Christian Landry Yapi¹, Yapo Hermann Aristide Yapi¹, David Léonce Kouadio¹, Kouassi Serge Gbamélé², Issifou Ouattara Mama¹, Brou Dibi^1
1Laboratory of Environmental Sciences and Technologies, Jean Lorougnon Guédé University, Daloa, Côte d’Ivoire.
²Laboratory of Environmental Sciences, Training and Research Unit (UFR) of Environmental Sciences and Management, Nangui Abrogoua University, Abidjan, Côte d’Ivoire.
DOI: 10.4236/ojapps.2026.1611234   PDF    HTML   XML   0 Downloads   1 Views   Citations

Abstract

Eutrophication of surface waters, driven by excessive phosphorus discharges, constitutes a major threat to aquatic ecosystems. The objective of this work was to identify the best conditions for preparing a cocoa husk biosorbent intended for phosphate removal, using a design-of-experiments approach. After the key factors had been selected with a Plackett-Burman screening matrix, a two-level factorial design was carried out. Although globally significant (p = 0.021), the resulting linear model proved inadequate (adjusted R² = 63.88%), justifying recourse to a central composite design. The resulting quadratic model exhibited excellent statistical performance (R² = 97.16%; adjusted R² = 95.13%; coefficient of variation = 0.72%), confirming its predictive robustness. Optimization via the desirability function identified a NaOH concentration of 1 N and an activation time of 8 hours as the optimal conditions. During validation tests, a mean removal rate of 98.23% was obtained, in agreement with the predicted value of 99.67%. These results confirm the efficiency of the biosorbent and its competitiveness relative to commercial adsorbents.

Keywords

Biosorbent, Cocoa Husks, Phosphate, Central Composite Design, Response Surface

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1. Introduction

Eutrophication of aquatic environments is currently one of the major environmental challenges worldwide [1] [2]. This phenomenon primarily results from an excessive enrichment of aquatic ecosystems with nutrients, particularly nitrogen and phosphorus, originating from intensive agricultural activities, industrial effluents, and insufficiently treated domestic wastewater [3]. This nutrient overload promotes excessive proliferation of algae and aquatic plants, leading to a decrease in dissolved oxygen, alteration of biodiversity, degradation of water quality, and significant disturbances to the functioning of aquatic ecosystems [4] [5]. Among the nutrients responsible for this phenomenon, phosphorus is widely recognized as the primary limiting factor of eutrophication in continental waters [6]. In aquatic environments, it occurs in various chemical forms, notably as inorganic phosphates, organic phosphorus compounds, oligophosphates, and polyphosphates [3]. Even at low concentrations, phosphorus is sufficient to stimulate the growth of photosynthetic organisms and accelerate eutrophication: recent studies place the ecological threshold for total phosphorus at around 0.04 mg·L⁻¹ for surface waters [7]. Under the effect of anthropogenic discharges, this value is nevertheless frequently exceeded in many regions of the world. Moreover, according to [8], a significant proportion of the world’s population still depends on untreated surface waters, such as rivers, lakes, and other water bodies, for domestic needs, which reinforces the need to develop water treatment technologies that are effective, economically accessible, and environmentally friendly.

To reduce phosphorus concentrations in effluents, several treatment processes have been developed and widely implemented in wastewater treatment plants. Biological treatments rely on phosphorus assimilation by microorganisms [9] whereas physicochemical routes rely mainly on chemical precipitation with Ca, Fe or Al salts [10] or on coagulation-flocculation using alum [3]. Despite their effectiveness, these techniques present several limitations, notably high operating costs, sometimes complex implementation, substantial consumption of chemical reagents, and the generation of large quantities of secondary sludge requiring further treatment [11]. These drawbacks have encouraged the development of cheaper and greener treatment options.

Among the possible alternatives, adsorption on biosorbents derived from agricultural residues appears as a particularly promising technology. This approach offers numerous advantages, including relatively low cost, abundant availability of raw materials, simple implementation, high efficiency in pollutant removal, and a significant reduction in environmental impact [12] [13]. The use of agricultural waste as adsorbent materials also fits within a circular economy approach, valorizing residual biomass while contributing to the protection of water resources.

