 (l-R)XF (2XF+1) fMAX - E + 2 2 - R x 3R XF 3 EEEU 1/3 3/2 XF cos-l / + 2h [02”) -J T A graph of fMAX versus XF for various values Of R is shown COS III-1A ~— in Figure III-7. Despite the apparent complexity Of Equa- tion III-1A, f is a well behaved function showing a slight MAX monotonic decrease with increasing values of XF until fMAX is equal to fLIM' E. Series Multi-Stage Reverse Osmosis Separation Calculations Using Equations III-6, 7, and 1A, the number of stages required for a given separation may be calculated from the specied feed and outlet conditions and the rejection factor. The calculation scheme is shown in Table III-1. Starting from the concentrate end and working toward the feed stage, XCl is set equal to the specified value Of the concentrate outlet concentration in step 1 to find XPl. The feed con- centration and the f factor for stage one is found by 69 ) ~31 R=O°1 1: M(__________.... 3‘ O .3) (350/ {Lm/ ... 9? o 0 xi: ’05), I KFI/ t~ CH 9Q)" — g 0 C. O , «A ‘9 *3 C— O. O:\\// g \V/ E“ £69" “T ‘6 :0 >4 s :0 \ / ' 009/ _~ on T G/ O S as H o “3 $4 to --l 0: ‘T U: "a n P" O O O O C II — F: m 0 I l I I, l O} CO [~— \0 Ln .3 m o o o o o o 0 c3 6 Table III-1. 70 Calculation Scheme for Series Multi-Stage Reverse Osmosis Separation System. 1. Calculate X = pi 2. Calculate 3. Calculate A. Calculate 5. Calculate X and f F1 1 by iteration. (1 - R fl) XCi the feed and permeate flow rates. the concentrate stream concentration for the next stage. 71 iterating until the value of XFl used to calculate fl in Equation III-1A agrees with the calculated value Of XFl from step 2. The value of fl is then used to calculate the flow rates F and FPl. In general the concentrate F1 stream from the next stage, FC , is equal to the dif— 1+1 ference between the feed stream FF and the permeate stream i from the stage below, FP . For the first stage FP is 1-1 i-l set equal to zero. The concentrate concentration of the stage above the first stage, X , is found by mass balance C2 in step 5. Calculations for the next stage may be carried out and continued until the permeate concentration calculated for the kth stage is less than the feed concentration. Calculations are then done from the permeate end of the system moving toward the feed stage until the calculated concentrate con— centration for the mth stage is greater than the feed con- centration. The total number of stages is then the sum Of the stages calculated in the two series calculations. An example of this type of calculation for different values of R is shown in Figure III-8. 72 .m .mm powwow z .wnHHH osswaa ¢||.m o.H m.o s.o m.o m.o muuilruwiiiiiu_ _ _ (A _ u a o// o/o/ ooo.a n as an Hoo.o u x Ho mmm.o u x mo.o u ex .3 H ¢—— 3389119 armaqurew pearnbag ,io .13qu CHAPTER IV REVERSE OSMOSIS SEPARATION ENERGY REQUIREMENTS AND EFFICIENTS A. The Work of Pressurization In the first step of a reverse osmosis separation the feed stream is pressurized. The work of pressurization, Wp, is due to compressing the feed stream from its initial volume to a final volume, i.e., wp =[VF p dV IV-l VI The degree that a substance is compressible is de- termined from its compressibility factor, B, where B is defined as, -1 3V _ B -V 5-5)T IV2 and V0 is the volume of the substance at a standard pres- sure po. Assuming B to be a constant, Equation IV-2 can be integrated, substituted into Equation IV—l, and the resultant equation integrated to yield, 73 7A 80 Vo 2 2 w. = Ts - p1) where the subscripts refer to the final, F, and the initial, 1, pressure. The compressibility factor B is largest at low pres- sures, rapidly decreases with increasing pressure, and then slowly decreases at high pressures. Using the compres- sibility factor for a substance at one atmosphere in equa- tion IV-3 will yield the maximum calculated work of pres- surization. From various Handbooks (Perry and Chilton, 1973) it may