LIBRARY OF THE UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN (&2, S l£<35o no. 51 - 52, ENGINEERING a ' ■' X The person charging this material is re- sponsible for its return on or before the Latest Date stamped below. Theft, mutilation and underlining of books are reasons for disciplinary action and may result in dismissal from the University. UNIVERSITY OF ILLINOIS LIBRARY AT URBANA-CHAMPAIGN J KfttRUWwa MOV 2 INTERL1BRAR 9 MAR 2 FEB. 2 4 J^AN ■1978, / LOAN nam 7 1978 pECD 8££B;MH0H SEP 35 L161— O-1096 Digitized by the Internet Archive in 2013 http://archive.org/details/applicabilityoft51java r ^ CIVIL ENGINEERING STUDIES SANITARY ENGINEERING SERIES NO. 51 »#* ■ 4 APPLICABILITY OF TWO MATHEMATICAL MODELS TO THE BATCH SETTLING OF ACTIVATED SLUDGE mrhiy of hwhb LIBRARY By ALI RASOOL JAVAHERI Supported by FEDERAL WATER POLLUTION CONTROL ADMINISTRATION U.S. DEPARTMENT OF THE INTERIOR RESEARCH PROJECT WP-01011 DEPARTMENT OF CIVIL ENGINEERING UNIVERSITY OF ILLINOIS URBANA, ILLINOIS JUNE, 1969 APPLICABILITY OF TWO MATHEMATICAL MODELS TO THE BATCH SETTLING OF ACTIVATED SLUDGE by Ali Rasool Javaheri THESIS Submitted in Partial Fulfillment for The Requirements of the Master of Science Degree in Sanitary Engineering Department of Civil Engineering University of Illinois Urbana, Illinois June, 1969 ~~C Q (? $(L ING,NEERING LIBRAIB ^ 5/'3i. ABSTRACT It was envisioned that the batch settling of activated sludge should follow the formula developed by Richardson and Zaki (1954) for hindered settling of uniform particles and the porous media theory advo- cated by Carmen and Kozeny (1937). The former equation is based on individual particle velocity, liquid-solid interface subsidence velocity and the porosity of the suspension. Experiments were designed to investigate the applicability of the two mathematical models mentioned. Laboratory tests were carried out with samples of activated sludge from three different waste treat- ment plants. It was intended to cover as large a range of concentrations of activated sludge as possible. Data were obtained for interface set- tling velocities of each sample of activated sludge placed in laboratory columns at different initial concentrations. In applying the models, uniform particle size was assumed for the settling aggregates at any specified concentration. This assumption can possibly be questioned; but, it provided a tool for analyzing aggre- gate sizes in different concentrations. It was shown that activated sludge follows these models with certain limitations. The average diameter of aggregates were calculated as a function of suspension concentration. The aggregate size decreased (or remained constant) as the concentration of suspension increased. The aggregate squeeze index was introduced to indicate the degree of compressibility of the sludge aggregates. This provided a means to characterize sludges with different settling behavior. From interpretation of aggregate size data, two flow patterns were discerned, i.e., interaaggregate flow (flow through aggregates) and interaggregate flow (flow between aggregates). A plot of logarithm of interface settling velocity versus con- centration sometimes showed a straight line relationship. This relationship can be useful in plotting the flux diagram which is used in the design of continuous thickeners. I I I ACKNOWLEDGEMENT The author wishes to express his sincere appreciation to Dr. Richard I. Dick, Associate Professor of Sanitary Engineering for his constant assistance and encouragement. Dr. Dick provided the guidance and criticism which helped the author to carry out this work. The author also wants to thank his laboratory assistant, Mr. B. Ebrahimi for his cooperation in performing the experiments. Thanks are also in order to Mr. Joseph Matherly, assistant research chemist, and Messrs. Robert Wood and James Schwing, graduate students, for their help in the preparation of this thesis. The investigation was supported by a research grant WP 01011 from the Federal Water Pollution Administration. Their support is great- fully acknowledged. IV TABLE OF CONTENTS Page ACKNOWLEDGEMENT iii LIST OF TABLES v LIST OF FIGURES vi I. INTRODUCTION 1 OBJECTIVE 1 II. BASIC THEORIES OF SEDIMENTATION 2 III. STUDY OBJECTIVES 9 IV. THEORY AND METHODS 10 MODEL I (Richardson-Zaki Equation) 10 MODEL II (Carmen-Kozeny Equation) 17 V. EXPERIMENTAL METHODS 20 INTRODUCTION 20 LABORATORY PROCEDURE . . 20 TIME OF FLOCCULATION 23 VI. RESULTS AND DISCUSSION 25 DATA ANALYSIS 25 SETTLING DATA AND INVESTIGATION OF MODELS 25 APPLICATION OF MODEL I (Richardson and Zaki Equation) 29 APPLICATION OF MODEL II (Carmen and Kozeny's Equation) 34 THE EFFECT OF CONCENTRATION ON INTERFACE SUBSIDENCE VELOCITY 36 VII. CONCLUSIONS 41 FIGURES . . . 44 REFERENCES 92 APPENDIX 95 LIST OF TABLES Table Page 1 DETERMINATION OF VOLUMETRIC SOLIDS CONCENTRATION 97 2 CALCULATIONS FOR MODELS I AND II 99 VI LIST OF FIGURES Figure Page 1 FLUX PLOT FOR CONTINUOUS THICKENING 44 2 EFFECT OF UNDERFLOW RATE ON TOTAL FLUX CURVE OF A CONTINUOUS THICKENER 45 3 REYNOLDS NUMBER VERSUS n(-^ -> 0) AFTER RICHARDSON AND ZAKI . . 46 4 DIAGRAM OF APPARATUS FOR SETTLING TESTS 47 5 TYPICAL BATCH SETTLING CURVE 48 6 DETERMINATION OF OPTIMUM TIME OF FILL FOR BATCH SETTLING 49 7 INTERFACE POSITION IN COLUMN VERSUS TIME — FIRST AND SECOND RUNS 50 8 INTERFACE POSITION IN COLUMN VERSUS TIME — THIRD AND FOURTH RUNS 51 9 INTERFACE POSITION IN COLUMN VERSUS TIME — FIFTH AND SIXTH RUNS 52 10 INTERFACE POSITION IN COLUMN VERSUS TIME — SEVENTH AND EIGHTH RUNS 53 11 INTERFACE POSITION IN COLUMN VERSUS TIME — NINTH AND TENTH RUNS 54 12 INTERFACE POSITION IN COLUMN VERSUS TIME — ELEVENTH AND TWELFTH RUNS 55 13 INTERFACE POSITION IN COLUMN VERSUS TIME — THIRTEENTH AND FOURTEENTH RUNS 56 14 INTERFACE POSITION IN COLUMN VERSUS TIME — FIFTEENTH AND SIXTEENTH RUNS 57 15 INTERFACE SUBSIDENCE VELOCITIES FOR ACTIVATED SLUDGE FROM PLANT I 58 16 INTERFACE SUBSIDENCE VELOCITIES FOR ACTIVATED SLUDGE FROM PLANT II — SAMPLE A 59 VI I Figure Page 17 INTERFACE SUBSIDENCE VELOCITIES FOR ACTIVATED SLUDGE FROM PLANT II — SAMPLE B 60 18 INTERFACE SUBSIDENCE VELOCITIES FOR ACTIVATED SLUDGE FROM PLANT II — SAMPLE C 61 19 INTERFACE SUBSIDENCE VELOCITIES FOR ACTIVATED SLUDGE FROM PLANT III 62 20 APPLICATION OF RICHARDSON AND ZAKI ' S EQUATION TO SEDIMENTATION OF ACTIVATED SLUDGE FROM PLANT I 63 21 VARIATION OF AGGREGATE VOLUME INDEX WITH SOLIDS CONCENTRATION — PLANT I 64 22 VARIATION OF AGGREGATE DIAMETER WITH SOLIDS CONCENTRATION — PLANT I 65 23 VARIATION OF AGGREGATE VOLUME WITH SOLIDS CONCENTRATION — PLANT I 66 24 VARIATION OF AGGREGATE SOLIDS CONTENT WITH SOLIDS CONCENTRATION — PLANT I 67 25 VARIATION OF NUMBER OF AGGREGATES WITH SOLIDS CONCENTRATION — PLANT I 68 26 VARIATION OF AGGREGATE DENSITY WITH SOLIDS CONCENTRATION — PLANT I 69 27 VARIATION OF VOLUME OF SUSPENSION AND AGGREGATES WITH SOLIDS CONCENTRATION — PLANT I 70 28 VARIATION OF ACTIVATED SLUDGE SUSPENSION POROSITY WITH SOLIDS CONCENTRATION — PLANT I 71 29 VARIATION OF FLUID DISPLACEMENT RATES WITH CONCENTRATION — PLANT I 72 30 VARIATION OF AGGREGATE SQUEEZE INDEX WITH SOLIDS CONCENTRATION — PLANT I 73 31 APPLICATION OF MODEL I TO SETTLING DATA FROM PLANT II SHOWN IN FIGURE 17 (SAMPLE B) 74 VI I I Figure Page 32 APPLICATION OF RICHARDSON AND ZAKI 1 S EQUATION TO SEDIMENTATION OF ACTIVATED SLUDGE FROM PLANT III 75 33 • VARIATION OF AGGREGATE VOLUME INDEX WITH SOLIDS CONCENTRATION — PLANT III 76 34 VARIATION OF AGGREGATE DIAMETER WITH SOLIDS CONCENTRATION — PLANT III 77 35 VARIATION OF AGGREGATE VOLUME WITH SOLIDS CONCENTRATION — PLANT III 78 36 VARIATION OF AGGREGATE SOLIDS CONTENT WITH SOLIDS CONCENTRATION — PLANT III 79 37 VARIATION OF NUMBER OF AGGREGATES WITH SOLIDS CONCENTRATION — PLANT III 80 38 VARIATION OF AGGREGATE DENSITY WITH SOLIDS CONCENTRATION — PLANT III 81 39 VARIATION OF VOLUME OF SUSPENSION AND AGGREGATES WITH SOLIDS CONCENTRATION — PLANT III 82 40 VARIATION OF ACTIVATED SLUDGE SUSPENSION POROSITY WITH SOLIDS CONCENTRATION — PLANT III 83 41 VARIATION OF FLUID DISPLACEMENT RATES WITH CONCENTRATION — PLANT III 84 42 VARIATION OF AGGREGATE SQUEEZE INDEX WITH SOLIDS CONCENTRATION — PLANT III 85 43 APPLICATION OF CARMEN AND KOZENY'S EQUATION TO SEDIMENTATION OF ACTIVATED SLUDGE — PLANT I 86 44 CHANGE IN AGGREGATE VOLUME INDEX WITH CONCENTRATION — PLANT I 87 45 SOLIDS FLUX CURVE — PLANT I 88 46 APPLICATION OF MODEL II TO SEDIMENTATION OF ACTIVATED SLUDGE — PLANT II (SAMPLE B) 89 47 APPLICATION OF CARMEN AND KOZENY'S EQUATION TO SEDIMENTATION OF ACTIVATED SLUDGE — PLANT III 90 48 VARIATION OF AGGREGATE VOLUME INDEX WITH CONCENTRATION — PLANT III 91 I. INTRODUCTION OBJECTIVE Sludge concentration is the largest unsolved research and development problem. The savings that could be effected in this area, alone, would go a long way in paving the way in improving other treatment processes and effluent. Vinton W. Bacon and Frank E. Dalton (1966) expressed their view as quoted above and explained that Chicago Metropolitan Sanitary District has not been able to concentrate activated sludge adquately either in the raw or digested form. This means