00001.tif

PDF

Download

Open document

Transcript (if available)

Content A STUDY OF THE EFFECTS OF POROSITY AND SURFACE AREA ON THE FILTERABILITY OF SILICIOUS MATERIAL A Thesis Presented to the Faculty of the Graduate School University of Southern California In Partial Fulfillment of the Requirements for the Degree Master of Science June, 1948 UMI Number: EP41713 All rights reserved INFORMATION TO ALL USERS The quality of thi3 reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. Dissertation Publishing UMI EP41713 Published by ProQuest LLC (2014). Copyright in the Dissertation held by the Author. Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 4 8 1 0 6 -1 3 4 6 C - k .. * ^ V H k 9 77j« thesis, written by * BDGAJi.H^-.iJDfFIiJG................ under the guidance of h Faculty Committee, and approved by all its members, has been presented to and accepted by the Council on Graduate Study and Research in partial fulfill ment of the requirements for the degree of Maa.ter..Qf...aclejn.c.e...la...GJhemlo.al.. Engineering Dean D^.J.lINE..19.4a. Faculty Committee °Cl Chairman ACKNOWLEDGEMENT The author is grateful for the many criticisms and suggestions pf Mr. J. W. Kenney, chief chemist of the Dicalite Company, and Dr. F. J. Lockhart of the University of Southern California. Likewise, the author wishes to thank the Dicalite Company laboratory for samples of diatomaceous earth and qugrtz and the use of their equipment, especially the bomb filter press. Also he wishes to thank W. Smittle of the Dicalite Company and Dr. R. Baker of the University of Southern California for their assistance in preparing photomicrographs of the samples. TABLE OF COMEM’ S CHAPTER PACE I. INTRODUCTION ...................................... 1 II. HISTORICAL DEVELOPMENT.................. . . . 3 Filtration • • • • • . . . • . . 3 Permeability . . . . . . . . . . . 7 III. CORRELATION BETWEEN FILTRATION AND PERMEABILITY . . 11 IV. EXPERIMENTAL WORK...................... 14 Materials . • • • • • • • • • • 14 Apparatus • • • • • • • • • • • 18 Filtration apparatus • • • • • • • • 18 Permeability apparatus • • • • • • • 22 Procedure . • • • • • • • • • . 25 Filtration t e s t s ............................. 25 Permeability tests . • • • • • • • • 27 Experimental data • • • . • • • • • 28 Sample calculations • • • • • . • • • 28 Summary of results • • • • • • • • • 32 V. DISCUSSION OF RESULTS.............................. 34 Estimated accuracy • • • • • • • • • 34 Filtration tests • • . • • • • • • 34 Permeability tests • • • • • • • • • 34 Comparison of filtration and permeability tests • 36 Filtration test • • • • • • • • • 36 JCHAPTER PAGE Permeability test • • • • • • • • • 39 Effect of precoat • • • • • • • • • 40 Surface Area • » • • • • • • • • 44 Porosity • • • • • • • • • • • 46 Average specific resistance • • • • • • 48 VI. CONCLUSIONS................................. 57 NOMENCLATURE ......................... 58 BIBLIOGRAPHY...................... 61 APPENDIX.................................... 65 LIST GF TABLES TABLE PAGE I. Some Chemical and Physical Properties of Quartz and Kieselguhr 16 II* Summary of Calculated Data • • • • • • • • 33 III; Comparison Between Air Permeability and Water Permeability Tests • • • • • • • • 41 IV* Time-Flow Data Illustrating Effect of Precoat • • • 44 V* Experimental Filtration Data • • • • • • • 66 VI* Calculated Filtration Data * . . • • • * . 68 VII, Experimental Permeability Data * • • • • • • 70 VIII, Calculated Permeability Data * * • * • * • • 72 LIST OF FIGURES' FIGURE fcAGE 1. Photomicrograph of Marine-Type Kieselguhr x 1100 • • , 17 2a* Photomicrograph of Unseparated Quartz (As Is) x 1100 • • 19 2b* Photomicrograph of 10-20 Micron Quartz x 1100 . • • • 19 3a, Photomicrograph ef 5-10 Micron Quartz x 1100 * * * * 20 3b, Photomicrograph of 3-5 Micron Quartz x 4-300 • • • • 20 4a* Photomicrograph of 2-3 Micron Quartz x 4-300 • • • * 21 4b* Photomicrograph of 1-2 Micron Quartz x 4-300 • • • « 21 5* Drawing of Filtration Apparatus * « • • • • • 23 6, Picture of Filtration Apparatus * • • • • • * 24- 7* Sketch of Permeability Apparatus * * * « , * • 26 3* Time-Flow Data of Run 26 * * . * • • * , * 31 9* The Distribution of Accuracy of Filtration Data * * * 35 10. The Distribution of Accuracy of Permeability Data . . . 37 11. The Distribution of Accuracy Between Filtration and Permeability Data • • • * • • • • • • 3& 12* Time-Flow Data Illustrating Effect of Precoat * * 4-3 13* Effect of Composition on Surface Area of Particles « « 4-5 14-* Effect of Composition on Porosity of Particles * * * 47 15* Effect of Composition on Filtration Resistance per Unit Weight, r^p * • « • » • • • • • 49 16, Effect of Composition on Permeability Resistance per Unit Weight, Tpp 50 FIGURE PAGE 17. Effect of Composition on Filtration Resistance per Unit Volume, • • • • • • * • • • 51 18* Effect of Composition on Permeability Resistance per Unit Volume, r , • • • • • • • • • • 52 p* 19. Correlation of Experimental Data with Kozeny*s and Walas* Equations • • • • • • • • • • 55 CHAPTER I INTRODUCTION The unit operation, filtration, may beat be defined as the separation of a liquid from solids suspended in the liquid by passing the liquid through a porous medium or septum and collecting the separated solids as a cake formed on the septum* The study of filtration, has advanced in recent years to the point where most of the factors affecting the resistance of a system to filtration have been combined in an equation dV _ P 'P d & - (1) where dV is the instantaneous rate of filtration in cc*/sec*, A is the area of filtration in sq* cm., P is the total pressure drop across the filter press in g*/sq* cm., Tf is the average specific resistance of a unit cube of the cake in sq* sec./cc., v is the volume of cake per unit volume of filtrate, q is the viscosity of the filtrate in poises, V is the volume of filtrate collected at any time %9 and R is the initial or septum resistance per unit area for a liquid of unit viscosity in sq* sec*/sq* cm* r^ is a function of the porosity of this cake* It is the purpose of this paper to determine the nature of the function. Likewise, from a practical standpoint, an insight into the variables affecting the average specific resistance of the cake could lead to better filtration procedure* Since, in many ways filtration is similar to fluid flow through porous beds, an attempt is made here to evaluate and compare the 2 average specific resistance calculated from a simple permeability test to that calculated from a constant pressure filtration test making use of equation (l). In industrial filtration one of the major problems has been a quick method of predicting accurately the filtration characteristics of a given slurry. Equation (1) may be integrated for either constant rate or constant pressure to give equations for determining the volume of filtrate to be obtained at a given time. However, these equations cannot be evaluated until numerical values of Tf, and v are found. One purpose of this paper is to show that accurate values of r^ and v can be obtained from a simple permeability test. CHAPTER II HISTORICAL DEVELOPMENT A. Filtration The development of equation (1) has extended over many years with many incorrect assumptions based on inaccurate experimental data holding up the progress# Hatscheck^ in 1908 recognized the function of the filter septum as being only the means of support of the cake — not the actual filter medium# He showed that it is the difference in the pressure across the filter medium alone that causes the filtrate to pass through the medium. Almy and Lewis developed the following equation based upon experimental data from constant pressure filtrations dV _ K. Pn d* " Vm where and all subsequent K*s are proportionality constants, and n and m are variable exponents# 3 Additional work by Baker led to an extension of the Almy and Lewis equation to include the effect of area d V = K A ' P * (3) ^ E. Hatschek, "The Mechanism of Filtration," Journal of the Society of Chemical Industry. 27:538 - 4A, 1908, 2 C. Almy and W# K# Lewis, "Factors Determining the Capacity of a Filter Press," Journal of Industrial and Engineering Chemistry. A:528 - 32, 1912. 3 F. C. Baker, "A Study of the Fundamental Laws of Filtration Using Plant-Scale Equipment, "Journal of Industrial and Engineering Chemistry. 13:610, 1921# Integration of this equation led to \Zm *'= Cm+Ortz A*Pn -6- <*> The value of m was found by plotting V raised to various powers against Q on logarithmic paper and using that value of (m + l) which gave the straightest line, n was found by running additional experiments at constant rate or, as pointed out by Waterman and Van Gilse^, from constant pressure data by use of the equation n = (5) /of P, - /<*? / = > z where 62 represents the time needed to collect a given amount of filtrate when the pressure was held constant at P^ and is the time to collect the same volume of filtrate under a pressure, P^. Baker-* showed that a value of m *1 usually produced the best results for a suspension of relatively incompressible solids. However, Ruth^ pointed out that Baker*s equation I /'-ZfcA'P*# (6) resulted in an appreciable error for the early stages of the run. He attributed this to the absence of any term denoting the initial or septum resistance in Baker's equation. Weber and Hershey introduced the concept of the average resistance 4 H. J. Waterman and J. P. M. van Gilse, Rec. Trav. Chim. Pays — Bas. 4-3:757, 1924, cited by B. F. Ruth, G. H. Montillon, and R. E. Montonna, "Critical Analysis of Filtration," Industrial and Engineering Chemistry. 25:76-7, 1933. 5 Baker, on. cit.. 611. ^ Ruth, Montillon, and Montonna, op. cit.. 77. 7 H. C. Weber and R. L. Hershey, "Some Practical Applications of the Lewis Filtration Equations," Industrial and Engineering Chemistry. 