MODELLING FOR DESIGN OF SEDIMENTATION OPERATIONS

Abstract

Sedimentation is the most widely used unit operation to remove the organic arid inorganic settling solids from waters or wastewaters. Based on the nature of solids and their concentrations, four types of settling are recognised, namely, class-I (discrete particles), class-II (light concentrations of flocculent particles), class-Ill (heavy concen trations of suspended solids) and class-IV (inter-particle contact, resting and compression). STUDIES ON CLASS-I SEDIMENTATION In class-I sedimentation, if v is the terminal settling velocity (also the overflow rate), the particles having settling velocities lesser than v will also be removed but only partially and in proportion to the ratio of their settling velocity (v ) to v . The existing practice for the design of class-I settling tanks is based on fixing the overflow rate for a particular particle size (smallest size intended to be removed). The actual removal will however, be much more than the expected removal because the particles smaller than the chosen smallest size will also be removed in proportion to the ratio of their settling velocities to the settling velocity of the chosen particle size. This existing design procedure thus, gives a better performance than the needed performance, and manifests a waste of capacity of the sedimentation units. With this view, the settling tank design would be much more rational and economical 111 IV if designed for a desired overall particle removal rather than for an overflow rate based on the smallest particle to be removed (Bhargava and Rajagopal, 1989a). The rational procedure involves the plotting of a cumulative size distribution curve of the suspended settling solids those present in the waters. From this curve, the overall removals should be worked out corresponding to the different settling velocities (overflow rates) through the numerical integration procedure. A plot can thus, be obtained between the overall removal and overflow rate and an overflow rate is then selected corresponding to the desired overall removal of the particles. Based on this overflow rate, the sizing of the settling tank should be done. To adopt the rational procedure for the design of class-I sedi mentation tanks, an overall removal predictive model was evolved invol ving the sieve-analysis parameters of the particles present in the tank influent and the overflow rate. To develop such a model, six sets of particle size distributions having, effective sizes of 0.01 mm, 0.05mm, 0.10 mm, 0.15 mm, 0.5 mm and 1.00 mm, each having a nonuniformity coefficient of 1.5, 2, 3 and 4 were drawn. The settling velocities were calculated for the various particle sizes. The specific gravity, the kinematic viscosity (temperature dependent) and the acceleration due . to gravity were assumed as 2.65, 0.8039 x 10 m Is (temperature 30 C) and 9.81 m/s respectively. On this basis, the 24 cumulative size distri bution (CSD) curves showing the size distribution versus the settling velocity (expressed as overflow rate) were prepared. For each such CSD curve, the overall percentage removals were evaluated corresponding to the various overflow rates from a numerical integration of the CSD urves. Plots between the evaluated overall percentage removals and the overflow rates corresponding to the above said effective sizes and nonuniformity coefficients were prepared. Using these plots, a predictive model was developed (Eq. 1) for evaluating the overall percentage removals (FJ from the sieve-analysis parameters [such as the effective size (EJ and nonuniformity coefficient (H^] of the discrete particles present ^n the tank influent, and the overflow rate (vq) (Bhargava and Rajagopal, 1989d). c N 1 (177.881 + 44.712 N ) F m InN +4.627 }J o exp[ (3.186x10 3Nu+2.036)lnEo+exp( 2^g09 )] ...d) 3, , 2 The constants of Eq. (1) were obtained with vq expressed in m/s/m and E expressed in mm. o Such a model (shown in Eq. 1) can thus, be used for a rational fixing of the design overflow rate to provide a desired removal of the particles of a given size distribution. The experimentally observed data of several other researchers are found to be in total agreement with the values predicted from the presented model. An alternate approach based on the polynomial fitting concept has also been used to develop the overall percentage removal predictive VI model in terms of the overflow rate (v ), effective size (E ) and nono o uniformity coefficient (N ) (Rajagopal and Bhargava, 1989e) as shown in Eq. (2) . F = 99.8044-28.5688 ln(v ) + 60.0487 ln(E ) + 4.8445 ln(N ) m o o u . + 0.1759 (lnv )2 + 9.7670 (lnv )(lnN ) - 19.6681(lnE ) o o u o (In Nu) (2) To use the above models (Eqs. 1 and 2 ), the particle size distribution of the suspension is required. In case of the primary clarif iers used in water