WEF Residuals and Biosolids Conference 2017

Transcription

1 A Laboratory Based Method for Predicting Dewaterability Zwelani Ngwenya 1, Matthew J. Higgins 1, Steven Beightol 1, Sudhir N. Murthy 2, 1 Bucknell University, Lewisburg, PA; 2 DC Water, Washington, DC ABSTRACT The goal of this research was to develop a lab-scale dewatering method that estimates dewatering characteristics such as polymer demand, cake solids and capture. The method replaces traditional centrifuge tubes with belt filter cups which are fitted with circular belt filter press fabric. Digestate is conditioned and then portions of the conditioned sludge is placed in the centrifuge cups and centrifuged at a set g-force for a defined time. The essential parameters defining the method were: (1) mixing the cake during centrifugation, (2) the time of centrifugation, and, (3) dry solids loading onto the belt filter cups. Mixing the cake during the centrifugation increased the final cake solids as did increasing the centrifugation time. However, cake solids decreases as solids loading increases. Using appropriate parameters, the method could accurately predict full scale belt filter press cake solids with only 0.15% difference relative to full scale. Overall, the method is well suited for use in the laboratory because it demands less equipment and also produces cake which can be further tested for other dewatering parameters such as odors. Key Words: Dewaterability; centrifuge; cake solids; conditioning; sludge; CST; OPD

2 INTRODUCTION Dewatering is employed by utilities to reduce the water content of sludges and digestate. Dewatering increases dry solids which in turn helps minimize costs associated with solids management. In addition to digestate volume reduction, the dewatering process also affects the nutrient and odor levels of solids. The need for assessment of dewatering parameters such as cake solids, nutrients, polymer demand and cake odors on digestate produced from pilot scale or lab reactors has led to the development of various laboratory scale dewatering methods. The two most popular dewatering methods used in large wastewater treatment plants are the centrifuge and belt filter press. Numerous lab-scale methods have been developed to simulate performance of these full scale devices in terms of cake solids, polymer demand predictions and other dewatering parameters. Because of the small volume of digestate produced in pilot and lab scale studies, lab scale dewatering methods that produce cake using small volumes of digestate samples, are needed to help characterize digestate dewaterability at a small scale. Furthermore, researchers also make use of lab-scale methods of dewatering to compare the dewaterability of different sludges. One of the most difficult and challenging aspects of sludge dewatering at a lab scale is the absence of a universally accepted dewatering method that is easy to use, requires less equipment and can estimate cake solids while also simulating full scale dewatering methods. While previous studies have developed different lab-scale dewatering methods that simulate fullscale mechanical dewatering devices, very few have used a relatively simple and accurate apparatus that s capable of simulating full scale methods. Previous attempts at developing lab scale dewatering methods have resulted in two distinct approaches. One group comprise methods that measure the rate of dewatering. Such surrogate methods of dewatering are the capillary suction time (CST), specific resistance to filtration (SRF) and the drying curve method. In many cases, researchers are interested in optimizing cake solids, hence methods that predict the extent of dewatering are usually used as substitute for or a complement to the surrogates of dewatering methods. Physical dewatering methods that produce cake and predict the extent of dewatering have been developed by previous researchers. These methods include, a bench scale centrifuge using centrifuge tubes, piston press and a crown press. Dewatering surrogates One of the earliest surrogates of dewatering previously used is the SRF, which was developed by Coakley et al., (1956). The SRF measures the permeability of a sludge layer deposited on a filter medium to which a vacuum has been applied. The method characterizes the sludge based on its filtration rate (Vesilind, 1988). A drawback of this technique is that it produces low cake solids which may not be representative of the actual extent of dewaterability of the digestate. Furthermore, while the method gives an indication of how well a sludge dewaters, it provides no information regarding solids capture efficiency. As a response to the difficulty of conducting the SRF test, Gale and Bakersville (1968) developed the CST apparatus. The CST test measures the rate of filtration and gives information on how well a sludge dewaters. Digestate that release their water slowly have high CST values while sludges that readily release their water have low CST values (Vesilind, 1988). The CST device was deemed to be a simple, quick and inexpensive means for measuring the dewaterability potential of 2 567

