Investigating the Steady-State Rheological Properties of Activated Sewage Sludge for Effective Post-Treatment

Abstract

Pipeline transportation has become an effective way to transport sludge from wastewater treatment plants due to its high transportation efficiency, low operating cost, and low environmental pollution. Before designing and optimizing the sludge-conveying pipeline, it is first necessary to analyze the rheological properties of the sludge. In this paper, activated sludge with varying volume concentrations (C_w) of 2.38%, 3.94%, and 5.39% was used as the research object. Under three temperature (T) conditions of 293 K, 298 K, and 303 K, the sludge concentration and temperature were investigated, and based on the results, a rheological model of activated sludge was established. The experimental results indicated that the upward and downward paths of the shear stress change curve were generally similar but did not overlap, and a hysteresis loop was formed between the two due to the characteristics of sludge shear thinning. The limiting viscosity of sludge with different concentrations increased with the increase in sludge concentration. This phenomenon was caused by the differences in the internal flocculent network structure of sludge with different concentrations and the different fluid flow effects. At different shear rates, the shear stress and sludge viscosity in the experiment decreased with the increase in temperature. The stability of the test sludge was weakened with the increase in temperature. Additionally, the viscosity of sludge decreased with the increase in shear rate and then stabilized, exhibiting shear thinning characteristics. The above rheological properties were described using the Bingham and Herschel–Bulkley models.

1. Introduction

Sludge from sewage treatment plants is a byproduct of the biochemical treatment process of wastewater, which contains a large amount of organic and inorganic pollutants, as well as heavy metals. If not properly treated and disposed of, it can seriously pollute the ecological environment. For most small- and medium-sized sewage plants, the investment and operating costs of sludge treatment and disposal projects are high and are often unaffordable [1,2]. Therefore, the centralized treatment and disposal of sludge in cities or regions can effectively reduce the burden on sewage plants in this regard, while also saving land around the city and reducing pollution to the ecological environment. Consequently, the centralized treatment and disposal of sludge have important practical significance in solving the problem of sludge outlets in sewage plants [3,4]. Based on the understanding of the above issues, the transportation of sewage sludge in sewage plants has become a link between sewage plants and sludge treatment plants. In terms of transportation methods, pressurized pipeline transportation has become the preferred choice due to its significant advantages, such as high transportation efficiency, low operating costs, easy management, and low environmental pollution, compared to traditional truck and barge transportation. And it has been applied in countries such as the United States, Japan, and the Netherlands [5,6,7,8].

The sludge from sewage treatment plants contains many solid particles, which makes its physical properties more complex than clean water, especially the hydraulic characteristics reflected in pipeline transportation. Therefore, it is necessary to first analyze the rheological properties of sludge when conducting hydraulic calculations and optimizing the design of sludge-conveying pipelines, as well as selecting conveying equipment [9,10]. Many scholars have carried out experimental studies on the rheological properties of different types of sludge, including activated sludge, kitchen waste anaerobic digestion sludge, oxidation pond sludge, oily sludge, membrane-thickening sludge, granular sludge in the up-flow anaerobic sludge bed reactor, and sludge after anaerobic or aerobic digestion [11,12,13,14,15,16]. In addition, so many environmental granular fluid mixtures, such as clay–soil, silt–rich soil, fine-grained natural debris, and fine-grained slurry–muddy debris, behave similarly to the sludge produced in sewage treatment plants. In recent years, the effect of grain concentration, grain sorting, and thixotropy have been investigated, and different rheological models (including the Bingham model and the Herschel–Bulkley model) have been successfully considered [17,18,19]. The research results indicate that the rheological properties of sludge are related to factors such as sludge type, sludge concentration, and temperature, and the transport characteristics of sludge are closely related [9,10]. Therefore, in this article, using activated sludge as the research object, the effects of sludge concentration and temperature on its rheological properties were investigated. On this basis, the sludge rheological model was established, which was used as the basis for the optimized selection of operating parameters for the sludge pipeline pressure transportation system. This study is important for improving the management level of the sewage sludge pipeline transportation system, reducing transportation energy consumption, saving the total transportation cost, and reducing the consumption of resources. Meanwhile, this research also has important practical significance for maintaining the sustainable development of environmental resources and social resources.