treatment, the discrete particle size distribution of the suspension can be obtained by the simple 'sieve-analysis' technique. But in the case of primary clarifiers used in sewage/wastewater treatment, the analytical technique of sieve-analysis is not possible, because the organic solids present in the sewage get deshaped apart from undergoing changes in their size, weight and specific gravity during their settling and due to the difficulty of maintaining their identify for sieve-analysis. For such solids, the presented methodology for size distribution is based on principles of differential settling (Rajagopal and Bhargava, 1989a). In the sedimentation process, the settling velocity of the discrete particles is determined by the Stoke' s law for the laminar flow (Reynolds number < 1). However, when the Reynolds number is > 1 (transition and turbulent flow), the settling velocity is calculated by other models involving a trial and error procedure of checking for the Reynolds number after each working out of the settling velocity from the model. The repeated trial and error calculations of working out the settling velocity and each time checking of the Reynolds number, is quite tedious, and Vll in order to generalise one model applicable for all ranges of the Reynolds number, nomograms have been developed (Bhargava and Rajagopal, 1989c) for this purpose in respect of the various particle diameters (ranging -5 -2 from 10 m to 10 m) in the specific gravity range of 2.65 to 1.001, and in the temperature range of 5 C to 40 C. Using these nomograms, a more general composited settling velocity model has been evolved (shown in Eq. 3 ) which can conveniently, instantly and directly be used to obtain the settling velocity of a particle of a known specific gravity and diameter at a given temperature without undergoing the tedious trial and error calculations (Bhargava and Rajagopal, 1989 i). v. = exp {-exp { -exp [1.7768 + 0.2798 In (In s )]} +exp {exp[ [exp(-2.4808-0.0471 Inv)]ln (In s ) + exp (-0.8067+0.0651nv)]} In (-In d ) j } (3) In Eq. . 3 , v represents the settling velocity in m/s, d repret P sents the particle diameter in m, v represents the kinematic viscosity 2 (temperature dependent) in m /s and s represents the specific gravity. The concept of polynomial fitting has also been used to develop an intergrated expression for the prediction of settling velocity of parti cles in relation to the particle diameter (d ) , specific gravity of the particle (s ) and kinematic viscosity of the liquid (v ). The integrated expression developed is shown in Eq. 4 (Bhargava and Rajagopal, 1990b). Vlll v = exp { -54.6322+40.4532 [ln(-lnd)] - 0.3367 [In(Ins )] t P - . 5 2 +8.2673 [ln(-lnv)]-12.5788 [ln(-lnd )] + 0.6165 [ln(-lnd )][ln(ln s )]} (4) The constants of Eq. 4 were obtained with v^, dp and Vexpressed in m/s, m, and m2/s respectively. Eqs. , 3 and 4 are applicable -5 -2 for particle size range of 10 m to 10 m. STUDIES ON CLASS-II SEDIMENTATION A class-II sedimentation basin performance involves several para meters including the detention time, overflow rate, depth of the tank and flocculent properties of the suspended materials. Column test results are processed to evaluate the class-II clarifier design parameters. To explore the effect of the above said parameters on class- II clarification, column settling tests were conducted for four different kinds of the suspended materials, viz. the particles contained in the sugar mill waste, domestic wastewater, aluminium hydroxide floes and ferric hydroxide floes. The initial suspended solids concentration were made in the 146 to 435 mg/L range for the sugar mill waste and in the 103 to 580 mg/L range for the domestic wastewater. The floes of alumi nium hydroxide and ferric hydroxide were created by using the aluminium sulphate [A12(S04)3 . 18 H20] and ferrous sulphate (FeS04 . 7H20) res pectively. For creating sufficient alkalinity, sodium hydroxide was used. The initial floe concentrations was made in the 40 to 257 mg/L range for the aluminium hydroxide floes and in the 52 to 215 mg/L range IX for the ferric hydroxide floes. To interpret the concentration of the suspended solids from a measurement of the turbidity (which is much simpler when compared to the tiring process of an analytical estimate of the suspended solids), standard curves were plotted between the turbidity of the samples and the corresponding suspended solids concen tration for each type of the suspended material. The equations developed (Rajagopal and Bhargava, 1989b) from these plots were used to determine the suspended solids concentrations of the samples collected at each sampling port at the different times. From the column test data (the percentage removal of the suspen ded solids at various column depths in respect of the various time inter vals) of sugar mill waste and aluminium