Environ. Sci. Technol. 2006, 40, 1280-1285
Chemical-Equilibrium-Based Model for Describing the Strength of Sludge: Taking Hydrogen-Producing Sludge as an Example GUO-PING SHENG AND HAN-QING YU* Laboratory of Environmental Engineering, School of Chemistry, The University of Science & Technology of China, Hefei, Anhui, 230026, China
A new model, based on chemical equilibrium theory, was established to evaluate the strength of sludges in biological wastewater treatment systems. The effectiveness of this model was demonstrated by the experimental results with an anaerobic hydrogen-producing sludge. The equilibrium dispersed mass concentration of the primary particles in the sludge solution was found to nonlinearly increase with the solid content and shear intensity, and could be well described by the model. The Gibbs free energy of adhesion (∆G°) under shear could also be calculated using this model. The equilibrium constant K° and ∆G°/ RT at a shear intensity of 800 1/s were estimated to be 6.54 ( 0.12 and 1.88 ( 0.02, respectively. The two parameters could be used to evaluate the strength of the hydrogenproducing sludge. In addition, the effectiveness of the established model was also confirmed by the results with activated sludge in the literature.
Introduction Solid/liquid separation efficiency in biological wastewater treatment systems is greatly affected by the sludge structure and its surface physicochemical characteristics (1-3). The structure of activated sludge has been observed using optical microscopy and confocal laser scanning microscopy (4-6). The influence of sludge surface physicochemical characteristics on its compressibility and settleability has also been documented (2, 3). However, sludge strength has not been given sufficient attention yet, although it is crucial for solid/ liquid separation in biological wastewater treatment systems. Primary particles erode from the sludge surface because of hydrodynamic shear force, and this has a significantly negative effect on the solid/liquid separation process (7). Although the complexity of sludge constituents and its chaotic structure make it difficult to study its strength characteristics, it is of engineering significance and has recently attracted increasing interest. Efforts have been made to characterize sludge strength through measuring the floc size changes under given shear conditions (8, 9). However, this method may not be adequate for describing such a separation process, in which the primary particle concentration is essential. The shear sensitivity of activated sludge, as the ratio of sludge volumes of sheared samples to those of nonsheared ones, was assessed to evaluate the sludge strength (10). A dissociation constant, defined as unit absorbance per * Corresponding author phone: +86 551 3607592; fax: +86 551 3601592; e-mail:
[email protected]. 1280
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gram of biomass washed, was also employed to characterize the sludge strength (1, 11). A physically relevant index for describing the total network strength of sludge with rheological tests was proposed (12). This index was hypothesized to correlate with the dewatering efficiency of flocculated sludge. However, the roles of solid content and shear intensity are not considered in these methods. Thus, the sludge characteristics cannot be predicted under other shear conditions, and cannot be compared with the results from other studies. Many attempts have been made to describe the concentration of primary particles in sludge suspension using mathematical methods based on sludge self-flocculation and adhesion process. A flocculation-deflocculation model was developed by Parker and co-workers (13) based on a mechanistic approach with consideration of the balance of flocculation-deflocculation process. This model is appropriate for describing the flocculation of activated sludge at low shear intensities (13). However, it was not applicable for describing the process at a high solid content or at a high shear intensity (14). Instead, based on Langmuir adsorption isotherm theory, an adhesion-erosion model (AE model) was established from a macroscopic viewpoint for quantifying the concentration of dispersed primary particles due to erosion under shear conditions (14). In this model, two independent equations were used to describe the effects of solid content and shear intensity on the concentration of equilibrium dispersed primary particles, and the sludge strength was correlated with some thermodynamic terms, such as the change in enthalpy and Gibbs free energy of the adhesion process. This model is successful in describing the sludge desorption phenomenon at a high shear intensity (7, 14). According to the AE model, at a high solid domain, the equilibrium was dominated by the upper limit value (14). Therefore, the AE model was effective for describing the sludge strength at solid contents below a limit. It would bring about some deviations at a high solid content. In recent years, harvesting hydrogen from organic wastes through an anaerobic process has attracted extensive attention (15, 16). The hydrogen-producing sludge with a high strength would be favorable for the solid/liquid/gas separation, and be beneficial for keeping a high sludge concentration in anaerobic hydrogen-producing reactors. In this study, the shear strength of hydrogen-producing sludge at various solid contents and shear intensities was investigated with a new model, which was established based on the chemical equilibrium theory. The results from this study might provide valuable information for the operation and design of a hydrogen-producing bioreactor.
