Model for prediction of the optimal dose of Jatropha curcas in FS dewatering

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.

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.

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)).

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 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.

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%.

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.

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 R² 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).

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.

The coefficient of determination R² and adjusted coefficient of determination R⁻² were computed. The R² was used to measure the model's usefulness for predicting the conditioner's optimal dosage as a response variable. The R² depicts how well explanatory variables can explain the response variable. R⁻² has a similar interpretation as R². However, it attempts to improve the estimation of R². R² takes on values between 0 and 1, and R⁻² is always smaller than R². The predictive power of explanatory variables increases as the values of R² 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.

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).

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.

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 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.

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).

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.

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.

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).

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.

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).

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.

The combined JC optimal dose model was the function of FS explanatory variables and JC stock solution concentrations. The coefficient of determination, R² 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.

Table 5

Stata output for FS explanatory variables, JC stock solutions concentrations and JC optimal dosage

.	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		R2 = 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		R2 = 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	***

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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).

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.

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.

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%.

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 (R²) 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.

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

The authors declare there is no conflict.