3 wastewater sludges (Vesilind, 1988). The technique has been used in wastewater and water treatment facilities to evaluate polymer demand as well as to detect changes in sludge dewaterability. Unfortunately, despite its widespread acceptance as a useful general measure of sludge dewaterability, the CST does not predict the extent of dewaterability, namely cake solids. Instead it measures the rate of water removal. In addition, it does not result in cake for solids analysis and cannot predict capture efficiency. Kopp & Dichtl, (2000) developed the drying rate curve method to predict digestate dewaterability. This method assumes that, of the three types of water found in sludges namely, free water, interstitial water and bound water, only the free water can be removed by mechanical dewatering means. The authors used thermogravimetric measurements to dry a sludge sample at constant temperature and airflow and produced a drying rate curve in which drying rate was plotted against moisture content, measured as mass of water per mass of suspended solids of the sludge. Using an arithmetic scale, the drying rate curve allows for the determination of the different types of water found in sludge. The curve is linear at the start of drying and then after a certain moisture content, it becomes nonlinear. The authors propose that this point of inflection marks the end of the free water content in the sludge. After determining the point of inflection and developing the equation of the tangent, the moisture content of the sample at the point of inflection is used to calculate the solids content of the sludge. The authors argue that this is the maximum cake solids achievable since the remaining bound and interstitial water cannot be separated from the sludge by mechanical dewatering. The authors showed that the method accurately predicted full cake belt filter press and centrifuge percent cake solids. While the method predicts percent cake solids accurately, it does not predict polymer requirements or capture efficiency and does not produce a cake that can be evaluated for odors or other parameters. Physical Dewatering Methods Using a bench scale centrifuge with centrifuge tubes has been a common method to approximate full scale dewatering process of the centrifuge. This method involves centrifuging the solids to relatively high g-force and then decanting the resultant supernatant. The cake solids are then determined by measuring the solids content of the resultant pellet in the centrifuge tube (Vesilind, 1970). While this method is quick, easy and results in cake solids for further testing, it often leads to an under prediction of cake solids as observed during preliminary phases of this work at Bucknell University. The thin water film that remains at the pellet/supernatant interface after decanting often leads to low cake solids prediction. Baskerville et al. (1978) used a piston press as a laboratory scale approximation of the full scale belt filter press. The apparatus consists of a cylindrical filtration cell and a freely moving pistol. The application of pressure to the non- porous piston causes the filter cake in the cell to dewater. In the simulation of full scale belt press pressures Baskerville et al. (1978) found out that pressures of 700kPa are sufficient and can be achieved using a compressed-air cylinder and pressure regulator. The resultant cake solids consistencies from the piston press were comparable to full scale BFP results. Severin and Collins (1992) used the Crown Press to simulate belt filter press (BFP) dewatering. They reported that the Crown Press produced cake solids similar to those produced on BFP

4 However, Galla et. al. (1996) reported that when improper belt tensions are used in pressing regime calculations, the crown press does not accurately simulate the operation of a BFP. The process of ensuring that proper belt tensions are applied makes the method cumbersome. Emery (1994) reported that the Crown Press was able to simulate the wedge zone and high-pressure zone of the BFP but on all Crown Press simulations, severe belt blinding was observed. Belt blinding prevents further drainage of water from the sludge resulting in low cake solids predictions. While previous studies have developed methods to simulate full scale mechanical dewatering devices, very few have used a relatively simple apparatus that s capable of producing reliable estimates of cake solids, polymer demand and capture efficiency. A reproducible laboratory dewatering method is needed to evaluate mechanisms of dewatering, and the effects of different upstream processes on dewatering at the lab scale and full-scale systems. In many cases, researchers use surrogates of dewatering such as CST or time to filter. Although these methods give an indication of dewatering rate, they do not provide information on the extent of dewatering. The development of a reliable method that is easy to use and can estimate cake solids while also simulating full scale dewatering methods would be of great value. The goal of this research was to develop a laboratory method that: (1) uses relatively small volumes of samples; (2) is predictive of polymer demand for conditioning; (3) is predictive of cake solids for a given full-scale process such as BFP; (4) is reproducible; (5) produces a cake that could be evaluated for parameters such as odors; and, (6) is easy to implement. MATERIALS AND METHODS Experimental Approach First, the method was developed using anaerobic digestate collected as effluent from pilot scale anaerobic digesters operated at Bucknell University. The reactors were part of a separate study and were operated under mesophilic temperatures with retention times of 10 and 15 days, respectively. In order to test and develop the method, anaerobic digestate was obtained from three different wastewater treatment plants (WWTPs) in Pennsylvania and Washington DC. Conventional and thermally hydrolyzed sludge were used. These samples were used to evaluate different parameters in the conditioning and dewatering test as described in the overview of the method section