Model Development In sludge suspension, the particle size distribution is bimodal, mainly containing two particle classes, i.e., primary particles (0.5-5 µm) and flocs (25-100 µm) (7, 17). The concentration of dispersed primary particles in sludge suspension depends on both shear intensity and solid content. The adhesion of particles to flocs and their erosion from flocs occur simultaneously under shear conditions (13, 14). There might be a dynamic equilibrium between the primary particles and flocs under shear conditions. This equilibrium between the dispersed primary particles and flocs would shift to the domination of the primary particles (14), as the shear intensity or solid content increases, as in a reversible chemical reaction. Assuming that the flocs are homogeneous and regardless of their formation process, the equilibrium between the primary particles and flocs under shear conditions could be treated 10.1021/es0518528 CCC: $33.50
2006 American Chemical Society Published on Web 01/14/2006
as a reversible chemical reaction:
chemical equilibrium, the effect of temperature on the equilibrium constant K° is governed by the change of enthalpy (∆H), as described by the van’t Hoff equation:
shear
R particles 798 flocs By the analogy to a reversible chemical reaction, the equilibrium established between primary particles and flocs is expected to depend on the solid content and shear intensity. The thermodynamic equilibrium constant K° without dimension at a constant shear intensity could be expressed as follows in terms of activity:
K° )
()
nF nP / n° n°
( )
nFm nPm / n°m n°m
R
)
( )
mF m P / m° m°
∆H 1 +q R T
(7)
where T is absolute temperate, R is the gas constant, and q is a constant without dimension. Neglecting the effect of temperature and replacing T with G, as done by Mikkelsen and Keiding (14), eq 7 is integrated into
R
(1)
where nF and nP are the number concentrations of total flocs and dispersed primary particles at equilibrium, respectively, n° is the standard sludge number concentration, and R is a sludge characteristic constant. In practice, the use of mass concentration is more convenient than number concentration. Thus, the equation above could be changed to
K° )
ln K° ) -
R
)
mT - md,∞ (m°)R-1 md,∞R (2)
in which mF and mP are the mass concentrations of total flocs and dispersed primary particles at equilibrium, respectively; m is the mass of one primary particle; mT is the mass of total solid content, i.e., mT ) mP + mF; m° is the standard sludge mass concentration and its value is assumed as 1.0 g of SS/L (SS, suspended solids). md,∞ represents the equilibrium mass concentration of dispersed primary particles and could be estimated from the desorption kinetic curves suggested by Mikkelsen and Keiding (14):
6 9 1 -N2Dt md,t ) md,∞ + (md,0 - md,∞) e π2N)1N2
∑
(3)
where md,0 and md,t are the dispersed mass concentration of primary particles at initial time and time t, respectively, N is an integer, and D is an effective diffusion constant. The Gibbs energy of adhesion at a constant shear intensity could be estimated from the following physicochemical equation:
∆G° ) -RT ln K°
(4)
On the basis of physicochemical principles, the change in Gibbs energy can show the direction of equilibrium shift between primary particles and flocs. The more negative value of ∆G° implies a greater stability of flocs. Equation 2 could be rearranged into
mT ) md,∞ + K°md,∞R
(5)
Equation 5 is linearized as
ln(mT - md,∞) ) ln K° + R ln md,∞
(6)
From a linear regression between ln(mT - md,∞)and ln md,∞, the values of K° and R could be calculated at a constant shear intensity. In the experiments for strength testing, an increase in shear intensity would cause a shear equilibrium shift to the direction of primary particles. The effect of shear intensity could be treated by analogy with that of temperature on a conventional chemical equilibrium, as suggested by Mikkelsen and Keiding (14). Such an analogy was successfully used for establishing the AE model (14). For a given conventional
ln K° ) -
∆H 1 +q R G
(8)
in which ∆H is the change of enthalpy of sludge adhesion, and is independent of shear intensity. Introduction of eq 2 to eq 8 gives
(
ln
)
mT - md,∞ md,∞
R
)-
∆H 1 +q R G
(9)
With this equation, a plot of ln[(mT - md,∞)/md,∞R] vs 1/G is expected to give a straight line with a slope of -∆H/R and an intercept of q.