that they have had to construct facil- ities to handle water which was about 28.5 times the weight of actual solids to be disposed. The annual savings to the District, if a one per- cent increase in solids (3.4 percent to 4.4 percent) concentration could be accomplished, would be $1,127,300. Concentrating sludge to higher concentrations by gravity thickening has been a problem since the acti- vated sludge process was introduced as a means of waste treatment. A great number of papers were introduced during the last two decades concerning the physical, chemical, and biological behavior of activated sludge with regard to its settling and thickening. Better understanding of the mechanism of sludge thickening will result in im- proved solids separation and concentration in activated sludge plants. This will indeed improve the effectiveness of activated sludge process. Also, significant cost reduction can be realized in disposing the large amount of waste solids from activated sludge plants, if the problem of thickening of waste solids into small volume can be solved by better gravity settling methods. II. BASIC THEORIES OF SEDIMENTATION The study of sedimentation characteristics of activated sludge with different methods has frequently been directed toward designing better final sedimentation tanks. The conventional procedure for design does not present a sound fundamental understanding of the overall opera- tion of the final tanks. Conventional procedures for design of final sedimentation tanks are based on the recommendations of the Great Lakes- Upper Mississippi River Board of Sanitary Engineers (I960) which advocate the surface settling rate as the only design criteria. There seems to be a lack of fundamental understanding of basic parameters which govern the sedimentation of activated sludge. In 1957, Lesperance advocated the analysis of sedimentation problem on the basis of area and volume requirements for final tanks. The area and volume requirements are based on the clarification and thick- ening functions of the sedimentation tanks (Dick, 1965). The former func- tion refers to the utilization of concentrated underflow from the final tank. The area required for clarification may be determined from the overflow rate considerations as explained by Hazen (1904) and Camp (1936), while the area required for thickening is founded on the works of Coe and Clevenger (1916). The larger of the two areas must be provided for satis- factory performance of the tank. The volume required for clarification is calculated by considering the flocculating characteristics of the suspen- sion (O'Connor and Eckenfelder, 1957). The volume requirement for thicken- ing can be determined from the consolidation characteristics of the suspension as described by Roberts (1949). Either clarification or thickening might regulate the area and volume requirements of the final tank. The volume requirement for the thickening function of a contin- uous thickener has not been analyzed as thoroughly as the area requirement. Hasset (1958) suggested a unified approach for the design of continuous thickeners. (Here the thickening was the only function of the settling basin for the specific suspension.) He suggested the area requirement as the only need for the satisfactory performance of continuous thickeners. He objected the need to calculate a volume for the thickener. Coe and Clevenger introduced the idea of solids handling capacity, G, in a batch settling test employing a slime suspension of concentration, C, V G= T -^ r (1) C C u where G = solids handling capacity C = concentration of suspension, less than C u C = ultimate concentration u V = interface subsidence velocity corresponding to concentration C. Coe and Clevenger showed that each concentration of a suspension has a certain capacity to discharge its solids. They concluded from their experimental work that the basis for determining the area required for optimum solids handling capacity is to find the limiting layer with minimum solids handling capacity. Hasset (1958a) derived the formula for solids handling capacity of a continuous thickener by applying the method of material balance to a continuous thickener. Accordingly, the solids flux at any layer below the feed layer is composed of two parts. The first component is due to the settling solids relative to the liquid.; and the second due to overall downward velocity imparted by solids withdrawal. Then G = V C + UC (2) c is the total solids flux through the continuous thickener. Here, C refers to solids concentration at any point along the height of the thickener. At the bottom where a higher concentration (discharge concentration C >C) prevails, the total flux G is G = C U (3) u By combining equation 2 and 3, the equation of solids handling capacity (equation 1) can be derived. One can describe the operation of a continuous thickener by plotting equation 2 for a given suspension and a range of underflow velocities. The term V C in equation 2 is due to solids flux in batch c ^ settling. The solids flux curve (V C versus C) is the characteristic curve of the suspension derived from laboratory batch settling tests. There is no exact theoretical formula which describes the relationship between inter- face subsidence velocity and solids concentration. This is the reason why one has to do batch settling tests in the laboratory to find out the characteristic batch flux curve of a given suspension. Later, it will be shown that a first order relationship between interface settling velocity V , and concentration C may estimate the batch flux curve for certain sludges. A typical flux curve for a continuous thickener is shown on Figure 1. The suspension was an industrial waste (Dick, 1968). The flux plot is composed of two parts. The first part is the characteristic batch flux curve (V C versus C) obtained from the batch settling tests performed in the laboratory. The second part is the superimposed flux curve (UC versus C) due to downward solids withdrawal. The downward velocity U is equal to the tangent of the angle 9 in Figure 1. The total flux curve for a continuous thickener is the graphical addition of these two flux components. Any point on Figure 1 refers to a feed loading specified by its flux (weight/time/area) and concentration (weight/volume). The minimum point on the total flux curve corresponds to maximum possible feed load and the limiting concentration C. . If a load G, more than G (limiting J L max 3 solids handling capactiy according to Coe and Clevenger) is applied to a thickener while keeping the underflow velocity U constant, the excessive load (G - G ) will go to overflow. Only the feed equal to or less than max 3 ' ^ G will concentrate from feed concentration to the limiting concentration max 3 C. , inside the thickener. Hasset (1958 b) argued that underflow concentra- tion C must be more than C. . He concluded from material balance that, G = V_, C. + UC. = UC (4) CL L L u and therefore C u = C L (l + \ L ) (5) It is important to note that with a higher underflow velocity U, , one may feed a higher load G , to the given thickener. This will 1 ' 3 maxl 3 result in lower underflow concentration C ,. This fact is graphically ul 3 r / represented on Figure 2, where U, > U. Note that a comparison can be made between Figure 1 and Figure 2 as follows: u x > U and G , > G , or G, , > G. maxl max LI L then C , < C ul u Here one is decreasing the underflow concentration (which might be the main objective of a thickener) for the sake of increasing the maximum possible load that the given thickener with a constant area can operate with, without turning the solids to overflow. Again it is to be noted that with a higher underflow velocity U, C approaches C. ; but they can never be equal. This can be demonstrated by drawing successively increasing underflow velocities (U, U, , U , ..., U ) and observing the corresponding underflow concentration (C , C ,, C „, ... 