Our earlier screening work, based on Plackett-Burma matrix, identified the operating parameters that most strongly govern phosphate uptake [14]. The present paper extends these results by optimizing the way the biosorbent is prepared. A linear (first-order) model derived from a two-level full factorial design (FFD) is tested first, and a central composite design (CCD), which yields a quadratic model, is applied if the linear model proves inadequate. The performance of the developed model is finally compared with results reported in the literature to assess the robustness, reliability, and relevance of the methodological approach adopted.

2. Material and Methods

2.1. Biosorbent Preparation

The cocoa husks, supplied by farmers in the Daloa area (Côte d’Ivoire), were prepared according to the protocol described in our previous work [14]. Briefly, after washing and air-drying at room temperature, the biomass was mechanically ground using a Retsch SK 100 knife mill, then sieved to obtain the desired particle size fractions. The powder was then activated by immersion in a NaOH or H₂SO₄ solution kept under magnetic stirring (350 rpm), at concentrations, durations, and temperatures that varied according to the trial. The activated materials were successively rinsed with tap water and distilled water, then dried before use.

2.2. Investigation of the Optimal Biosorbent Preparation Conditions

Optimization of the biosorbent preparation conditions was carried out using experimental design methodology, a statistical approach that allows the simultaneous study of several parameters and of their interactions within a single series of runs, which the conventional one variable at a time strategy cannot achieve [15]. The phosphate ion removal rate (R, in %) was retained as the single response for evaluating the material’s efficiency. A preliminary screening study, carried out using a Plackett-Burman design (PBD), addressed seven preparation variables: biomass nature, particle size, activation time, activation temperature, solid/liquid ratio, type of activating agent, and concentration of the activating solution. Three parameters emerged as significant from this screening and were carried forward to the optimization step: activation temperature (X₁), activation time (X₂), and sodium hydroxide concentration (X₃) [14]. Their experimental domain is given in Table 1. These boundaries were defined based on the screening results, particularly the marked positive effect of the activating agent concentration. These three factors were subsequently studied by means of a full factorial design.

Table 1. Experimental domain of the full factorial design.

Factors	Low level	High level
Temperature (X1)	40˚C	80˚C
Duration (X2)	3 h	6 h
Normality (X3)	0.5 N	2.5 N

The design implemented is thus a duplicated three-factor full factorial design (2³), corresponding to 16 experimental runs.

The resulting first-degree polynomial model from this design is given by Equation (1).

$R=a_0+{\displaystyle {\sum }_{i=1}^k{a}_i{x}_i}+{\displaystyle {\sum }_{ij}{a}_{ij}{x}_i{x}_j}$ (1)

Here, $a_{ij}$ denotes the coefficients of the two-factor interactions. Response surface methodology was then applied through a central composite design (CCD) in order to model the removal rate and locate the optimum. A CCD combines three groups of runs: the 2^k points of a two-level factorial design (k being the number of factors), the axial (star) points, and replicated center points. It leads to the second-order polynomial of Equation (2):

$R=a_0+{\displaystyle \sum a_i{X}_i}+{\displaystyle \sum a_{ij}{X}_i{X}_j}+{\displaystyle \sum a_{ii}{X}_i^2}$ (2)

The $a_{ii}$ coefficients account for the curvature of the response (quadratic effects). Minitab 19 software was used to build the design matrices, estimate the regression coefficients and compute the statistical values for the different experimental designs.

2.3. Methods for Coefficient Evaluation and Model Validation

Each coefficient was tested by multiple linear regression and the overall model by analysis of variance (ANOVA) at the 5% significance level; terms with p > 0.05 were discarded. A model was regarded as adequate when its residual sum of squares was lower than one third of the regression sum of squares [16]. The quality of fit was further judged from R² and adjusted R² [17] and from Fisher’s F-test [18]. Predictive accuracy was expressed through the coefficient of variation (CV), defined as:

$C_V=\frac{1}{n}\left[{\displaystyle {\sum }_{i=1}^n\left|\frac{R_{\exp }-R_{\text{cal}}}{R_{\exp }}\right|}\right]\times 100$ (3)

where n is the number of runs, and R_exp and R_cal are the measured and predicted removal rates, respectively. A CV below 5% was taken as the acceptance criterion [19]. The optimum was located from the contour and three-dimensional response surface plots and then refined with the desirability function of Minitab 19.

