*3.3.3 Yield stress*

The process conditions affecting the yield stress were evaluated. The experimental yield stress values obtained during the test runs ranged from to 0.86 Pa to 48.70 Pa. No transformation of the data was required according to the Box-Cox theory. In this case, parameters B, C, aB, and BD were found to be significant at the 5% level as shown in **Table 5**. In the case of the yield stress, the linear screen speed is not significant, but there is an interaction between belt speed and linear screen speed. The adjusted R2 is 0.78.

Eq. (6) shows the coded equation and Eq. (7) the actual equation.



$$\text{Yield stress} = 24.1843 + 2.24613\mathbf{a} + 4.38\mathbf{B} - 13.38\mathbf{C} - 1.277\mathbf{D} + 1.581\mathbf{E} + 3.833\mathbf{a}\mathbf{B}$$

$$-5.554\mathbf{B}\mathbf{D} - 3.0768\mathbf{D}\mathbf{E} - 5.33\mathbf{D}^2$$

$$\begin{aligned} \text{Yield stress} &= -848 - 333\mathbf{a} + 334\mathbf{B} - 1.35\mathbf{C} + 30.5\mathbf{D} \\ &+ 5.84184\mathbf{E} + 754\mathbf{a}\mathbf{B} - 10.6\mathbf{B}\mathbf{D} - 0.1223\mathbf{D}\mathbf{E} - 0.194\mathbf{D}^2 \end{aligned} \tag{7}$$

(6)

#### *3.3.4 Solid capture*

The experimental values obtained for solid capture ranged from 66.5 to 95.6%. The significant model terms are C, aC, aD, aE, CD, DE, and B<sup>2</sup> as shown in **Table 6**.

Eq. (8) shows the coded equation and Eq. (9) the actual equation.

$$\begin{aligned} \text{Solid capture} &= 93.5726 + 1.213 \mathbf{\hat{a}} + 0.787295 \mathbf{\hat{B}} - 2.380 \mathbf{\hat{C}} - 1.369 \mathbf{\hat{D}} - 0.608 \mathbf{\hat{E}} \\ &+ 2.82703 \mathbf{\hat{a}} \mathbf{\hat{C}} + 3.24954 \mathbf{\hat{a}} \mathbf{D} + 1.78 \mathbf{\hat{a}} \mathbf{\hat{E}} - 1.84 \mathbf{\hat{C}} \mathbf{D} - 2.34 \mathbf{\hat{D}} \mathbf{E} - 3.71 \mathbf{\hat{B}}^2 \end{aligned} \tag{8}$$
 
$$\begin{aligned} \text{Solid capture} &= -31.33 - 1256.6 \mathbf{\hat{a}} + 369.42 \mathbf{\hat{B}} - 0.215 \mathbf{\hat{C}} + 5.005 \mathbf{\hat{D}} + 2.912 \mathbf{\hat{E}} \\ &+ 6.11 \mathbf{\hat{a}} \mathbf{\hat{C}} + 12.36 \mathbf{\hat{a}} \mathbf{D} + 6.45 \mathbf{\hat{a}} \mathbf{\hat{E}} - 0.035 \mathbf{\hat{C}} \mathbf{D} - 0.1032 \mathbf{\hat{D}} \mathbf{E} - 361.3 \mathbf{\hat{B}}^2 \end{aligned} \tag{9}$$

The normal probability plot (**Figure 8**) of the residuals is approximately linear. Removing run 4 from the analysis could improve the adjusted R2 from 68% to 71%, but the assumption that Run 4 is due to experimental error and based on experience it is not. Such a change to improve the statistics will also result in significant factor changing from polymer dosing ( B2 ) to linear screen speed (E2) in the final equation.


**Table 6.** *ANOVA for solid capture.*

**Figure 8.**

*Normal probability plot of residuals for solid capture.*

### **4. Results and discussion**

In order to understand the effect of the process conditions on belt filter press performance, 3D surface plots are utilized **Figure 9a** shows FSS as a function of sludge feed and polymer dosing at the lowest polymer concentration, belt speed, and linear screen speed. The filtrate suspended solids were all below 1 g/L. A minimum value of FSS is obtained at the maximum sludge flow rate and a medium polymer dosing rate due to process interaction. The situation remains the same if all the conditions are set at the maximum values as shown in **Figure 9b**.