3 r 3 u ul u2 C ). From this one can observe that the difference between limiting un 3 concentrations and corresponding underflow concentrations decreases. Or (C u" C L )>(C ul- C L1> >(C U2- C L2» >- (7) Kynch (1952) analyzed sedimentation theory with the basic assumption that "at any point in a dispersion the velocity of fall of a particle depends only on the local concentration of particles." Kynch showed that the continually decreasing slope of the suspension-Liquid interface versus time curve can be interpreted as the successive inter- section of slower subsiding, more concentrated layers with the interface. Dick (1965) analyzed the batch settling behavior of activated sludge with Kynch's theory. He found that the Kynch model applies to ideal suspensions like sand. With activated sludge there is a deviation from ideal suspen- sion settling behavior measured by the retardation factor which is expressed in units of time. He also related the retardation factor to the rheological properties of activated sludge. Dick recognized Kynch's contribution as a mathematical formulation of the experimental procedure of Coe and Clevenger. Talmage and Fitch (1955) adopted the Kynch model and argued that multiple batch settling tests are not necessary for determination of the limiting solids handling capacity as advocated by Coe and Clevenger. They proposed a graphical method to determine settling velocity and con- centration at any time of settling from a single batch settling test. There has been some controversy about the validity of either multiple batch set- tling tests according to Coe and Clevenger or single batch settling tests according to Talmage and Fitch for the determination of solids concentra- tion and settling velocity at any stage of settling. Shannon _et _a_l. (1964) who worked with a suspension of glass beads reported similar results from both techniques. Shannon and Tory (1965) who worked with calcium carbonate slurries noticed differences between the two methods. They felt that multiple batch settling tests were more valid. Alderton (1963) directed plant-scale operation with gold mine slurries and showed that the Coe and Clevenger method of multiple batch settling test was more valid. Fitch (1962) advocated multiple batch settling tests rather than the single batch settling test which he previously recommended. Apparently some factors other than local solids concentrations effect the rate of settling. III. STUDY OBJECTIVES Although many investigators have contributed to the basic knowledge of thickening, the thickening behavior of nonideal suspensions like activated sludge is still not well defined. Presumably, some physical factors like sludge aggregate size and compressibility play significant roles in settling and thickening of activated sludge. Knowledge of the variation of these physical parameters which take place during subsidence of activated sludge would be useful in developing methods for effective th icken ing. In this work, two sedimentation models were applied to study the activated sludge aggregate properties. Model I was an equation for inter- face subsidence velocity of concentrated suspensions developed by Richardson and Zaki (1954). Model II was the equation of porous media theory developed by Carmen and Kozeny (1937). Application of these models provided the tool to investigate the nature of activated sludge aggregate size variations and liquid displacement from within aggregates. The nature of the models and the related qualifying assumptions will be discussed in the next paragraphs. 10 IV. THEORY AND METHODS MODEL I (Richardsor>-ZaJ < 26 > Equation 24 can be written as 9 (p k - p w )d 2 (1 - A 5 k ) 3 V c " t 36 K f ^ substituting k, for the bracketed term in equation 27, or (27) (V c # k ) 1/3 = K^ 3 (1 - A $ k ) (28) (V c $ k ) 1/3 = K x 1/3 - (k^A) # k (29) As explained previously, the values of V and §> were obtained experi- C K mentally for the suspensions of activated sludge. To apply the Carmen- 1/3 Kozeny equation, then (V $,) was plotted as a function of $, . From the slope of the plot obtained at any specified concentration, the value of aggregate volume index A and K, could be calculated. Since the value of K (equation 27) was unknown, the equivalent aggregate diameter, d, could not be determined. 20 V. EXPERIMENTAL METHODS INTRODUCTION Batch settling tests to determine sludge settling velocities were run on sludge samples taken from a local activated sludge waste treatment plant and two other activated sludge waste treatment plants in neighboring towns. Data obtained consisted mainly of sludge inter- face subsidence velocities with corresponding sludge concentrations. LABORATORY PROCEDURE The sludge was taken from the plant to the laboratory and was aerated for about 15 hours before beginning the settling tests. This was to bring the samples to room temperature (20+ 2 C) . Also 5 this pre-aeration helped to minimize the change in settling velocity of the sludge in the first few hours after it was taken to the laboratory. Dick (1965) observed that significant changes in sludge settling occured during the first 10 to 20 hours after sampling of the sludge from the treatment plant, while such changes became minimal after 24 hours. The settling velocities obtained after 15 hours of pre-aeration were con- sistently equal to the settling velocities measured initially. Settling tests to determine the zone settling velocity of sludge were conducted in the apparatus shown in Figure 4. The apparatus con- sisted of four plexiglass columns, 3.5 in. in diameter, and 4 ft in height, Column 2 and 3 were equipped with identical stirrers driven by small 21 electric motors which were located at the top of columns. The stirrers were constructed from 1/8 in. diameter aluminum bars. Thirteen angles, 3 in. x 3 in. in size were welded on 3 in. centers at the midpoint of one leg to the main vertical bar. The stirrers were easily removable from column 2 and 3. They had a constant rotational speed of one revolution per minute. The sludge was pumped from the reservoir on the right side to any of the columns desired. The tests were run at con- stant initial height of sludge in columns equal to 3.5 ft. Upon filling the column at a predetermined rate, the activated sludge was allowed to settle. The procedure of filling the columns from the bottom was de- scribed by Dick (1965). This method of filling the columns with the suspension was expected to produce a homogeneous concentration of solids at any point in the filled column soon after filling was finished. A plot of typical settling behavior is shown in Figure 5. Here, the height of the interface from the bottom of the column is drawn versus time for a specific sludge with a particular initial suspended solids concentration, Before beginning settling tests, the suspended solids concentra- tion and volumetric solids concentration were determined for the sludge in the reservoir. Solids concentrations were determined by taking four 15 ml sludge samples from the reservoir. The Gooch crucible method (Gratteau and Dick, 1968) was used for determination of solids concentra- tion. The average of four determinations was assumed to be representative of the solids content of reservoir sludge. The volumetric concentration of solids, §,, and solids density, p, , were determined by use of 50 ml pycnometers. Each pycnometer was 'S-9215, E. H. Sargent and Co. 22 filled with great care from a different height at the reservoir and it was capped very carefully. The pycnometers were then transferred to a constant temperature room (20 C) . After about one hour the pycnometers were removed from the constant temperature room and the levels of the sludge were adjusted to a consistent level in the capillary head of the pycnometer with a fine syringe. The pycnometers were then weighed with an accurate balance to determine the weight of sludge and pycno- meter together. A similar procedure was followed for calibration of pycnometer with distilled water at 20 C. A typical calculation is shown in Appendix A. The average of three values for the volumetric concentration of solids was assumed to be the volumetric concentration of solids in the reservoir. The volumetric and gravimetric concentra- tions of a specific sludge were directly proportional because the density of the solids remained constant. Settling data was obtained with samples of sludge of different initial solids concentrations with or without the presence of stirrers. For the latter case, stirrers could easily be removed from the columns. One column at a time was filled from the reservoir through the valved part in each column. The solids concentration was that determined pre- viously for the reservoir. The sludge remaining in the reservoir was diluted with its own supernatant to an approximate desired concentration. Another column was then filled at predetermined rate with less concentra- ted sludge to the height of 3.5 ft. Solids concentrations of the new diluted sludge in the reservoir were determined using the procedure described before. Type B5-Mettler, Mettler Instrument Corp., N. J 23 The settling tests were run for lower and lower concentrations as described above. The pipes and columns were washed with tap water to avoid deposition of solids in different parts of the apparatus. The settling tests were usually conducted twice for a specific concentration in order to check the accuarcy of the results. Experience showed that the settling tests for the two columns of the same initial concentration were reproducible. So in experiments involving both stirred and unstirred samples, two columns, one with and one without stirrer (columns 1 and 2 or 3 and 4) were filled with sludge of the same concen- tration and replicate tests were not made. This procedure avoided repeti- tion of settling tests and was mostly a time saving one. The results of settling tests were similar to Figure 5. They will appear in the next chapter of this thesis. TIME OF FLOCCULATION Figure 5 shows a non-linear portion at the beginning of settling test. The time corresponding to the point of intersection of a horizontal line drawn from the initial height of suspension interface with the exten- sion of the linear part of settling curve is arbitrarily called the time of f locculat ion. This is a measure of initial turbulence and homogeneity of initial solids concentration in the total volume of the column. A higher rate of fill of the column increases the degree of turbulence and conse- quently the time of f locculat ion. A lower rate of fill, though, does not assure a homogeneous initial solids distribution along the height of the column, but it decreases the time of floccula t ion. 24 The consequence of either low or high column fill time has been shown experimentally to be higher initial settling velocities than are obtained at intermediate filling rates. This is attributed to non- homogeneous distribution of solids. This change in settling velocities due to fill time has been observed with different suspensions at different initial concentrations. Figure 6 shows the results. The optimum fill time should be small enough (high rate of flow) to produce sufficient turbulence to assure a homogeneous mixed liquor suspended solids. It should also be large enough (low rate of flow) to avoid the consequence of high turbulence in the column. The optimum fill time was found to be about one minute. The time of fill in all of the settling tests was then adjusted to one minute by opening or closing the throttling vavle (Figure 4) . 