Materials and Methods Hydrogen-Producing Sludge. The anaerobic hydrogen production experiments were conducted with a 5-L fermentor (Baoxin Biotech Ltd., Shanghai). The fermentor was equipped with an impeller and four baffles and was operated in a batch mode. The seed sludge was originally collected from a fullscale upflow anaerobic sludge blanket reactor treating citrateproducing wastewater for methane production. The methaneproducing sludge was heated at 102 °C for 2 h to inactivate hydrogen-trophic methanogens and to enrich hydrogenproducing bacteria. A 1000-mL heat-treated seed sludge of volatile suspended solids at 20 g/L and 3.0 mL of nutrients solution were added to the fermentor. The nutrient solution was composed as follows (units in mg/L): NH4HCO3, 2025; K2HPO4‚3H2O, 800; CaCl2, 50; MgCl2‚6H2O, 100; FeCl2, 25; NaCl, 10; CoCl2‚6H2O, 5; MnCl2‚4H2O, 5; AlCl3, 2.5; (NH4)6Mo7O24, 15; H3BO4, 5; NiCl2‚6H2O, 5; CuCl2‚5H2O, 5; ZnCl2, 5. After addition of sucrose at 20 g/L as substrate, the fermentor working volume was adjusted to 3 L with distilled water. Prior to operation, the fermentor was purged with nitrogen for 10 min to ensure anaerobic conditions. The pH, temperature, and agitation rate of the fermentor were kept at 5.5, 35 °C, and 120 rpm, respectively. The specific hydrogen production potential achieved was 11.8 mmol of H2/g of sucrose, and the maximum hydrogen production rate reached 14.8 mmol of H2 L-1 h-1 under these conditions. At the end of the hydrogen production test, the sludge was sampled from the fermentor, washed three times with tap water, and then settled for 2 h at 4 °C to remove rudimental primary particles and the fermentative products. After that, the sludge was thickened to 20-30 g of SS/L. Thereafter, the sludge was diluted with tap water to 0.8-20.0 g of SS/L, and was then placed at 4 °C for 6-12 h without shear. Shear Tests. Shear tests were performed in a baffled reaction chamber with a cover. The hydrogen-producing sludge was sheared with continuous purging of nitrogen at 4 °C. The initial sludge volume was kept at 1000 mL. The shear intensity was characterized by the root-mean-square velocity gradient (G): G ) xP/ηV, where P is the power input, η is the fluid viscosity, and V is the suspension volume (7). The shear intensity was continuously controlled using a mechanic mixer (JJ-4, JCGS Instrument Co., Jiangsu, China). The release of dispersed primary particles as a result of shear was characterized with the changes of the supernatant VOL. 40, NO. 4, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 2. Linear regression between ln(md,∞) and ln(mT - md,∞) at various solid contents of hydrogen-producing sludge.
FIGURE 1. Dispersed mass concentration of primary particles versus shearing time for hydrogen-producing sludge: (a) at various solid contents and fixed G value of 800 1/s; (b) at various G values and fixed solid content of 1.65 g/L. turbidity. Samples of 3 mL were taken from the chamber at predetermined time intervals. Supernatant turbidity was measured as absorbance at 650 nm using a spectrophotometer (UV751GD, Analytical Instrument Co., Shanghai, China), following a 2-min centrifugation at 2200 rpm (14). The value of md,t was then estimated using the turbidity/SS mass concentration conversion factor according to Wahlberg et al. (13). Measurements of SS were conducted according to Standard Methods (18).