2. Materials and Methods

2.1. Preparation of Sludge Samples

The sludge used in the test was obtained from the Xijiao Sewage Treatment Plant in Changchun City and was prepared by diluting the dewatered sludge with the effluent of the sewage plant. It was determined that the moisture content of the original dewatered sludge was 75.2%. The three samples of the dewatered sludge were prepared by mixing it with the effluent of the sewage plant according to the volume ratio of 1: 9.42, 1: 5.29, and 1: 3.60, and the test sludge samples with a water content of 97.62%, 96.06%, and 94.61% were obtained, respectively. Therefore, the volume concentrations of the three test sludge samples were 2.38%, 3.94%, and 5.39%, and their basic physical properties are shown in

Table 1. Basic physical properties of test sludge.

Serial Number	Moisture Content (%)	CW (%)	Density (kg/m3)
1	97.62	2.38	1005.26
2	96.06	3.94	1009.05
3	94.61	5.39	1014.96

Note: C_w stands for volume concentration of sludge.

.

2.2. Determination of Sludge Particle Size and Shape

Before and after the experiment, the particle size distribution of sludge was measured using a laser particle size analyzer (BT9300S, Dandong Baite Instrument Co., Ltd., Dandong, China). The particle size distribution before the experiment is shown in Figure 1. It can be seen from Figure 1 that sludge particles with a particle size of about 100 μm appear most frequently, and the cumulative frequency of sludge particles with a particle size of less than 45 μm is 23.26%, after which the slope of the cumulative frequency curve increased significantly. The cumulative frequency of sludge particles with particle size less than 200 μm reached 87.17%, and the slope of the cumulative frequency curve began to decrease significantly. This showed that the particle size of sludge particles was mainly between 45 and 200 μm. The particle shape was measured using a high-frequency pulse particle size analyzer (QICPIC-LIXELL, Synpatec Co., Ltd., Clausthal-Zellerfeld, Germany) to observe the changes in the sludge particle shape before and after the experiment.

2.3. Steady-State Rheological Test

The steady-state rheological properties of sludge were measured using a rotary rheometer (ARES-G2, TA Instruments, New Castle, DE, USA) at three temperature conditions in the raising order from low to high: 293 K, 298 K, and 303 K. For the testing procedure, 14 shear rates were set (15.5–996.3 s⁻¹), and a rotation test was conducted in order of low to high and then high to low at a specific temperature. The shear stress corresponding to each shear rate under each temperature condition was recorded, and the rheological curve of the sludge sample was derived. During the above testing process, a constant-temperature water bath was used to keep the temperature of the sludge sample constant, with a temperature error not exceeding ±0.1 °C. All the above testing processes were subjected to three parallel tests. Via rheological property testing, the measured shear stress, shear rate, apparent viscosity, and limiting viscosity (i.e., the stable value of the corresponding apparent viscosity when the shear rate approaches infinity) were directly recorded.

2.4. Rheological Model Simulation

The non-Newtonian flow behavior of sludge suspension is usually described by the following model, as shown in Equation (1):

$$\tau ={\tau }_0+{\eta }_p{\dot{\gamma }}^n$$

(1)

where:

• τ—shear stress (mPa);
• τ₀—the yield stress (mPa);
• η_p—the plastic viscosity (mPa·s);
• $\dot{\gamma }$—the shear rate (s⁻¹);
• $n$—the rheological index.

During the rheological testing of sludge, when the applied stress was less than the yield stress, τ₀, the fluid did not flow, indicating elasticity. When the stress exceeded τ₀, the system only flowed, and the fluid showed viscosity at this time. In the formula, if n = 1 in the equation, the stress is linearly related to the shear rate, which is called Bingham plastic fluid; if n ≠ 1, the fluid exhibits nonlinear shear thinning (n < 1) or thickening (n > 1) flow behavior, known as Herschel–Bulkley plastic fluid [17,20].

