## Abstract

*Jatropha curcas* (JC) is a highly effective conditioner in dewatering fecal sludge (FS); however, there are limited studies on the model predicting its optimal dose. This study presents the results of the developed model for predicting JC optimal doses. The developed model assessed the FS parameters and JC stock solution. We analyzed the FS samples from a mixture of a pit latrine and septic tank at the water quality laboratory of the University of Dar es Salaam. The multiple linear regression model was used to establish a relationship between JC optimal dose as a function of FS characteristics (pH, electrical conductivity, total solids, total suspended solids and concentration of the JC stock solution). The results indicated that 90.4% of the JC optimum dosage was determined and contributed by FS characteristics and JC stock solution concentrations. Also, the main explanatory factors determining the JC optimal dose were the JC stock solution concentration, followed by the pH of FS. The model results showed a good agreement between the predicted and observed JC optimal dose with a coefficient of determination of *R*^{2} = 0.904 and 0.7879 for calibration and validation, respectively. Therefore, the model can be adapted to determine the JC optimal dose without running the jar test experiment.

## HIGHLIGHTS

Effects of physical–chemical characteristics of fecal sludge on

*Jatropha curcas*dose.Physical–chemical predictor of fecal sludge on dewaterability.

Concentration of

*J. curcas*solution on the optimal dose of*J. curcas*.*J. curcas*optimal dose model.*J. curcas*optimal modal validation.

## INTRODUCTION

Globally, the eruption of the COVID-19 crisis caused enormous disruption to Sustainable Development Goals (SDGs). Nevertheless, even before the pandemic, the world was totally off track to meeting the United Nations Global SDG, especially sanitation-related target 6.2. Recently research reported that only 600 million people are using improved sanitation services (WHO and UNICEF 2019). About one-third of the world's population is estimated to rely on on-site sanitation systems (OSSs). The rest either practice open defecation or use unimproved facilities (WHO and UNICEF 2019). Communities in low- and middle-income countries are grappling to meet SDG 6 on basic sanitation services (Chandana & Bakul 2022). About 80% of the population in Sub-Saharan African (SSA) countries still depend on poor and inadequate OSSs as a solution to achieving SDG 6, target 6.2 (Alix *et al.* 2021). For example, in Dar es Salaam, the fastest-growing city in Tanzania, about 90% of its population uses the OSS for their sanitation needs (Artwell *et al.* 2021; Seleman *et al.* 2021). The enormous amount of water in fecal sludge (FS) is one of the significant challenges and concerns of FS management (FSM) (Strande *et al.* 2018).

This enormous amount of water in FS typically causes the problem of high cost in transporting liquid sludge and difficulty in subsequent treatment processes (Semiyaga *et al.* 2017). Therefore, FS must be dewatered before any other treatment process (Getahum *et al.* 2020). It was reported that the common, simplest, cheapest technology for dewatering FS is sand-drying beds. However, this technology takes a long time to dewater FS and occupies large areas (Gold *et al.* 2016). Several strategies are available to enhance FS dewatering with different conventional conditioners like aluminum sulfate. However, in developing countries, there are disadvantages such as a relatively higher cost and they contaminate the soil due to their high ion concentrations (Semiyaga *et al.* 2017; Djeffal *et al.* 2021).

The local physical conditioners, including sawdust and char material, and animal-based (chitosan) and plant-based (*Moringa oleifera* and *Jatropha curcas* (JC)) conditioners, have been analyzed in enhanced dewatering of the FS (Gold *et al.* 2016; Semiyaga *et al.* 2017). In addition, studies indicate that JC efficiently tackles the challenges of conventional conditioners on sand-drying beds. It contains proteins that enhance the FS dewatering process at an optimal dose (Gold *et al.* 2016). The jar test is a common method that has been widely used to obtain the optimal amount of conditioners including JC for FS dewatering (Gold *et al.* 2016; Semiyaga *et al.* 2017); but this is an uneconomical method as it is a trial-and-error practice that consumes a lot of time and materials.

Although FS characteristics and conditioner concentration are known to influence the optimal dose of JC required for FS dewatering, its relationship with the JC optimal dose has yet to be investigated and documented. Therefore, this study attempted to develop an empirical relationship explaining the factors determining the JC optimal dosage to improve FS dewatering. A multiple linear regression (MLR) model was used to determine the relationship. The investigated factors include the FS characteristics and concentration of the JC stock solution.

## MATERIALS AND METHODS

### Study approach

### Data collection approach

#### The source of FS and the sampling procedure

*et al.*2017). We collected about 180 samples in the first phase for model calibration and 30 samples for model validation. Samples were collected from six FS trucks from pit latrine and septic tanks and were analyzed, whereby a total of 120 trucks were involved in the study. The trucks had varying capacities ranging from 10 to 15 m

^{3}. Samples were collected directly from the truck during discharging. The sampling process involved three phases: the first phase was at the beginning of the truck discharging of the sludge when the truck tank volume was full. Second, a 20-l sample was collected in the middle of discharge when the truck tank volume was half full, as indicated by the gauge. The last one is at the end of the disposal. The trucks collected 10 m

^{3}of FS samples from the pit latrine and septic tank at three different sampling intervals. The samples from all three phases were thoroughly poured into mixing tanks to harmonize them. After that, the composing sample was re-sampled in 10-l containers for laboratory analysis, as shown in Figure 2. We adopted this sampling protocol from the study by Bassan

*et al.*(2013), and we repeated the same process in the analysis of all samples.