Results The typical sludge desorption curves at various solid contents and shear intensities are shown in Figure 1. The supernatant turbidity rapidly increased after the sludge was exposed to turbulent shear, and then leveled off after 3 h. The desorption rates were significantly affected by both solid content and shear intensity. A regression was performed with the data in Figure 1 using eq 3, and the values of md,0 and md,∞ were estimated and are listed in Table 1. Effect of Solid Content on md,∞. The effect of solid content on md,∞ for the hydrogen-producing sludge at various shear intensities is illustrated in Figure 2, in which the curves are
drawn with the linear regression results of eq 6. To accurately estimate R values, the six independent data at G ) 800 1/s were used for linear regression. The estimates of R and K° values at G ) 800 1/s are listed in Table 2. The high correlation coefficient indicates such a treatment was reasonable. The md,∞ value significantly increased with increasing solid content. The data were fitted by eq 6, yielding the same slope value for the sludge at various shear intensities (Figure 2). This suggests that the parameter R was independent of the shear intensity and was thus a sludge characteristic constant. The high correlation coefficient (R2 ) 0.999) implies that eqs 5 and 6 were able to effectively describe the effect of solid content on md,∞. The different line intercepts at various shear intensities shown in Figure 2 indicate that the equilibrium constant K° was dependent on the shear intensity. However, when the shear intensity was higher than 1100 1/s, the K° value remained almost unchanged (Figure 2), suggesting that the K° value initially increased with shear intensity, but leveled off at a high shear intensity domain. To confirm the validity of eqs 5 and 6 in a relatively large range of sludge content, two additional experiments were conducted at G of 800 1/s with solid contents of 14.88 and 19.57 g of SS/L. The measured and calculated results with the established model and the AE model are listed in Table 3 for comparison. The relative deviations between the measured and calculated values were -2.2% and -6.3% for solid contents of 14.88 and 19.57 g of SS/L, respectively. This suggests that the model established in this study was able to describe the sludge strength well at high solid contents. Effect of Shear Intensity on md,∞. For the hydrogenproducing sludge, the estimated md,∞ values at different shear
TABLE 1. Effect of Solid Content and Shear Intensity on Estimates and Standard Deviations (in Parentheses) of md,∞ and md,0 for Hydrogen-Producing Sludge
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mT (g of SS/L)
G (1/s)
md,∞ (g of SS/L)
md,0 (g of SS/L)
R2
0.82
270 500 800 1100 1400
0.034 (0.003) 0.051 (0.001) 0.096 (0.003) 0.143 (0.002) 0.142 (0.003)
0.017 (0.002) 0.014 (0.002) 0.018 (0.004) 0.019 (0.004) 0.022 (0.005)
0.489 0.918 0.913 0.964 0.942
1.65
270 500 800 1100 1400
0.074 (0.004) 0.146 (0.005) 0.202 (0.005) 0.269 (0.005) 0.257 (0.004)
0.046 (0.002) 0.024 (0.005) 0.033 (0.007) 0.030 (0.009) 0.040 (0.008)
0.533 0.900 0.929 0.956 0.954
3.56
270 800 1400
0.196 (0.012) 0.421 (0.005) 0.689 (0.008)
0.035 (0.006) 0.025 (0.009) 0.015 (0.016)
0.823 0.980 0.983
5.78
800
0.707 (0.012)
0.012 (0.017)
0.974
8.00
800
1.026 (0.017)
0.020 (0.024)
0.977
10.67
800
1.533 (0.019)
0.049 (0.027)
0.987
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TABLE 2. Estimates and Standard Deviations (in Parentheses) of Model Parameters from Eqs 1-9 for Three Types of Sludge sludge
K° a
∆G°/RTa
∆H/R (1/s)
q
r
reference
AAE sludge HS sludge hydrogen-producing sludge
12.3 (0.1) 14.7 (0.5) 6.54 (0.12)
-2.51 (0.01) -2.69 (0.03) -1.88 (0.02)
-437.8 (20.0) -435.6 (20.6) -426.2 (37.8)
1.96 (0.02) 2.36 (0.02) 1.22 (0.07)
0.74 (0.01) 0.65 (0.03) 0.88 (0.07)
14 14 this study
a
Obtained at G ) 800 1/s.
TABLE 3. Deviation between Experimental Results and Values Estimated by the Present and AE Models for md,∞ at High Solid Content and G ) 800 1/s solid content (g of SS/L)
measd (g of SS/L)
est of present model (g of SS/L)
rel dev (%)
est of AE model (g of SS/L)
rel dev (%)
14.88 19.57
2.28 (0.06) 3.16 (0.05)
2.23 2.96
-2.2 -6.3
2.46 3.60
7.9 12.5
FIGURE 3. Effect of shear on equilibrium dispersed mass concentrations of hydrogen-producing sludge.