During the data analysis process, Origin 9.0 (Origin Lab, Northampton, MA, USA) was used to fit the Bingham and Herschel–Bulkley models to the rheological data to obtain the values of characteristic parameters, such as τ₀, η_p, and n.

3. Results and Discussion

3.1. Analysis of Typical Rheological Properties of Sludge

Under the three temperature conditions of 293 K, 298 K, and 303 K, the rheological characteristic curves of sewage plant sludge with three concentrations of 2.38%, 3.94%, and 5.39% are shown in Figure 2. The experimental results in Figure 2 indicated that the rheological curves of sludge with different concentrations under different temperature conditions had certain similarities. Therefore, the rheological characteristic curve of 2.38% concentration sludge at the T = 293 K temperature condition (Figure 2a) was taken as an example for analysis.

From Figure 2a, during the process of shear rate from low to high, and then from high to low, the shear stress change curve was divided into an upward path and a downward path, with similar but not overlapping trends. In the ascending path, when the shear rate was low, the shear stress rapidly increased with the increase in the shear rate. However, when the shear rate was greater than 57.79 s⁻¹, its ascending rate began to decrease, but it had a relatively stable curve slope; that is, the plastic viscosity remained basically stable. This phenomenon was maintained until the end of the ascending path, that is, when the shear rate was equal to 996.3 s⁻¹. In the subsequent descent path, the shear stress decreased with the decrease in shear rate, and the downward trend was relatively stable. Meanwhile, according to the apparent viscosity curve in Figure 2a, the apparent viscosity decreased rapidly with the increase in the shear rate when the shear rate was less than 99.62 s⁻¹. Subsequently, as the shear rate increased, the apparent viscosity continued to decrease, but the rate of decrease gradually decreased. Under high shear rate conditions, the apparent viscosity tended to be relatively stable at approximately the corresponding limit viscosity (2.47 mPa·s).

The above phenomenon indicated that the sludge suspension exhibited different flow states under different shear rate conditions, and there was also a significant difference in its viscosity. Under low shear rate conditions, the sludge was in a laminar flow state, and the flocculent network structure formed between particles due to flocculation was sufficient to resist a certain amount of external force. Therefore, it was necessary to overcome the initial yield stress before flow occurs, and the viscosity of the fluid was high [21]. With the continuous increase in shear rate, the floc network structure had been damaged, so the sludge suspension exhibited almost homogeneous flow characteristics, and its viscosity remained basically unchanged [22].

In addition, it can be seen from Figure 2a that the shear stress in the descending path was smaller than that corresponding to the same shear rate in the ascending path, forming a hysteresis loop between the two, which showed that the sludge sample had the characteristics of thixotropy or shear thinning [23]. From the perspective of the internal structure of sludge, the appearance of this hysteresis loop specified that when the shear rate increased to a certain value, the flocculent network structure inside the sludge was damaged and exhibited relaxation characteristics, resulting in the arrangement direction of molecular chain segments inside the sludge tending to be consistent with the flow field direction. At the same time, due to the fast shear process, the system did not have enough time to reconstruct the floc network structure, which led to the deviation of the molecular chain segments in the sludge from the equilibrium conformation, and the relative flow resistance between oriented molecules was reduced. Therefore, in the descending path, the shear stress exhibited at the same shear rate was somewhat weakened compared to the ascending path, and the plastic viscosity of the sludge was reduced. At this time, the properties exhibited by the fluid conform to the characteristics of Bingham plasticity or yield pseudo-plasticity [22,23].