18:341 - 5, 1926. ' / - > * per unit cube of cake, • into the equation to replace the permeability coefficient K, where Kg= Their equation for homogeneous sludges is l/~= * 2 A P (7) where 1-x replaces n* Their equation for heterogeneous sludges is much 8 more complicated and has since been proven incorrect by Underwood • Likewise, their equation is not accurate for the early part of the run as noted by Ruth?. Sperry^»H*1^ and others, notably Hinchley, Ure, and Clarke^ and Underwood^- developed equations based upon Poiseuille*s law for the flow of fluids through capillary beds and the concept of filter base resistance. Poiseuille's law could be written - - 4 A <8> A& 1L where L is the thickness of the cake at time 0 in cm. If the permeability constant K3 were replaced by l/r^ then the equation 8 A. J. V. Underwood, Proceedings of the World Engineering Congress. Tokyo. 1929. 31*245, 1931, cited by Ruth, Montillon, and Montonnaj op. cit.. 78 9 Ruth, Montillon, and Montonna, op. cit.. 78 10 D. R. Sperry, "The Principles of Filtration — I," Rhamlcal and Metallurgical Engineering. 15*198-203, 1915. 11 D. R* Sperry, "The Principles of Filtration — II, "Chemical and Metallurgical Engineering. 17*161-6, 1917. 12 D. R. Sperry, "Effect of Pressure on Fundamental Filtration Equation when Solids are Non-Rigid or Deformable," Industrial and Engineering Chemistry. 20*892-5, 1928. 13 J. w. Hinchley, S. G. M. Ure, and B. W. Clarke," Studies in Filtration," Journal of the Society of Chemical Industry. 45*1T-10T,1926, 14 A. J. V. Underwood. "Filtration Equations for Compressible Sludges," Journal of the Society of Chemical Industry. 47*325T-8T,1928. for the instantaeous rate would be d V = P A d 0 rf qt_ If the total pressure, F, were made up of a part, Pc, the pressure drop through the cake, and Pg, the pressure drop through the septum, then d V _ R A _ PsA__________PA , 1nv d& $ -7 L ~ 1R ~ ' ' L - vV since it was assumed that the thickness of the cake at any time A was proportional to the volume of solids present in the cake and that the latter was proportional to the volume of filtrate collected at that time. Therefore, ... . z di/ __ P A ________ d-9- fj(rf vV+PA) ( 1) which is equation (1). This equation integrates for constant pressure » - a n which fits the experimental data much better than equation (7). Ruth^** developed an equation along empirical lines which he showed to be based on sound theory and which also accounted for the initial resistance (v + c)‘ = k 4 (d +e0) (12) where C and 0 are correction factors and O « 2 A* P O'ms) . . . . Ki----(13) S is the weight of filterable solids per weight of prefilt, m^ is the weight of the wet cake per weight of dry cake, f> is the density of the filtrate in g./ce., cx is another average resistance of the solids where _ e</)5 (14.) v ( / - m ‘ s) b. F. Ruth, G. H. Montillon, and R. E. Montonna, "Fundamental Axiom of Constant Pressure Filtration," IndustHand Englneerimr Chemistry. 25:153-61, lf33« 7 Both equations (11) and (12) represent the data for the filtration of incompressible solids within the limits of experimental error* In many cases it may be more convenient to express the cake resistance as the average specific resistance per unit weight of the solids, rf±f in sq. cm./g., In this case r]C= rv (15) where c is the weight of solids per unit volume of filtrate. Equation (11) then becomes o- V* ,___9 * V___ (16) 2.PA* PA ’ B. Permeability Soon after the presentation of Poiseuille’s law in 184-0 for the flow of fluids through capillary tubes D’Arcy^ published his law covering the rate of flow through porous beds. V „ Ks PA fl7N 0 " L V A great deal of experimental data has shown the rate of flow through porous beds to be inversely proportional to the viscosity of the fluid so equation (17) may be written _vi_ = «‘P A ,18) * n l (18' which is quite similar to Poiseuille*s law. A (19) V _ ci*PtA & 32 L where d is the capillary diameter and g is the acceleration due to gravity* The diameter of the pores in a porous bed is difficult to ^ H. P. G. D'Arcy, Les Fontaines Publioues de la Ville de Pi .ion. Paris: Victor Delmont, 1856, cited by P. G. Carman, nFundamental Principles of Industrial Filtration,” Transactions — Institute of Chemical Engineers (London). 16:171, 1938. measure and is not uniform anyway. However, Seelheisr^ showed that equation (IS) could be changed to include a tens for the average diameter of the particles. His empirical equation was shown to be satisfactory for sand beds of a porosity of 0.367 — = O. 5 8 5 (20) V v *~ where d^ is the average diameter of the particles. He obtained the average diameter as that of a spherical particle with an average weight 18 found by weighing and counting. Hazen showed that the value of the permeability constant varied with the porosity of the bed. His correction coefficient, based on sieve sizes, empirical and artificial though it is, enjoys wide usage among soil engineers. In 1863 Dupuit^ set forth the belief that the fractional free area of a sand bed is constant for a given bed and equal to the porosity 20 of the bed. That this is true is pointed out by Carman in his discussion of regular and random packing. Then the true linear rate of flow in the bed would be— — where € is the fractional void volume or & A e porosity. Then equation (18) would be V __ /fV edm PA /pil ■9- ~ tjL *7 S e e l h e i m , g. Anal. Chem.. 19*387, 1880, cited by Carman, op. cit.. 171. 1® A. Hazen, 2Ath Annual Report of the State Board of Health. Massachusetts. 1892, 554-, 1892, cited by Carman, oj>. cit., 171. 19 a. J. DuPuit, Etudes Theoretiques et Pratiques sur le Mouvement des Eaux. 1863, cited by Carman, oj>. cit.. 171. Carman, op. cit., 171-2. Though this equation is an improvement it still does not fully account for the effect of the porosity* Since at best dm is only a hypothetical diameter it was realized that better results would be obtained if the surface per unit volume of solids, SQ, were considered as the variable influencing the flow* The basis for this work is the fact that the frictional resistance to flow of the fluid depends upon the amount of surface in contact with the fluid. Likewise, it is a quantity which has a real meaning and is calculable for a mixture of particles* Kruger^ in 1918, proposed an equation rising these variables for sand with porosities varying from 0*30 to 0*40* _V______n.s6 PA (22) & - S'/jl. where S is the surface per unit volume of the bed and is related to SQ ^ S = C/-e)Sa < 23> This equation was found to be satisfactory over the narrow range of porosities that he investigated but was inaccurate for more extreme porosities. 22 23 In 1927, Kozeny * proposed an analogy between the flow through pipes of non-circular cross-seetion* He suggested that the surface per unit pore volume, *1 corresponding to the mean hydraulic radius, be used* Kozeny*s equation is 21 Kruger, Int. Mitt* Bodenkunde. 8:105, 1918, cited by Carman, op. cit.. 172* 22 j. Kozeny, Ber. Wien. Akad., 136as271, 1927, cited by Carman, op. dit., 172. 23 j. Kozeny, Wasserkraft und Wasserwirtschaft. 22:67, 86, 1927f cited by Carman, op. cit*. 172. Carman‘ ^ ^', p tested this equation over a wide range of conditions with £* P & A €* P g A 10 (24) many materials and found it to he extremely accurate when a value of Kgs 5*0 was used. In fact, so enthused wag he with the accuracy of this equation that he proposed it as a method of obtaining surface area from permeability measurements. By combining equations (8) and (24) and letting Kg = 5.0 1937. ^ P. C. Carman, "The Determination of the Specific Surface of Powders,1 1 Journal of the Society of Chemical Industry. 57*225T, 1938. or < - * € so sfO-Q* * - s o sfO-e)% (25) ( 26) P. C. Carman, "Fluid Flow Through Granular Beds," Transactions — Institute of Chemical Engineers. (London) 15*150-66 ^ P. C. Carman, "Fluid Flow Through Granular Beds," CHAPTER III CORRELATION BETWEEN FILTRATION AND PERMEABILITY Walas^ attempted a correlation between filtration resistance and particle size and porosity. His data resulted in an empirical equation which held for various materials. <x = 3.3 *10 (27) where p* is the density of the solids in g./cc. He found d^ from o 3 Oden's sedimentation method and used Ruth's method for obtaining <x . His results differ from the theoretical considerations of Kozeny^,' ’ aEK* 6 Fair and Hatch who envisioned the resistance as being an inverse function of the square of the diameter. He attributed this deviation to absorbed fluid films and to the distwntion of the compressible particles which would restrict the cross-sectional area available to How. ^ S. M. Walas, "Resistance to Filtration," Transactions of the American Institute of Chemical Engineer's. 42:783-93, 194&. 2 S. Oden in J. Alexander, Colloid Chemistry (New YorksRheinhold Publishing Company, 1926) I, 861 cited by Walas, op. cit.. 787 3 B. F. Ruth, G. H. Montillon, and R. E. Montonna, "Fundamental Axiom of Constant Pressure Filtration", Industrial and Engineering Chemistry. 25:156, 1933. 4 J. Kozeny, Ber. Wien. Akad.. 136d:271, 1926, cited by Walas, op. cit.. 788. 5 J. Kozeny, Wasserkraft und Wasserwirtschaft. 22:67 and 86, 1927, cited by Walas, op. cit.. 788. ^ G. M. Fair and L. P. Hatch, "Fundamental Factors Governing the Streamline Flow of Water Through Sand," Journal of the American Water Works Association. 