be seen that the maximum value of B for water, or- ganic and inorganic liquids is approximately 10'“ recipro- cal atmospheres. Using a specific density of 0.8 grams per milliliter and initial and final pressures of one and one hundred atmospheres results in a calculated work of pres— surization of 6.332 x 10'2 joules per gram liquid pres— surized. The true value for Wp must be below this cal- culated value. Of course working pressures for reverse osmosis separations may be much less than one hundred atmospheres which would also lead to lower values for the work of pressurization. B. The Work of Separation and Transport Once the feed has been pressurized, liquid will start to flow across the membrane. This liquid will have a 75 different concentration than the liquid on the high pres— sure side. Steady state concentrations for the permeate and concentrate streams are reached when the solute con- centration of the concentrate stream is equal to the solute concentration in the reverse osmosis stage. The time re- quired for this to occur is a function of the feed stream flow rate and the volume of the stage. To maintain this steady state flow work must be done to maintain a steady pressure. The pressure-volume work done on the volume of liquid which moves across the membrane con- Invite-Ar 1L- sists of the work of separation and the work of transport. The work of separation is the work required to separate a volume of liquid of one concentration from another volume at a different concentration and is equal to the difference in Gibb's free energy of the two solutions at the same tem- perature and pressure as the separation stage. This dif- ference may be called the free energy of separation, AGS, and is equal to the negative Of the Gibb's free energy of mixing for the process where the two solutions are re-mixed. The work of separation is then equal to the negative of the Gibb's free energy of mixing, AGMIX’ ttgt, NS = - AGMIX IV-A The free energy Of mixing of the two solutions may be cal— culated from standard thermodynamic properties and mixing 76 rules. The work of transport is the pressure—volume work done on the permeate liquid to overcome the frictional forces which impede the membrane flow. This work is equal to the volume of the permeate liquid times the difference between the ap- plied pressure and the osmotic pressure due to the concen— tration gradient across the membrane, i.e., - p ) IV-S A where V1: is the volume transported, p sure, and p ap is the applied pres- osm is the osmotic pressure. An approximate value of W may be calculated using the equilibrium osmotic t pressure due to the solvent concentration difference ac- ross the membrane (Equation 1—2) for the value of posm' C. Power Requirements and Efficiencies The power required to perform a separation can be cal- culated from experimental measurements using the following formula, P = p v A J IV—6 where P is the power required to move one gram of liquid ac- ross the membrane, V is the specific volume of the permeate flow, Jp is the permeate flux in grams per square centimeter (ff-fl I... 1 Jun!“ ‘ I!“ 77 per second, and A is the area required, given Jp, for one gram per second of permeate to flow. The power can be divided into the power required to move one gram of permeate solution across the membrane re— versibly, P and the power required to overcome the rev’ frictional forces of the process. The reversible power can be calculated using an equation Of the same form as Equation IV-6 using the reversible pressure rather than the applied pressure. For a reverse osmotic separation the reversible pressure is the equilibrium osmotic pressure, peq OSITl _ eq A Prev - posm V A J IV-7 The efficiency of the reverse osmosis process, n, can be equated to the ratio of the reversible power to the total power requirement, eq _ Prev _ Posm 8 n - P - p IV- ap Some values of required powers and efficiencies are listed in Table V-l. As shown, the power does not vary greatly for a given pressure no matter which solute is used. However the area needed to produce a flow of one gram per second does fluctuate with solute type. Efficiencies are maximized for low applied pressures, and high rejection coefficiencies. 