#### FS sample analysis

Physical–chemical parameters of FS that affect FS dewaterability were analyzed. These parameters include temperature, pH, electrical conductivity (EC), total solids (TS), total suspended solids (TSS) and total volatile solids (TVS). All FS parameters were analyzed according to the Standard Methods for Examination of Water and Wastewater (APHA *et al.* 2017). In addition, the pH and temperature of the FS were measured *in situ* using a digital pH measuring kit with a probe (pH meter PT-15), and the EC was measured in the field with a Metrohm E587 conductivity meter. Finally, the laboratory used the gravimetric method to determine TS, TSS and TVS.

#### Source and preparation of JC seed powder

*et al.*1995). The dry seeds were blended by using a kitchen blender to make seed powder (Figure 3(b)).

##### Oil extraction ad preparation of fine JC seed powder

*et al.*2017). First, 40 g of powder was determined on an analytical balance (Sartorius BS 124S, Germany). Next, the weight was put into a thimble (Porous cartridge). The thimble was set into the Soxhlet apparatus for condensation (Figure 4(a)). The match condenser pipe was connected to tap water for cooling. The reaction applied 400 ml of petroleum ether as a solvent. An electric iron stove was used for heating at 100 °C for 4 h to allow complete extraction of oil. The oil and solvents were collected in the bottom of the conical flask. The mixture was discharged as waste, and the defecated cake yield was retained as a resource for other processes.

The cake was removed from the thimble bag and dried at room temperature for 15 min to allow total dryness (Figure 4(a)). Then, the cake was crushed to obtain fine particles; the fine particles were sieved using a sieve of 0.8, 0.78, 0.75, 0.7, 0.68, 0.65, 0.6 and the last sieve size obtained in the chemistry laboratory of 0.58 mm to get very fine seed powder (Figure 4(c)).

#### Preparation of the JC conditioner stock solution

The conditioner stock solution was prepared separately using salt (0.6 M of NaCl). Active coagulant agents from conditioners were extracted by dissolving 4–7 g of seed powder in 100 ml of distilled water and 100 ml of NaCl solution. Fifteen samples of FS were used to test FS dewatering performance to get an appropriate solvent that maximizes coagulants agents' extraction. The salting effect improved the extraction process by eluting more coagulation agents from yield conditioners JC seed powder (Ndabigengesere *et al.* 1995). The active coagulant of *JC* seed was extracted by dissolving 1–10 g of powder in 100 ml of NaCl solution (0.6 M) to make a 1–10 w/v% solution. The solution was blended using a magnetic stirrer for about 30 min. To be accurate and systematic, all suspension was filtered first with 0.2–0.85 mm pore size filters. The filter size belongs to 0.2 mm clogging where no filtrate is obtained, and for a filter size greater than 0.85 mm, most of the solid particles pass through the filter and cause chemical oxygen demand (COD) in the solution. Because the active agent was obtained after filtration, the concentration of the active coagulant was expressed in milliliter of the added amount per FS volume using the jar test experiment.

#### The functionality of the JC optimal dosage models

The optimal dosage models for *JC* conditioner enhance the dewatering of mixed FS from pit latrine and septic tanks. The powdered seeds, which extracted oil using petroleum ether for 4 h, were used. The stock solution concentration of conditioners is made up using salt (NaCl) solution with 0.58 mm of fine seed powder.

#### Determination of the appropriate concentration of the JC conditioner stock solution

Three trial experiments were conducted to determine the JC stock solution that would give the best FS dewaterability results. It was undertaken for 30 different FS samples tested with JC stock solution concentrations ranging from 1 to 10 w/v%. First, FS samples were tested with a stock solution of 1–2 w/v%. Second, FS samples were dosed with a stock solution of 3–5 w/v%; finally, FS samples were dosed with a concentration of 5–10 w/v%.

#### Determination of JC optimal dosage

##### Jar test experiment

*et al.*(2017), the commonly and widely used method was the jar test experiment to determine the optimal dose. Each of six beakers of 1,000 ml was filled with 800 ml of FS samples. The samples were placed in the jar tester, with one of them being a control. Paddles were inserted in each beaker; the paddles were set at a stirring speed of 100 rpm for 1 min after the prepared stock solution of conditioner JC was dosed (Figure 5). The dosage was done separately for three w/v (%) −5 w/v (%) by varying volumes of the stock solution ranging from 5 to 50 ml depending on the concentration of the stock solution and FS characteristics. Each dosage was done for the JC conditioner; the process was repeated for 280 dosages. Later on, the stirring speed was reduced to 35 rpm for 20 min. This was done to promote flocs formation by enhancing particle collision. 20 and 50 ml of samples were taken immediately after the mixer was switched off. As optimization parameters, the samples were taken to analyze dewatering time, extent and settling particles.