25:1551-65, 1933* 12 also found that the porosity was a function of the final or maximum pressure to which the cake was subjected which, in turn, explained the deviations of o< with pressure* He claims that by using equation (27) the determination of partiele size, density, and porosity as a function of pressure will "define completely the filtration behavior of any slurry"• 7 Likewise Ruth attempted to correlate filtration characteristics with permeability and particle size. He found that the permeability of a particle bed to the flow of a liquid was less than to the passage of air. He attributed this to a fraction of the void volume which took no part in the passage of the liquid and which he called "dead" volume . His definition of void volume, , differs from porosity in that it is the volume of voids per volume of solids while porosity is the volume of voids per volume of cake. He determined the value of \?0 by plotting the permeability of a constant weight of filter solids against the void volume. An extrapolation to zero permeability gave \ie . His equation for the average specific resistance is <* - K, ------4^-,------- t (28) where f > ' is the density of the solids. He calculated c< from permeabil ity data for a calcium carbonate slurry and found it to be about 15% less than from a filtration of the same material. He attributed this to aging as a considerable time lag occurred between the two tests. He ^ B. F. Ruth, "Correlating Filtration Theory with Industrial Practice," Industrial and Engineering Chemistry. 38:564-71, 194-6. also noted that the void volume was a function of the maximum pressure stress and gave several empirical equations relating them. CHAPTER 17 EXPERIMENTAL WORK A. Materials It was desired to investigate systems in this study which are chemically inert so as to eliminate, as much as possible, changes in physical properties caused by aging and chemical activity* Likewise, it was recognized that when working with heterogeneous systems, electro- kinetic effects might occur which would cause trouble in obtaining reproducable results* However, systems were required which varied widely in porosity, surface area, and specific resistance in order to adequately test the correlation between filtration and permeability. To accomplish these objectives it was decided to blend various amounts of a chemically inert material, quartz, with an equally inert and chemically similar material, diatomaceous silica. Although they are chemically and electrokineticly similar — both have negative charges — they have a marked difference in physical properties. Quartz is made up of rhombohedral crystalline particles with low porosities — about 0.40. The diatomaceous silica or kiesselguhr used in these experiments is the calcined skeletal remains of marine plant life called diatoms. It exists naturally in many sections of the world and very pure deposits are being worked along the Pacific coast. The diatoms are primarily amorphous silica having many shapes varying from long pencil like spicules to plate-like discs. Among their more important physical properties are the very high porosity, 0.80 to 0.90, and large surface 15 area* They form beds which are extremely permeable to the passage of fluids and yet are able to trap colloidal particles and remove them from the fluid* For these reasons they enjoy widespread usage as filter aids* Table I gives a comparison between some of the chemical and physical properties of quartz and kieselguhr* Figure 1 shows a sample of the marine-type diatomaceous earth used in these tests magnified 1100 times* It is seen to be made up of discs and spicules* The disc shown in the photomicrograph has a diameter over #120 microns* Likewise, many of the spicules are over 400 microns in length. Their thicknesses may be only 2 or 3 microns* Thus it is extremely difficult to assign and average value of diameter to such a system* Another factor is that many of the discs and spicules are fractured during processing which further complicates the picture* However, this photomicrograph makes it easier to understand how a cake made up of these discs and spicules exhibits such a high porosity — up to 90 per cent void volume* In order to obtain an even wider range of resistances the quartz was separated by successive settlings into the following particle size ranges: 1-2, 2-3, 3-5, 5-10 and 10-20 microns* The particles were assumed to be spherical and to obey Stoke*s i*" tt. adiSlp '-rt /© * 1 where u is the linear velocity in em./see* and d& is the diameter of a spherical particle in centimeters* The quartz was dispersed in water and allowed to settle at a uniform known temperature* For example, at 20° C., all particles TABLE I SOME CHEMICAL AND PHYSICAL PROPERTIES OF QUARTZ AND KIESELGUHR QUARTZ Weight Per Cent KIESELGUHR Weight Per Cent Chemical Analysis Si02 99.2 90.9 A!2°3 0.3 4.6 Fe2°3 0.3 1.9 CaO 0.1 1.4 MgO 0.1 0.4 Ignition Loss 0.3 Undetermined w » « » SUft Physical Analysis 100.0 100.0 Specific Gravity (H20 -1.00) 2.65 2.25 Appearance Uniform, Multi-shaped, crystalline amorphous Porosity 0.371 0.856 an 17 (i W # f • « f : . : i i t 1*t1 < < 1 .* T a 4 • » . * i Marine-Type Diatomaceous Earth, x 11G0 One small division equals, 2,9 microns FIGURE I greater than twenty microns settled below a mark five centimeters from the surface of the water in 135 seconds* The suspension above this mark was siphoned off and transferred to another beaker* It contained no particles greater than twenty microns* The particles in the suspension were redispersed and allowed to settle for such a time that all particles greater than ten microns had settled below a given mark* The suspension above this mark, containing only particles less than ten microns, was siphoned off* The suspension below the mark contained particles in the 10-20 micron range plus smaller particles which did not have to settle as far* It took five or six successive settlings and decantations to obtain a uniform narrow 10-20 micron cut* This procedure was repeated for the 5-10, 3-5, 2-3, and 1-2 micron ranges* RLgueps 2, 3, and 4 - are photomicrographs of the quartz* The 1-2, 2-3, and 5-5 micron samples were taken with an electron microscope and are magnified 4-300 times. The original or "As Is” quartz, 5-10, and 10-20 micron samples are magnified 1100 times* An examination of these photomicrographs shows the majority of the particles to fall within the micron range designated for them. This means that although the particles of quartz are not spherical they are regular and an average diameter may be assigned to them. These results also illustrate the reliability of the successive settling method for separating particles into narrow size ranges* B. Apparatus 1. Filtration Apparatus All filtrations were made using a laboratory bomb filter press- * - • ^ Instruction Manual for Bomb Filter. Technical Department, Dicalite Company, Los Angeles, California, 194-5, p*4* Unseparated Quartz (As Is) x 1100, One small division equals 2.9 microns FIGURE 2a t / Micpon Quartz (10-20) x HOO, One division equals 2.9 microns FIGURE' ,2b Micron Quartz (5-10) x 1100, One small division equals 2.9 microns FIGURE 3a I Micron Quarts (3-5) x 4300, One centimeter equals 2.33 mi FIGURE 3b microns < 4 1 4 t % 4 9 H F Micron Quartz (2-3) x 4300, One centimeter equals 2,33 microns FIGURE 4a r 0 £ 4 t W 1 1 ' 4 # * 0 a : Micron Quartz (1-2) x £300, One centimeter equals 2.33 microns FIGURE 4b — the essential features of which are shown in Figure 5. Figure 6 is a photograph of the filtration equipment. It consists of two small pressure vessels made of ten gage, 13-8 stainless steel, with a capacity of 2000 cc. The bottoms are conical sections from which the slurry passes through an external filter area. The two vessels are used to hold the prefilt and may be used in conjunction or in series by regulating the outlet valves, A side arm and valve lead from the drain age arm and enable a precoat to be applied before the filter operation, A removable pressure tight gasketed lid Is fitted to the top of the pressure vessel and is held in place by four bolts. Compressed air passing through an air regulator valve into the bottom of the pressure vessel creates the pressure differential in the press and provides agitation by bubbling up through the suspension, A pressure release valve is in the lid. The pressure drop is measured by a mercury manometer, one end of which is attached to a valve in the lid and the other end is open to the atmosphere. The leaf is made of two parts, the upper of which is attached to the drainage arm of the press. The filter cloth fits over the bottom part and is held in place by a gasket, A clamp fits the two parts together when the cloth is in place. The lower part of the leaf is corrugated to enable free flow of the filtrate. The leaf is in a horizontal position. This has the advantage of preventing the precoat from collapsing with jarring which might take place with a verticals leaf, A baffle plate is attached to the upper part of the leaf to prevent washing away of the cake, 2, Permeability Apparatus The permeability tests were made with very simple laboratory 23 TO MANOMETER PRESSURE RELIEF VALVE PRESSURE GAGE AIR REGULATOR VALVE FROM COMPRESSOR VALVE B PRECOAT LINE CAKE SPACE BAFFLE PLATE GASKET ----- FILTER CLOTH VALVE A FILTER LEAF FILTRATE OUTLET SECTION A A THERMOMETER WELL VALVE B PRECOAT LIQUOR VALVE A N> V*» DRAWING OF F IL TR A TIO N A P P A R A T U S - FIGURE 5 FIGURE 6 PICTURE OF FILTRATION APPARATUS 25 equipment whose essential parts are shown in Figure 7. A circular glass tube, graduated to 0.1 ec., having a volume of 15 cc., and a cross- sectional area of 1.77 sq. cm. is used as the measuring cylinder. It is made to fit into a one-hole rubber stopper with a filter cloth between it and the stopper. A coarse wire gauze acts as a support for the cloth. The stopper fits into a filter flask which is in turn connected to a vacuum pump. C. Procedure 1. Filtration Tests Two grams of the solids to be filtered were dispersed in 1000 cc. distilled water* The slurry was poured into the bomb press with valve A closed (see Figure 5). The air regulator was set so as to allow a continuous stream of air to bubble through for agitation. The lid was placed on the press and the four bolts were tightened to hold the lid in place. The pressure relief valve was cracked slightly to allow continuous agitation. The air regulator valve was opened until the mercury manometer read the desired pressure drop, ten lbs./sq. in. gage. The filter cloth was fit into place on the leaf, held with a cork gasket, and clamped in place. Another slurry of diatomaceous earth in distilled wateri/as made and placed in a 1000 cc. graduate. Enough of this was drawn through the leaf by means of a vacuum pump so as to lay down a precoat equal to ten lbs./lOO sq. ft. of filter area. Valve B was then closed. Valve A was opened and a stopclock was started with the appearance of the first drop of the filtrate. Volume readings were taken after thirty seconds, 1, 2, 3, 5, 7, 9, 11, 13 and 15 minutes. The temperature of the filtrate was CN W H O' <>0 . 