5 Overview of the method Figure 1 summarizes the major steps of the dewatering method. Step 1 involves conditioning using a cationic polymer. The sample is placed in baffled cylindrical container and then mixed with the polymer using a variable speed mixer. Step 2 is free draining the conditioned sludge. Sludge is drained for a minute and the mass of the wet solids measured. In step 3, wet solids are transferred to belt filter cups and dewatered in bench scale centrifuge. Finally, after centrifugation, cake is placed in a 105 o C oven and total solids are determined. 2) 1) 4) 3) Figure 1: Overview of dewatering method showing key dewatering steps Conditioning: A high molecular weight cationic polyacrylamide (SNF FLOPAM FO 4440) was used for conditioning. The powdered polymer was made up to a concentration of 0.5% active content. The solution was mixed at 400 rpm for 30 minutes. The prepared polymer was then allowed to age for approximately 45 minutes. Next, increasing dosages of polymer were added to 500 ml samples of digestate. The polymer was mixed at a velocity gradient, G, of 500/s for 10 s, and then a G of 100/s for 90 s. The initial high speed mixing ensures that the polymer is well mixed with the sludge for optimal coagulation. The slow speed allows for complete mixing without excessively shearing the sludge. After mixing, the CST was measured, and the optimum dose was considered as the dose that gave the minimum CST. This dosage was then used for the dewatering step. Free draining: The conditioned wet solids are free drained through a belt filter press fabric. A spatula is used to mix the wet solids to allow for faster drainage. The wet solids are mixed for a 5 570

6 minute for complete draining. The mass of the free drainage wet solids is measured and serves as an input to the developed spreadsheet that calculates target mass of wet solids to be added to centrifuge cups (discussed in the following section) for dewatering. Dewatering: The dewatering method used is a modification to the bench scale centrifuge test and is primarily targeted at eliminating the thin layer of water that forms on the surface of the dewatered cake when using the traditional centrifuge tubes. Since this often leads to an under prediction of the percent cake solids, the new method was designed to keep the dewatered cake separate from the centrate. The traditional centrifuge tubes were replaced with centrifuge cups as shown in Figure 2, which had a piece of belt filter press fabric supported about half way up the cup. 2 : After free draining, a portion of the free drained solids is added to the cup and the mass of solids added to these cups depend on the total solids (TS) concentration to achieve a desired loading rate on the belt filter fabric. Table 1 shows the sample spreadsheet used to calculate mass of wet solids to be added to the centrifuge cups

7 Table 1: Sample spreadsheet for the calculating of mass of wet solids to add in BFP cups Volume of digestate (ml) 500 TS (%) of sludge before dewatering 3.09 Target dry solids (g) Mass of dry solids in sample sludge 1 (g) Mass of wet solids after Free draining (g) Mass of wet solids to placce in BFP Cup 2 (g) The mass of dry solids in sample sludge are calculated using equation 1: 1 Mass of dry solids in sample sludge = Target dry solids (g) 100 TS (%) (1) Where: TS is sludge total solids prior to dewatering. Equation 2 calculates the mass of wet solids to place in the BFP cup: 2 Mass of wet solids to place in BFP cup = [ Mass of dry solids in sample sludge (g) Volume of sample (ml) ] Mass of wet solids after free draining (g) (2) The samples are then centrifuged at 140 x g for 2 minutes, and then at 350 x g for an additional 2 minutes to seat the cake on the belt fabric. Next, the cake is centrifuged at 2075 x g for a defined time. Centrifugation is stopped at different time intervals to mix the cake on the fabric using a spatula to redistribute the cake and allow better drainage. After centrifugation at 2075 x g for 10 minutes, the centrate drains to the bottom of the cup while the dewatered cake solids remain suspended on the filter cloth. The different x g values were calculated using Equation 3 which accounts for the distance of cake from the centrifuge rotor center: Converting rpm to times gravity (x g) x g = 1.118*10-5 *R*S 2 (3) Where: R is the distance between the center of the centrifuge rotor and the surface of the cake in the centrifuge cup. S is rotor speed in revolutions per minute (rpm) 7 572