##### Dewatering rate (CST experiments)

*et al.*2017). 20 ml of sample from the jar test experiment was divided into portions of 5 ml for analysis. The test was done in triplicates for every new batch of samples to minimize errors. The analysis was done using the CST instrument (Type 304, Triton, England, UK), equipped with an 18-mm diameter reservoir funnel and chromatography paper. Triplicate readings of CTS were recorded for distilled water for every new batch of CST. Then, the CST (seconds) was obtained by subtracting the CST reading of distilled water (seconds) from the CST reading of the sample (seconds). The sample determined the optimal dosage with a dewatering rate of at least 75% (Equation (1)).where blank = sample without conditioner and sample = sample with conditioner.

##### Dewatering extent (%TS in dry cakes) experiment

The dewatering extent was done to determine the percentage of solids in the cake using a centrifuge apparatus (APHA *et al.* 2017). 50 ml of sample from the jar test experiment was filled in a centrifuge tube and centrifuged at 3,000 rpm for 20 min in a MISTRAL 1000-type UK machine. The supernatant, after centrifugation, was decanted. The remaining solids were transferred into an empty crucible placed in an oven operating at 105 °C to determine TS. The sample with a high concentration of TS or less water content was regarded as the sample with a suitable dosage.

### Data analysis

#### Analysis of general optimal dose predictors

Descriptive statistics were used to analyze the FS dewaterability predictors. Q–Q diagrams and Shapiro numbers were used to analyze the normality of FS explanatory variables. The factor analysis (FA) was used to determine all factors that affect the JC optimal dose model (Landau & Everitt 2004). The MLR model was used to understand the relationship between the explanatory variables (FS parameters and the JC stock solution) and the response variable (JC optimum dose) (Mendenhall & Sincich 2012; Keith 2014). The Variance Inflation Factor (VIF) was used to analyze the multi-collinearity among a set of explanatory variables (Landau & Everitt 2004). A scatter plot diagram was employed to determine the linear relationship between each explanatory variable (*X*-values) and the response variable (*Y*-values). Plots of the standardized residuals and predicted values were used to test the homoscedasticity. The *R*^{2} values were used to determine the performance of the developed model (Montgomery & Runger 2014). The model development was performed using R-software. Furthermore, the Kruskal–Wallis test was performed to examine the significance of the explanatory variables in the model (Montgomery & Runger 2014). The *p*-value for the *F*-statistic was used to test the significance of the model at the level of significance of *α* ≤ 0.05 (Mendenhall & Sincich 2012; Gold *et al.* 2018).

#### Model development

##### MLR for JC optimal dosage model development

*Y*, and the explanatory variables are represented by

*X*

_{1},

*X*

_{2}and

*X*

_{3}for pH, EC, TS, TSS of FS, and

*X*

_{4}for a concentration of conditioners’ stock solution. Coefficients of the explanatory variable denoted by , this explained the influence of the explanatory variables on the optimal dosage model. The relationship between the response and the explanatory variables is represented by the following equation.where ,

*j*= 0, 1, 2, 3, 4……….

*K*are regression coefficients for explanatory variables and is an error term assumed to be normally distributed with the properties. The MLR model was developed starting with the linear combination of the response variable with the explanatory variables. The process of developing and analyzing the model was performed using R-software to obtain the following equation

#### Model assumptions and their tests

In this study, three critical assumptions were made to satisfy the application of the MLR model and establish its validity. The assumptions include multi-collinearity, independence of errors and homoscedasticity. The assumption was tested using the statistical package and R-software. The linear relationship between each explanatory variable and the response variable was determined by constructing a scatter plot for the explanatory variables against the response variable *Y*.

*Multi-collinearity* among a set of explanatory variables was examined by a VIF. The VIFs above 10 are a cause of multi-collinearity among explanatory variables. Therefore, the explanatory variables with a high VIF (VIF above 10) imply that another explanatory variable can explain their effects on the model within the model, and they are excluded (Landau & Everitt 2004).

*The Durbin–Watson statistic* was used to determine the independence of error. The Durbin–Watson statistic is generally ranging from 0 to 4. The values between 1.5 and 2.5 mean that the errors are independent of one another (uncorrelated). If the value approaches 0, it indicates an increasingly stronger positive correlation and values toward 4 show stronger negative correlations (Garson 2012).

*Homoscedasticity,* the plot of the standardized residuals (the errors) against the standardized predicted values, is used to test the variance of the error term. When this assumption is satisfied, residuals typically form a non-pattern cloud of dots around the regression line (Keith 2014) when the assumptions of the MLR model (1) were satisfied.

#### Validation of the developed MLR model

The coefficient of determination *R*^{2} and adjusted coefficient of determination *R*^{−2} were computed. The *R*^{2} was used to measure the model's usefulness for predicting the conditioner's optimal dosage as a response variable. The *R*^{2} depicts how well explanatory variables can explain the response variable. *R*^{−2} has a similar interpretation as *R*^{2}. However, it attempts to improve the estimation of *R*^{2}. *R*^{2} takes on values between 0 and 1, and *R*^{−2} is always smaller than *R*^{2}. The predictive power of explanatory variables increases as the values of *R*^{2} move from 0 to 1. Suppose the extreme value of the coefficient of determination is zero. In that case, it implies that the model explains none of the variability of the response data around its mean. If it is one, it indicates that the predictor variables explain all variations in the suggested model and that the fit is perfect.