78 mm.mm momz.o Hano.m mmmm.a mmmw.m mm.omm amm>.o :>.mH mm.wm cow A wm.mam wwom.HH mm.:a mm.mm cow mm.wm maom.o HH>>.H noma.o mmmm.m mm.oom m:mm.m wH.wH mm.mm co: H:.mm mwmo.o ommm.o ammo.o 3500.5 mo.om omm.ma m:.: Hw.m oom A.m om.m H:.m oom A.Hm mmmo.o mmom.o wmma.o mmw:.m :m.mm me.m mm.m om.m co: :HHoooo m a c Ampumzv ANEV Ampumsv Afimdv AmmEo\wv Maps Map: Afimdv Aocmmnsozv >opa mop< a Show :oa.ah Qom Hopsoefipoaxm mo modam> Oopooaom .H.>H oaome CHAPTER V CONCLUSION AND SUMMARY The experimental results presented in this work show re- verse osmosis separations of organic solute - organic solvent feed streams can be carried out using asymetric cellulose acetate and aromatic polyamide membranes. While these or- ganic feed streams are not found in commercial separation processes, the experimental results arising from their sepa- ration do have implications as to the opportunities and dif- ficulties Of applying reverse osmosis to industrial nonelectro- lytic separations. The relationship between feed solute concentration and permeate solute concentration was used as a probe of the mem- brane structure. While no general trend could be discerned, the results support the theory that as the membrane becomes more dense the membrane structure changes from porous to nonporous. As shown by the membrane selection of alkenes and C10 compounds the mechanism of selection does not appear to be based on the relative mobility of the solute and solvent mole- cules within the membrane. As shown in Tables II—3 through 11—6, relative mobilities could account for only a small fraction of the observed selection. If selection does not occur inside the membrane it must occur at the membrane - bulk solution interface. Two different mechanisms for this 79 80 selection process can exist. In the first, the solute and solvent molecules distribute themselves between the bulk phase and the membrane phase. In this case the concentra- tion of each feed solution component in the bulk solution to its concentration in the membrane could be related through a distribution coefficient as described by Equation II—2, where each coefficient is independent from the other distri- bution coefficients. A second possibility for the membrane selection process would be that the feed solution nearest to the membrane face interacts with the membrane surface in some manner. This in- teraction leads to the solute molecules seeing the solution next to the membrane as being different from the bulk solu- tions. The differences in solute concentration in the bulk region and the region next to the membrane could again be related through a distribution coefficient as shown in Equation II-A. Membrane selection can be affected by solute feed con- centration. This is seen for the l-decene - ethanol and decalin - ethanol feed systems. As the solute concentrate concentration for these systems increased so did the permeate solute concentration but at a decreasing rate. This effect was explained as being due to the movement of lstructural solvent' into or out of the membrane which caused the mem- brane to change either its density or the average size of the membrane pore. Alternatively, such behavior could be at- tributed to a concentration dependence Of the selection 81 mechanism itself, i.e., that the distribution coefficients were concentration dependent. The 'structural' explanation appears more plausible than a solute concentration effect on the selection mechanism for two reasons. First it readily explains the existence of a minimum solute