25 VI. RESULTS AND DISCUSSION DATA ANALYSIS The settling curves obtained in this study were analyzed to determine the applicability of the models and more specifically to achieve the objectives mentioned before. The procedure used for this analysis is described in the following paragraphs. SETTLING DATA AND INVESTIGATION OF MODELS Settling curves were obtained for samples taken from three dif- ferent plants. The plants will be designated as plant I, II, and III. Plant I was a municipal treatment plant (Danville, Illinois). It em- ployed conventional activated sludge process. The population equivalent of the waste treated was about 165,000. The average hydraulic loading of the plant was 8 million gallons per day. The BOD loading was around 50 lb BOD per 1000 cubic foot or about 0.3 lb BOD per lb of mixed liquor suspended solids. The mixed liquor suspended solids in aeration tanks varied from 1500 mg/1 to 4000 mg/1 depending on the amount of sludge returned from the final settling tanks and the operation of the plant. The percent volatile solids varied depending on the amount of industrial waste received by the plant and averaged about 65 percent. The retention time in aeration tanks was about 5 hours. The settling behavior was very satisfactory with 26 an SVI of less than 80. The sludge sample was collected from the return sludge piping and taken to the laboratory. Plant II was a municipal waste treatment plant (Urbana-Champa ign, Illinois) employing a combination of the Kraus and Contact Stabilization modifications to the conventional activated sludge process and the trickling filter process. The population equivalent of the waste treated by the plant exceeded 120,000. The average hydraulic loading was nearly 11 million gallons per day. The BOD loading on the plant was about 0.2 lb BOD per lb of sludge solids or about 50 lb of BOD per 1000 cubic foot of aeration tank. The retention times were about 2 hours in the contact tanks and 5 hours in the stabiliza- tion tanks. The solids concentration in contact tanks was around 2000 mg/1 and that in stabilization tanks was around 5000 mg/1. About 30 percent of sludge solids was volatile. The sludge settling behavior was normally satisfactory with SVI around 100. The samples were collected from the contact tanks. Plant III was a small municipal activated sludge plant (Sullivan, Illinois) with a fair amount of carbohydrate waste loading from the local industries. The population equivalent of the waste treated by the plant exceeded 10,000. The plant used the contact stabilization modi- fication to activated sludge process. The BOD loading was about 50 lb per 1000 cubic foot of aeration tank or 0.45 lb BOD per lb of suspended solids. Solids concentration was less than 1000 mg/1 in the contact tank and about 2000 mg/1 at stabilization tank. The retention times were about 2 hours in contact tank and 5 hours in the stabilization tank. About 75 percent of the sludge was volatile. The settling behavior of the sludge 27 was very poor with SVI of more than 150. Samples were collected from the effluent end of the contact tank. A comparison of results obtained by analyzing settling data with and without stirring by use of Model I afforded a measure of the effect of stirring. It should be noted, however, that Vesilind (1968) has found that the beneficial effect of stirring is to minimize the arti- ficial effects created in laboratory settling columns. Hence, data from the stirred columns are considered to be more indicative of thicken- ing as it actually occurs in full scale settling basins. The results of a series of settling tests conducted for a sample of activated sludge from Plant I are shown in Figures 7 to 14. It should o be noted that zone settling velocities with slow stirring (V ) were always greater in magnitude than the quiescent settling velocities (V ) at relatively high concentrations (Figures 7 to 10). The quiescent settling velocities were not sometimes measurable when settling tests were conducted with highly concentrated sludge or due to gas production (Figures 7 and 8). It was noted that stirring did not have any effect on zone settling velocities at relatively low concentrations. However, stirring decreased the flocculation time in such instances (compare Figures 11 and 12). At even lower concentrations, stirring did not result in any decrease in flocculation time; but it did influence sub- sidence after high concentrations were reached in the process of thick- ening (Figures 13 and 14). 28 The results of settling tests from Plant I is summarized in Figure 15. Similar settling curves were obtained for sludges from Plants II and III. Figure 16 shows the settling data for a stirred sample (sample A) from Plant II. Figures 17 and 18 show settling data for two different samples (Samples B and C) from Plant II. The SVI in the plant at the time sample B was collected was 110 and that for sample C was 140 due to unusual application of higher organic loadings. Analysis of the data from Plant II will illustrate the changes in aggregate charac- teristics of the sludge due to operational parameters which effect the settling property of the sludge. Figure 19 shows the settling data from Plant III. Significant differences between the settling characteristics of the three activated sludges may be noted. The concentration ranges for the three sludges were appreciably different because of variations in sludge characteristics caused by the particular operating conditions in the three plants. The concentration range used for each sludge was con- sidered to represent the thickening conditions which could exist in the respective plants. For simplicity of presentation, Model I will be applied first to the settling data from the three plants. Results for the stirred samples of sludge from Plant I will be discussed in detail. Results of anal- ysis of unstirred samples from Plant I and all samples from Plant II will be mentioned briefly. Results of analysis for both the stirred and unstirred samples from Plant III will be presented to illustrate the typical effect of mixing. Model II will be applied later to the settling data from the 29 three plants. The results obtained from the application of the two models will be compared at appropriate instances. APPLICATION OF MODEL I (Richardson and Zaki Equation) Q 1/4.65 Figure 20 shows a plot of V versus the volumetric solids concentration, $, , for sludge from Plant I (Figure 15). The relationship between *, and the gravimetric concentration, C, as established by use of pycnometers is shown on the figure. The fact that the curve in Figure 20 is not linear indicates (from equation 21) that the settling velocity of an individual aggregate, V , and the aggregate volume index, A, changed with concentration. Values of A and V were obtained by drawing tangents o to the curves at selected concentrations and solving for the equations of the tangent lines according to equation 21. From the values of V obtained, the equivalent aggregate diameter, d, was calculated at various concentra- tions by use of equation 19. Results are shown in Figures 21 and 22. The figures show that in concentrating from about 5000 mg/1 to 19,000 mg/1, the diameter of aggregates was reduced from about 1.9 mm to 0.5 mm and the volume of water associated with each volume of solids was reduced from about 56 to 28. From these data it was possible to compute the number of aggre- gates which existed at any concentration as well as their volume and density Also, the volume and weight of actual solids in each aggregate could be calculated as could the porosity of the suspension at any concentration. 