8 Total Solids Determination: Total solids measurement was measured following Standard Methods 2540 B (APHA, 2012). The slight modification to the method was that solids were left in the oven for at least 24 hours to ensure that a constant weight was obtained. Total solids were measured twice for each dewatering cycle. TS were measured pre- and post-dewatering. First, digestate TS was calculated for use as input in the spreadsheet that calculates the mass of wet solids to be loaded on the belt filter cups, and secondly, it was measured on dewatered cake to determine the cake solids. Cake Thickness: The thickness of the belt filter fabric was measured using a Vernier caliper. After centrifugation, the cake and the belt filter fabric was carefully removed from the cup and the thickness was measured. The actual cake thickness was calculated by subtracting belt filter fabric thickness from total thickness of belt filter fabric and the cake. Since the cake surface was not uniform, cake thickness was measured at four evenly spaced points around the cake. The average thickness was then calculated. Parameters of Interest: The development of the method involved investigating the following impacts on cake solids and cake thickness: 1. Mixing and non-mixing during centrifugation 2. Number of times cake is mixed during centrifugation 3. Target dry solids loaded on the belt filer cup, in terms of kg dry solids per m 2 of belt fabric 4. Time of centrifugation at 2075 x g Statistical Analysis: Microsoft excel was mainly used to generate graphs, tabulate data and perform basic statistics such as mean and standard deviation calculations. R software package was used to perform tests for: equal variances; one-way analysis of variance (ANOVA) to compare the mean values of the data sets for statistical differences at the 0.05 significance level. RESULTS AND DISCUSSION The development of this method was aimed at assessing the impact of four major parameters, namely; 1. Mixing and non-mixing during centrifugation 2. Number of times cake is mixed during centrifugation 3. Target dry solids loaded on the belt filer cup, in terms of kg dry solids per m 2 of belt fabric 4. Time of centrifugation at 2075 x g Impact of cake mixing and loading rate The first parameter studied was the impact of mixing the cake during the ten minute period of the 2075 x g force. To ensure that all other conditions remained the same during dewatering, the mixing and no mix centrifuge cups were placed in the centrifuge at the same time. The two cakes 8 573

9 were subjected to the same temperature, time, pressure and force. Mixing was done once at the high speed centrifugation phase. The cake was mixed using a spatula at the 5 th minute time interval of ten minutes. Mixing allows for the release of water that remains trapped in the cake as it compresses due to high speed centrifugation. A schematic presentation of the mixing sequence is shown in Figure x g 350 x g 2075 x g Figure 3: Overview of the mixing sequence of cake in the centrifuge. Number of times cake is mixed and the duration of centrifugation is varied only at the 2075 x g phase. Percent cake solids were statistically different for cake mixing and no mixing, indicating that mixing does increase cake solids as shown in Figure 4. Cake Solids (%) With Mixing No Mixing Full Scale Cake Dry solids added on BFP cup (kg/m 2 ) Figure 4: Effect of mixing, and increasing dry solids added onto the BFP cup on solids cake content using thermally hydrolyzed sludge from pilot digesters at Bucknell University. Error bars represent one standard deviation. Cake was mixed once at 2075 x g

10 Visual inspection also showed that the cake without mixing developed a thin water layer after centrifugation at 2075 x g. The presence of this layer of water also explains the lower cake solids obtained for the no mix regime. Also higher solids loading are shown to lead to decreased percent cake solids as depicted in Figure 4. This is mostly due to the longer drainage path generated by increased thickness of cake. The cake thickness as a function of dry solids loading is shown in Figure 5. Cake Thickness (mm) Mixing No Mixing Dry solids added on BFP cup (kg/m 2 ) Figure 5: Effects of dry solids loading on cake thickness for thermally hydrolyzed sludge from pilot digesters at Bucknell University. The typical range of the cake solids from the full-scale belt filter press is also shown on Figure 4, and this lab method does produce cake solids within this range depending on the loading and mixing conditions. Figure 4 also highlights the flexibility of the method. If a study is performed to simulate belt filter performance, then dewatering without mixing at low dry solids loading (between 0.6 and 2 kg/m 2 ) yields cake solids comparable to full scale belt filter press performance. On the other hand, if the goal of a dewatering study is to maximize cake solids, without any need to predict full scale performance, then dewatering with mixing yields higher cake solids at lower dry solids loading. To attain cake solids comparable to full scale belt filter performance using the mixing regime, high dry solids loading yield percent cake solids within the full scale range. Based on Figure 4, the appropriate solids loading to predict full scale cake solids is approximately 5 kg/m 2. The non-mixing regime leads to lower cake solids at higher dry solids loading. The percent change between mixing and non-mixing cake solids increased linearly with increased target dry solids loading as shown in Figure