#### Coefficient of explanatory variables

The model parameters were estimated using R-software sample data to give the observations’ best fit (Montgomery & Runger 2014). The values of explain well the influence of parameters on the optimal model. Furthermore, the significance of the model was examined using statistical tools/tests where the hypothesis was tested. The null hypothesis test that (intercept-only model) against the alternative hypothesis. At least one of the parameters listed differs from (the predictor dependence model) (Mendenhall & Sincich 2012).

##### Interrelationship of model predictors

The correlation between the explanatory variable was determined using R-software. For the variable that shows the same influence in the model, only one variable was taken to develop the model.

#### Level of significance of the model

The *p*-value for the *F-*statistic was used to test the significance of the model at the level of significance of *α* = 0.05. The model with predictors is considered significant if the *F*-value is greater than the significance level (i.e., relationships exist between the response variable and explanatory variables). On the other hand, suppose the *F*-value is less than the significance level. In that case, the model with no predictor is significant (no relationship between the response variable and explanatory variables) (Graybill & Iyer 1994; Mendenhall & Sincich 2012).

## RESULTS AND DISCUSSION

### Description of FS characteristics and JC concentration

Results of FS physical–chemical characteristics and concentration of a JC stock solution and that of existing literature values are presented in Table 1. The FS characteristic values and the variability observed in this study are similar to those reported in other studies. The average TSS concentration from this study was in the range of reported average TSS concentrations of 1,048–7,568 mg/l. However, the TS concentration ranged from 4,587 to 22,572 mg/l, implying that the values of 10,063 + 8,434 mg/l were at the low end of the published range. FS samples from this study were a mixture of FS from pit latrines and septic tanks, which had dilution effects due to the use of water for anal cleansing. Moreover, TVS concentration values from this study were in the 130–30,256 mg/l range, whereas the published range was 200–38,480 mg/l. The findings indicated that the minimum EC values were lower than those reported in previous studies, which were 2,000 μS/cm.

Parameters . | Descriptive statistics of explanatory variables . | ||||||
---|---|---|---|---|---|---|---|

N
. | Min . | Max . | Mean . | STD . | p-values (α = 0.05)
. | Mean literature values . | |

T (^{o}C) | 180 | 25 | 31 | 26.95 | 1.99 | 0.68 | N/A |

pH | 180 | 5.6 | 8.8 | 6.9 | 0.07 | 0.0041** | 6.9–8.5^{a,c} |

EC (μS/cm) | 180 | 151 | 5,400 | 2,582 | 1,417 | 0.0023** | 2,000–18,000^{d} |

TS (mg/l) | 180 | 4,587 | 22,572 | 9,063 | 4,650 | 0.001** | 1,000–52,000^{b,d} |

TSS (mg/l) | 180 | 1,048 | 7,568 | 4,047 | 1,976 | 0.002** | 1,300–19,900^{f,g} |

TVS (mg/l) | 180 | 130 | 30,256 | 4,010 | 10.36 | 0.52 | 200–38,480^{e} |

Concentration (mg/l) | 180 | 3 | 5 | 4 | N/A |

Parameters . | Descriptive statistics of explanatory variables . | ||||||
---|---|---|---|---|---|---|---|

N
. | Min . | Max . | Mean . | STD . | p-values (α = 0.05)
. | Mean literature values . | |

T (^{o}C) | 180 | 25 | 31 | 26.95 | 1.99 | 0.68 | N/A |

pH | 180 | 5.6 | 8.8 | 6.9 | 0.07 | 0.0041** | 6.9–8.5^{a,c} |

EC (μS/cm) | 180 | 151 | 5,400 | 2,582 | 1,417 | 0.0023** | 2,000–18,000^{d} |

TS (mg/l) | 180 | 4,587 | 22,572 | 9,063 | 4,650 | 0.001** | 1,000–52,000^{b,d} |

TSS (mg/l) | 180 | 1,048 | 7,568 | 4,047 | 1,976 | 0.002** | 1,300–19,900^{f,g} |

TVS (mg/l) | 180 | 130 | 30,256 | 4,010 | 10.36 | 0.52 | 200–38,480^{e} |

Concentration (mg/l) | 180 | 3 | 5 | 4 | N/A |

### Fitness of explanatory variable in model development

The results of FA and model fitness information (*p*-values) on the assessment of suitable parameters (explanatory variables) determined that temperature (°C) and TVS (mg/l) had insignificant influence on the JC model development. This is due to low values of FA (<0.05) and higher *p*-values (>0.05) as compared to other explanatory variables (Table 2).