30 Figures 23 and 24 indicate the decrease in individual aggregate volume, ■V- , and the volume of actual solids in each aggregate, ¥, , which occurred a k as concentration increased. Figure 25 indicates the rapid increase in number of aggregates, N, as the concentration of the suspension increased, Figure 26 shows the increase in the aggregate density, p , as calculated a from equation 17 which accompanied an increase in concentration. Figure 27 shows a plot of the total volume of suspension, ¥ , and the total volume of aggregates per gram of suspension, 2¥ , as a function of concentration. The difference between the two curves repre- sents the amount of water between aggregates. The porosity, e, at any -V- - sv s a concentration is given by — 77 . Figure 28 shows the relationship a between porosity and concentration and indicates that porosity decreased from about 70 percent to about 50 percent as the sludge from Plant I thickened from 5000 mg/1 to 19,000 mg/1. It is of interest to know whether the volume reduction which accompanies thickening at any particular concentration is caused by elimination of water from between aggregates or by squeezing of water from within aggregates. Figure 29 shows the rate of change of suspen- sion volume, -V- , and total aggregate volume, £V , with respect to con- S 3 centration as given by the slopes of the curves in Figure 27. To give a measure of the significance of particle squeeze during thickening, A(£V) the quantity _ ,. defi ned as the " Aggr e 9 a t e S q uee 2 e Index," ASI. The ASI indicates the fraction of clarified liquid which originated from within aggregates as thickening took place. ASI would be zero for imcompressible aggregates and would achieve a maximum value of 1.0 when all displaced fluid originated from within aggregates. Figure 30 31 shows how the ASI varied with solids concentration with sludge from Plant I. About 15 percent of the total water being displaced from the consolidating sludge mass was coming from inside aggregates when the suspended solids con- centration was about 7000 mg/1 but that this fraction about doubled by the time the sludge concentration reached 15,000 mg/1. Figures 23, 24, 25, and 26 show that as thickening took place, the activated sludge aggregates became smaller, contained less solids than the initial aggregates, increased in number, and also that the density of aggregates increased. It is suggested that these phenomena were brought about by the two physical mechanisms, "squeeze" and "split." By the pro- cess of squeezing, the water content of activated sludge aggregates is reduced. By the process of splitting, an aggregate is divided into smaller aggregates, each of which contains only a portion of water and solids from the original aggregate. The experimental results show that both mechanisms prevailed during thickening of the activated sludge from Plant I because the aggregates became smaller, denser, and they increased rapidly in number. To explain the changes which take place during thickening in a different manner, two different flow patterns may be considered (Scott, 1966) Some of the liquid originating from the body of aggregates and from the interstices between aggregates is displaced from the subsiding sludge mass by "interaggregate flow" or flow between aggregates. Some of the liquid, however, is displaced by flowing through aggregates and this can be termed "intraaggregate flow." In applying Richardson and Zaki's equation to settling data, the manifestation of intraaggregate flow is a reduction of the apparent size of the basic settling units or aggregates. 32 The analysis of unstirred data from Plant I (Figure 15) indi- cated that the variations in aggregate diameter, d, and aggregate volume index, A, were equal to those of stirred samples up to the concentration of 8500 mg/1. At this concentration, an abrupt change occurred in the values of d and A and the values continued to remain constant at 8500 mg/1 and higher concentrations. A similar analysis was carried out for samples from Plant II (Figures 16, 17, and 18). For stirred samples (Figure 16) the nature of variations of AVI, and aggregate diameter were comparable to those des- cribed for the sludge from Plant I„ With unstirred samples from Plant II a plot of Model I in the form of equation 21 gave a straight line over the range of concentrations indicated in Figures 17 and 18. A plot of . 1/4.65 V versus §, for data of Figure 17 is shown in Figure 31. A similar plot can easily be obtained for the data of Figure 18. The aggregate diameter, d, and the aggregate volume index, A, were constant for the unstirred samples from Plant II. The calculated values are shown below: Aggregate Diameter Aggregate Volume Index, Unstirred Tests (Plant II) d, mm. A Sample B 2.54 80.0 Sample C 1.38 60.0 It is seen that the calculated values of d and A are different for the two unstirred settling experiments from the same plant. The differences in magnitudes of aggregate diameter and aggregate volume index between samples B and C were due to the difference between settling velocities of the samples which was indeed brought about because of unusual loading to the plant as explained previously. 33 Data from Plant III (Figure 19) were analyzed completely to indicate the typical effect of mixing. Figure 32 shows the application of Model I to the sedimentation of stirred and unstirred samples of the poorly settling sludge from Plant III. The curvature of Figure 32 again indicates that the aggregate size varied during the thickening process. The decrease in aggregate volume index, A, and aggregate size, d, with increasing concentration is indicated in Figures 33 and 34. Similarly, Figures 35 and 42 are plotted for the sample from Plant III by the methods described previously. Note that considerable differences existed between aggregate characteristics in the stirred and unstirred samples. At a given concentration, the aggregates of a stirred sample were smaller, denser, and larger in number than those of the unstirred sample (Figures 35, 37, and 38). The suspension porosity and the aggregate squeeze index of the stirred sample increased with concentration; while these variables decreased with concentration for unstirred samples (Figures 40 and 42). While it may seem unreasonable that porosity should be greater in slow- settling, high concentrated suspensions than in more dilute suspensions, it should be noted that the individual aggregate settling velocity, V , decreased at higher concentrations and that this change could offset an increase in porosity (see equation 11). Presumably, stirring destroyed bridge networks in the suspension, enhanced squeezing of the aggregates, and produced a greater aggregate squeeze index in the concentrating sus- pension of activated sludge. As before, both the squeeze and the split mechanisms were prevalent during the thickening of the stirred and the unstirred samples from Plant III. 34 Comparison of results for the stirred samples from Plants I and III indicates several significant points,, The poor settling sludge from Plant III had a much larger aggregate squeeze index (Figure 42) than the better settling sludge from Plant I (Figure 31). This means that a large fraction of the fluid clarified from the poor settling sludge originated from the bodies of the aggregates. The poor settling sludge also had a smaller porosity (Figure 40) than the better settling sludge (Figure 28) in the respective concentration ranges of the two sludges. It seems that a good settling sludge is characterized by its high porosity and low aggregate squeeze index (ASI) . When sludge char- acteristics are such that squeeze of aggregates must be relied upon to achieve higher concentrations, thickening does not take place readily. APPLICATION OF MODEL II (Carmen and Kozeny's Equation) As described previously, the value s of A (aggregate volume 1/3 index) and K, could be determined by plotting (V §, ) versus f. (equation 29). Figure 43 shows the plot for the activated sludge sample from Plant I. The decrease in the aggregate volume index, A, with concen- tration is indicated in Figure 44. The values agreed closely with those obtained by use of Richardson adn Zaki's equation (Figure 21). Since the value of k (equation 27) was not known, the equivalent aggregate diameter, d, could not be calculated. This is one of the disadvantages of using the Carmen-Kozeny equation for analysis of settling data. Another disadvantage of the equation is that as $, approaches 1/3 zero, (V §,) ' also approaches zero. Note that V $, is directly C K C K 35 proportional to solids flux (G = CV ) which is commonly used in analysis of thickening (Hasset 1964, and Shannon and Tory, 1966). The solids flux curve (G versus C) has the characteristic shape shown in Figure 45. Now, 1/3 (V §,) is directly proportional to the cube root of the ordinate values in solids flux curve. If a smooth curve has to be drawn in Figure 43 in order to apply the Carmen-Kozeny equation, the data should represent the values of G following G . The Carmen-Kozeny equation r 3 max can not be applicable then to settling data at concentrations corres- ponding to solids flux values at the left side of G . The values 3 max omitted from the curve in Figure 43 indicate this point. Application of Carmen-Kozeny ■ s equation to the values only on the right side of G in Figure 43 can provide an estimate of the aggregate volume index as shown later. The disadvantages mentioned limited the utility of Carmen- Kozeny's equation as a means of aggregate size analysis of activated sludge. Application of Model II to the unstirred data from Plant I indicated that the variations in aggregate volume index were equal to those of stirred samples from the same plant up to the concentration of 8500 mg/1 (Figure 44). The aggregate volume index remained constant after this concentration. In a similar manner, the data from Plant II were analyzed. The aggregate volume index decreased as concentration increased for the stirred samples from Plant II (Figure 16). The variations of aggregate volume index were comparable to those obtained when Model I was applied. With unstirred samples from Plant II, a plot of Model II in the form of equation 29 gave a straight line. A plot of 1/3 I $, ) versus $, 1/3 (V ^..) versus $, based on the data in Figure 17 is shown in Figure 46. 