## Introduction

Black liquor (BL) is one the most known by-products of the pulp and paper industry. It is highly appreciated for its caloric value as industrial fuel and correspondingly unattractive from the environmental point of view1. Due to their environmental toxicity, both the chemical content and the colour of the black liquor containing effluents are of major concern. Therefore, numerous physicochemical treatments and decolorization methods have been proposed over the years. Examples include: coagulation and precipitation2,3, electrocoagulation4,5, adsorption6, wet oxidation7, ozonation8,9, photochemical degradation10, biodegradation and other advanced oxidation processes11,12, each having its own advantages and drawbacks. In the context of technical progress of pulp and paper industry and with the continuous tightening of the environmental standards and regulations, these methods must continually prove their economical and practical viability. Thus, in order to increase efficiency and reduce costs, great efforts were made to enhance and to optimize the existing treatment methods and to find the optimal operational parameters13,14,15,16,17,18,19,20.

Proposed in the 60 s by Box and Hunter, one of the classical optimization approaches used for studies regarding the degradation and decolorization of pulp and paper effluents12,21,22,23 is Response Surface Method (RSM) based on central composite design (CCD)24. Currently, the outstanding progress of computational science and engineering allows the application of a variety of algorithms for optimizing real-world problems25,26,27,28,29,30. These optimizers can be classified in various ways, but the most used criterion divides then into deterministic and stochastic31. The difference between the two consists in the characteristics of the solutions obtained. If starting from the same point, the deterministic approaches will always provide the same solution. On the other hand, the stochastic ones will generate different solutions that can be distributed in the search space or tightly packed together. Due to their effectiveness and general applicability, the stochastic approaches are often used as alternatives to the classical optimization variants. Therefore, in this work, along RSM modelling, a stochastic approach represented by a bio-inspired metaheuristic—Differential Evolution (DE)32- was used as an alternative to the RSM optimization.

The goal of the current work is twofold: (i) to study and identify the optimal condition for decolorization of a black liquor obtained in laboratory from corn stalks; and (ii) to demonstrate that the classical approaches can be improved to keep up with the novel decolorization processes. To this means, a three-step procedure is used:

1. (i)

experimental (where an experimental plan is set-up and followed). Two extensively studied decolorization procedures10,33,34,35,36 were selected and used in lab-scale experiments: active carbon decolorization (ACD) and TiO2 promoted photochemical decolorization (PCD). The role of specific key parameters and their interactions were evaluated for each procedure;

2. (ii)

modelling (where data gathered from the previous step is statistically modelled in order to determine a set of mathematical relations that can describe the processes). The method used to perform this step is represented by RSM;

3. (iii)

optimization (where the previously determined model in combination with an optimizer is used to identify the optimal process parameters). The algorithm used to perform the optimization is represented by DE.

The chosen decolorization methods (ACD and PCD) were selected based on their simplicity, reduced cost and ease of implementation. Moreover, the base materials for the ACD and PCD methods, active carbon and respectively TiO2 are highly valued, with countless applications in environmental protection. The active carbon-based materials were extensively studied as adsorbents. In order to increase their functionality, various strategies for their production and activation were developed37,38. In the latest years, the focus was on converting low value lignocellulosic biomass (renewable crops, agriculture waste, and invasive plants) into active carbon and on their application for wastewater treatments39,40,41,42,43. This conversion involves pyrolysis (anaerobic thermal activation or physical activation) that can be preceded or followed by complementary chemical activation42,44. By varying the nature of the raw materials, the pyrolysis temperature, and the nature of the chemical reagents (commonly ZnCl2, H3PO4, NaOH or KOH), the active carbon surface area can be controlled and enhanced41,42,43,44. On the other hand, TiO2 (titania) has multiple applications as pigment (white) and as photocatalyst45. Nowadays, the research is focused on new strategies to improve the photocatalytic activity46,47. Two main directions can be distinguished: altering the materials crystallinity (rutile/anatase ratio)48,49,50 and the use of doping with non-metals such as C, N and S, transition metals such as Al, Fe, Cu, V, Ni or noble metals47,51,52,53.

The aim of the current work is not to prove which of the two processes is better but to demonstrate that novel computational techniques can provide additional strategies to improve their efficiency beyond the standard performance levels reported so far. Since the focus is not on particular properties, the materials used (active carbon and TiO2) are commercially available and were used as such, without any alteration or supplementary treatment. To the author’s knowledge, the combination of ACD and PCD with the modelling/optimization techniques (RSM and DE) has never been studied in such manner before.