When the polymer concentration is minimized with maximum belt and linear screen speed, the FSS is above 1 g/L. However, an acceptable FSS can be obtained by dosing the polymer at 0.5 m<sup>3</sup> /hr, which is the midpoint. This interaction between polymer dosing and sludge flow rate is very useful to obtain acceptable FSS at high production rates as shown in **Figure 9c**. Furthermore, the amount of polymer usage can be reduced by decreasing the linear screen speed to the minimum and the sludge feed rate to just under the maximum at 59 m<sup>3</sup> /hr; the resulting FSS will be below 1 g/L as shown in **Figure 9d**.

#### **Figure 9.**

*3D surface plot of FSS as a function of sludge feed and polymer dosing.*

To ascertain the performance of the filter cake, the prediction of cake solids is presented under the similar conditions as for the FSS. In contrast to the FSS, the cake solids increase linearly with increasing polymer dosage, with no minima or maxima observed at maximum sludge feed rate. **Figure 10a** shows that at the minimum settings for polymer concentration, belt and linear screen speed, the maximum cake solids of almost 14% can be obtained at the maximum polymer dosing rate and maximum sludge feed rate. Increasing the parameters has a detrimental effect on the cake solids, unlike the case of filtrate suspended solids, and a maximum of 13% cake solids are obtained at the minimum sludge feed rate and maximum polymer dosing as

#### **Figure 10.**

*3D surface plot of cake solids as a function of sludge feed and polymer dosing.*

shown in **Figure 10b**. However, surprisingly, by minimizing the polymer concentration, production can be increased and maximum sludge feed rate and maximum polymer dosing with result in 13% cake solids. It should also be noted that the design point is higher than the prediction under these conditions as shown in **Figure 10c**. Similarly to the FSS, when reducing the linear screen speed, the cake solids can be improved by nearly 1% as seen in **Figure 10d**. Even though better FSS can be obtained

*Optimization of Polymer Dosing for Improved Belt Press Performance in Wastewater… DOI: http://dx.doi.org/10.5772/intechopen.108978*

**Figure 11.**

*3D surface plot of solid capture as a function of sludge feed and polymer dosing.*

at the medium polymer dosing rate, the maximum polymer dosing rate is required for the maximum cake solids, and based on the prediction, the FSS will still be within the 1 g/L limit. A detailed study of polymer cost versus cake removal costs is needed to manage these limits to an optimum.

For the solid capture, similar graphs are presented in **Figure 11**. These are the inverse of FSS with a maximum obtained at the maximum sludge feed rate and the medium polymer dosing rate (**Figure 11a**). Running all conditions at maximum has


#### **Table 7.**

*Summary of significant main factors and interactions.*

limited impact on the performance of the belt filter press as shown in **Figure 11b**. Reducing the polymer concentration impacts the performance of the belt filter press negatively as the solid capture is reduced to less than 70% (**Figure 11c** compared with 90% under all minimum or all maximum conditions. Reducing the linear screen speed at the minimum polymer concentration improves the solids capture but only to midor low sludge feed rates as shown in **Figure 11d**, but it is ultimately the reduction of the belt speed at lower polymer concentration that will ensure maximum solid capture at high sludge flow rates (**Figure 11a**) at the mid-range polymer dosing rate.

A summary of the significant main factors and interactions is provided in **Table 7**. It shows that the polymer concentration is much more important than polymer dosing rate in interactions with the other conditions. Current practice in the plant is to keep the polymer concentration constant and to change polymer dosing rate. This work demonstrates that a control system that can incorporate changes to concentration is required for a fully automated polymer control system to reduce cost.

### **5. Conclusion**

A factorial trial was conducted at a WWTW to establish correlations to predict the filter belt press performance as a function of process conditions. Correlations to predict the FSS, Cake solids, Yield stress, and Solid Capture were developed based on the factorial trial design. From the results obtained, it was found that a power-law relationship exists between FSS and the yield stress. There is no relationship between the yield stress and the cake solids. The cake solids are affected by the linear screen speed and the interaction between the polymer concentration and sludge feed. It is recommended that more work be done around the optimization of the cake solids based on this information. It is also the only parameter for which the linear screen is the most significant factor, and the belt speed is insignificant in this case. An important outcome from this work is that it shows that changes in polymer concentration rather than polymer dosing rate are more important in the control system. This is contrary to current practice where the polymer concentration is constant and only the polymer dosing rate is adjusted.