3.2. The Effect of Concentration on the Rheological Properties of Sludge

The experimental results of the limiting viscosity of sludge with different concentrations under different temperature conditions in the experiment are shown in Figure 3. From Figure 3, under the same temperature condition of 293 K, the limiting viscosity of the three different concentrations of sludge, at 2.60 mPa·s, 3.21 mPa·s, and 5.95 mPa·s, shows an upward trend with the increased sludge concentration. In addition, when the sludge concentration was relatively small (such as 2.38% and 3.94%), the limiting viscosity of sludge slowly increased with the increase in sludge concentration, but when the sludge concentration was high (such as 5.39%), its limiting viscosity increased rapidly. Similarly, under the temperature condition of 298 K, the effect of sludge concentration on its limiting viscosity was like that at 293 K. The limiting viscosity of the three concentrations of sludge reached 2.45 mPa·s, 2.91 mPa·s, and 5.78 mPa·s. In addition, under the temperature condition of 303 K, the limiting viscosity of the three concentrations of sludge, at 2.32 mPa·s, 2.78 mPa·s, and 3.69 mPa·s, showed a stable upward trend with the increase in sludge concentration. The limiting viscosity did not show a sudden increase when the sludge concentration reached 5.39%.

The above phenomenon indicated that sludge concentration was one of the important factors affecting its limiting viscosity mainly due to the increased resistance caused by the deformation of the streamline near the solid particles [24,25]. If there were fewer solid particles in the sludge, then this flow only involved the influence of the solid on the fluid. However, if there were many solid particles, that is, if the concentration of sludge was high and the distance between the sludge particles was very small, then this bypass effect inevitably involved the mutual influence between the solid particles. In addition, in the sludge composed of solid–liquid phases, the influence of solid particles with different particle sizes on the viscosity of the sludge was different [25]. The fine particles were interconnected to form a flocculent network structure due to flocculation, enclosing a considerable amount of free water in the middle of the flocculent network and becoming so-called closed water, which moved together with the flocculent network. This led to a decrease in the flow of water between particles, an increase in the attraction between sludge particles, and an increase in viscosity. As the concentration increased, the flocculent network structure between sludge particles became stronger, increasing shear stress that needed to be overcome when relative motion occurred between flow layers. The macroscopic manifestation was an increase in apparent viscosity. For coarse particles, in a solid–liquid two-phase system dominated by fine particles, although their intervention also caused an increase in sludge concentration, it had a certain contribution to the reduction in sludge viscosity [24,25,26,27]. The reason for this was that, when fine particles coexist with coarse particles, the fine particles filled the voids between the coarse particles, thereby preventing the formation of overly strong flocculent structures between the fine particles and increasing the viscosity of the sludge.

In this experiment, and as can be seen in Figure 1, the number of sludge particles with a particle size of less than 100 μm accounted for 56.89% of the total number of particles, the number of particles with a particle size of less than 500 μm accounted for 97.07% of the total number of particles, and the number of particles with a particle size of less than 800 μm accounted for 100% of the total number of particles. From this, it can be inferred that the composition of the above sludge samples was mainly composed of fine particles, and the formation of the flocculent network structure was the main reason for the increase in the viscosity of the sludge system. Moreover, as the sludge concentration increased, the flocculent network structure became sturdier, and the macroscopic performance showed that the limiting viscosity of the sludge also increased accordingly.

The particle size distribution and shape of sludge solid particles before and after steady-state rheological testing were measured and observed in the experiment. The changes in sludge particle size are shown in Figure 4, and the changes in particle shape are shown in Figure 5.

As shown in Figure 4, there was a significant change in sludge particle size before and after the experiment. After the experiment, the peak of the sludge particle size distribution shifted to the left, indicating that the overall sludge particle size decreased compared to before the experiment. This phenomenon occurred because sludge flowed under the shear stress applied by the rheometer, and the relative motion between flow layers caused shear friction between particles and between particles and the instrument wall, resulting in a decrease in the particle size of sludge due to wear. On the one hand, as the size of sludge particles decreased, it was easier to achieve homogenization in the two-phase medium composed of sludge particles and water, which was beneficial for reducing flow resistance [28]. However, at the same time, the decrease in sludge particle size may have led to an increase in the number of small particles in the solid–liquid two-phase system, which in turn led to an increase in fluid viscosity, which was detrimental to reducing flow resistance [28,29]. It can be deduced from Figure 5 that, while the sludge particle size decreased after the experiment, the surface of the sludge particle also became smoother due to hydraulic shear friction, and its shape tended to become spherical, which was beneficial for reducing the frictional resistance between flow layers.