Explanatory variables . | p-values
. | FA values . |
---|---|---|

Temp (^{o}C) | 0.992 | 0.02 |

pH | 0.0003*** | 0.901 |

EC (μS/cm) | 0.041*** | 0.953 |

TS (mg/l) | 0.041*** | 0.977 |

TVS (mg/l) | 0.069 | 0.02 |

TSS (mg/l) | 0.044*** | 0.834 |

Concentration (w/v, %) | 0.0001*** | 0.987 |

Explanatory variables . | p-values
. | FA values . |
---|---|---|

Temp (^{o}C) | 0.992 | 0.02 |

pH | 0.0003*** | 0.901 |

EC (μS/cm) | 0.041*** | 0.953 |

TS (mg/l) | 0.041*** | 0.977 |

TVS (mg/l) | 0.069 | 0.02 |

TSS (mg/l) | 0.044*** | 0.834 |

Concentration (w/v, %) | 0.0001*** | 0.987 |

*Note:* Significant difference at *p* ≤ 0.05 and factor loading 0.3.

Similar observation on the influence of pH, EC, TS and TSS on FS dewatering was reported by Ward *et al.* (2019) and Gold *et al.* (2016). Moreover, the insignificant influence of temperature might be due to the small range of temperature variation in FS sludge samples.

### Normality of explanatory variable

*et al.*(2019), Ward

*et al.*(2019) and Semiyaga

*et al.*(2017). Therefore, all FS explanatory variables were analyzed using non-parametric tests.

### Interrelationship of explanatory variables

All the values of the relationship parameters involved in model development are within the range of −1 to +1 and less than 0.05 (Table 3). Therefore, every parameter is involved in the model development since no effect of one parameter on other parameters is observed. Moreover, the relationships between TS and pH, TSS, EC, and concentration of 3 w/v% are linear-positive. Therefore, an increase in TS leads to an increase in these parameters. This means that at 3 w/v%, a high amount of stock concentration is used to reach an optimal dosage at a high amount of TS. In addition, 4 and 5 w/v% show a negative linear relation with all other parameters (Table 2), which means increasing concentration decreases in the other parameters. As a result, at a high amount of TS, TSS, EC, and a small pH amount of stock concentration, conditioners of either 4 or 5 w/v% are desirable to meet the optimal dosage.

. | TS . | TSS . | EC . | pH . | 3 w/v% . | 4 w/v% . | 5 w/v% . |
---|---|---|---|---|---|---|---|

TS | 1.00 | ||||||

TSS | 0.0048 | 1.00 | |||||

EC | 0.039 | 0.00098 | 1.00 | ||||

pH | 0.0012 | −0.0024 | −0.0025 | 1.00 | |||

3 w/v% | 0.0039 | 0.0060 | 0.00053 | −0.0028 | 1.00 | ||

4 w/v% | −0.0023 | −0.0054 | −0.0058 | 0.0017 | −0.0029 | 1.00 | |

5 w/v% | −0.009 | −0.0033 | −0.0037 | −0.00014 | −0.00015 | −0.00019 | 1.00 |

. | TS . | TSS . | EC . | pH . | 3 w/v% . | 4 w/v% . | 5 w/v% . |
---|---|---|---|---|---|---|---|

TS | 1.00 | ||||||

TSS | 0.0048 | 1.00 | |||||

EC | 0.039 | 0.00098 | 1.00 | ||||

pH | 0.0012 | −0.0024 | −0.0025 | 1.00 | |||

3 w/v% | 0.0039 | 0.0060 | 0.00053 | −0.0028 | 1.00 | ||

4 w/v% | −0.0023 | −0.0054 | −0.0058 | 0.0017 | −0.0029 | 1.00 | |

5 w/v% | −0.009 | −0.0033 | −0.0037 | −0.00014 | −0.00015 | −0.00019 | 1.00 |

### Effects of the JC stock solution concentration on FS dewaterability performance (rate and extent)

A total of 10 stock solutions (1–10 w/v%) was prepared and tested for their dewaterability performance, and showed that no changes in dewatering time and dewatering extent (%TS in dry cake) were found for JC concentration of 1–2 w/v%. However, the stock solution of 3–5 w/v% showed a significant change, while 5–10 w/v% showed no further substantial changes in dewatering time and extent compared to that of 5 w/v% (Table 4).

Concentration of JC stock solution (w/v%) . | Dewatering time CST(s) . | Dewatering extent (%TS in dry cake) . | p-values (α ≤ 0.05)
. |
---|---|---|---|

Unconditioned (0) | 418 | 20 | 1 |

1 | 407 | 24 | 0.31 |

2 | 405 | 25.4 | 0.42 |

3 | 85 | 76.8 | 0.001 |

4 | 52 | 82 | 0.001** |

5 | 32 | 92 | 0.0001** |

6 | 31.5 | 92.5 | 0.0001** |

7 | 30.5 | 93 | 0.002** |

8 | 30 | 93.2 | 0.0001** |

9 | 29.5 | 94.2 | 0.001** |

10 | 29.3 | 94.8 | 0.0001** |

Concentration of JC stock solution (w/v%) . | Dewatering time CST(s) . | Dewatering extent (%TS in dry cake) . | p-values (α ≤ 0.05)
. |
---|---|---|---|