11 Increase in cake solids due to mixing relative to no mixing (%) Figure 6: Percent increase in cake solids vs. dry solids loading for thermally hydrolyzed sludge obtained from pilot digesters at Bucknell University. The effects of a longer drainage path become more pronounced at higher solids loading (between 5 and 7 kg/m 2 ) and therefore mixing of the cake has a greater impact. Centrifuge Time and Cake Mixing R² = Dry solids added on BFP cup (kg/m 2 ) After demonstrating that incorporating mixing and using lower dry solids loading on the modified centrifugal method yields high percent cake solids; different times of centrifugation at high speed were tested. For this arrangement, the loading rate of 0.64 kg/m 2 and number of times the cake solids were mixed at 2075 x g was kept constant. The cake solids were mixed only once midway during the high g-force centrifugation time. The no mix regime was also employed for comparison. The cake solids were increased with increased time of centrifugation at 2075 x g as shown in Figure

12 Figure 7: Effect of varying centrifuge time on cake solids at 2075 x g. Conventional sludge was used as sample. Additionally, Figure 7 further supports the conclusion that mixing is a necessary step in order to attain higher percent cake solids. Embedded in Figure 7, is the full-scale belt filter press cake solids range for this conventional sample. With cake mixing, it takes less than 20 minutes to produce cake comparable to full scale dewatering. Without mixing, producing cake in the range of full scale cake solids would take approximately four times as long. Frequency of Mixing The impact of the frequency of mixing was investigated for the time interval of 20 minutes at a force of 2075 x g. The 20 minute time interval was selected because it allowed for a wider range of mixing frequency (0 to 5) with reasonable time spacing between mixing. Figure 8 shows that increasing the frequency of mixing leads to an increase in cake solids. Mixing frequently reduces the drainage path and exposes water trapped with the sludge. This facilitates maximum release of water leading to high cake solids. Additionally, mixing frequently reduces the amount of water trapped in the sludge as the cake compresses at high g force

13 Cake solids (%) Number of times cake is mixed Figure 8: Impact of increasing the number of times cake is mixed at high 2075 x g for a 20 minute time interval Mixing five times during the 20 minute time interval is rather tedious. In order to make the method shorter in terms of time, the lower end of the centrifugation time spectrum (from Figure 7) was further developed in order to produce cake comparable to full scale at minimum centrifugation time. To get high cake solids at lower centrifuge time, the frequency of mixing at 10 min and 20 min intervals was increased. Previously, the cake was mixed only once midway the high speed centrifugation time interval. The frequency of mixing was increased to 2 times within each high speed time interval. The times at which centrifugation was stopped to allow for mixing was evenly split during this time interval. Table 2 shows that mixing twice at the 20 minute interval overestimates full scale cake solids by over 4 percent. In contrast, mixing twice at the 10 minute interval resulted in accurate predictions of full scale cake solids. On average, mixing at 10 minute interval only under predicted the cake solids by 0.36 percent and this difference is shown to be statistically insignificant at a 95% confidence level. Table 2: Impact of mixing twice at 2075 x g for the 10-and 20-minute interval. Percent cake solids compared to full scale belt filter press results on conventional sludge Time interval at 3000 x g centrifugation (minutes) Number of times cake mixed Cake solids (%) Standard Deviation (%) Percent difference relative to fullscale Full scale