concentration below which no separation occurs as is seen in the l-decene - ethan- ol system at 1.26 wt % and in the decalin - ethanol system at 0.6 wt %. An effect based on concentration dependence of the selection mechanism would tend to disappear as the solute concentration decreased but the selection mechanism should remain Operational. Secondly, no concentration effect is seen in the 1-hexadecanol — ethanol system or the l-decanol - ethanol system. It is not apparent why the selection mechanism for these systems would be unaffected by changing the solute concentration while the previously mentioned 1- decene and decalin systems show such pronounced effects. Membrane selection is also affected by the size of the pressure gradient imposed across the membrane. As the pressure gradient is increased the rejection coefficient percentage, % R, for the alkenes and the C compounds 10 also increases. It is unlikely that very great pres- sure differences will be seen in the solution at or near the membrane surfaces, thus the membrane selection mechan- ism would see no great pressure gradients. Also, increases in the scalar pressure are known to have little effect on equilibrium constants such as distribution coefficients. 82 Therefore it is unlikely that a direct pressure effect on the selection mechanism can explain the observed changes in selection. Instead the mechanical compression of the mem— brane material and subsequent reduction in membrane leaks appears to best explain increased solute rejection with increased pressure. This compaction mechanism is supported by the experimental evidence for fresh membranes presented in Figures II—10 and 11-11 where the change in permeate con- centration of decalin with time follows the same type of curve as the reduction of flux of pure solvent. Based on the above experimental evidence, reverse os- mosis membranes appear to operate in the following manner. Bulk solution molecules move toward the membrane face. Near or at the membrane surface a selection mechanism Operates which favors the passage of one Of the types of feed solution molecules into the membrane interior. This mechanism can be represented by distribution coefficients which are probably not greatly affected by changes in solute concentration or applied pressure. The composition of the stream moving through the membrane interior remains constant. The stream does suffer a significant pressure drop due to the frictional interactions with the membrane material. Lastly, the stream emerges from the membrane and flows into the low pressure bulk solution. Based on this working model the interior of the membrane serves no practical purpose. Indeed it is seen as the major source of inefficiency in the separation process. 83 Theoretically, by reducing the thickness of the membrane interior the size of the membrane flux can be increased with no corresponding reduction in membrane selection. However as the membrane thickness is reduced any membrane surface irregularities will tend to become leaks which will reduce the overall membrane selection. Also thinner membranes may have a looser structure and be more affected by the movement of structural solvent than the thicker membranes. This in turn may increase the minimum level at which selection will occur. Thinner membranes will also be more prone to deform than thicker membranes. Here the true nature of the membrane structure will become important. Porous structures are weaker than nonporous structures and tend to buckle sooner under identical loads. Thus a porous membrane will have to be thicker than a nonporous membrane to withstand the same applied pressure. Alternatively, a porous membrane of the same thickness as a nonporous membrane will have to be Operated at lower applied pressures and thus more total membrane area will be required to get the same through put. The valuecfi‘the