27 recorded. Then valve A was closed and the pressure release valve was slowly opened while the air pressure was slowly reduced. When the pressure within the bomb returned to atmospheric the lid was unclamped and the filter leaf broken down. After cleaning, the press was ready for another filtration. 2. Permeability Tests One tenth gram of diatomaceous earth of a different color than that used in these experiments was dispersed in distilled water. This slurry acted as a precoat to prevent any of the fine silica from pass ing through the cloth. It was applied by putting it in the tube and applying 20.36 inches of mercury vacuum (ten lb./sq. in. gage) through the side ana of the filter flask. Distilled water was added to the tube before the precoat had a chance to blow dry and the time for one cc. of clear distilled water to pass through the cake and cloth was obtained by passing eight cc. through and dividing the time for eight cc. by eight. From one to four grams of sample to be tested, depending upon the percentage of diatomaceous earth, were dispersed in distilled water. The diatomaceous earth is much more porous than the quartz and cakes made from it are more voluminous. The variationsin the weight of the sample used were made to obtain a farly uniform volume of cake. This slurry was added before the precoat blew dry. To minimize settling, a fine glass tube was set down into the measuring cylinder at a height about one-half inch above the cake and a fine stream of air was bubbled through the tube. When all solids had formed a cake, distilled water was added carefully before the cake blew dry, and the time for one cc. to pass through the cake was noted. Two such runs were made for each sample and the average of the two runs minus the time for one cc. of water to flow through the cloth and precoat alone were used as the reciprocal rate of flow in the calculations. The temperature of the water was recorded and the volume of the cake (minus the precoat) was noted. The thickness of the cake was calculated from the volume of the cake and the cross-sectional area of the tube. D. Experimental Data Filtration and permeability tests were made on each of the separated samples of quartz and on mixtures of 25 per cent diatomaceous earth — 75 per cent quartz; 50 per cent of each; and 75 per cent quartz — 25 per cent diatomaceous earth. The experimental data are tabulated in Tables V and VII of the Appendix. E. Sample Calculations Average specific resistances of the cakes were calculated from both the filtration and permeability tests. The methods of calculating r and r^ are best shown by sample calculations. For the system containing 100 per cent (3-5) micron quartz — the calculations are based upon the following test data from run no. 25, Table VII, and run no. 26, Table V in the Appendix. Permeability Test Weight of sample, W • Density of sample, p‘ Volume of cake, V1 • A»0 g. • 2.65 g./cc. . 3.40/cc. Permeability Test (continued) 29 Thickness of cake, L • • Cross sectional area of cake, A Pressure, P . . . Temperature, T . . • Viscosity of water, t ) Reciprocal rate, -y Reeiprocal rate through cloth and precoat alone • 1*92 cm. • 1.77 sq. cm. . 704. g./sq. cm. . 23.6° C 0.00923 poises 155.2 sec./ec. • 0.2 sec./cc. From this data the porosity of the eake may be calculated from € * /- W V'P' (29) from which From equation (9) f - 0.556 €* - 0.172 ( / - € ) ' = 0.197 PA (v/«) 7 L From equation (25) r g . ( . m ) 11,771. (1^5) . P (0.00923) (1.92) r10.90 x 10^ sq. sec./cc. M er s.o (t-e) * ■ 080) (0172) ( / o . 30) Oo*) (S O) (0.197) =18.70 x 108 SQ ® 4.33 x 10^ sq. cm./cc. of particles The value of ^ , the specific resistance per unit weight of sample, is calculated from he 30 /£, * 9.^0 x J.u sq. sec./g. Filtration Test Temperature, T 25° C. Grains of solids per cc. of filtrate, c 0.002 Viscosity of Filtrate, Pressure, P 0.008937 poises 704. g./sq.cm. = 10 lbs./sq.in Area of Filtration, A 4-.63 sq. cm. Time — minutes, Q 1/2 1 2 3 5 7 9 11 13 15 Volume of filtrate — cc., V 33 57 98 127 175 217 253 286 316 3AA When equation (16) is divided ty V it becomes which is the equation of a straight line when ^ is plotted against V on rectangular coordinate paper. The slope of the line, b, is 7 c 2 PA* and the V intercept is yy-—* • Figure 8 shows the above time — volume data plotted as ? against V. From Figure 8 b * 91.5 x 10 from which r^ _ 2bPA^ (2) (91.5) (IQ"6) (704) (A.63) (0.008937) (0.002) 20 0 .0 4 •H <P1> 0.02 10 0.01 FIGURE 8 TIME-FLOW DATA. 400 0 100 200 V, VOLUME OF FILTRATE, cco min rf t = 155200 (min.) (sec.)/g. = 9.30 x 106 sq. sec./g. Tf,the resistance per unit volume, is obtained from r^ since % V where v, the cake volume per unit filtrate, is obtained from c V= (/-£)/*> - 0.002 " (0.444) (2.65) = 0.0017 rf = ,(9»3S, xAQ6.)-iQiQQ2l (0.0017) = 10.93 x 10^ sq. sec./cc. F. Summary of Results The summarized results are given in Table II. The average porosities, surface areas, and specific resistances are listed as well as the percentage deviation from the average of the latter. The data for each test are given in Tables, V, VI, VII aid VIII in the Appendix. TABLE II SUMMARY OP CALCULATED DATA * D E refers to diatomaceous earth V rfl» so» Average Average Average rpl» Average Filtration Permeabil Average Filtra Average Per Per SiOp Surface Cake Re ity Cake Per Cent tion Cake Permeabil Average Cent Cent *5r Microns Average Area of sistance Resistance Deviation Resist ity Cake Per Cent BE * Si02 Porosity Particles per unit per unit for r ance per Resist Deviation sq. cm./cc. volume volume unit wt. ance per for r^ sq. sec./ sq, sec./ cc. x KT6 sq. sec./ unit wt. cc. x 10** g. x 10** sq. sec./ g. x 10-6 0 100 As Is 0.3710 19175 14.52 ‘ 13.08 5.22 8.645 7.83 4.94 25 75 As Is 0.6625 42000 3.50 3.475 0.36 4.155 4.04 1.40 50 50 As Is 0.7760 50000 1.364 1.152 8.44 2.485 2.103 8.32 75 25 As Is 0.8253 64500 1.149 1.108 1.81 2.795 2.705 3.27 0 100 (1-2) 0*4610 202900 622.5 652.0 2.32 437.5 457.0 2.24 25 75 (1-2) 0.5975 147250 84.3 72.3 7.68 81.65 70.45 7.37 50 50 (1-2) 0.7325 150500 21.0 20.6 0.96 32.02 31.45 0.86 75 25 (1-2) 0.8125 109050 3.98 3.39 8.21 9.055 7.69 8,18 0 100 (2-3) 0.5620 60900 20.25 16.57 9.99 17.45 14.31 9.87 25 75 (2-3) 0.6465 68200 10.86 10.48 1.78 12.01 11.625 1.63 50 50 (2-3) 0.7370 72950 4.70 4.34 3.75 7.29 6.725 4.05 75 0 25 (2-3) 0.8153 79900 2.075 1.95 3.09 4.715 4.475 2.61 100 (3-5) 0.5560 43500 11.02 10.01 4.89 9.37 8.42 5.33 25 75 (3-5) 0.7005 57550 4.30 4.265 0.41 5.75 5.57 1.59 50 50 (3-5) 0.7910 66400 1.975 1.90 1.93 3.85 3.69 2.12 75 25 (3-5) 0.8295 74300 1.435 1.191 9.30 3.585 2.985 9.14 0 100 (5-10) 0.6030 26500 2.52 2.403 2.37 2.40 2.275 2.67 25 75 (5-10) 0.7170 37550 1.565 1.701 4.17 2.17 2.37 4.41 50 50 (5-10) 0.7960 50900 1.085 1.127 1.90 2.175 2.25 1.69 75 25 (5-10) 0.8330 66900 1.095 0.987 5.19 2.79 2.51 5.28 0 100 (10-20) 0.5810 12A55 29600 0.701 0.708 0.04 0.632 0.636 0.04 25 75 (10-20f 0.7365 0.786 0.800 0.88 1.195 1.19 0.21 50 50 (10-20) 0.7990 46800 0.876 0.908 1.79 1.78 1.845 1.79 75 25 (10-20) 0.8330 61050 0.91© 0.983 3.85 2.32 2.51 4.11 100 0 0.8527 76450 1 .067 0.991 3.59 3.187 2.97 3.52 CHAPTER V DISCUSSION OF RESULTS The calculations of the specific resistances were made on both weight and volume bases* The advantage of using r^, the resistance per unit weight, is that it makes the calculations of the filtration data completely independent of the permeability data, i.e., it is not necessary to know the porosity of the cake in order to calculate r^. On the other hand the resistance based upon a unit volume of cake best illustrates the effect of filteraids in increasing the porosity and decreasing the resistance to flow. A. Estimated Accuracy 1. Filtration Tests Duplicate tests were made on all filtrations to determine the precision of the filtration tests. The average precision for 56 filtration tests was A.63 per cent for r^ and A.53 per cent for r* The distribution of accuracy is shown in Figure 9 for both weight and volume tests. The errors within the filtration tests are most likely due to agitation in the press. This particular problem is quite important, for inadequate agitation leads to settling and an uneven formation of the filter cake. Too much agitation could lead to erosion of the particles and increased resistance. 2. Permeability Tests The average precision within the 51 permeability test is 1.65 35 30 25 20 15 10 0 PER CENT OF DATA. FIGURE 9 THE DISTRIBUTION OF ACCURACY OF FILTRATION DATA 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 19 16 17 18 PER CENT DEVIATION OF r*. 