hydroxide floes, families of curves were developed between the overall percentage removals versus the overflow rates and detention times at a column depth of 1.2 m (Rajagopal and Bhargava, 1989d and Bhargava and Rajagopal, 1989b). A model was evolved for sugar mill waste to predict the overall percen tage removal at a column depth of 1.2 m (measured from the top of the column) in relation to the overflow rate and the initial suspended solids concentration (Rajagopal and Bhargava, 1989d). Such a model and the stated families of curves can be used for a rational design of the clarifiers handling the sugar mill waste and aluminium hydroxide floes. The column tests data for the various kinds of the suspended materials were also utilised to develop the predictive percentage removal models. The models were developed in the form of polynomial expre ssions , to determine the percentage removal of the suspended solids in relation to the time, depth of the column and initial suspended solids concentration as shown in Eq. 5* (Bhargava and Rajagopal, 1989g). R(z,t,C ) = b +blZ+b t+b_C +b,t2+bcC2+b,tC (5) o ol23o4 5o6o In Eq. (5), R represents the percentage removal of the suspended solids (at any -time t, at column depth z, for initial suspended solids concentration C ), and b , b, , b_ .... b, are the function constants, o o 1 I 6 The function constants were evaluated through a regression analyses of the column test data for the above said suspended materials. Such a model as shown in Eq. 5 , can also be exploited to determine the overall percentage removals at any depth, time, etc. The methodology for estimating the overall percentage removals from Eq. 5 is much simpler and convenient compared to the traditional method of estimation of overall percentage removals using the isopercentage lines (Rajagopal and Bhargava, 1990a). Using the same data, the isopercentage lines were drawn for each type of the suspended material having different initial suspended solids concentrations. From the isopercentage lines, the overall percen tage removals were calculated at different times for various column depth in respect of each of the initial suspended solids concentration present in the various types of the suspended materials. A general predictive model presented in Eq. 6 has been evolved to determine the overall percentage removals (F )• in relation to the depth of the column (z), initial suspended solids concentration (C ) and overflow rate (v ) for o o the above said suspended materials (Bhargava and Rajagopal, 1989h). XI (z/vq) Fo exp [c+d ln(C )] +{exp [e+f (1/C )]•} z/vq The coefficients c, d, e and f were evaluated for each of the various types of the stated suspended materials. The evaluated values of c, d, e and f were 5.4875, -2.7213, -4.6267 and 175.732 for sugar mill waste, -3.7579, -1.0972, -4.3423 and 45.3504 for domestic wastewater, 4.320, -2.927, -4.6535 and 48.155 for aluminium hydroxide floes and, 2.602, -2.608,-4.6736 and 50.1169 for ferric hydroxide floes respectively. The model evolved can be used conveniently for evaluating the design parameters (such as the overflow rate and detention time, for a desired overall percentage removals and at the desired depth of the tank)of a class-II settling tank for any given initial suspended solids concentration, without conducting the tedious column tests for the various types of the suspended materials. In class-II clarification, for the same initial suspended solids concentration, the removal efficiency of one type of waste may be diff erent from the other and the clarifier design parameters need a rational evaluation. To explore this aspect, column settling tests were conducted for different kinds of the floe materials such as the sugar mill waste, domestic wastewater, aluminium hydroxide floes and ferric hydroxide floes. The initial suspended solids concentration was kept about 230 mg/L for all types of the suspended materials. For each type of the waste, the percentage removals were worked out at various depths and times of sampling. Using the results obtained, isopercentage lines xii were drawn for each waste and the overall percentage removals were worked out at the various times corresponding to a column depth of 1.20 m. For a given overflow rate, much variation in the overall per centage removals was not visible between the ferric hydroxide floes and aluminium ' hydroxide floes (both representing the chemical floes). Similar trend was also seen between the domestic wastewater and sugar mill waste (both containing the organic material). But there is a wide variation in the overall percentage removals (for a given overflow rate and for the same initial suspended solids concentration) between the chemically formed floes to the wastewaters. Thus, there is need to evaluate some coefficient a which is in some way describes the floe