3.3. The Effects of Temperature on the Rheological Properties of Sludge

In addition to sludge concentration, temperature is also an important factor affecting the steady-state rheological properties of sludge.

Table 2. Effect of temperature on rheological parameters of 2.38% concentration sludge.

Shear Rate (s−1)	Temperature
	293 K		298 K		303 K
	Shear Stress (Pa)	Viscosity (Pa·s)	Shear Stress (Pa)	Viscosity (Pa·s)	Shear Stress (Pa)	Viscosity (Pa·s)
15.5009	0.14362	0.00926	0.1356	0.00875	0.09587	0.00618
19.2330	0.16653	0.00866	0.1608	0.00836	0.12303	0.0064
26.7254	0.21378	0.008	0.19496	0.00729	0.1705	0.00638
37.1364	0.26573	0.00716	0.24001	0.00646	0.22361	0.00602
51.6009	0.3278	0.00635	0.29581	0.00573	0.27112	0.00525
71.6997	0.38507	0.00537	0.36755	0.00513	0.30855	0.0043
99.6266	0.45399	0.00456	0.43603	0.00438	0.34095	0.00342
138.426	0.53565	0.00387	0.49387	0.00357	0.39709	0.00287
192.333	0.62979	0.00327	0.5623	0.00292	0.49716	0.00258
267.233	0.75763	0.00283	0.68807	0.00257	0.66374	0.00248
371.334	0.9528	0.00257	0.94998	0.00256	0.89543	0.00241
516.003	1.4622	0.00283	1.25161	0.00243	1.23022	0.00238
716.984	2.33272	0.00325	1.87687	0.00262	1.73887	0.00243
996.296	3.76797	0.00378	2.95372	0.00296	2.46221	0.00247

provides the specific rheological parameters of sludge with a volume concentration of 2.38% at test temperatures of 293 K, 298 K, and 303 K. As shown in Table 2, under different shear rate conditions, as the temperature of the sludge increased, the shear stress and viscosity of the sludge in the experiment decreased accordingly. From a microscopic perspective, this indicated that, at higher temperatures, the thermal movement of water flowing between sludge particles was more intense, and the strength of the flocculent network structure formed by flocculation between particles was weakened. The bonding force between the same phases and between two phases in the solid–liquid phase medium was weakened [30]. Therefore, macroscopically, this was manifested as a decrease in sludge viscosity and an increase in its fluidity.

Many scholars have studied the influence of temperature on the viscosity of sewage sludge. Baudez et al. [31] considered that the variation in temperature will affect the spatial structure and composition of sludge and change its rheological properties irreversibly. Baroutian et al. [32] believed that when sludge was heated, the cohesion between molecules decreased due to the thermal movement, which led to the decrease in shear stress and viscosity. Meanwhile, studies have shown that the increase in temperature will enhance the activity of microorganisms in sludge, which also leads to a decrease in cohesion between sludge particles and a decrease in dynamic viscosity [11]. Dong Yujing et al.’s [25] research results showed that when the temperature rose from 283 K to 343 K, the limiting viscosity of sludge with a concentration of 32.1 × 10³ kg/m³ decreased from 26.3 mPa·s to 7.9 mPa·s. They attributed this phenomenon to the weakening of the network structure strength between particles at higher temperatures. All the above conclusions were basically consistent with the results of this experiment.

3.4. Sludge Rheological Model

From Figure 2, the viscosity of sludge decreased with the increase in shear rate, exhibiting shear thinning characteristics, and then tended to relatively stabilize. The rheological properties of sludge can be described using the Bingham or Herschel–Bulkley models (Equation (1)) [20,33].