20 15 10 0 PER CENT OF DATA 0 1 2 , 3 5 6 7 8 9 10 11 12 13 14 19 16 17 16 PER CENT DEVIATION OF rfl per cent for r^ and 1.79 per cent for r. The distribution of accuracy for both r^ and r is shown in Figure 10. The greatest source of error in this test is the accurate determination of the cake volume• The surface of the cake is not always horizontal. This would occur if any non-uniform settling took place. It is impossible to completely prevent settling. So, if some large particles were to congregate at one side of the cake they would offer less resistance to flow than the rest of the cake, hence more flow would take place through these particles and the cake would build up unevenly. This might lead to an error in reading the volume of the cake and, therefore, the thickness of the cake. However, the very slight deviations from the average which occured show that these errors are only of minor importance. 3» Comparison of Filtration and Permeability Tests The resistance to flow calculated from permeability tests compares very favorably with the resistances based upon filtration tests. The average deviation from the average of*about 3.62 per cent for r^, is even less than the precision within the filtration tests. Since the filtrate volume collected at any time is inversely proportional to the square root of the average resistance, the error in predicting the filtrate volume from permeability data would be less than the error in obtaining the average resistance and would be, in any event, only a slight error. The distribution of accuracy is shown in Figure II*. B. Filtration Test The variables controlling filtration are more easily handled P E R C E N T O F DATA 35 30 25 FIGURE 10 THE DISTRIBUTION OF ACCURACY OF PERMEABILITY DATA 20 15 10 0 35 30 25 20 15 10 5 ■ ■ o 0 1 2 3 4 5 6 ? 8 9 1 0 pi 2' 3 4 ^ 5 7“ PER CENT DEVIATION 9 10 38 , FIGURE 11 THE DISTRIBUTION OF ACCURACY BETWEEN FILTRATION AND PERMEABILITY DATA 0 1 2 3 4 5 6 7 8 9 10 r 0 1 2 3 4 5 6 7 8 9 10 PER CENT DEVIATION OF r x 39 with the bomb filter press than with any other filtration equipment. Most of the early work was done with plant-scale equipment and large volumes of prefilt. Variations in pressure drop, solids concentration, and temperature and lack of means of accurately determining the rate of flow plus the inability to control settling led to erroneous results. No data in the literature are available from which the accuracy of the equipment used may be determined since duplicate runs were never reported. However, results obtained in the Dicalite company laboratory have shown that the bomb filter press is an accurate laboratory instru ment for predicting plant-scale filtration. Also the duplication of results in these tests produced an accuracy well within design limitations. C. Permeability Test The permeability test used in these experiments has several advantages over other test methods. Carman^- used a method whereby a known weight of dry solids was introduced into a cylinder, similar in design to Figure 7, and gently tapped until the dry cake settled as much as possible. Then a water permeability test was made. Although he seemed to have obtained reasonable results his method is open to the objection that channeling could easily take place. Peehukas and Gage , commenting on various air permeability tests, 1 P. C. Carman, "The Action of Filter Aids," Industrial and Engineering Chemistry. 31*1047, - 1050, August, 1939. 2 Alphonse Peehukas and F. W. Gage, "Rapid Method for Determin ing Specific Surface of Fine Particles," Industrial and Engineering Chemistry — Analytical Edition. 18:370-3, June, 1946. pointed out that it was necessary to pack the powder in tightly in the test cylinder in order to prevent channeling. Comparative tests made by the author showed that the calculation of surface area by air permeability tests agree with that calculated by the water permeability test but that the former method requires more packing to prevent chan neling and therefore, results in decreased porosity. Table III gives the results of these tests* The air permeability test is quite useful in determining surface area but is of little value for obtaining the average resistance. Even on a weight basis the resistance from the air permeability test is over three times as great as the resistance from the water permeability test. This is due entirely to the low porosity obtained in the former. The plausability of the author's permeability method as a test for filtration resistance is apparent when it is realized that the cake formed in this test is of the same nature as that formed in an actual filtration. This eliminates all chances for channeling and provides an accurate means of obtaining the porosity of the filter cake. D. Effect of Frecoat A precoat of ten lbs./lOO sq. ft. of filter area of diatomaceous earth was applied on most of the filtrations. Its purpose was to present a uniform porous, non-penetrable filter septum for all tests* The method of applying the precoat precludes a high degree of accuracy which accounts for most of the minor deviations in R, the initial or septum resistance. For many of the runs the precoat was applied in heavier amounts, especially for those containing high percentages of 41 ■TABLE III COMPARISON BETWEEN AIR PERMEABILITY AND Water permeability tests Weight of sample — g* Density of sample — g./cc. Volume of cake — cc* Temperature — °C Viscosity — poises Reciprocal rate — sec./cc* Pressure drop through cake — g./sq* cm. Cross-sectional area of cylinder — sq* cm* Thickness of cake - cm* Porosity of cake Surface area of cake — sq. cm./ce* of solids Resistance of cake — sq* sec./cc. of cake Resistance of cake ~ sq. sec./g. solids Air Permeability 0.4876 2.25 0.756 21.0 0.000185 8.87 704 0.378 2.0 0.714 74600 6.37 x 10c Water Permeability 2.0 2.25 5.90 22.5 0.00947 27.3 704 1.77 3.33 0.849 74300 9.89 x 10* 6 1.077 x 10^ 3.17 x 10c 42 fine quartz# Generally, the cake resistance was found to be independent of the septum resistance, although there is some indication that a high initial resistance yields higher cake resistance# In any event if too heavy a precoat is applied it usually takes longer for the cake resistance to become noticeable# This is illustrated in Figure 12# Three filtrations were made with the same material, a mixture of 25 per cent diatomaceous earth and 75 per cent of the (5-10) micron silica-,* The filtrations differed only in the amount of precoat applied. A had no precoat, B had a 10 lbs#/ 100 sq. ft. precoat, and C had a precoat of 15 Ibs./lOO sq. ft. The plot Q of v against V is a straight line for all of the data of B, whereas about one-half of the runs were required to smooth out the data for A and C. The precoat resistance was of such a magnitude in C that it over - shadowed the cake resistance for much of the run. If C had been carried out for a longer time more points on the $ vs. V diagram might have shown the slope to be more in line with that of B# Likewise, no precoat results in unusually high initial flow and often leads to plugging of the filter eloth. The excessively high initial flow is due to the inability of the cloth to retain the solids which results in less resistance to flow but also in poorer clarity. This is illustrated in Figure 12 by run A# The early points in this run were above the line and the intercept was negative which indicates too low an initial resistance. Similarly to C, a longer filtration cycle would have produced more points on the y vs. V diagram and might have brought the slope more in line with B# min./cc. . A3 FIGURE 12 TIME-FLOW DATA . ILLUSTRATING EFFECT OF FRECOAT q > | i > s 10 lb. Pre i coat rv 0.01 No Precoat Vjtf 800 1000 600 400 200 VOLUME OF FILTRATE, cc. 44 The time-flow data for these filtrations are given in Table IV. TABLE IV THE TIME-FLOW DATA ILLUSTRATING EFFECT OR PRECOAT Time - minutes 0.5 1 2 3 5 7 9 11 13 15 Filtrate Volume - cc. A - No pre coat 187 267 375 475 602 700 782 856 928 990 B - 10 lb./lOO sq. ft. precoat 117 181 269 337 450 538 617 689 756 818 C - 15 lb./lOO sq. ft. precoat 40 65 112 160 236 307 374 435 493 543 Several of the runs with precoats had negative intercepts which shows that those runs had insufficient precoats and that some of the solids might have passed through the thin precoat. This tendency was greatest for those runs in which no additional diatomaceous earth was added to the slurry. E. Surface Area If no attrition oceured it Is logical to assume that the surface areas of mixtures of particles should be additive. Figure 13 shows this to be the case for when SQ, the specific surface area in sq. meters per cc. of the powder, is plotted against the volume percentage of diatom aceous earth a straight line generally results. With only two exceptions the data fit this relationship within ten per cent* FIGURE 13 EFFECT OF COMPOSITION OH SURFACE AREA OF PARTICLES 1-2 micron cut 2-3 micron cut ' 3^5 micron cut 5-10 micron cut 10-20 micron cut — + . . . . . 10 C Q 100 0 PER CENT DIATOMACEOUS EARTH BY VOLUME The calculation of surface area may be made by several other methods, notably nitrogen or other gaseous adsorption methods and microscopic particle counts. The latter method is unsuitable for these systems because of the odd shapes of the diatomaeeous earth particles. The gas adsorption method as outlined by Emmett^ most likely gives more precise values for surface area though it is more complicated. However, the surface area in these calculations is used as a measure of the frictional resistance to flow and the permeability method gives sufficiently accurate and reproducable results. The results obtained in these experiments bear this out for most of the data fall well within the eight per cent margin which Carman^- claims to be the accuracy of this test. Also Anderson, McCartney, Hall and Hofer^ reported surface areas determined from the nitrogen adsorption test on the same grade of diatomaeeous earth as used in these experiments as 7.88 sq, meters/ec. This compares quite favorably with the 7.645 sq, meters/cc, which was the average value obtained from the permeability method, F. Porosity Figure 14 shows the porosity plotted against the weight per cent 3 P. H. Emmett, "Gas Adsorption Methods for Measuring Surface Area of Adsorbents," Industrial and Engineering Chemistry. 