2.4. Method for Evaluating the Phosphate Ion Removal Rate

The efficiency of each material was assessed through batch adsorption runs. In each run, 1 g of biosorbent was shaken with 25 mL of a 50 mg/L synthetic phosphate solution in a 100 mL Erlenmeyer flask. The pH was set at 4.7 with 1 N H₂SO₄ or 1 M NaOH, following [3]. The suspensions were stirred magnetically at 300 rpm for 2 h at room temperature and then centrifuged at 4000 rpm for 12 min. The residual phosphate concentration in the supernatant was measured by UV-Visible spectrophotometry at 880 nm, and the removal rate was calculated as follows:

$R=\frac{C_0-C_e}{C_0}\times 100$ (4)

R: phosphate ion removal rate (%)

C₀: initial phosphate ion concentration (mg/L)

C_e: residual phosphate ion concentration (mg/L)

3. Results and Discussion

3.1. First-Degree Model: Full Factorial Design (FFD)

Figure 1 reports the removal rate R (%) obtained for the eight factorial combinations, each run in duplicate.

Removal varied from 66.2% (run 1) to 85.0% (run 8). The lowest response is higher than the lowest one recorded during the screening stage, which indicates that the biosorbent was improved. The mean and median of the responses (76.8% and 79.3%, respectively) are close to each other, which points to a roughly symmetrical distribution of the data [20].

Figure 1. Results of the full factorial design.

Regression of the factorial data in Minitab gave the following linear model, where R₁ is the predicted removal rate:

$\begin{array}{c}{R}_1=44.2+0.134X_1+5.63X_2+18.5X_3-0.019X_1\ast X_2\\ -0.205X_1\ast X_3-2.90X_2\ast X_3+0.036X_1\ast X_2\ast X_3\end{array}$ (5)

The ANOVA of the factorial model is reported in Table 2.

Table 2. Analysis of variance for the full factorial design.

Sources	DF	Adj SS	Adj MS	F-value	p-value
Model	7	632.249	90.321	4.9	0.021
Error	8	150.845	18.856
Pure error	4	3.411	0.853
Total	15	783.094
R2	80.74%
${\text{R}}_{\text{A}}^2$	63.88%

With a p-value of 0.021, below the 0.05 threshold, the ANOVA in Table 2 shows that the linear model is significant as a whole; in other words, the factors studied do affect the removal efficiency [15].

However, closer examination of the other statistical parameters reveals that the linear model cannot be validated, in accordance with the methodological criteria reported by [3] [21]. Indeed, although the model sum of squares is relatively high (632.249), the error sum of squares remains substantial (150.845), reflecting non-negligible dispersion of the residuals [3]. This situation indicates that the model fails to satisfactorily explain the variability observed in the experimental data. Moreover, the presence of a low pure error (3.411) compared to the total error suggests that the observed discrepancy is mainly due to model inadequacy rather than random experimental error [21]. This confirms that the linear structure of the model does not correctly describe the actual behavior of the system studied [11]. Furthermore, the coefficients of determination shown in the table reinforce this conclusion. While R² is 80.74%, meaning that about four fifths of the total variability is accounted for by the model, the adjusted R² drops to 63.88%, revealing a significant loss of explanatory power once the number of factors and interactions is accounted for [11]. This marked difference between R² and adjusted R² reflects over-parameterization and insufficient predictive capacity of the model [22]. Thus, despite apparent statistical significance, the first-degree model shows major limitations in terms of adequacy and robustness. In line with recommendations from the literature [23], these results justify rejecting the linear model and highlight the need to resort to a second-order model [3] based on a response surface design, in order to better capture the joint and non-linear effects of the factors. Prior to building this second-order model, the relative weight of each factor and interaction was examined with a pareto chart (Figure 2), so as to single out the variables that actually govern removal efficiency.

Figure 2. Pareto chart of the standardized effects of the three factors and their interactions.

As can be seen in Figure 2, over 80% of the variability in the response is attributable to the activation time (X₂), the sodium hydroxide concentration (X₃), and the interaction between NaOH concentration-activation temperature-duration (X₁·X₂·X₃). The most influential factor is the activation time (X₂). Next came the normality and the interaction between NaOH concentration-activation temperature-duration (X₁·X₂·X₃), with respective contributions of 30.0% and 8.0% [11]. The contributions of temperature (X₁), the interaction between activation temperature and activation time (X₁·X₂), and the interaction between activation time and normality (X₂·X₃) each contribute less than 15%. The main effects plot (Figure 3) shows the direction and magnitude of the effect of each factor and indicates which level favors phosphate removal.