The rheological properties of sludge at a temperature of 293 K and concentrations of 2.38%, 3.94%, and 5.39% were fitted using these two models. The fitting results are shown in Figure 6, Figure 7 and Figure 8. The results showed that the fitting accuracy of the Bingham model for three concentrations of sludge was high, with regression coefficients, R²,reaching 0.9795, 0.9871, and 0.9808. At the same time, the flow of sludge had an initial yield stress, and the yield stress values, which were 6.657 mPa, 30.823 mPa, and 98.727 mPa, increased with the increase in concentration.

When the Herschel–Bulkley model was used to fit the experimental data, the model accuracy was also adequately high, with regression coefficients, R²,reaching 0.9496, 0.9681 and 0.9667. Furthermore, the rheological indexes, n, corresponding to the Herschel–Bulkley model of sewage sludge experimental data with three different concentrations were 0.9221, 0.7481 and 1.1295, indicating that the sludge showed the characteristics of shear thinning when the concentrations were 2.38% and 3.94%, while the sludge had the shear expansion characteristics when the concentration was high enough, such as C_w = 5.39%. This phenomenon was consistent with the results of the influence of concentration on the rheological properties of sludge discussed above.

3.5. Case Study for Effective Post-Treatment

The purpose of investigating the steady-state rheological properties of sewage sludge is to determine the limiting viscosity of sludge, which can be used as the basis for calculating pipeline transportation resistance and selecting a pump. Taking a circular, long, and straight pipeline as an example, the calculation process of flow resistance and pump power during sludge transportation were briefly analyzed using the following steps:

(1)

Calculate the Reynolds number of the flow using the limiting viscosity obtained in the experiment with Equation (2):

$$Re=\frac{vd}{\nu }$$

(2)

where:

• Re—Reynolds number;
• $v$—velocity of flow (m/s);
• $d$—pipe diameter (m);
• $\nu$—kinematic viscosity coefficient, that is, the ratio of limiting viscosity to sludge density.

(2)

Use the Muddy diagram to obtain the friction coefficient $\lambda$ combined with the relative roughness coefficient ($\frac{k_s}{d}$) of the pipe and Re:

$$\lambda =\lambda \left(\mathit{Re}, \frac{k_s}{d}\right)$$

(3)

where:

• $\lambda$—friction coefficient;
• $\frac{k_s}{d}$—relative roughness coefficient.

(3)

Calculate the frictional head loss using the Darcy–Weisbach formula:

$$h_f=\mathsf{\lambda }\frac{l}{d}·\frac{v^2}{2g}$$

(4)

where:

• $h_f$—frictional head loss, m;
• $l$—pipeline length, m;
• $\mathrm{g}$—acceleration of gravity, m/s².

(4)

Determine the pump power N:

$$\mathit{N}=\mathit{\rho }\mathit{gQH}/1000\mathit{\eta }=\mathit{\rho }\mathit{gQ}({\mathit{H}}_{\mathit{S}\mathit{T}}+{\mathit{h}}_{\mathit{f}})/1000\mathit{\eta }$$

(5)

where:

• N—power of delivery pump, kW;
• H—pump lift, m;
• ρ—density of sludge, kg/m³;
• η—efficiency of delivery pump, %;
• H_ST—static lift of delivery pump, m.

4. Conclusions

In the experimental analysis, to examine the effect of sludge concentration and temperature on the sludge rheology, it was deduced that, under the action of shear stress, the flocculent network structure inside the sludge was destroyed and exhibited relaxation characteristics; that is, the sludge sample had the characteristics of thixotropy or shear thinning. The rheological properties of sludge can be described using the Bingham and Herschel–Bulkley models. Concentration had a great influence on the rheological properties of sludge. In the experiment, the limiting viscosity of sludge with different concentrations showed an upward trend with the increase in concentration, which was caused by the differences in the internal flocculent network structure of sludge with different concentrations and fluid flow effects. Therefore, the influence of sludge concentration should be considered in the design of sludge-conveying pipeline. Again, under the same concentration, the viscosity of sludge decreased with the increase in temperature, so increasing the temperature of sludge properly is beneficial to reduce the flow resistance of sludge. In actual operation, running the sludge-conveying pipeline at a low temperature should be avoided, or it should be properly insulated.