37:639-44, 1945. ^ Canaan, op. cit., p. 1049, ^ R. B. Anderson, J. T. McCartney, W, K. Hall, L.J. E. Hofer, "Kieselguhrs, Suitability as Carriers In Catalysts," Industrial and Engineering Chemistry, 39:1627, December , 1947, 0.80 0.75 o 0u 0.65 0.50 FIGURE 14 EFFECT OF COMPOSITION ON POROSITY OF PARTICLES 1-2 micron cut 2-3 micron cut 3^-5 micron cut 5-10 micron cut 10-20 micr&n cut As Is 0.40 0.3 25 50 75 PER CENT DIATOMACEOUS EARTH BY WEIGHT 100 of diatomaeeous earth. A porosity of 0.371 for the unseparated quartz is in line with the values obtained for the random packing of sand beds (0.36 - O.A5)^. However, the porosity of the various fractions seems higher than would be expected. One reason for this higher porosity is that the cuts are not perfect and contain small percentages of both larger and smaller particles. These particles tend to force the uniform particles further apart but are not small enough to fit in the voids between the regular particles. On the other hand the diatomaeeous earth has a high porosity because of its shape. A cake formed from this material has a very porous brushwork pattern. Mixtures of these materials result in porosities intermediate in value between the two. It is interesting to note that the rate of porosity increase is greatest for mixtures of diatomaeeous earth and unseparated quartz, containing up to fifty per cent diatomaeeous earth. Above this figure the rate of increase drops rapidly. This helps in explaining why relatively small amounts of filter aid often produce such marked improvement in the filtration properties of difficult filterable systems. When this increase in porosity is combined with a decrease in surface area, as is the case with mixtures of the 1-2 micron cut, the improvement in filtration properties is the greatest. G. Average Specific Resistance A graphical presentation of the data for the average specific resistance is given in Figures 13, 16, 17, and 18. In Figures 15 and 16 --1 Z--------— P. C. Carman, "Fundamental Principles of Industrial Filtration," Transactions of the Institute of Chemical Engineers - (London).16:168- 188, 1938. FILTRATION RESISTANCE; PER UNIT WEIGHT, sq. sec./g.x/O 4 , 9 500 ■ FIGURE 15 EFFECT OF COMPOSITION ON FILTRATION 200 •RESISTANCE PER UNIT 2-3 micron cut 3-5 micron cut 5-10 micron, cut 10-20 micron cut As Is . 100 20 10 F— t 100 0 PER CENT DIATOMACEOUS EARTH BY WT. t l PERMEABILITY RESISTANCE PER UNIT WEIGHT, sq* sec./g.*/<> 50 1000, FIGURE 16 EFFECT OF COMPOSITION ON PERMEABILITY RESISTANCE PER UNIT WEIGHT, r, 1-2 micron cut 2-3 micron cut 3-5 micron cut 5-10 micron cut 10-20 micron cut As Is 0 25 ^o 75 100 PEE CENT DIATOMACEOUS EARTH BY WT. 51 o X • o o X * o ® - » • • cr m tA ih ts (X, B SS- & - * CO * - ) CO £5 t e - o M Se &4 1006 500 POO FIGURE 17 EFFECT OF COMPOSITION O N FILTRATION RESISTANCE PER UNIT VOLUME, 1-2 micron cut 2-3 micron cut 3-5 micron cut 5-10 micron cut 10-20 micron cut As Is 0 .5 100 PER CENT DIATOMACEOUS EARTH BY VOL. PERMEABILITY RESISTANCE PER UNIT VOLUME, sq. sec./cc**'<> 52 1000J FIGURE 18 • EFFECT OF COMPOSITION - ON PERMEABILITY ?00 RESISTANCE PER UNIT \jUKJmi> p X 1-2 micron cut ’ -2-3 micron cut■ 3-5 micron cut . 5-10 micron cut 10-20 micron cut 200 100 20 10 p . u .75. 100 PER CENT DIATOMACEOUS EARTH BY VOL. the resistance per gram of 1 to 1 and 3 to 1 mixtures of nAs-Isn quartz and diatomaeeous earth is less than the resistance of either. This is explainable by the fact that the particle size distribution of these mixtures is such that the porosity and especially the porosity function , approach that of the straight diatomaeeous earth while the surface area, being additive, is considerably less. This unusual circumstance also occurs in mixtures of the 5-10 micron quartz and diatomaeeous earth. Figures 17 and 18 show that when the resistances are calculated on a volume basis the addition of diatomaeeous earth generally decreases the average specific resistance. Even though the surface area and, therefore, the frictional resistance are greater for the diatomaeeous earth than for all quartzes other than the 1-2 micron range, the resist ance per unit volume of cake is less because of the marked increase in the porosity of the cake. For the 10-20 micron quartz the increase in porosity does not balance the increase in surface area and so the addition of diatomaeeous earth results in an increased average specific resistance# If the particles are assumed to be spherical an average diameter may be calculated from the surface area data since for a sphere d • *jT— (31) Kozeny's equation may then be written 54 In Figure 19 the diameter calculated from surface area data is plotted against the function /-_€_____ e* p' Equation,(32) is drawn in as line A while line B is Walas* equation corrected to equivalent units. The points represent the experimental data* The data obeys Kozeny’s equation very closely whereas Walas* equation is in considerable difference. Walas* equation is empirical and he recognized it as being in disagreement with theory* The compressible systems with which he worked cause problems which exist to a much lesser degree with incompressible systems* If one of the more conventional means of obtaining an average diameter, i*e* microscopic slides, a weighted average screen diameter, or from a Sedimentation curve, is used and the value obtained is substituted into equation (32), the calculated value of r^ would be in disagreement with that obtained from filtration tests. As an example of this consider the (1-2) micron quartz. From both a sedimentation curve and the (1-2) micron photo-micrograph (Figure 4b) an average diameter would be approximately 1.5 microns* Substitution of this value for d and the values for f>' from Tables VII and VIII in the Appendix into equation (32) gives a value for r^, equal to 17 x 1G4 sq. sec./g* The actual filtration resistance for this system, r ^ (see Table VI — Appendix) is 4-57 x 104 sq. see./g. The diameter calculated from the surface area by the use of equation (31) is 0.296 microns and the substitution of this value for d in equation (32) gives a value of r^ equal to 438 x 104 sq. sec./g* This illustrates the fact that the 10, e r a 20 10 0.? 0.2 0.01 0.02 0. 0? 0.1 55 FIGURE 19 CORRELATION OF EXPERIMENTAL DATA WITH KOZENY'S AND WALAS* EQUATIONS A - EOZENY'S EQUATION B - WALAS* EQUATION ° « ® EXPERIMENTAL DATA resistance to flow is a function of.the surface area and not the diameter and that unless the particles are spherical the diameter obtained from any of the conventional methods would give misleading results when used to calculate the resistance to flow. Then to make use of equation (32) a shape factor would have to be introduced relating the actual shape of the particle to that of a sphere. It is much easier to use an equation, such as (33), with the surface area as a parameter of resistance thus ob viating the necessity of using a shape factor K = S '°jS*n~€) (33) g € fi It was noted in the course of separating the quart2 that the unseparated fraction formed a hard, difficult-to-disperse cake at the bottom of the settling beakers. On the other hand the separated fractions formed soft cakes which were easily dispersable. The most easily dispersed samples were those in which the separation was the best. It might be possible to correlate ease of dispersion with degree of fractionation. This type of correlation might prove of some value to paint formulators who often have a major problem in hard settling* CHAPTER VI CONCLUSIONS’ The principle attainments of this work led to the following conclusions^ 1. A simple permeability test is adequate for obtaining an accurate value of the average specific resistance which, in turn, may be used in predicting filtration characteristics of the given system. 2. The average specific resistance calculated from filtration data is shown to be equal to that calculated from permeability data and to be the following (Kozeny) function of surface area and porosity: r = 5.0 So2 (1 -e)Z g €3 or r_ = 5.0 So2 ( 1 -O - 1 p‘g e3 Several supplementary conclusions became apparent in the course of this investigation. They were: 3. Both air and water permeability tests give similar results for the calculation of surface area, although an air permeability test cannot be used to calculate r or r^ because of inherent porosity errors. 4. It is the marked increase in porosity that is primarily responsible for the decrease in resistance and the increase in flow rate when diatomaeeous silica filteraids are added to prefilt systems. 5. Both the bomb filter press and the permeability test equipment as described are excellent laboratory apparati and accurate reproducible results are obtainable with them. NOMENCLATURE 59 NOMENCLATURE A area of filtering surface, sq. em. C correction factor for the initial resistance in Ruth*s equation, cc. (v+c)2 * k (©*<%) to proportionality constants L thickness of filter cake, cm, P total pressure drop across both cake and cloth, g./sq.cm. Pc pressure drop across cake alone, g./sq.cm. Pg pressure drop across septum or cloth alone, g./sq.cm. so that * " V P. E septum resistance per unit area for a liquid of unit viscosity, sq. sec./sq.cm* S surface area per unit volume of cake, sq. cm./cc. SQ surface area per unit volume of solids, sq. cm./cc. T temperature of filtrate, °C V volume of filtrate collected at any time, cc. cake volume — cc. W weight of cake solids, g. b slope of the line in the equation, e- * c 1/ R . tf r, c__ v = Z P A X * P A ' c weight of solids per unit volume of filtrate, g./cc. d capillary diameter, cm. d j j , average diameter of particles 60 f subscript referring to filtration g acceleration due to gravity * 980 cm./sq.see. m1 weight of wet cake per weight of dry cake m variable exponent n variable exponent p subscript referring to permeability r^ average specific resistance of cake on a weight basis, sq. sec./g. r average specific resistance of a unit cube of cake, sq. sec./cc. s weight of filterable solids per weight of prefilt v volume of cake per unit volume of filtrate x exponent of pressure in the equation r = r1!