membrane selection for nonelectrolytes is smaller than that for electrolytes (ttgt, R 5 0.5 versus R E 0.9). Thus multistage (counter current) separation will be needed in industrial applications. These multistage reverse osmosis units would differ from distillation or 8A absorption multistage units in that the fraction of feed which goes on to the next stage is controlled by the Operator and not by the physical properties of the solution. A calculation scheme based on Optimizing the total separation of solute and solvent at each stage was devised and an example separation process computation was carried out to determine the number of stages required for a given rejection coefficient. This is shown in Figure III—8. For R equal to 0.5 or greater N the number of stages re- quired is twenty or less. This does not appear to be an unworkably large number of stages. Finally, the power required to perform the experimental reverse osmosis separations was calculated along with the respective areas and efficiencies. These are tabulated in Table IV-l. The required power ranged from 3.AA watts per gram permeate solution produced at A00 psi applied pressure to 7.05 watts per gram at 800 psi applied pressure. While separations carried out at lower applied pressure had higher efficiencies, they also required greater membrane areas. For example, a feed stream of 3.5 wt % decalin dissolved in ethanol was separated with a 6% efficiency at A00 psi as compared to a 3% efficiency at 800 psi. The area required 2 however for the lower applied pressure was 0.19 m , nearly twice the area needed at the higher applied pressure. REFERENCES REFERENCES Anderson, J., S. Hoffman, and C. 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Geiger, J., "Design, Energy, and Economic Analysis of Small Scale Ethanol Fermentation Facilities", M.S. Thesis, Department of Chemical Engineering, Michigan State University, 1981. Jacazio, G., R. Probstein, A. Sonin, and D. Yung, "Electro- kinetic Salt Rejection in Hyperfiltration Through Porous Materials. Theory and Experiment". Kopecek, J., and S. Sourirajan, "Performance of Porous Cel— lulose Acetate Membranes for the Reverse Osmosis Separa- tion of Mixtures of Organic Liquids", Ind. Eng. Chem. Process Des. Develop. 9, 5 (1970). 85 86 Lakshminarayanaiah, N. Transport Phenomena lg Membranes, Academic Press, New York (1969)? Lonsdale, H., U. Merten, and R. R. Riley, "TranSport Prop- erties of Cellulose Acetate Osmotic Membranes", J. Appl. Polymer Sci. 2, l3Al (1965). Matsuura, T., and S. Sourirajan, "Reverse Osmosis Transport Through Capillary Pores Under the Influence Of Surface Forces", Ind. Eng. Chem. Process Des. Deve. 29, 273 (1981). Merten, U. (ed), Desalination %% Reverse Osmosis, The MIT Press, Cambridge, Mass (19 ). Michelsen, D. "The Transport of NaCl and Water Through Com- pressed HydrOphilic Films", in Membranes from Cellulose and Cellulose Derivatives, Turbak, A.7(ed), Interscience Publishing (1970). Nomura, S., M. Yoshida, H. Seno, H. Takahashi, and T. Yamobe, "Permselectivities of Some Aromatic Compounds in Organic Medium Through Cellulose Acetate Membranes by Reverse Osmosis", J. Appl. Poly. Sci. gg, 2609 (1978). Perry, R., and C. Chilton, Chemical Engineer's Handbook, 5th Ed. McGraw-Hill Book Company'(l973), p. 2-9. Reid, C., and E. Bretor, "Water and Ion Flow Across Cel- lulosic Membranes", J. Appl. Polymer Sci. l, 133 (1959). Reid, R., J. Prausnitz, and T. Sherman, The Properties gt Gases and Liquids, McGraw-Hill Book Company (1977). Reid, 0., and H. Spencer, "Ultrafiltration of Salt Solutions by Ion—Excluding and Ion-Selective Membranes", J. Appl. Polymer Sci. 3, 3-A (1960). Sourirajan, S., "The Mechanism of Demineralization of Aque— ous Sodium Chloride Solutions by Flow, Under Pressure, Through Porous Membranes", I & EC Fun. 2, 51 (1963). Sourirajan, 8., Reverse Osmosis, Academic Press (1970). Turbak, A. (ed), Membranes from Cellulose and Cellulose Derivatives, Interscience Publishing (19707? APPENDIX DATA APPENDIX A. Expgrimental Data The experimental values used to construct Figures II—3 through II-ll are listed in this section. Figure II-3. AP = A00 psi AP = 800 psi Cp CC Cp CC 2.3 A.7 '3.0 5.0 2.7 A.7 2.7 5.2 A.7 9.6 A.8 9.8 5.1 9.3 A.8 9.7 6.9 1A.5 7.1 1A.8 9.6 19.3 9.9 19.6 13.0 25.1 17.1 31.4 87 Figure II—A. 88 O O p c 1.8 5.0 1.1: 11.3 1.6 A.6 3.6 9.7 3.6 9.7 5.7 1A.3 5.1 14.3 7.5 19.7 7.5 l9.A 10.7 2A.6 10.7 21m 12.3 30.5 12.7 28.9 Figure 11—5. 