36 A similar plot can be obtained for the data in Figure 18. The constant aggregate volume index values calculated for the two unstirred settling data from Plant II were as follows: Unstirred Tests (Plant II) Aggregate Volume Index A Sample B Sample C 71.0 55.0 It is significant that the values of aggregate volume index obtained by the application of both models were comparable. Application of the Carmen-Kozeny equation to the settling data from Plant III is illustrated in Figure 47. The values of the aggregate volume index, A, are shown in Figure 48. The computed values of the AVI compared closely to those obtained by using the Richardson- Zaki equation (Figure 33) . The decrease in the aggregate volume index with increasing concentration found by application of the Carmen-Kozeny equation indi- cated squeezing of the aggregates. Splitting of the aggregates could not be shown by the application of the Carmen-Kozeny equation, since aggregate diameters could not be calculated. THE EFFECT OF CONCENTRATION ON INTERFACE SUBSIDENCE VELOCITY The settling data obtained from the three plants were plotted in Figures 15 to 19. It was noted that some of the plots appear as 37 straight lines in the semilog paper. The data were not numerous enough to make any statistical inference about the validity of the first order relationship between settling velocity and concentration. However, similar results can be found in the literature (Vesilind, 1968). The relationship between the settling velocity and respective gravimetric solids concentration in such instances can be written as V = V e" kC (30) co . where k = slope of straight line of log V versus C, Equation 30 can be used instead of a flux plot to determine the relationship between the operational parameters of a continuous thickener. The total flux equation for a continuous thickener is, G = V C + UC (31) c Substitution of equation 30 into equation 31 results in G = V Ce' kC + UC (32) o Differentiating equation equation 32 with respect to concentration C and equating the results to zero, -"kC -kC L -^ = V e "- kC.Ve + U = (33) dC o L o wh ere C. stands for limiting concentration (see Figure 1) . 38 2 2 Note that d G/dC > for the limiting concentration, C. . This would require the condition kC > 2. From equation 33, -kC. U = V Q e L (kC L - 1) (34) But since, G, = UC (35) L u and G L = V a C L + UC L (36) Then from equations 34 and 35, -Tc G. = V e L (kC. - 1) C (37) L o L u and from equations 34 and 36, -kC. -kC, __ G L = (V Q e L ) C L + V Q e L (kC L - 1) C L (38) Equating equations 37 and 38 and solving for C , kC, 2 C u ■ TC^ (39) 39 Solution of equation 39 for C. will result in, c in c l=K + t< c u 2 - 4 f u > (40 > Equation 40 shows the relationship between limiting solids concentration and the ultimate concentration in a continuous thickener. Although in Equation 40, C appears to be independent of U, the underflow concentra- tion, C , is a function of withdrawal rate, U(see Figures 1 and 2). From equations 35 and 36, G L = V CL C L + r C L (41) u Solving equation 41 for G. , C L " C u which is equivalent to equation 1 and represents the limiting point in the flux curve (Figure 1). Assuming that equation 30 is valid, one can experi- mentally determine the value of k which would be a characteristic constant of the given activated sludge. Then he may choose a practical value for C and calculate the limiting concentration from equation 40. The values of limiting flux, G. , and underflow velocity, U, can then be obtained from equations 42 and 35, respectively. By repeating the cacluations for a series of practical ultimate solids concentrations, one can calculate and plot the relationships between C , U, and G. to determine the operational parameters of a given thickner with the given suspension. However, it has 40 to be emphasized that much effort should be put in examination of the validity of first order relationship between settling velocity and concentration before such a procedure can be used. 41 VII. CONCLUSIONS 1. The equation of reduced settling velocity of a suspension developed by Richardson and Zaki (Model I) provides the means to obtain informa- tion regarding the fundamental behavior of activated sludge during thickening. The nature of liquid displacement from aggregate particles, and the manner in which aggregate particle size varies as consolidation takes place, can be studied using this equation. 2. The equation of porous media developed by Carmen and Kozeny (Model II) is a less fruitful means of analysis of sludge aggregate variations. This equation can not be used to calculate the variations in aggregate diameter as thickening takes place. The following specific conclusions may also be drawn: 3. As the concentration of activated sludge increases, the aggregates which comprise the sludge are squeezed to eliminate water and are split into smaller aggregates. The combined effect of "squeeze" and "split" is that aggregates become smaller, more numerous, and more dense as thickening takes place. 4. The fluid eliminated from subsiding sludge masses originates from within aggregate particles and from the interstices between aggregates. The "aggregate squeeze index" (ASI) has been introduced to describe the role which aggregate "squeeze" plays in thickening. It is the fraction of the total water being eliminated at any particular concentration which is originating from within aggregate particles. Based on the settling characteristics of sludges from the plants studied here, 42 activated sludges with good settling characteristics have low ASI and high porosity values and thickening to high concentrations occurs primarily by elimination of intersticial water. In con- trast, sludges with poor settling properties have high ASI values and low porosities. That is, much of the water removed in the course of thickening of poor settling sludges comes from inside the aggregates. 5. Slow stirring during laboratory settling tests alters the settling velocity of high concentrations of activated sludge appreciably. The faster settling velocities commonly observed in stirred columns may be caused by the fact that stirring increases the aggregate squeeze index. However, the low ASI values associated with unstirred columns may reflect the bridging in laboratory settling columns and may not be a factor in prototype settling basins. 6. The thickening of activated sludges brings about two flow patterns with the mass of aggregates. Some of the total displaced fluid which originates from the interstices of the suspension and bodies of the aggregates travels between the subsiding aggregates. This is referred to as interaggregate flow. At the same time, some of the fluid travels through the subsiding aggregates. This is referred to as intraaggregete flow. Intraagregate flow accompanies the split of aggregates to smaller ones. 7. Assuming that the experimentally observed first order relationship between interface settling velocity of activated sludge and its 43 concentration is a valid one, the design and operation of a con- tinuous thickener can be very much facilitated by using simple equations to determine the relationship between solids flux, underflow concentration, and solids withdrawal rate. 44 o LU m <_> cvj i— i ^^ X w H O o X 3 z O O E 1- z o o *— ' cr •k o ;U Li. O c _J o Q_ in k V- X y —J § u. o c • o o 8 *Dp/ ? W/sq| *xny spnos 45 Iv o \ ° -« V «» -1 o _i \ /- \ X ° o ID i + / o f — II % o \ A \ o o \ \ I CD c O II 5" e> ii 8 E CD 1 s- w \ 1 1 1 1 ^\ - 'o x 8 3 o c .2 C_> CO o o o Li- CD o x 3 < o U c 3 o —I Li- ar uj Q z 3 o LU CM UJ CD o 8 8 o 8 *op/ w/sqi »*n|j spjios 46 47 ro M CO LU O LU CO CC o 2 < CL CL < o C9 < CC C3 48 o CD _3 O o c o o 0. «.o 1 1 1 I 1 3.5 — 3.0 — \ /-Slope = Zone Settling Velocity, V c - 2.5 — — 2 — 1.5 — — 1 0.5 n 1 l 1 I i 10 20 30 40 50 60 Time, min. FIGURE 5. TYPICAL BATCH SETTLING CURVE 49 0.12 0.10 o o 0> o> 0) C/> 0.40 0.60 0.80 1.00 1.20 1.40 Time to Fill 3.50 ft, min. FIGURE 6. DETERMINATION OF OPTIMUM TIME OF FILL FOR BATCH SETTLING 50 •> o> % ♦ CO 3 a: O o o z < I- co UJ 2: CO 8 I 4-> LU 3 > i S o o 8 Z E 5 8 CO o o. UJ o < u. UJ cc JD U 'mmpo m yofiiwy 51 en H- cc z> o L. O 2 < Q C E CO O O CO o a. < 00 LU o ujOMoq ujoi| 4| *uu«|00 uj uofiftotj ■ 52 to z => on X t— I to Q 2 < to =3 to • LU «? > -2 3: • E o o o I— I H i-t to o 0l LU < LL. on LU LU OH CD UIOMOq lANMJ 4| 'UUJWtOQ U| UOfHtOd 53 c c F E N v. V. N» t £ ? O 5 SP CM CVJ O 8 0> 0) O O o O o M ii It II u u (/) J • > o> ■«■ £ £ CD l-H LU 8 o z < X 1- z LU > LU CO ? 