* « > c average specific resistance of the solids p density of filtrate, g./cc. p' density of solids, g./cc. viscosity of the filtrate, poises time of filtration, min. or sec. ^ correction for initial time in Ruth*s equation (V-»C)^ • K € fractional void volume or porosity "V volume of voids per volume of solids \ dead void volume per volume of solids BIBLIOGRAPHY 62 BIBLIOGRAPHY Alexander, J..Colloid Chemistry. New Yorks Rheinhold Publishing Company, 1926, Vol. I. pp. Almy, C. and W. K. Lewis, "Factors Determining the Capacity of a Filter Press, "Journal of Industrial and Engineering Chemistry. As528-32, 1912. Anderson, R. B., J. T. McCartney, W. K. Hall, and L.J.E. Hofer, "Kieselguhrs, Suitability as Carriers in Catalyst", Industrial and Engineering Chemistry. 1618-1628, 194-7. Baker, F. C., "A Study of the Fundamental Laws of Filtration Using Plant-Scale Equipment," Journal of Industrial and Engineering Chemistry. 13:610, 1921. Carman, P. C., "Fluid Flow Through Granular Beds," Transactions- Institute of Chemical Engineers (London). 15:150-66, 1937. "The Determination of the Specific Surface of Powders," Journal of the Society of Chemical Industry. 57:225T, 1938. "Fundamental Principles of Industrial Filtration," Transac tions -Institute of Chemical Engineers (London), l6sl68-88, 1938 "The Aetion of Filter Aids," Industrial and Engineering Chemistry. 31:1047-50, 1939. Df Arcy, H. P. G., Les Fontaines Publicrues de la Ville de Dijon. Pariss Victor Delmont, 1856. DuFuit, A. J., Etudes Theoreticrues et Practioues sur le Mouvement des Eaux. 1863. Emmett, P. H., "Gas Adsorption Methods for Measuring Surface Area of Adsorbents," Industrial and Engineering Chemistry. 37:639-44, 1945. Fair, G. M. and L. P. Hatch, "Fundamental Factors Governing the Stream line Flow of Water Through Sand," Journal of the American Water Works Association. 25:1551-65, 1933. Hatscheck, E., "The Mechanism of Filtration," Journal of the Society of Chemical Industry. 27:538-44, 1908. Hazen, A., 24th Annual Report of the State Board of Health. Massachu setts. 1892* 63 Hinchley, J. W., S. G. M. Ure, and B. W. Clarke, "Studies in Filtra tion," Journal of the Society of Chemical Industry. 4-5:lT-10T, 1926. Instruction Manual for Bomb Filter. Technical Department, Dicalite Company, Los Angeles, California, 194-5 . 24- pp. Kozeny, J., Ber. Wien. Akad., 136a:271, 1927. . Wasserkraft und Wasserwirtschaft. 22:67-86, 1927. Kruger, E., Int. Mitt. Bodenkunde. 8:105, 1918* Pechukas, Alphonse and F. W. Gage, "Rapid Method for Determining Spe cific Surface of Fine Particles, "Industrial and Engineering Chem- isty. Analytical Edition. 18:370-73, 194-6. Ruth, B. F., G. H. Montillon, and R. E. Montonna, Critical Analysis of Filtration, "Industrial and Engineering Chemistry, 25:76-82, 1933. ______ , "Fundamental Axiom of Constant Pressure Filtration," Industrial And Engineering Chemistry, 25:153-61, 1933. Ruth, B. F., "Correlating Filtration Theory with Industrial Practice," Industrial and Engineering Chemistry. 38:564.-71, 194-6. Seelheim, Z. Anal. Chem.. 19:387, 1880. Sperry, D. R., "The Principles of Filtration-I," Chemical and Metallur gical Engineering. 15:198-203, 1915. . "The Principles of Filtration-II," Chemical and Metallurgical Engineering. 17:161-66, 1917 ______ , "Effect of Pressure on Fundamental Filtration Equation when Solids are Ron-Rigid or Deformable," Industrial and Engineering Chemistry. 20:892-95, 1928. Underwood, A. J. ¥., "Filtration Equations for Compressible Sludges," Journal of the Society of Chemical Industry. 4-7:325T-28T, 1928. Proceedings of the World Engineering Congress. Tokyo, 1929, fT*245, 1931. Walas, S. M., "Resistance to Filtration," Transactions of the American Institute of Chemical Engineers. 42:783-93, 194-6. 64 Waterman, H. J., and J. P. M. van Gilse, Rec. Trav. Chim. Pays-Bas. 43:757, 1924. a Weber, H. G., and R. L. gershey, “Some Practical Applications of the Lewis Filtration Equations,” Industrial and Engineering Chemistry, 18:341-45, 1926. APPEMDIX: TABLE V EXPERIMENTAL FILTRATION DATA Area= 4.63 sq. cm• Pressure* 704 g./sq.cm .a10 lb./sq. in gage c=0.002 g. solid/cc. filtrate • % « % T-°C , 1 . Volume of Flow — ml. at 0 in minutes Run D E SiO? Si0? H -poises 1/2 1 2 3 5 7 9 11 13 15 F-l 0 As Is 100 23 0.009358 83 119 171 209 268 316 357 394 427 458 F-2 0 As Is 100 24 0.009142 85 122 170 207 264 309 348 383 a5 444 F-3 25 As Is 75 27 0.00854-5 80 122 187 2a 315 383 445 503 549 580 F-4 25 As Is 75 29 0.008180 87 125 187 2a 330 402 462 515 561 599 F-5 50 As Is 50 29 0.008180 130 194 286 350 470 562 648 723 790 852 F-6 50 As Is 50 29 0.008180 120 183 273 343 458 553 635 711 777 840 F-7 75 As Is 25 28.5 0.008270 94 145 219 279 376 456 528 591 646 699 F-8 75 As Is 25 29 0.008180 100 152 228 289 390 473 542 6 0 9 667 724 *F-9 0 (1-2) 100 26 0.008737 10 19 34,5 48.5 71 92 113 130 146 159 *F-10 25 (1-2) 75 26.5 0.0086a 70 115 181 233 313 375 426 473 518 557 *F-11 25 1-2) 75 27 0.008545 79 127 196 249 329 393 447 495 538 577 *F-12 50 (1-2) 50 26 0.008737 92 152 245 317 426 509 508 664 731 782 *F-13 50 (1-2) 50 27 0.008545 114 186 289 367 486 579 657 725 787 845 F-U 75 (l-2) 25 26 0.009737 28 50 87 118 168 210 247 281 312 340 F-15 75 (1-2) 25 28 0.008360 57 88 142 181 242 291 334 372 407 439 F-16 0 2-3) 100 25.3 0.008870 61 86 118 145 187 220 249 273 298 317 F-17 0 (2-3) 100 25.1 0.008917 77 107 144 174 219 255 287 314 340 364 F-18 0 (2-3) 100 23.3 0.009293 68 95 133 162 206 242 273 299 327 350 F-19 25 (2-3) 75 24.7 0.009030 102 131 169 200 250 295 325 350 362 370 F-20 25 (2-3) 75 23.5 0.009250 80 108 144 176 224 265 296 320 3a 360 F-21 50 (2-3) 50 24.0 O.QO9142 93 130 180 218 281 326 370 409 445 476 F-22 50 (2-3) 50 25.0 0.008937 99 135 184 226 287 339 383 423 460 493 F-23 75 (2-3) 25 28.0 0.008360 1 16 162 227 276 354 a3 473 518 558 596 F-24 75 (2-3) 25 23.0 0.009358 104 152 210 258 334 400 458 502 540 575 F-25 0 (3-5) 100 27.0 0.008545 88 125 174 211 268 314 355 391 423 453 F-26 0 (3-5) 100 25.0 0.008937 33 57 98 127 175 217 253 286 316 344 F-27 0 (3-5) 100 27.0 0.008545 88 125 174 212 269 316 356 392 425 456 F-28 25 (3-5) 75 25.0 0.008937 74 114 169 212 280 335 384 427 467 504 * A 17.85 sq. cm. TABLE ¥ (continued) EXPERIMENTAL FILTRATION DATA Area =4.63 sq, cm# Pressure = 70A g./sq.cm. = 10 lb./sq. in. gage c= 0.002 g. solid/cc. filtrate % % Volume of Flow — ml. at Q in minutes__________ Run D E SiOp SiO? T-°C j rpoises 172 1 2 3 5 7 9 11 13 15 F-29 25 (3-5) 75 26.0 0.008737 73 110 F-30 50 (3-5) 50 26.0 0.008737 97 1A2 F-31 50 (3-5) 50 26.0 0.008737 97 1A7 F-32 75 (3-5) 25 25.0 0.008937 101 152 F-33 75 3-5) 25 25.5 0.008837 91 1A3 F-34 0 (5-10) 100 21.0 0.009810 56 100 F-35 0 (5-10) 100 23.6 0.009271 79 118 F-36 0 (5-10) 100 21.0 0.009810 30 53 F-37 0 (5-10) 100 26.0 0.008737 135 200 F-38 25 (5-10) 75 25.5 0.008837 115 171 F-39 25 (5-10 75 25.5 0.008837 39 6A F-40 25 (5-10) 75 28.5 0.008270 117 181 F-41 50 (5-10) 50 25.0 0.008937 A3 76 F-42 50 (5-10) 50 21.0 0.009810 33 61 F-43 50 (5-10) 50 26.0 0.008737 129 192 F-44 50 (5-10) 50 2A.0 0.0091A2 113 185 F-45 75 (5-10) 25 25.0 0.008937 AS 82 F-A6 75 (5-10) 25 26.0 0.008737 51 85 F-A7 75 (5-10) 25 2A.0 0.009142 112 171 F -AS 0 (10-20) 100 2A.0 0.0091A2 106 191 F-A9 25 (10-20) 75 19.0 0.010299 97 1A8 F-50 25 (10-20) 75 21.0 0.009810 157 229 F-51 50 (l0-20) 50 23.0 0.009358 122 ISA F-52 50 (10-20) 50 19.0 0.010299 82 12A F-53 75 (10-20) 25 19.0 0.010299 127 186 F-54 75 (10-20) 25 19.0 0.010299 11A 120 F-55 100 0 2A.0 0.0091A2 35 61 F-56 100 — 0 26.0 0.008737 108 160 16A 206 272 328 377 419 458 495 206 256 335 401 457 511 555 597 219 275 363 436 500 557 611 657 226 284 376 451 517 575 628 680 219 278 369 442 510 567 622 673 166 220 307 382 445 504 556 606 20A 266 366 450 525 593 655 713 95 134 204 268 326 379 431 780 296 367 479 569 648 728 792 849 251 313 425 508 580 646 707 764 UO 151 226 292 353 409 462 512 269 337 450 538 617 689 756 818 135 189 277 355 424 484 541 595 110 153 226 291 350 405 456 504 276 342 449 537 615 685 747 807 271 339 448 537 615 689 750 807 141 191 283 342 405 462 516 565 146 197 280 351 416 475 530 580 25A 318 422 507 580 646 705 761 326 441 625 780 915 1035 1135 1200 232 302 423 526 619 695 766 840 335 421 564 682 786 880 968 1049 276 346 461 585 640 715 784 848 191 248 343 424 496 560 620 677 269 336 439 526 602 668 731 788 250 313 415 500 575 642 705 760 104 144 216 278 335 388 437 481 239 299 393 471 536 597 653 705 3 TABLE VI CALCULATED FILTRATION DATA 68 Run b. Slope of e/v vs. V, x lO-o *LJk PA o/v . Intercept R, Septum resistance sq.sec./sq.cm. rfi, Cake resistance per unit wt. sq. sec./ g. x 10“° Per cent deviation from average rfl v, let to dry cake weight ratio rf, Cake resistance per unit wt. sq. sec./ cc. x 10”° Per cent deviation from average rf F-l 74 -0.00111 -23200 7.18 8.43 0.001198 12.00 8.25 F-2 85 -0.00425 -91000 ' 8.48 8.43 0.001198 14.16 8.25 F-3 38.3 0.003a 78100 4.07 0.75 0.002320 3.50 0.72 F-4 36.0 0.00335 80100 4.01 0.75 0.002320 3.45 0.73 F-5 18.28 0.00182 43600 2.08 1.07 0.003650 1.14 1.00 F-6 19.00 0.00209 50000 2.125 1.07 0.003650 1.163 1.00 F-7 24.50 o.ooa9 99000 2.70 0.18 0.00488 1.105 0.27 F-8 24.30 0.00331 79200 2.71 0.18 0.00488 1.11 0.27 *F-9 298.0 0.04690 15600000 457 0.001402 652 ■ ■ *F-10 45.7 0.00170 571000 71.1 0.93 0.001950 ^2.9 0.83 *f-h 44.5 0.00180 612000 69.8 0.93 0.001950 