character. A model was evolved (Eq. 7 ) to predict the overall percen tage removals (F ) in relation to the overflow rate (v&) and the sediment character coefficient a for the above said floe materials (Bhargava and Rajagopal, 1989f). F o r8-571 x 10"5 ] + [ 0.277 , (?) I „a _- i1.9Q3u0n JJ v^o, LL arv ++ 1144..773322J The constant for the above equation were obtained for a Cq value of 230 mg/L at a column depth 1.2 m. The values of a were assumed as 10.8, 7.9, 2.7 and 2.6 for the ferric hydroxide floes, aluminium hydro xide floes, domestic wastewater and sugar mill waste respectively. The systematic variation in the evaluated values of the function constants of Eq. 5 (i.e., bQ, by etc.) and the model coefficients of Eq. 6 (i.e. c, d, e and f) for the different types of the suspended materials showed that the function constants and coefficients may depend on some characteristics of the suspended material such as the specific xin gravity, biochemical oxygen demand (BOD), chemical oxygen demand (COD), and sludge volume index (SVI). Through trial correlations, it was inferred that except for the sludge volume index, other stated para meters did not show correlation with the evolved function constants and coefficients of Eqs. 5 and 6 . Hence, some of the function constants of Eq. 5 (such as b , b_, bc and b,) and the model coefficient o i b o e of Eq. 6 were correlated with the determined average values of sludge volume index of the different types of the suspended materials (Bhargava and Rajagopal, 1990a) and are presented in Eqs. 8 to 12 . b = -86.8463 + 1233.333 (1/SVI) (8) b3 = -1.2813 + 0.5218 In (SVI) (9) b5 = 2.1443 x 10~4 - 2.1356 x 10~5 (SVI) (10) b6 = -exp [-8.0843 + 0.0203 (SVI)] (11) SVI -0.1934 - 0.2125 (SVI) (12) The constants of the above equation were obtained with sludge volume index (SVI) expressed in ml/g. The determined average values of sludge volume index were 110 ml/g, 99 ml/g, 16 ml/g and 24 ml/g for the ferric hydroxide floes, aluminium hydroxide floes, domestic wastewater and sugar mill waste respectively. STUDIES ON CLASS-III SEDIMENTATION (ZONE SETTLING) The settling behaviour in zone settling depends on the character istics of the suspension, initial suspended solids concentration, etc. XIV The design parameter (the thickener area) is obtained through batch settling tests. To study the effects of the nature of the suspended material present in the waters and the initial suspended solids concen tration , • etc. on zone settling, batch settling tests were conducted for the various types of the suspended materials such as ferric hydroxide floes, aluminium hydroxide floes, calcium carbonate, bentonite and grey soil, present in different initial suspended solids concentrations. Through trial runs, the minimum concentrations at which the zone settling could occur, were estimated as 0.50 g/L, 1.0 g/L, 65.0 g/L, 20.0 g/L and 58.0 g/L for ferric hydroxide floes, aluminium hydroxide floes, calcium carbonate, bentonite and grey soil respectively. Knowing the minimum concentration, the batch settling tests were conducted for the initial suspended solids concentration range of 0.557 g/L to 5.617 g/L, 1.643 g/L to 4.381 g/L, 69.070 g/L to 304.457 g/L, 20.582 g/L to 61.640 g/L and 59.254 g/L to 176.168 g/L respectively for the above said suspended materials. The data pertaining to the fall of the interface between the sludge blanket and clarified supernatant with respect to time for each of the various types of the suspended materials of different initial suspen ded solids concentration were observed. Using the graphical method developed by Talmadge and Fitch, the time required to reach the desired underflow sludge concentrations (several assumed values) were estimated for each of the initial suspended solids concentration for the different kinds of the suspended materials. For the assumed underflow sludge concentrations, the thickener areas were determined for each of the various types of the suspended materials having different initial suspended solids concentrations, in terms of the influent flow rate. The results XV thus obtained have been utilised to develop the models for predicting the thickener area for any given suspended solids concentration and for a desired underflow sludge concentration. To incorporate a factor to indicate in some way the characteristics of the various types of the suspended material in the model, trial correlations were attempted between the various model constants and the various parameters such as the specific gravity, BOD, COD, etc. representing the characteristics of the suspended materials. A success was met only with the specific gravity and thus the same was incorporated in the predictive model (Bhargava and Rajagopal, 1989e) as shown in Eq. 13 . t u __ [ H o exp {[exp(2.3407 - 0.9973s )]+d1(C )} +[e, +CfU1 (Cu) ]1" Co ] <13> In Eq. 13 , t