Figure 3. Main effects plot of the factors.

As shown in Figure 3, removal efficiency rises with normality (X₃): the mean removal rate goes from about 74% to 80% when the NaOH concentration is raised from 0.5 N to 2.5 N, i.e. a gain of about 6 percentage points. Extending the activation time (X₂) from 3 h to 6 h has an even stronger effect, the mean removal rate increasing from about 69% to 82%. Both parameters therefore improve the performance of the biosorbent. A longer and more concentrated alkaline treatment is likely to hydrolyze a larger fraction of lignin and hemicellulose, thereby opening up the porosity and generating oxygen-bearing functional groups that are known to participate in phosphate binding [14]. Similar trends have been reported for activated biosorbents [11] and for activated clays [3]. In contrast, the Pareto chart (Figure 2) shows that activation temperature (X₁) has no statistically significant effect, and Figure 3 even suggests a slight decrease in removal at its high level. Consequently, only activation time and NaOH concentration were kept for the next step. The second-order model used to describe and optimize the response is presented in the following section.

3.2. Central Composite Design (CCD)

The CCD was built with two factors (k = 2), namely NaOH concentration (X₁) and activation time (X₂). It comprised 13 runs distributed as follows:

4 factorial runs (2²);

4 axial (star) runs (2k);

5 replicated runs at the center of the domain.

With α = (2k)^1/4 = 1.414, the coded levels of each factor range from −1.414 to +1.414, which corresponds to 1 - 3 N for NaOH concentration and 4 - 8 h for activation time. The measured responses R₂ (Exp), the values predicted by the model R₂ (Cal) and the corresponding coefficients of variation are listed in Table 3.

Table 3. Matrix, experimental design, removal rate, and coefficients of variation for the central composite design.

Test	Normality	Duration	R2 (Exp)	R2 (Cal)	Residual	Cv (%)
1	1.29	4.58	90.08	90.43	−0.35	0.39
2	2.70	4.58	82.34	81.84	0.5	0.6
3	1.29	7.41	93.4	93.11	0.29	0.31
4	2.70	7.41	86.42	85.28	1.14	1.32
5	1	6	95.95	95.69	0.26	0.27
6	3	6	83.14	84.08	−0.94	1.13
7	2	4	83.42	83.29	0.13	0.16
8	2	8	86.79	87.61	−0.82	0.94
9	2	6	83.1	83.27	−0.17	0.2
10	2	6	84.62	83.27	1.35	1.6
11	2	6	82.77	83.27	−0.5	0.6
12	2	6	83.75	83.27	0.48	0.58
13	2	6	82.23	83.27	−1.04	1.26

All CCD runs gave removal rates above 80% (Table 3), which confirms the improvement achieved after the factorial stage. Figure 4 presents the distribution of residuals as a function of fitted values. The residuals appear randomly distributed around zero, with no systematic trend.

No residual exceeds 2 in absolute value, showing close agreement between measured and predicted responses. Fitting the CCD data gave the second-order model of equation (6), in which R₂ is the predicted removal rate:

$R_2=176.8-93.3X_1-6.03X_2+26.47X_1^2+0.545X_2^2+0.380X_1\ast X_2$ (6)

In this equation, the coefficients express the individual, interaction and quadratic effects of the factors. The ANOVA used to validate the model is summarized in Table 4.

Figure 4. Distribution of residuals versus fitted values.

Table 4. Analysis of variance for the central composite design.

Sources	DF	Adj SS	Adj MS	F-value	p-value
Model	5	232.664	46.533	47.90	0.000
Error	7	6.800	0.971
Lack-of-fit	3	3.389	1.130	1.33	0.383
Pure error	4	3.411	0.853
Total	12	239.464
R2	97.16%
${\text{R}}_{\text{A}}^2$	95.13%
CV	0.72%

In line with the criteria of [24], the residual sum of squares (6.800) is far below the regression sum of squares (232.664), and the model is highly significant (p < 0.001). The lack-of-fit test is not significant (p = 0.383 > 0.05), so the quadratic form describes the data adequately. Pure error (3.411) represents only 1.42% of the total sum of squares and can therefore be neglected [25]. R² (97.16%) and adjusted R² (95.13%) are both high and close to each other, which shows good agreement between measured and predicted values and rules out over-fitting. Finally, the mean CV (0.72%) is well below the 5% limit. Together, these results validate the proposed quadratic model [24]-[26].