Unconditioned (0) | 418 | 20 | 1 |

1 | 407 | 24 | 0.31 |

2 | 405 | 25.4 | 0.42 |

3 | 85 | 76.8 | 0.001 |

4 | 52 | 82 | 0.001** |

5 | 32 | 92 | 0.0001** |

6 | 31.5 | 92.5 | 0.0001** |

7 | 30.5 | 93 | 0.002** |

8 | 30 | 93.2 | 0.0001** |

9 | 29.5 | 94.2 | 0.001** |

10 | 29.3 | 94.8 | 0.0001** |

This implies that the usability of JC stock solutions of 1–2 and 6–10 w/v% are not economically viable for FS dewaterability. Because 1–2 w/v% have shown no changes since it has the same meaning as unconditioned sludge. Moreover, the 6–10 w/v% showed no further changes from the JC stock concentration of 5 w/v%. Hence, instead of using the higher ranges (6–10 w/v%), the 5 w/v% serves the purpose. This study analyzed stock solution concentrations of 3–5 w/v% to determine the optimal dosage. A similar result of the JC stock solution concentration was reported by Gold *et al.* (2016), which showed 5 w/v% as the appropriate JC stock solution concentration in the dewatering of FS.

### Relationship between FS characteristics and the JC stock solution on dewatering time and extent

#### Relationship between TS and TSS on the dewaterability performance of FS in different JC stock concentrations

*p*= 0.0001,

*p*= 0.002 and

*p*= 0.007, respectively.

Similar results were reported by Gold *et al.* (2016), whereby the stock solution concentration of 5 w/v% demonstrated the variation of TS increase with CST reduction. This was associated with filter media clogging during the FS filtration process (Strande *et al.* 2014). Sidewise, the dewatering extent (%TS in dry cakes) increased linearly with the JC stock solution concentration for the same TS (mg/l) concentration. For an average TS concentration of 8,752 mg/l, the %TS in dry cakes were 59, 68 and 76% for 3, 4 and 5 w/v%, respectively (Figure 7(b)). Similar results were reported by Gold *et al.* (2016), that it is important to determine the optimal dosage of FS at high or low concentrations of JC stock solutions.

The results found that the TSS concentration (mg/l) negatively correlated with CST reduction (s), whereby increased TSS led to decreased CST. With mean FS TSS values of 1,461 mg/l, the CST was found to increase from 181, 398 and 500 s with an increased JC stock solution concentration of 3, 4 and 5 w/v%, respectively (Figure 7(c)). Gold *et al.* (2016) state that increasing TSS significantly influences CST reduction at a fixed stock solution concentration. TSS caused clogging of filter media during the dewatering process and hence prolonged the dewatering time of FS (Strande *et al.* 2014; Gold *et al.* 2016).

#### Relationship between EC and pH on dewaterability performance of FS in different JC stock concentrations

A positive correlation was observed for pH and CST reduction (s) in that the increased FS pH resulted in increased CST reduction time. Furthermore, the higher CST reduction time required a higher JC stock solution concentration dose. For a mean pH of 6.2, the CST reduction (s) was increasing from 181, 308 and 465 s for 3, 4 and 5 w/v%, respectively (Figure 8(c)). According to Abidin *et al.* (2011), the phenomenon is due to electrochemical factors affecting surface charge and coagulation properties. Similarly, the FS pH influenced the increasing concentration of %TS in dry cakes at varying JC stock solution concentrations. Also, the increased JC stock solution concentration led to an increasing concentration of %TS in dry cakes. For a mean pH of 5.1, the %TS in dry cakes was found to increase from 59, 68 to 76% for JC stock solution concentrations of 3, 4 and 5 w/v%, respectively (Figure 8(d)).

So, to reduce the dewatering time at concentrated pH, TS, EC and TSS in FS during the dewatering process, the JC stock solution concentration of optimal dosage of JC would be required. The optimal dosage concentration of the JC stock solution introduces the amino acid with positive charges, which dissolves in the negative charges introduced by FS with a high concentration of TS and TSS. The solutions' combination of positive and negative charges facilitates the floc formation. The amino acid in the JC stock solution concentration fastens the release of the surface charges between bonds of FS, reducing the time for releasing water from solids (Abidin *et al.* 2011). Also, a high amount of TS in dry FS is produced at the optimal dose due to the enhancement of large flocs formation. The dose is determined to be found at the JC stock solution concentration of 5 w/v%. A similar finding was reported by Gold *et al.* (2016), whereby the JC stock solution concentration of 5 w/v% was found to be the desired concentration in the determination of optimal dosage. This is important to be done to avoid the excessive usage or minimal usage of the stock solution concentration, which has high-cost implications. Using the high concentration of more than 5 w/v% stock solution concentration has no significant difference hence it makes no sense to use them. Therefore, the optimal JC stock solution was found to be a concentration of 5 w/v%, the usage of less or more stock solution concentration would not be economical and efficient. Using less concentration would not serve the purpose, and using more concentration would be economical.

### Influence of FS characteristics and concentrations of stock solution on JC optimal dose model

#### Influence of pH and stock solution concentration on JC optimal dose model

*et al.*(2011), whereby at lower pH values, the FS requires lower optimal dosage than at high values since, at low pH, the positive charges at amino acid make up the molecular protein dominates and hence enhance coagulation.