represents the time required to reach the desired under flow sludge concentration in min, H represents the initial height of the interface in m, C represents the initial suspended solids concentra tion in g/L, C represents the desired underflow sludge concentartion in g/L, s represents the specific gravity of the suspended material and d, , e, and f, , are the constants. The values of s , d, , e, and f, were determined as 1.0026, g 1 1 1 0.1301, 3.4599 and 0.4863 for ferric hydroxide floes, 1.0017, 0.0257, -3 1.2355 and 0.4016 for aluminium hydroxide floes, 1.1762, -2.6351 x 10 , 438.1743 and 0.4574 for calcium carbonate, 2.051, 4.7300 x 10 , 7.1671 -4 and 0.7398 for bentonite and, 2.662, -7.697 x 10 , 102.8708 and 0.665 for grey soil respectively. XVI The evolved predictive model would eliminate the need for con ducting enormous and tiring settling tests and graphical analyses for the various types of the suspended materials, which are necessary to fix the thickener area under the existing methodology. ANALYSIS OF COMPRESSION SETTLING In compression settling, the settling behaviour depends on the initial suspended solids concentration, characteristics of the suspended materials present in the waters, etc. To explore this aspect, the data pertaining to the fall of the interface between sludge blanket and the clarified supernatant in the zone of compression were observed for the different types of the suspended materials such as ferric hydroxide floes, aluminium hydroxide floes, calcium carbonate slurry, bentonite and grey soil, present in different initial suspended solids concentration. For all types of the suspended materials, the interface height was seen to have reached almost a constant value within two days although on trial basis, the tests were continued for about a month and hence the settling tests were conducted for all types of the suspended materials for about two days . From the experimental data of the height of sludge (h ) at time t = 0, and the height of sludge (h ) at any time t, the firstorder rate constants k and the height of sludge (h ) at time t = L OO were determined from Eq. 14 . -let (h - h ) = (h - h ) (1 - e Kt) (14) Z Zn Zoo Zq XV11 The rate constants vary from 3.1053x10 4 min l to 1.1378x10 " min ' [for an initial suspended solids concentration (Cq) range of 5.617 g/L to 0.557 g/L], 5.5943xl0"4 min"1 to 1.5789x10" min" (for a Cq range of 4.381 g/L to" 1.643 g/L), 1.0403xl0"3 min" to 1.6799x10 " min " (for aC range of 304.457 g/L to 69.070 g/L), 8.3988xl0"4 min"1 to 1.8149xl(f- ° -3 min"1 (for a Cq range of 61.640 g/L to 20.582 g/L) and 1.0315x10 " min"1 to 1.9209xl0"3 min"1 (for a Cq range- of 176.168 g/L to 59.254 g/L) for ferric hydroxide floes, aluminium hydroxide floes, calcium carbonate, bentonite and grey soil respectively. Since the rate constants k are varying with the initial suspen ded solids concentration (Cq) , the values of k were correlated with C as shown in Eq. ,15 . o I = a + b C (") k o In Eq. (15), a and b are the coefficients. The values of a and b were evaluated for the above said suspended materials. To incorporate in some way, the characteristics of the suspended materials in Eq. 15 trial correlations were attempted between the coefficients a and b of Eq. 15 and the various sludge characteristics parameters such as the specific gravity, BOD, COD and sludge volume index. A success was met only with sludge volume index and thus the same was incor porated in Eq. 15 and a predictive model (shown in Eq. 16) was developed to determine the value of the rate constant k for the given initial suspended solids concentrations and the sludge volume index (Bhargava and Rajagopal, 1990c). XV111 I = a + [-8.0162 + 1.9862 (SVI)] Co (16) o In Eq. 16 , k represents the rate constant expressed in min , SVI represents the sludge volume index expressed in ml/g and Cq represents initial suspended solids concentration expressed in g/L. The determined values of a and SVI were 384.5762 and 233 ml/g for ferric hydroxide floes, -23.0891 and 229 ml/g for aluminium hydroxide floes, 506.8938 and 3.5 ml/g for calcium carbonate, 230.4403 and 13.8 ml/g for bentonite and 315.2241 and 5.1 ml/g for grey soil respectively. - The predictive model (shown in Eq. , 16) can be used to deter mine the rate constant k for the stated suspended materials for the given C values without doing enormous and time consuming settling tests. SUMMARY Based on extensive laboratory settling and column tests, several predictive models were developed in respect of each class of sedimen tation. Such evolved predictive models can be used for the rational fixing of the design parameters for the different categories of sedimenta tion units, and thus significantly simplify and rationalize the design technology of the various types of sedimentation basins used in water and wastewater treatment.