71.7 0.83 *F-12 20.3 0.00330 1095000 31.1 1.11 0.003050 20.4 0.97 *F-13 20.2 0.00100 340000 31.8 1.11 0.003050 20.8 0.97 F-H 81.3 0.00840 188000 8.33 8.33 0.004530 3.67 8.25 F-l 5 64.5 0.00650 152000 7.05 8.33 0.004530 3.11 8.25 F-16 151.5 -0.00170 -37500 15.60 9.00 0.001725 78.05 9.05 F-17 129.0 -0.00370 -81200 13.17 7.96 0.001725 15.27 4.22 F-18 143.5 -0.00270 -56800 14.15 1.11 0.001725 16.40 1.02 F-19 110 -0.00050 -10820 11.10 4.51 0.002220 10.00 3.91 F-20 123.5 -0.00500 -105500 12.15 4.51 0.002220 10.95 3.91 F-21 68,5 -0.00120 -25400 6.83 1.56 0,003105 4.40 1.38 F-22 65.3 -0.00170 -37200 6.62 1.56 0.003105 4.28 1.38 F-23 42.6 -0.00080 -18700 4.62 3.23 0.004610 2.01 3.08 F-24 44.4 0.00070 14600 4.33 3.23 0.004610 1.89 3.08 F-25 77.0 -0.00210 -48100 8.13 3.45 0.001702 9.56 4.40 F-26 91.5 0.01240 272000 8.98 6.65 0.001702 10.86 8.60 F-27 77.5 -0.00200 -45700 8.16 3.09 0.001702 9.60 4.00 F-28 52.7 0.00310 67800 5.39 3.24 0.002615 4.13 3.17 F-29 55.0 0.00320 71700 5.75 3.24 0.002615 4.40 3.17 * A 17*85 sq, cm* TABLE VI (continued) CALCULATED FILTRATION DATA 69 Run b, Slope of eA vs, V, x 1G-6 n r t t eA Intercept R, Septum resistance sq. sec,/sq.cm. r-fi, Cake resistance per unit wt, sq. sec./, g. x 10’6 Per cent deviation from average rfl v, Wet to dry cake weight ratio Tf, Cake resistance per unit wt, sq. sec./ cc. x lO*® Per cent deviation from average rf F-30 39*3 0.00170 38100 A.10 11.A0 0.003905 2.11 11.05 F-31 31.5 0.00230 61600 3.28 11 .AO 0.003905 1.69 11.05 F-32 29.5 0.00210 A5900 2.99 0.16 0.00A990 1.192 0,83 F-33 29.1 0.00290 6A1G0 2.98 0.16 0.00A990 1.190 0.83 F-3A 29.1 0.00720 1A3500 2.69 18,25 0.001905 2.83 17.75 F-35 21.0 0.00610 127500 2.06 9.A5 0.001905 2.17 9.70 F-36 25.3 0.01930 38A500 2.33 2.86 0.001905 2.A6 2.37 F-37 19.8 0.00100 1A000 2.06 9.A5 0.001905 2.17 9.70 F«*38 23.2 0.00210 29100 2.37 0.00 0.002780 1.70 0.01 F-39 2A.5 0.01680 372000 2.50 5.A9 0.002780 1.795 5.58 F-AO 20.3 0.00210 A9700 2.2A 5.A9 0.002780 1.61 5.35 F-Al 22.9 0.01160 255000 2.33 3.55 0.00A020 1.161 3.02 F-A2 26.7 0.01550 309000 2.A5 8.88 0.00A020 1.222 8. A3 F-A3 21.6 0.00260 58300 2.20 2.22 0.0QA020 1.097 2.66 F-AA 20.7 0.00170 36A00 2.03 9.78 0.00A020 1.028 8.78 F-A5 25.1 0.01120 2A5000 2.555 1.79 0.005110 1.001 1.A2 F-A6 25.9 0.01070 23AO00 2.68 6.77 0.005110 1.050 6. AO F-A7 23.3 0.00210 A5000 2.32 7.57 0.005110 0.910 7.82 F-A8 6.38 o.ooaoo 85700 0.636 — — 0/001800 0.708 — « F-A9 1A.95 0.005A0 102500 1.32 10.90 0.002975 0.888 11.00 F-30 11 .A 0.002A0 A7800 1.06 10.90 0.002975 0.711 11.00 F-51 17.85 0.00260 5A300 1.73 6.23 0.00AG75 0.851 6.28 F-52 22.2 0.00690 131300 1.96 6.23 0.00A075 0.96A 6.28 F-53 22.5 0.001A0 26700 2.A9 9.80 0.005110 0.976 0.71 F-5A 22.8 0.002A0 A5700 2.53 0.80 0.005110 0.990 0.71 F-55 30.3 0.01660 355000 3.01 1.00 0.006030 1.000 0.91 F-56 28.3 0.00170 38000 2.95 1,00 0.006030 0.982 0.91 % TABLE VII EXPERIMENTAL PERMEABILITY DATA Pressure = 704 g./sq. cm* Run Per cent DE SiOg, microns Per cent Si02 W, Dry ttt. of sample, g* r Density of solids* g./cc. vi Cake volume, cc. Cake thick ness, cm. Cross Sec tional area, sq.cm. T,°C 7 Liquid Viscosity, poises ©/V Reciprocal flow rate, sec./ce. Prl 0 As Is 100 2.0 2.65 1.20 0.679 1.77 22.0 0.009579 75.7 P-2 0 As Is 100 2.0 2.65 1.20 0.683 1,76 23.0 0.009358 76.1 P-3 25 As Is 75 2.0 2.55 2.35 1.33 1.77 19.7 0.010250 39.2 P-4 25 As Is 75 2.0 2.55 2.30 1.305 1.76 20.4 0.009950 35.9 F-5 50 As Is 50 2.0 2.45 3.70 2.09 1.77 21.0 0.009810 22.4 P-6 50 As Is 50 2.0 2.45 3.60 2.045 1.76 21.5 0.009695 21.9 P-7 75 As Is 25 2.0 2.35 4.90 2.765 1.77 24.0 0.009142 23.5 P-8 75 As Is 25 2.0 2.35 4.85 2.755 1.76 23.7 0.009207 23.4 P-9 0 tt-2) 100 1.0 2,65 0.70 0.395 1.77 26.0 0.008737 1725.0 P-10 0 (1-2) 100 1.0 2.65 0.70 0.396 1.76 24.0 0.009142 1830.0 P-ll 25 1-2 75 2.0 2.55 1.90 1.072 1.77 28.2 0.008324 568.0 P-12 25 (1-2) 75 1.0 2.55 1.00 0.567 1.77 26.2 0.008700 355.0 P-13 50 (1-2) 50 2.0 2.45 3.10 1.75 1.77 24.5 0.009040 256.0 f-14 50 (1-2) 50 2.0 2.45 3.00 1.70 1.76 22.7 0.009424 282.0 P-15 75 (1-2) 25 2.0 2.35 4.60 2,60 1.77 23.5 0.009250 76.0 P-16 75 (1-2) 25 2.0 2.35 4.50 2.55 1.76 22.5 0.009470 78.8 P-17 0 2-3 100 2.0 2.65 1.65 0.93 1.77 23.0 0.009360 147.0 P-18 0 (2-3) 100 1.0 2.65 0.90 0.508 1.77 24.0 0.009142 73.0 P-19 25 (2-3) 75 2.8 2.55 3.00 1.695 1.77 22.6 0.009460 136.1 P-20 25 (2-3) 75 2.0 2.55 2.30 1.31 1.76 26.2 0.008700 102.8 50 (2-3) 50 2.0 2.45 3.10 1.75 1.77 23.0 0.009358 61.8 p-22 50 (2-3) 50 2.0 2.45 3.10 1.76 1.76 22.8 0.009400 62.8 P-23 75 (2-3) 75 2.4 2.35 5.55 3.14 1.77 25.4 0.008857 44.0 P-24 75 (2-3) 75 2.0 2.35 4.60 2.61 1.77 26.2 0.008700 38.8 TABLE. VII (continued) . EXPERIMENTAL PERMEABILITY DATA Pressure = 704. g./sq.cm. Run i Per cent D E SiQg, Per cent microns SIO2 W, Dry Ht* of sample g. Density of solids, g./cc. V* Cake volume cc. h Cake thick ness, cm. A, Cross Sec tional area, sq. cm. T,°C , 1 Liquid Viscosity, poises o /v Reciprocal flow rate, sec./cc. £-25 0 (3-5 J 100 4.0 2.^5 3.40 1.92 1.77 23.6 0.009230 155.0 P-26 0 (3-5) 100 4.0 2.65 3.40 1.92 1.77 22.2 0.009535 I64.O P-27 25 (3-5) 75 4.0 2.55 5.10 2.88 1.77 22.5 0.009470 91.0 P-28 25 (3-5) 75 4.0 2.55 5.40 3.05 1.77 23.6 0.009230 101.0 P-29 50 (3-5) 50 4.0 2.45 7.80 4.40 1.77 23.0 0.009358 64.3 P-30 50 (3-5) 50 4.0 2.45 7.80 4.40 1.77 22.0 0.009579 68.0 P-31 75 (3-5) 25 2,0 2.35 5.00 2.94 1.77 23.6 0.009228 31.2 P-32 75 (3-5) 25 2.0 2.35 5.00 2.94 1.77 23.6 0.009228 31.4 P-33 0 (5-10) 100 2.0 2.65 1.95 1.10 1.77 22.1 0.009583 22.1 P-34 0 (5-10) 100 2.0 2.65 1.85 1.05 1.76 21.6 0.009672 21.9 P-35 25 (5-10) 75 2.0 2.55 2.80 1.58 1.77 22.6 0.009446 19.3 P-36 x 25 (5-10) 75 2.0 2.55 2.75 1.56 1.76 22.7 0.009424 18.1 P-37/ 50 (5-10) 50 2.0 2.45 4.00 2.26 1.77 23.1 0,009336 18.1 P-38 50 (5-10) 50 2.0 2.45 4.00 2.27 1.76 22.8 0,009400 19.0 P-39 75 (5-10) 25 2.0 2.35 5.10 2.88 1.77 22.0 0.009579 24.5 P-4.0 75 (5-10) 25 2.0 2.35 5.10 2.89 1.76 21.5 0.009695 24.8 P-41 0 (10-20] 100 2.0 2.65 1.80 1.015 1.77 22.50 0.009468 5.41 P-42 0 (10-20; 100 2.0 2.65 1.80 1.015 1.77 23.0 0.009358 5.35 P-4-3 25 (IO-20; 75 2.0 2.55 3.00 1.695 1.77 23.5 0.009250 9.85 P -44 25 (10-20, 75 2.0 2.55 2.95 1.665 1.77 24.0 0,009142 9.60 P-45 50 (10-20] 50 2.0 2.45 4.00 2.26 1.77 23.8 0,009185 15.0 P-46 50 (10-20 50 2.0 2.45 4.10 2.315 1.77 22.8 0.009400 14.9 P-47 75 (10-20 ( 25 ' 2.0 2.35 5.10 2.875 1.77 23.3 0.009286 19.6 P-48 75 (10-20; 25 2.0 2.35 5.10 2.875 1.77 22.5 0.009470 19.8 P-49 100 — 0 2.0 2.25 6.20 3.50 1.77 22.7 0.009420 27.4 P-50 100 — 0 2.0 2.25 5.90 3.33 1.77 22.5 0.009470 27.3 P-51 100 —— 0 2.0 2.25 6.00 3.39 1.77 22.8 0.0C9400 27.2 /2 TABLE VIII . CALCULATED PERMEABILITY DATA Run e Porosity 3 e (1-6 )2 SL, Specific Surface Area of powder, sq. cm./cc. r-, Cake resistance per unit weight, , sq. sec./g.xKT0 i Per cent deviation from average ... rp,Cake resistance per unit volume , sq. sec./ce.xLO Per cent deviation from average rP P-l 0*371 0.051 0.395 19150 8.62 2.89 14.48 2.41 P-2 0.371 0.051 0.395 19200 8.67 2.89 14.55 2.41 P-3 0,666 0.295 0.111 43200 4.21 1.36 3.58 2.29 P-4 0.659 0.287 0.116 40800 4.10 1.32 3.42 2.29 P-5 0.779 0.474 0.0487 50900 2.51 1.00 1.360 0.29 P-6 0.773 0.463 0.0515 49100 2.46 1.00 1.368 0.29 P-7 0.826 0.565 0.0302 65100 2.83 1.18 1.158 0.78 P-8 0.8245 0.560 0.0307 63900 2.76 1.18 1.140 0.78 P-9 0.461 0.098 0.290 203000 438 0.10 623 0.08 F-10 O.46I 0.098 0.290 202800 437 0.10 622 0.08 P-31 0.587 0.202 0.170 135500 75.1 8.03 79.1 6.17 P-12 0.608 0,225 0.154 159000 88.2 8.03 89.5 6.17 P-13 0.737 0.400 0.0691 151500 31.3 2.19 20.2 3.81 P-14 0.728 0.386 0.0739 149500 32.7 2.19 21.8 3.81 P-15 0.8145 0.540 0.0343 110100 9.04 0.16 3.94 1.12 P-16 0.8105 0.532 0.0399 108000 9.07 0.16 4.03 1.12 P-17 0.543 0.161 0.208 56500 17.35 0.57 21.0 3.69 P-18 0.581 0.196 0.175 65300 17.55 0.57 19.5 3.69 P-19 0.634 0.255 0.134 62800 11.70 2.58 10.58 2.63 P-20 0.659 0.287 0.116 73600 12.32 2.58 11.15 2.63 P-21 0.737 0.400 0.0691 72900 7.28 0.13 4.69 0.10 P-22 0.737 0.400 0.0691 73000 7.30 0.13 4.70 0.10 P-23 0.816 0.545 0.0338 79000 4.56 3.29 1.97 3.57 P-24 0.8145 0.540 0.0343 80800 4.87 3*29 2.12 3.57 P-25 0.556 0.172 0.197 43300 9.27 1.06 10.90 1.09 P-26 0.556 0.172 0.197 43700 9.47 1.06 11.14 1.09 P-27 0.692 0.332 0.091 54600 5.53 3.83 4.17 3.14 . P-28 0.709 0.352 0.0845 60500 .. . ______ 3.83 • ---4.44 ! Un/versfty of Southern California Library 7 3 TABLE ?III (continued) CALCULATED PERMEABILITY DATA i Run c Porosity 3 c (i-6)2 SQ, Specific Surface AREA OF powder, sq. cm./cc. r_,, Cake resistance per unit weight , sq.sec./g.xLO”0 Per cent deviation from average rpl r , Cake resistance per unit volume jr sq. sec./cc.xlO Per cent deviation from average rP P-29 0.791 0.495 0.0435 65800 3.78 1.82 1.94 1.77 P-30 0.791 0.495 0.0435 67000 3.92 1.82 2.01 1.77 P-31 0.8295 0.572 0.0291 74200 3.57 0.18 1.43 0.35 P-32 0.8295 0.572 0.0291 74400 3.60 0.18 1.44 0.35 P-33 0.613 0.231 0.150 27800 2.43 1.25 2.49 1.19 P-34 0.593 0.209 0.165 25200 2.37 1.25 2.55 1.19 P-35 0.719 0.372 0.079 38500 2.25 3.69 1.61 2.87 P-36 0.715 0.364 0.081 36600 2.09 3.69 1.52 2.87 P-37 0.796 0.505 0.0415 50500 2.14 1.60 1.068 1.56 P-38 0*796 0.505 0.0415 51300 2.21 1.60 1.102 1.56 P-39 Q.833 0.580 0.0278 67100 2.82 1.07 1.105 0.91 P-40 0.833 0.580 0.0278 66700 2.76 1.07 1.085 0.91 P-41 0.581 0.197 0.175 12450 0.631 0.08 0.700 0.07 P-42 0.581 0.197 0.175 12460 0.632 0.08 0.701 0.07 P-43 0.739 0.405 0.068 30100 1.225 2.50 0.783 0.44 P-44 0.734 0.396 0.0705 29100 1.165 2.50 0.790 0.44 P-45 0.796 0.505 0.0415 46700 1.80 1.12 0.900 2.69 P-46 0.802 0.517 0.0391 46900 1.76 1.12 0.853 2.69 P-47 0.833 0.580 0.0278 61200 2.33 0.42 0.915 0.49 P-48 0.833 0.580 0.0278 60900 2.31 0.42 0.906 0.49 P-49 0,8565 0.614 0.0206 77750 3.20 0.41 1.032 3.29 P-50 0.8495 0.607 0.0227 74200 3.17 0.53 1.077 0.94 P-51 0.8520 0.610 0.0218 76400 3.19 0.09 1.063 0.37 <3 VO I

Linked assets