*R*

^{2}= 0.717. This means that pH and stock solution concentration significantly contribute to model development with

*p*= 0.001 and

*p*= 0.0001, respectively, at

*α*≤ 0.05. The optimal dose model for pH at different concentrations of the JC stock solution was developed as in Equation (4). The equation verifies that the JC stock solution concentration significantly influences reducing the amount of optimal dose with a 66.45 coefficient. Furthermore, the optimal dosage of JC is also lowered by pH, with a coefficient of 15.01. Meaning that the lower the pH, the low the optimal dose consumption

#### Influence of TS and stock solution concentration on JC optimal dose model

*et al.*(2016), where the dose was found to increase with increasing TS concentration of FS at a stock solution concentration of 5 w/v%.

*R*

^{2}= 0.826. This means that TS and the stock solution concentration influence model development with

*p*= 0.003 and

*p*= 0.0005, respectively, at

*α*≤ 0.05. The optimal dose model for TS at different concentrations of the JC stock solution was developed in R-software as in Equation (5). This equation justifies the good influence of the JC stock solution concentration on reducing the optimal dose amount with a 7.444 coefficient. However, the optimal dosage of JC is raised by increasing the TS concentration of FS with a coefficient of 0.004

#### Influence of EC and the stock solution concentration on JC optimal dose model

*et al.*(2019), where the dewatering is affected by EC concentrations of FS.

*R*

^{2}= 0.850. Furthermore, the results suggested that the combination of EC and concentration of stock solution predictors strongly contributed to the model development with

*p*= 0.002 and

*p*= 0.0004, respectively, at

*α*≤ 0.05. The optimal dose model for EC at different concentrations of the JC stock solution was developed as in Equation (6). From the equation, it can be concluded that the JC stock solution concentration has a fair influence on reducing the optimal dose amount with a 7.511 coefficient. Nevertheless, the optimal dosage of JC is raised by increasing the EC concentration of FS with a coefficient of 0.007.

#### Influence of TSS and the stock solution concentration on the JC optimal dose model

*et al.*(2016), whereby the TSS was found as an influencing variable in the determination of optimal dose.

*R*

^{2}= 0.882. The results indicated that a combination of TSS and concentration of stock solution predictors each have a fair contribution to the model development with

*p*= 0.004 and

*p*= 0.0003, respectively, at

*α*≤ 0.05. The optimal dose model for EC at different concentrations of the JC stock solution was developed as in Equation (7). Based on the equation, the JC stock solution concentration has a fair influence on the optimal dose reduction with a coefficient of 7.802. On the other hand, the TSS increases the optimal dose consumption with a coefficient of 0.002.

### MLR model for JC optimal dose

The combined JC optimal dose model was the function of FS explanatory variables and JC stock solution concentrations. The coefficient of determination, *R*^{2} value explained by all explanatory variables (FS explanatory variables and JC stock solution concentration), was found to be 0.904 (Table 5). Moreover, it was found that the explanatory variables contributed significantly to the prediction of JC optimal dose. The contribution was determined at *F*-statistic (*F*(5, 133) = 141.261) with *p* < 0. 0.001 at *α* = 0.05. Also, it was found that 90.4% of the JC optimum dosage was determined and contributed by FS characteristics and JC stock solution concentrations.

. | SS . | df. . | MS . | Number of observations = 180 . | . |
---|---|---|---|---|---|

Model | 26,946 | 5 | 5,389 | F(5, 133) = 141.261 | |

Residual | 2,861 | 75 | 38.15 | Prob. >F = 0.001 | |

Total | 29,807 | 80 | R^{2} = 0.904 | ||

R-Adjusted = 0.898 | |||||

Y . | coefficient . | Sth. err . | t . | p < ||t||
. | (95% Conf. interval) . |

Constant | 54.445 | 8.947 | 6.086 | 5.056 | *** |

pH | −4.101 | 1.046 | −3.922 | 0.003 | *** |

EC | 0.002 | 0.003 | 0.453 | 0.004 | *** |

TS | 0.004 | 0.001 | −0.917 | 0.002 | *** |

TSS | 0.001 | 0.001 | 4.007 | 0.004 | *** |

Conc. | −7.454 | 0.850 | −8.772 | 0.000 | *** |

. | SS . | df. . | MS . | Number of observations = 180 . | . |
---|---|---|---|---|---|

Model | 26,946 | 5 | 5,389 | F(5, 133) = 141.261 | |

Residual | 2,861 | 75 | 38.15 | Prob. >F = 0.001 | |

Total | 29,807 | 80 | R^{2} = 0.904 | ||

R-Adjusted = 0.898 | |||||

Y . | coefficient . | Sth. err . | t . | p < ||t||
. | (95% Conf. interval) . |

Constant | 54.445 | 8.947 | 6.086 | 5.056 | *** |

pH | −4.101 | 1.046 | −3.922 | 0.003 | *** |

EC | 0.002 | 0.003 | 0.453 | 0.004 | *** |

TS | 0.004 | 0.001 | −0.917 | 0.002 | *** |

TSS | 0.001 | 0.001 | 4.007 | 0.004 | *** |

Conc. | −7.454 | 0.850 | −8.772 | 0.000 | *** |

### Model assumptions

#### Multi-collinearity of explanatory variables

The multi-collinearity of explanatory variables, established by the VIFs and tolerance levels of numerical values for explanatory variables, was found to be less than 3. This means that each explanatory variable causes changes in the optimal dose of JC (*Y*) without disturbance from each other (Table 6).