89 Decalin:EthanOl l-DecenezEthanOl AP = A00 AP 800 AP = u00 AP 800 0p 0 0p 0 0p 0 0p 0 2.u 3.5 2.2 3.0 5.3 5.8 A.6 6.3 2.1 .9 2.3 3.A 5.0 5.8 u.5 5.8 5.9 3.9 6.3 5.3 7.0 A.8 5.8 .2 5.7 3.9 6.2 A.8 5.3 5.3 5.6 5.3 8.5 5.1 8.7 9.0 11.8 8.u 12.u 5.3 8.3 A.8 8.6 9.0 11.u 9.2 12.3 6.5 10.3 5.7 10.8 9.2 11.8 13.8 22.6 6.6 10.u 5.7 10.7 15.5 22.3 1A.7 22.3 7.6 12.7 6.8 13.3 16.3 21.9 lA.7 22.3 7.6 12.7 6.6 12.9 16.3 21.6 1A.6 22.9 9.3 16.0 8.0 15.9 17.18 23.1 16.8 36.7 9.3 15.9 7.9 16.0 17.1 2u.0 17.0 37.5 10.5 18.3 8.7 19.0 19.7 35.8 16.8 38.u 10.3 18.6 9.5 21.3 20.6 35.5 18.u A6.0 11.1 20.5 9.3 21.A 20.2 36.2 18.5 A6.u 10.9 20.5 10.6 2u.u 19.9 36.2 18.0 A6.0 11.7 23.8 10.3 23.9 22.3 A5.5 l2.A 23.5 11.3 27.u 21.8 uu.3 13.u 27.2 10.8 27.6 21.u uu.3 12.7 27.0 10.1 24.2 12.5 23.5 9.9 2u.7 12.0 23.9 90 Figure 11-6 % R AP (psi) 200 “00 600 800 Comgound l-Decene 21.1 33.8 “1.7 “5.1 l-Tetradecene 59.1 68.8 72.2 76.2 l-Hexadecene 67.3 79.“ 8“.2 87.6 Figure 11-7. % R AP (psi) 200 “00 600 800 ComEound Decalin 36.2 58.0 67.7 72.0 1-Decene 21.1 33.8 “1.7 “5.1 1-Decanol 12.3 15.3 16.8 16.8 n-Decane “0.7 56.1 62.9 71.“ 91 Figure 11-8. Cp (ppm) CC (ppm) “7 90 86 “13 125 628 163 909 206 109“ 2“7 1395 291 1677 Figure 11—9. 92 Time (Hr) Flux - 10” (g/cmzs) 0 Start 0.27 “.8251 0.53 3.6779 0.85 3.“593 1.13 3.5058 1.“5 3.3986 1.87 3.“515 2.65 3.“208 3.12 3.“O6“ 3.60 3.““6“ “.12 3.3551 93 Figure II-lO. Time (Hr) Flux - 10“ (g/cmzs) 0 Start 0.25 31.0728 0.50 29.093“ 0.75 28.1776 0.77 refill 1.12 25.3128 1.37 23.6828 1.6“ 22.7033 1.67 refill 2.02 21.7887 2.27 20.9920 2.52 20.381“ 2.77 19.9980 2.80 refill 3.37 19.1900 3.92 18.7273 9“ Figure II-ll. Time (min) 0 (wt%) CC (wt%) Flux-10“ (g/cmzs) p Start 10.3“ CDO\J:O 1“.7101 10 13.1 11 9.“ 16 1“.0 t 18 9.1 20 Refill 22 13.9 26 12.9186 28 13.6 30 8.8 36 13.“ 38 8.5 39 12.6675 “1 Refill “5 13.8 “7 8.5 “9 12.1920 53 1“.1 55 8.“ 60 11.602“ 95 B. Concentration and Flux Measurements. 1. Concentration Concentrations were determined using refractive index. Standard solutions were made and refractive index measured. These measurements were fit to a linear expression using a least squares technique. The error in these linear expressions was assumed to be equal to the largest dif- ference found between any standards'known concentration and the calculated value using the expression. EXAMPLE: For the decalin-ethanol system a sample with a measured refractive index of 1.3599 is found to have a decalin concentration of 2.“:0.53 weight percent, i.e. Wt% A°RI-B 92“.93 - 1.3599 - 1255.“ 2.“:O.53 96 A_1 B Error Range Solvent Solute (RI ) (wt%) (wt%) Ethanol Decalin 92“.93 1255.“ 0.53 0-“0 n—Decane 2019.9 27“2.2 1.00 0-50 1-Decanol 1337.6 1816.1 1.50 0-50 1-Decene 1696.2 2303.2 1.26 0-50 1-Hexadecanol 1212.7 16“6.0 1.12 0-50 1-Hexadecene 1226.1 l66“.6 1.35 0-30 l-Tetradecene 13““.3 1825.3 l.“7 0-60 Water Ethanol 1561.1 2077.3 0.88 0-25 Ethanol -2327.6 17“8.9 97-100 2. Flux A flux is the amount of material passing through a given area in a given time. The diameter of the membrane was three inches. For a sample collected for two minutes whose mass was found equal to 2.0673 grams the flux was calculated to be 3.7777-10-u g/cm2s, i.e., _ mass _ 2.0673 g Flux - Area-Time - 2 5“ cm 2 (1.5 in X —;i;r——) -l2OS = 3.7777 10'“ g/cmZS. lHllllfllHllll l‘I’lY 1 178 234 303 312