1 LU SI l-H 1- co CO (0 az • LU ♦» > 3 o C z X. & ID _J O m O « Z E l-H o CVJ K z l-H h~ l-H CO 0. LU CJ < Lu- o OD es: LU 1— LU CC CJ uuoMoq ujojj \\ 'inun|03 ui uotiftod 54 1 c : < > 2 > 5 c ft/mi 00 o o d 05 8 CO z q 2 < 3: $ CO CO a: ■*- o c 1 Z o CJ • z F § z I- o 1— 1 1- HH CO o Q- LU O < u. ac o LU 00 1- a: ukmoq wojj i| 'uumioo u| uojijtod 55 . 5 i 1 „ * i | fs, -j e CD CM CM o X pfi 9 a § ° ^^^ o o B d £ ""^ «5 S o^ $ ♦* 8 g a: t o z < 8 s or .6 c 1 2 C « ! 5 ^ M n ■ 7370 = 0.00< t0^\ • >°Oi O CO => C/1 3 a: c LU > E z 2: => » _i «> o E o 8 Z g GO o < Li. a: LU a: Z> C3 IO fj ujouoq uioi| \\ 'uumioo u| uoufscy 56 o csj ca 6 6 M N CM CM O O 6 8 •> o> to cc ZD O o z < I— I I- to to a: o <_> to o 0. < LU a: 3 C3 uiOMoq ujojj u 'uumfoo u| aci*|tOd 57 \ 1 1 5 e e > cs| eg £ q O O CM O 5 ■ ii ■ H i • °03 ■ n ? ft * i c 9 8 O C E m 8 I X CO O < UJ t UJ 3: CO CO on LU > o 8 CO o a. < LU C3 uiOMoq uio.ij ii 'uiunfco «) uotutoy 58 1.0 c o>° ■o c o •>° u > 0) o c "w 3 0) o o «*- a> c 10 -1 10 10 O With Stirring ( V c ) • Without Stirring ( V c ) # With and Without Stirring 4000 8000 12,000 16,000 20,000 Concentration C, mq/Jl FIGURE 15. INTERFACE SUBSIDENCE VELOCITIES FOR ACTIVATED SLUDGE FROM PLANT I 59 c u o> c o •>° o o a> > o c 0) -O a CO a> o o »^ k- a> c 10,000 Concentration C , mg// FIGURE 16. INTERFACE SUBSIDENCE VELOCITIES FOR ACTIVATED SLUDGE FROM PLANT II — SAMPLE A 60 c 'E o o> X3 C o •>° u o > o c a> ;o "«/> 3 o o «*- \_ a> c 2000 4000 6000 8000 10,000 Concentration C , mg// FIGURE 17. INTERFACE SUBSIDENCE VELOCITIES FOR ACTIVATED SLUDGE FROM PLANT II — SAMPLE B 61 c 1 o o> C o •>° u o > o c a> ;o " (/) a> o o «+- c 10,000 Concentration C , mg/^ FIGURE 18. INTERFACE SUBSIDENCE VELOCITIES FOR ACTIVATED SLUDGE FROM PLANT II — SAMPLE C 62 c "E u o> c o •>° o o a> > u c a> ;o c/) a> o o <*- 2000 4000 6000 8000 10,000 Concentration C , mg/,f FIGURE 19. INTERFACE SUBSIDENCE VELOCITIES FOR ACTIVATED SLUDGE FROM PLANT III 63 0.900 .C E o> 0.800 700 0.600 500 0.400 300 200 0100 C = 1085 « 10 f k ,mg/Jt p = 1085 gm/cm 3 50 100 150 200 250 Volumetric Solids Concentration , *\x 10 FIGURE 20. APPLICATION OF RICHARDSON AND ZAKI'S EQUATION TO SEDIMENTATION OF ACTIVATED SLUDGE FROM PLANT I 64 60.0 X © •a c E O © w < 50.0 — 40.0 30 — 200 10.0 — 5000 10,000 15,000 20,000 Concentration C , mg/J£ FIGURE 21. VARIATION OF AGGREGATE VOLUME INDEX WITH SOLIDS CONCENTRATION — PLANT I 65 2 50 E E l-o E o ® 8 < 50 5000 10,000 15,000 Concentration C, mg/J EOPOO FIGURE 22. VARIATION OF AGGREGATE DIAMETER WITH SOLIDS CONCENTRATION — PLANT I 66 6 E E o > o o> 2 o» < o c 20,000 Concentration C , mg/J FIGURE 23. VARIATION OF AGGREGATE VOLUME WITH SOLIDS CONCENTRATION — PLANT I 67 E E 9 < C O o 9 E 3 iopoo 15,000 20PO0 Concentration C , mg/$ FIGURE 24. VARIATION OF AGGREGATE SOLIDS CONTENT WITH SOLIDS CONCENTRATION — PLANT I 68 5 E o w o Q. I - 9 E z 5000 10,000 15,000 Concentration C , mg/Jt 20,000 FIGURE 25. VARIATION OF NUMBER OF AGGREGATES WITH SOLIDS CONCENTRATION — PLANT I 69 1.0050 10000 5000 lOpOO 15,000 Concentration C , mg/fl 20,000 FIGURE 26. VARIATION OF AGGREGATE DENSITY WITH SOLIDS CONCENTRATION — PLANT I 70 300 s < 9 E 250 — 200 — 150 — 1 E a. co co o *« E *o — E O • > 0. 100 5000 10,000 15,000 Concentration C, mg/fl 20P00 FIGURE 27. VARIATION OF VOLUME OF SUSPENSION AND AGGREGATES WITH SOLIDS CONCENTRATION — PLANT I 71 1.00 15,000 20g0OO Concentration C , mg/i FIGURE 28. VARIATION OF ACTIVATED SLUDGE SUSPENSION POROSITY WITH SOLIDS CONCENTRATION — PLANT I 72 ?h E|6 < X) c o < 030 025 020 015 010 — 005 Total Fluid Displacement Rate From Suspension, AV t Fluid Displacement — Rate From Aggregates , A(IV ) AC 5000 10,000 15,000 Concentration C , mg/A 20,000 FIGURE 29. VARIATION OF FLUID DISPLACEMENT RATES WITH CONCENTRATION — PLANT I 73 100 < 3 3 o i s < 80 0.60 — 0.40 0.20 5000 10,000 ISpOO 20 pOO Concentration C , mg/4 FIGURE 30. VARIATION OF AGGREGATE SQUEEZE INDEX WITH SOLIDS CONCENTRATION — PLANT I 74 0.700 0.400 FIGURE 31 100 Volumetric Solids Concentration, ^ x 10 K APPLICATION OF MODEL I TO SETTLING DATA FROM PLANT II SHOWN IN FIGURE 17 (SAMPLE B) c 8 4 - o o> 1 5 „ • > 0«00 9 950 500 450 400 — 350 0.300 250 200 75 C= I0€6il0% fc , mg/i Unstirred 10 20 30 40 so •o Volumetric Solids Concentration , + x I0 4 FIGURE 32. APPLICATION OF RICHARDSON AND ZAKI ' S EQUATION TO SEDIMENTATION OF ACTIVATED SLUDGE FROM PLANT III 76 300 1000 2000 3000 4000 Concentration C,mg// sooo 6000 FIGURE 33. VARIATION OF AGGREGATE VOLUME INDEX WITH SOLIDS CONCENTRATION — PLANT III 77 3 00 E E It," w ® E o b o © w < 2.50 — 2.00 — 1.50 — I 00 50 2000 3000 4000 5000 6000 Concentration C, mg/l FIGURE 34. VARIATION OF AGGREGATE DIAMETER WITH SOLIDS CONCENTRATION — PLANT III 78 E E E O > o o> w < a "O c 7000 FIGURE 35, 1000 2000 3000 4000 5000 6000 Concentration C , mg/fl VARIATION OF AGGREGATE VOLUME WITH SOLIDS CONCENTRATION — PLANT III 79 E E a> o ? s < c o o 0) a> E 1000 2000 3000 4000 5000 6000 7000 Concentration C , mg/jt FIGURE 36. VARIATION OF AGGREGATE SOLIDS CONTENT WITH SOLIDS CONCENTRATION PLANT III 1000 2000 3000 4000 Concentration C , mg /St 5000 6000 FIGURE 37. VARIATION OF NUMBER OF AGGREGATES WITH SOLIDS CONCENTRATION — PLANT III 81 E E 9 55 o 9 1 OOI4 1 1 1 1 I I 0012 - I 0010 - Stirred -n — i oooe ' 1 — 10006 Unstirred — ' r I""* - 10004 10002 1 OfKV) 1 1 1 | 1 — 1000 2000 9000 4000 8000 Concentration C , mg/i FIGURE 38. VARIATION OF AGGREGATE DENSITY WITH SOLIDS CONCENTRATION — PLANT III •000 82 CO 9 £ 5 600 500 400 £ (A C O C « 200 2 E u 300 (A "O O CO ^_ 100 o E o w CD 1000 2000 3000 4000 Concentration C , mg/J 5000 6000 FIGURE 39. VARIATION OF VOLUME OF SUSPENSION AND AGGREGATES WITH SOLIDS CONCENTRATION — PLANT III 83 I oo 080 — m 5 o £ S (/> 60 — 040 0.20 — 1000 5000 2000 3000 4000 Concentration C, mg/J? FIGURE 40. VARIATION OF ACTIVATED SLUDGE SUSPENSION POROSITY WITH SOLIDS CONCENTRATION — PLANT III 6000 84 ^ e u 6 o < T3 C o >1o < < 100 1 | 1 I i l~ Total Fluid Displacement / Rate , AV, AC 075 — 0050 Fluid Displacement — Rate From Aggregates, A(IV a ) ^sn r- Stirred — 0.025 A C 1 1 Unstirred -* I 1 1 1000 2000 3000 4000 Concentration C,mg/$ 5000 6000 FIGURE 41. VARIATION OF FLUID DISPLACEMENT RATES WITH CONCENTRATION — PLANT III 85 1000 2000 3000 4000 Concentration C , mg/Jt 5000 6000 FIGURE 42. VARIATION OF AGGREGATE SQUEEZE INDEX WITH SOLIDS CONCENTRATION — PLANT III lOOf OK) OOIO 070 c £ u 0> 060 050 — 040 0030 020 I 1 C = I 085 x 10* + k ,mq/l P k = 1.085 om/cm s T 50 100 150 200 Volumetric Solids Concentration. A* I0 4 86 250 FIGURE 43. APPLICATION OF CARMEN AND KOZENY'S EQUATION TO SEDIMENTATION OF ACTIVATED SLUDGE — PLANT I 87 > < x * E O > o ® 5000 10,000 15,000 Concentration C , mg/£ 20,000 FIGURE 44. CHANGE IN AGGREGATE VOLUME INDEX WITH CONCENTRATION PLANT I 88 o CD x 3 (A 2 (8 5000 10,000 15,000 20,000 Concentration C , mg// FIGURE 45. SOLIDS FLUX CURVE — PLANT I 89 0.075 0.040 100 Volumetric Solids Concentration , ^ R x 10 FIGURE 46. APPLICATION OF MODEL II TO SEDIMENTATION OF ACTIVATED SLUDGE — PLANT II (SAMPLE B) 90 0059 050 045 040 o> o 035 C o •>° 0030 025 0020 015 C = I066x 10* ♦ k ,mg/l Unstirred to 20 30 40 50 SO Voknwtric Solids Conctntration , ^ k x 10 FIGURE 47. APPLICATION OF CARMEN AND KOZENY'S EQUATION TO SEDIMENTATION OF ACTIVATED SLUDGE — PLANT III 91 300 2 50 200 X c — 150