Variables . | Multi-collinearity status . | |
---|---|---|

Tolerance . | VIF . | |

pH | 0.912 | 1.075 |

EC (μS/cm) | 0.814 | 1.336 |

TS (mg/l) | 0.930 | 1.256 |

TSS (mg/l) | 0.795 | 1.096 |

Conc. (mg/l) | 0.914 | 1.417 |

Variables . | Multi-collinearity status . | |
---|---|---|

Tolerance . | VIF . | |

pH | 0.912 | 1.075 |

EC (μS/cm) | 0.814 | 1.336 |

TS (mg/l) | 0.930 | 1.256 |

TSS (mg/l) | 0.795 | 1.096 |

Conc. (mg/l) | 0.914 | 1.417 |

#### Homoscedasticity

The errors between explanatory variables are small and independent from one another because the autocorrelation analysis done by using Durbin–Watson statistics was found to be 1.169. The value is lower than the accepted range of 1.5–2.5. The value of any two explanatory variables close to 2 is said to be in correlation with one another. Hence, the errors were uncorrelated and were all independent of different variables.

#### Linearity of explanatory variables over the response variable

### Model validation

The measured values of JC dose using the second data set were found to be near the same as predicted by the model (Table 7). Furthermore, the results after descriptive statistics of the explanatory variables showed no statistically significant difference between the mean dose obtained after laboratory analysis (experimental variables) and that obtained by the model (predicted optimal dose) at *p* = 0.003 with *α* = 0.05.

Descriptive statistics . | Characteristics of FS parameters . | MO stock solution parameters . | |||||
---|---|---|---|---|---|---|---|

pH . | EC (μS/cm) . | TS (mg/l) . | TSS (mg/l) . | Conc (w/v%) . | Predicted dose (mg/l) . | Lab dose (mg/l) . | |

N | 30 | 30 | 30 | 30 | 30 | 30 | |

Min | 6.8 | 151 | 4,587 | 1,048 | 4 | 25.3 | 22.1 |

Max | 6.92 | 5,400 | 22,572 | 7,568 | 7 | 60.3 | 56 |

STD | 0.07 | 1,417 | 4,650 | 1,976 | 1.14 | 9.7 | 9.2 |

Mean | 6.9 | 2,582 | 9,063 | 4,047 | 5.5 | 40 | 37 |

p-values (α = 0.05) | 0.0042** | 0.0024** | 0.0011** | 0.0211** | 0.001** | 0.003 | 0.003 |

Descriptive statistics . | Characteristics of FS parameters . | MO stock solution parameters . | |||||
---|---|---|---|---|---|---|---|

pH . | EC (μS/cm) . | TS (mg/l) . | TSS (mg/l) . | Conc (w/v%) . | Predicted dose (mg/l) . | Lab dose (mg/l) . | |

N | 30 | 30 | 30 | 30 | 30 | 30 | |

Min | 6.8 | 151 | 4,587 | 1,048 | 4 | 25.3 | 22.1 |

Max | 6.92 | 5,400 | 22,572 | 7,568 | 7 | 60.3 | 56 |

STD | 0.07 | 1,417 | 4,650 | 1,976 | 1.14 | 9.7 | 9.2 |

Mean | 6.9 | 2,582 | 9,063 | 4,047 | 5.5 | 40 | 37 |

p-values (α = 0.05) | 0.0042** | 0.0024** | 0.0011** | 0.0211** | 0.001** | 0.003 | 0.003 |

*R*

^{2}. It was found that the experimental results were well fitted to the predicted one, hence strongly correlated to each other with

*R*

^{2}= 0.7879 (Figure 15).

The validation verified that the model could predict the JC optimal dose in the FS dewatering process. The main explanatory variables that influence the JC optimal dose model are the JC stock solution concentration (w/v%), pH, TS (mg/l), EC (μS/cm) and TSS (mg/l). Moreover, the optimal dose was found at the JC stock solution concentration of 5 w/v%.

## CONCLUSION AND RECOMMENDATION

Upon analysis of the stock solution concentration, the JC stock solution concentration ranging from 3, 4 and 5 w/v% fitted the model development. The CST reduction and %TS in dry cakes increased with increasing JC stock solution concentrations. Moreover, the stock solution concentration was the highest influence in developing the optimal model for both JC. The optimal dose for JC was found at a stock solution concentration of 5 w/v%. Additionally, the coefficient of determination (*R*^{2}) for JC was 0.904. Also, following model validation, the accuracy of the JC model is 78.79%. Using the model was found to meet the aim of dewatering by reducing time and increasing dry solids (%TS in dry sludge). This is the economic potential to meet SDG6 targets 6.2 and 6.3. The developed model is essential and can be applied for optimal dose prediction for FS dewatering in FS treatment plants.

## DATA AVAILABILITY STATEMENT

All relevant data are included in the paper or its Supplementary Information.

## CONFLICT OF INTEREST

The authors declare there is no conflict.