14 The impact of mixing frequently at higher time interval such as 20 minutes could be used as the method s approximation of the centrifuge performance. Full scale comparison utilized in this study have drawn from plants using the belt filter press for dewatering. The 4 percent cake solids difference between the 20 minute- and 10 minute- two time mixing intervals is comparable to the full scale difference between the centrifuge and belt filter press cake solids, respectively. To assess this prediction, samples from plants with different dewatering devices such as belt filter press and centrifuge will be collected and tested in the lab as a way of applying the developed method. Conditioning The CST vs polymer dose profile for each sample dewatered was plotted to determine the optimum polymer dose (OPD). The OPD was considered to be the dose that resulted in the lowest CST as shown as circled data point in Figure CST (s) OPD Polymer Dose (g) Figure 9: Capillary suction time (CST) polymer dose profile used to determine the OPD for conventional and thermally hydrolyzed sludge during conditioning A plot of minimum CST against cake solids was made for different samples tested during the development of the method. Figure 9 shows that the minimum CST values achieved during conditioning did not correlate with cake solids. This lack of correlation was consistent with observations made by Higgins et al., (2015). Some previous studies have used CST as an indicator of dewaterability (Ormeci & Vesilind, 1999), but CST values do not necessarily correlate with final dewaterability as measured in terms of cake solids. Figure 9 demonstrates that CST may be used to assess the rate of dewaterability but may not be reliable in predicting the extent of dewatering

15 Cake Solids (%) R² = CST (s) Figure 9: Minimum CST after conditioning vs cake solids for anaerobic digestate Reproducibility of the method The reproducibility of the method was tested by dewatering five samples of the same sludge, sampled at different dates, and analyzing the variance. The samples were dewatered for a 10 minute time interval at 2075 x g and the cake mixed twice. Table 3 shows that the confidence intervals were rather small which demonstrates that the method is reproducible. Table 3: Reproducibility parameters of the dewatering method for conventional digestate Conventional sludge Cake solids (%) Mean Range Standard deviation 0.96 Coefficient of variation 0.05 Confidence interval at 99% 1.97 Confidence interval at 95% 1.19 Confidence interval at 90%

16 SUMMARY AND CONCLUSIONS The modified centrifugal method presented in this study results in the production of cake solids which can be used for further testing and analysis such as odor content. It was demonstrated that the method gives cake solids comparable to full scale when the solids loaded on the belt filter press cup are minimized and the time of centrifugation at 2075 x g set to 10 minutes. High cake solids were also produced when the cake was mixed twice during the high speed centrifugation phase. The method was proven to be reliable and reproducible, with a very small 95 percent confidence interval. The method can be used in the laboratory for accurate comparison of the dewaterability of different sludges. ACKNOWLEDGEMENTS This research was funded by the Water Environment and Reuse Foundation (WERF). The authors gratefully acknowledge this support

17 REFERENCES Baskerville, R. C., & Gale, R. S. (1968). A simple automatic instrument for determining the filterability of sewage sludges. Water Pollut. Control, 67(3), Baskerville, R. C., Bruce, A. M., & Day, M. C. (1978). Laboratory techniques for predicting and evaluation the performance of a filter belt press. Filtration & Separation, 1-5. Coakley, P., & Jones, B. R. S. (1956). Vacuum sludge filtration, I. Interpretation of results by the concept of specific resistance. Sewage Ind. Wastes, 28, Emery, B.P. (1994). Predicting Belt Filter Press Performance Using Laboratory Techniques. Master s Thesis. Dept. of Civil Engineering. University of Illinois at Urbana-Champaign. Galla, C. A., D.L. Freedman, B.F. Severin, and B.Y. Kim. (October 1996). "Laboratory Prediction of Belt Filter Press Dewatering Dynamics," Proceeding of the Water Environment Federation 69th Annual Conference, Residual and Biosolids Management Symposium, Dallas, TX. Graham, T. M. (1999). Predicting the performance of belt filter presses using the Crown Press for laboratory simulation. CLEMSON UNIV SC COLL OF ENGINEERING. Kopp, J., & Dichtl, N. (2000). Prediction of full-scale dewatering results by determining the water distribution of sewage sludges. Water Science and Technology, 42(9), Örmeci, B., & Vesilind, P. A. (2000). Development of an improved synthetic sludge: a possible surrogate for studying activated sludge dewatering characteristics. Water Research, 34(4), Severin, B. F., & Collins, B. H. (1992). Advances in predicting belt press performance from lab data. In Wat Env Fed, 65th Ann Conf & Expo (pp ). Vesilind, P. (1988). Capillary Suction Time as a Fundamental Measure of Sludge Dewaterability. Journal (Water Pollution Control Federation), 60(2), Vesilind, P. A. (1970). Estimation of sludge centrifuge performance. Journal of the Sanitary Engineering Division, 96(3),