o £ < 00 50 Stirred 1000 2000 3000 4000 5000 6000 Concentration C , mg/JL FIGURE 48. VARIATION OF AGGREGATE VOLUME INDEX WITH CONCENTRATION PLANT III 92 REFERENCES Alderton, J. L. 1963. Discussion of Analysis of Thickener Operation, by Behn, V. C. 1963. J. Sanit. Enq . Div. Am. Soc. Civil Enqrs. 89;SA6, 57-59." Bacon, V. W. and Dalton, F. E. 1966. Chicago Metro Sanitary Discrict Makes No Little Plans. Public Works , _97: 1 1 , 66. Camp, T. R. 1936. A Study of the Rational Design of Settling Tanks. Sewage Works J. 8:742-758. Carmen, P. C. 1937. Fluid Flow Through Granular Beds. Trans. Inst. Chem. Engr. _15 : 150- 166. Coe, H. S. and Clevenger, G. H. 1916. Methods for Determining the Capacities of Slime Settling Tanks. Trans. Am. Inst, of Mining Enq. 55 :356-384. Coulson, J. M. 1949. The Flow of Fluids Through Grandular Beds: Effect of Particle Shape and Voids in Streamline Flow. Trans. Inst. Chem. Engr. 27:237-257. Dick, R. I. 1965. Applicability of Prevailing Gravity Thickening Theories to Activated Sludge. Doctoral Thesis, Department of Civil Engineering, University of Illinois, Urbana, Illinois. Dick, R. I. and Ewing, B. B. 1967. Evaluation of Activated Sludge Thickening Theories, J. Sanit. Eng. Div. Am. Soc. Civil Engrs. 93:SA4:9-29. Dick, R. I. 1968. Associate Professor of Sanitary Engineering, Civil Engineering Department, University of Illinois, Urbana, Illinois, Private Communication. Fitch, B. 1962. Sedimentation Process Fundamentals. Trans. Soc. Mining Engr. 223 :129-137. Fitch, B. 1966. Current Theory and Thickener Design. Ind. and Engr. Chem. 58:18-28. Fitch, B. 1966. A Mechanism of Sedimentation. Ind. and Engr. Chem. Fundamentals . J: 129- 134. Fuerstenau, M. C. I960. The Mechanism of Thickening Kaolin Suspensions. Doctoral Thesis, Massachusetts Institute of Technology, Cambridge, Mass. 93 Gratteau, J. C, Dick, R. I. 1968. Activated Sludge Suspended Solids Determination. Water and Sewage Works . 115 : 468-472. Great Lakes — Upper Mississippi River Board of Sanitary Engineers. I960. Recommended Standards for Sewage Works. Hasset, N. J. 1958a. Design and Operation of Continuous Thickeners. Ind. Chemist. 34: 116-120. Hasset, N„ J. 1958b. Design and Operation of Continuous Thickeners. Ind. Chemist. _34: 169-172. Hasset, N. J„ 1958c. Design and Operation of Continuous Thickeners. Ind. Chemist. 34: 489-494. Hasset, N. J. 1964. Concentrations in a Continuous Thickener. Ind. Chemist . 40:29-33. Hazen, A. 1904. On Sedimentation. Trans. Am. Civil Engrs. 53:45-88. Krone, R. B. 1968. Discussion of Evaluation of Activated Sludge Thick- ening Theories by Richard I. Dick and Benjamin B. Ewing. Jour. Sanitary Engineering Division ASCE , _94: SA3:554-558. Kynch, G. J. 1952. A Theory of Sedimentation. Trans. Faraday Soc. 48:166-176. Lesperance, T. W. 1957. Application of Fundamentals to Waste Treatment Sedimentation Design. Biological Treatment of Sewage and Industrial Wastes , Vol. II (McCabe, B. J. and Eckenfelder, W. W. Jr., Eds.) Reinhold, New York. 182-195. Lewis, W. K., Gillard, E. R., and Bauer, W. C. 1949. Characteristics of Fluidized Particles. Ind. Eng. Chem. 41: 1104-1117. Michaels, A. S., and Bolger, J. C. 1962. The Plastic Flow Behavior of Flocculated Kaolin Suspensions. Ind. Eng. Chem. Fundamentals. Vol. 1:153-162. Maude, A. D., and Whitmore, R. L. 1958. A Generalized Theory of Sedimen- tation. Brit. Jour. Appl. Phys. _9:477-490. O'Connor, D. J., and Eckenfelder, W. W. , Jr. 1957. Evaluation of Labora- tory Settling Data for Process Design. Biological Treatment of Sewage and Industrial Wastes , Vol. II. (McCabe, B. J., and Eckenfelder, W. W. , Jr., Eds) Reinhold, New York. 171-181. 94 Richardson, J. F. and Zaki, W. N. 1954. Sedimentation and Fluidizat ion: Part I. Trans. Inst. Chem. Enqr. 32: 35-53. Roberts, E. J. 1949. Thickening — Art or Science? Mining Eng. _l:6l-64. Scott, K. J. 1966. Mathematical Models of Mechanism of Thickening. Ind. Eng. Chem. Fundamentals. _5_:109-113. Shannon, P. R., Dehaas, R. D., Stroupe, E. P., and Tory, E. M. 1964. Batch and Continuous Thickening. Ind. Eng. Chem. Fundamentals. _3:250-260. Shannon, P. T., and Tory, E. M. 1965. Settling of Slurries. Ind. Eng. Chem. _57: 18-25. Shannon, P. T., and Tory, E. M. 1966. The Analysis of Continuous Thick- ening. Soc. of Min. Engrs. of AIME Trans. , 235:375-382. Steinour, H. H. 1944. Rate of Sedimentation. Nonf locculated Suspensions of Uniform Spheres. Ind. Eng. Chem. 36: 618-624. Stokes, G. G. 1945. On the Theories of Internal Friction of Fluids in Motion, and of the Equilibrium and Motion of Elastic Solids. Trans. Cambridge Phil. Soc , 8:287-297. Talmage, W. P. and Fitch, E. B. 1955. Determining Thickener Unit Areas. Ind. Eng. Chem. _47: 38-41. Visilind, P. A. 1968. The Influence of Stirring in Thickening of Biologi- cal Sludge. Doctoral Thesis. School of Public Health, Chapel Hill, North Carolina. Void, M. J. 1963. Computer Simulation of Floe Formation in a Colloidal Suspension. J. Colloidal Science, Vol. 18:684-695. 95 APPENDIX A CALCULATION OF VOLUMETRIC SOLID CONCENTRATION, $ k The solids volumetric concentration of activated sludge was determined by three pycnometers, each having about 50 ml of volume. Since the density of solids remained constant for a particular sample of activated sludge, it was only necessary to determine i. value for one value of suspended solids concentration C. The values of $ . at other suspended solids concentrations were found by linear proportion. The fol- lowing equations were used to find the $, value in one pycnometer filled with the activated sludge of known gravimetric concentration. Weight of Suspension = Weight of Solids + Weight of Liquids or a b + c (43) and Volume of Suspension = Volume of Dry Solids + Volume of Liquid or d e + f (44) By definition (45) a is measured and b can be calculated from the pycnometer volume and the known value of suspended solids concentration C. The value of c then, can be determined from equation 43. The value of c (weight of liquid) is converted to f (volume of liquid) by assuming a density of 96 one for the liquid (the absolute density of water at 20 C is 0. 9992). More accurate measurements can be made to determine the density of the liquid; but this assumption is good enough for the total experimental accuracy. The error due to this assumption is quite small. Since d and f are known in equation 44, e (volume of solids) and §, can be determined. Calculation of volumetric solids concentration for a sample from Plant II (Figure 17) is shown on Table 1. The known gravimetric concentration of the sludge is 6550 mg/1 . Along with this calculation, p, (mass density of solids) is also calculated. 97 TABLE 1 DETERMINATION OF VOLUMETRIC SOLIDS CONCENTRATION Pycnometer No. 1 2 3 Weight filled with suspension (gm) 70.2671 67.1730 65.8376 * 3 Volume of pycnometer, d(cm ) 48.9781 50.5130 49.6850 Weight of pycnometer (gm) 21.2673 16.6385 16.1368 Weight of suspension, a (gm) 48.9998 50.5354 49.7008 Suspended solids concentration C (mg/1) 6550 6550 6550 Weight of dry solids, b(gm) 0.3209 0.3309 0.3254 3 Volume of liquid, f(cm ) 48.6789 •50.2045 49.3754 3 Volume of solids, e(cm ) 0.2992 0.3085 0.3096 Volumetric solids concentration, * k (e/d) 0.00612 0.00610 0.0623 Mass density of solids, p, or b/e (girt/cm^) 1.076 1.072 1.050 Average §, = 0.00615, at C = 6550 mg/1. 3 Average p, = 1.066 gm/cm and C = 1.066 x 10 6 $ k mg/1. Volume of pycnometers was determined with distilled water at 20 C. 98 APPENDIX B APPLICATION OF MODEL I AND MODEL II The calculations related to Figures 17, 31, and 46 are shown on Table 2 as an example. The volumetric solids concentrations were calculated from the relationship, C = 1.066 x 10 $ mg/1, determined on Table 1. The values of V are those shown in Figure 17. A plot of V 1/4 * b vs# a W as made in Figure 31 according to equation 21. From the c k ordinate intercept at zero $, and the slope of the straight line, the values of A = 80.0 and V = 0.566 ft/min were determined. Average o 3 aggregate diameter, d, was then calculated from equation 19 where (p, -P )d u =i! k w o 18 ii A r w and substituting, 3 p, = 1 .066 gm/cm 3 p = 1 .00 gm/cm w u, = 0.01 poise ^w g = 980 cm/ sec The value of d was found to be 2.54 mm. 1/3 A plot of (tf $ ) versus §, was made in Figure 46 according to equation 28. From the ordinate intercept at zero $, and the slope of the straight line, the value of A = 71.0 was determined. The aggregate volume indices determined by two models were comparable. 99 TABLE 2 CALCULATIONS FOR MODELS I AND II c \ • V c (v c )>'«- 65 W mg/1 -- ft/min ,, w . v 1/4.65 (ft/min) (ft/min) 1/3 7000 .00640 .0233 .440 .0530 6550 .00615" .0260 .465 .0539 6250 .00573 .0322 .488 .0570 4960 .00455 .0543 .550 .0628 4700 .00430 .0700 .579 .0671 4000 .00367 .0936 .617 .0701 3770 .00345 .1050 .631 .0713 Calculated for C = 6550 mg/1 in the laboratory. 100 APPENDIX C Symbol Quant i ty Dimensions A Ratio of the aggregate volume to the — volume of solids in the aggregate ASI Aggregate squeeze index, -rrr — AVI Aggregate volume index, same as A — 3 C Gravimetric solids concentration F/L 3 C. Initial gravimetric solids concentration F/L 3 C. , C. , , Limiting gravimetric solids concentrations F/L C L2' "" C Ln 3 C , C ,, Ultimate gravimetric solids concentrations F/L u ul 3 u2 un d Diameter of the spherical particle L d Equivalent aggregate diameter L D Diameter of settling column L 2 g Gravitational constant L/T G Solids flux F/L 2 T 2 G Maximum solids flux F/L T max 2 G., G., Limiting solids flux F/L T 3 k Slope of Log V vs C curve L /F K Constant of Carmen and Kozen's equation — K, Term in bracket in equation 27 L/T L Length of porous bed L N Number of aggregates per unit weight 1 /F of solids 101 Symbol Quant i ty Dimens ions n Exponent in Richardson and Zaki's equation — 2 AP Pressure difference F/L 3 SVI Sludge volume index L /F u Upward velocity based on total cross L/T sectional area V Independent settling velocity of an L/T individual aggregate V Suspension interface subsidence velocity L/T M . Limiting suspension interface subsidence L/T velocity o V Interface subsidence velocity with stirring L/T • V Interface subsidence velocity without stirring L/T Volume 3 U, U,, U oJ ..., U Underflow rates L/T 12 n 2 4 p Density FT /L $ Volumetric concentration — 2 |i Absolute viscosity FT/L e Suspension porosity — Additional Subscript Notations: a Aggregate — k solids — m spherical particle — s suspension of activated sludge — w liquid —