FIGURE 5. Effect of shear on equilibrium dispersed mass concentration for (a, b) AAE sludge and (c, d) HS sludge. The data are from Mikkelsen and Keiding (14).
FIGURE 4. Effect of solid contents on equilibrium dispersed mass concentration of activated sludge for (a) AAE and (b) HS sludge. The data are from Mikkelsen and Keiding (14). intensities and regression results are shown in Figure 3. All these experimental results could be well fitted with the model (Figure 3a). This demonstrates that the present approach was appropriate for describing the effect of shear intensity on md,∞. An increase in shear intensity always resulted in an nonlinear increase in md,∞. However, shear intensity had a slight effect on md,∞ at a high shear intensity domain. From the linear regression between ln[(mT - md,∞)/md,∞R] and 1/G, the values of ∆H/R and q were estimated and are listed in Table 2. The high correlation coefficient value (0.949) suggests that the present model is valid and that the assumptions for the model development are appropriate. Model Verification. To verify the validity of eq 9, data available in the literature were used for calculations. Mikkelsen and Keiding (14) evaluated the effects of solid content and shear on the dispersed degree of activated sludge from the Aalborg East (AAE) and Horsens (HS) Wastewater Treatment Plants, Denmark. Figure 4 shows the regression curves with eq 5 for the AAE sludge and HS sludge at G ) 800 1/s. The correlation coefficients were both greater than 0.99, suggesting that the predictions with eq 5 were in good agreement with the experimental results. From the regression, the parameter R were estimated to be 0.74 and 0.65 for the AAE sludge and HS sludge, respectively. The effects of shear on the equilibrium dispersed concentration for the activated sludge samples are illustrated in Figure 5a,c, whereas the
linear fittings of the experimental data to eq 9 are shown in Figure 5b,d. The high values of correlation coefficients imply that the present model was able to fit the experimental results of Mikkelsen and Keiding (14) very well. From the slopes and intercepts of the lines in Figure 5b,d, the values of ∆H/R and q for the two sludge samples were estimated and are also listed in Table 2 for comparison.
Discussion In the present study, a macroscopic approach based on chemical equilibrium was established to evaluate the strength of sludge. This approach provided good fits to the equilibrium between the primary particles and flocs for different types of sludges, including activated sludge and anaerobic hydrogen-producing sludge.The model was able to describe the effects of solid content and shear intensity on the equilibrium dispersed sludge concentration. The relationship between the thermodynamic parameters and sludge strength was also established. At a fixed solid content and shear intensity, the quantity of the dispersed particles could reflect the sludge strength. Comparison between the Present Model and AE Model. Both the present model and AE model are able to describe the effect of solid content and shear intensity on the equilibrium dispersed mass concentration of primary particles. The model established in this study was based on chemical-equilibrium theory, whereas the AE model was based on the Langmuir adsorption isotherm theory. The present model coupled the effect of solid content and shear intensity into one equation. In this way, it is convenient to estimate the dispersed particle concentrations at various solid contents and various shear intensities (Figures 2 and 3). The AE model, however, used two independent equations to VOL. 40, NO. 4, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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describe the effects of solid content and shear intensity on the dispersed particle concentrations (14). In addition, the present model is appropriate for a broad range of solid content, even for a solid content higher than 15 g of SS/L, as evidenced by the low relative deviations (Table 3), while the AE model was developed for cases with solid contents below a limiting SS (7, 14). According to the present model, for high solid contents, md,∞ was dependent on both K° and R values. Equation 5 could be simplified to
md,∞ 1 ) mT 1 + K°/m
1-R
(10)
d,∞
Equation 10 implies that only a small fraction of the dispersible sludge could be eroded into effluent at a relative higher solid content. Furthermore, the shear intensities of biological wastewater treatment bioreactors are not always high. According to eq 8, a high value of K° could be obtained, corresponding to a large value of K°/md,∞1-R. For K°/md,∞1-R . 1, eq 10 could be further simplified to
md,∞ ) (mT/K°)
1/R
(11)
From eq 11, a low md,∞ value could also be obtained at a relatively high solid content. This is able to explain the phenomena that a low effluent SS content could be achieved for wastewater treatment plants with various sludge concentrations. This also indicates that the model established in this study is applicable to more actual conditions, even at high solid contents (e.g., >15 g of SS/L) or low shear intensities (e.g.,