3.3. Optimization of the Phosphate Ion Removal Rate

The optimum was first sought graphically from the contour plot in Figure 5, which shows that removal rates above 95% can be achieved without leaving the experimental domain. The optimal region corresponds to combinations of NaOH concentration (X₁) and activation time (X₂) that place the response on or beyond the 99% contour (darkest blue zone). The problem therefore consists in finding the coded values of X₁ and X₂, within the design limits, that maximize R₂ as described by the second-degree polynomial.

Figure 5. Contour and response surface plots.

These coded values were then calculated with the desirability function of Minitab (Figure 6), the target being the maximum phosphate removal rate.

Figure 6. Desirability function.

According to Figure 6, a desirability of 1 is reached for a predicted removal rate of 99.67%. This optimum lies at −1.414 for NaOH concentration and +1.414 for activation time in coded units, which, after conversion to real units, gives 1 N NaOH and 8 h of activation. The 95% confidence interval of this prediction ranges from 94% to 100% (Table 5). Since the optimum lies at the boundary of the experimental domain, slightly better conditions outside the studied range cannot be excluded. Three additional (control) runs were performed under these conditions.

3.4. Control Test Results

Table 6 gives the results of the confirmation runs.

Table 5. Response prediction.

Factors	Settings
Normality	1 N
Duration	8 h
Response	Fitted value 99.67%
Removal percentage	95% CI (94 - 100)

Table 6. Control test results under optimal biosorbent preparation conditions.

Test	NaOH Concentration	Duration (H)	R2 cal (%)	R2 exp (%)	Mean removal rate (%)
1	1	8	99.67	97.2	98.23
2	1	8	99.67	98.8
3	1	8	99.67	98.7

The three control tests gave a mean removal rate of 98.23% (standard deviation 0.90). The difference from the predicted value (99.67%) is 1.44 percentage points, well within the 5% tolerance, which validates the model. This level of performance agrees with recent biosorption studies: comparable removal efficiencies, for various pollutants, have been reported for biosorbents prepared from Saba senegalensis hulls [11], argan shells [27], green walnut hulls [28], cocoa pod husks [29] and waste perlite [30], and they are of the same order as those of activated carbons [31] [32]. This high efficiency results both from the statistical optimization of the preparation conditions [21] [33] [34] and from the NaOH activation step, which enhanced the adsorption capacity of the material.

4. Conclusion

This work optimized the preparation of a cocoa husk biosorbent for phosphate removal using design-of-experiments tools. Following a preliminary screening, three variables were examined: activation temperature, activation time and NaOH concentration. The full factorial design showed that temperature had no significant effect, whereas activation time and NaOH concentration were the dominant factors. These two variables were then optimized by combining a central composite design, response surface analysis and the desirability function of Minitab 19. The best results were obtained with 1 N NaOH for 8 h, which gave a mean removal rate of 98.23%, close to the 99.67% predicted by the model and thus confirming the reliability of the approach. Cocoa husks therefore represent a low-cost and sustainable biosorbent for phosphorus removal, with an efficiency comparable to that of activated carbons, while turning an agro-industrial residue into a useful material in line with circular economy principles. Further work is still needed to assess the industrial feasibility of the process, including a techno-economic analysis. A detailed characterization of the material (FTIR, SEM, BET, pHPZC) will also be required to identify the functional groups involved, its morphology and textural properties, and the adsorption mechanisms before any scale-up.

Acknowledgements

We thank the management of the Laboratoire des Sciences et Technologies de l’Environnement, Université Jean Lorougnon Guédé (Daloa, Côte d’Ivoire), for providing laboratory facilities and for their support during this study.

Author Contributions

Christian Landry Yapi: Conceptualization, Methodology, Investigation, Formal analysis, Data curation, Visualization, Writing-original draft. Yapo Hermann Aristide Yapi: Methodology, Validation, Writing-review & editing. David Léonce Kouadio: Formal analysis, Validation, Writing-review & editing. Kouassi Serge Gbamélé: Investigation, Resources, Writing-review & editing. Issifou Ouattara Mama: Methodology, Validation, Writing-review & editing. Brou Dibi: Conceptualization, Supervision, Project administration Writing-review & editing. All authors have read and agreed to the published version of the manuscript.

Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.

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