This work is organized as follows. "Materials and methods" section describes the materials and methods used from both an experimental and simulation point of view. "Results and discussion" section presents and discusses the results obtained from multiple perspectives: experimental, modelling and optimization. The last section concludes the paper.

## Materials and methods

### Materials

The black liquor used in this study was obtained from a laboratory scale system for cellulose production and it was based on pulping of corn stalks. The corn stalks come from unprotected corn plantations and were gathered from the Iasi region, Romania with the permission of the farmers, following the national rules for agricultural waste collection. In a typical pulping experiment, about 440 g stalks (10% humidity) were used. The material was pulped with 48 g NaOH and 3600 cm3 distilled water (corresponding to 12% NaOH alkali charge and a solid to liquid ratio of 1:9). Following reactor closing, heat was applied to reach a temperature of 120 °C (25 min). This temperature was maintained for 40 min. These conditions were determined as optimum in a previous study focusing on the soda pulping of corn stalks54. After pulping time was completed, a sample of the liquid phase was withdrawn from the pulping reactor, cooled to room temperature and filtered to remove any remaining solids. The resulted liquor had a characteristic darkish brown colour, a relatively high alkalinity (pH = 11) a conductivity of 24.5 mS/cm and organic load (Chemical Oxygen Demand – COD = 40 g O2/L). The solid content of the black liquor was further determined according to the TAPPI test method (TAPPI T650, 1989). Organic to inorganic ratio was determined taking into account the ash content values (TAPPI 625 cm–85). The simplified schema of the steps used in the processing of corn stalks is presented in Fig. 1, where the blue colour indicates the focus of the current paper.

Common commercial TiO2 powder (M-1319) supplied at FCC purity grade by Mayam55 was used as such. The powder was characterized by SEM and EDX analysis and, in a previous study, was successfully applied for photochemical decolorization of methylene blue56.

The experiments were performed using irregular shape particles of active carbon supplied by Buzău Romcarbon Company (Romania), active carbon that was characterized in the study of57: specific microporous volume 0.48 cm3/g, total microporous volume 0.66 cm3/g, mean pore size 1.62 nm, BET surface 1403 m2/g, external surface 38 m2/g and total surface 631 m2/g. Prior to the experimental study, the particles were classified by sieving, the average diameter ranging between 2.5 and 3.15 mm.

### Equipment

The UV light source was a Biocomp UV-lamp with a wavelength of 253.7 ± 0.8 nm. An analogue UV light sensor GUVA S12SD was used to measure the intensity of incident UV radiation. The UV–VIS spectra and the absorbance values were recorded using a JASCO V-550 UV–VIS spectrophotometer. The COD mg O2/L was measured using a standard Hach-Lange kit LCK 114. A BHG Hermle Z 229 Centrifuge: 220 V, 50 Hz, 1.1 A, 240 W, maximum number of revolutions 15,000 rpm was also used.

### Experimental design

In order to determine the optimal parameters for BL decolorization three representative independent variables were considered for each method, as depicted in Table 1. These parameters and their limits were selected based the data provided by literature58. Following the design of experiments approach (DOE) proposed by Box and Hunter24, a minimum number of experiments were statistically programmed as presented in Table 2, where ηACD (%) represents the decolorization efficiency for the active carbon decolorization and ηPCD (%) for the TiO2 promoted photochemical decolorization. In Table 2 both the coded and the decoded variables were presented, the notations being the same as the ones used in Table 1. The bold columns from Table 2 indicate the experimental results obtained with the variables determined by the DOE approach.

### Experimental procedure

The BL was used as such, underprivileged of any pH chemical regulations, at room temperature. Bi-distilled water was used to reach the required dilution ratio for each experiment. In order to avoid settling (and to ensure a constant exposure of the mixture) the slurry was stirred constantly during all the experiments involving the presence of TiO2 powder or active carbon particles.

In the case of active carbon decolorization, for well-defined periods of time, 100 mL samples of specifically diluted BL solutions were mixed with the adequate amount of active carbon, according to the data presented in Table 2. Disposable disc filters 0.45 µm were used for particles separation.

In the case of TiO2 promoted photochemical decolorization, 50 mL samples of BL solutions (with 1:100 dilution ratio) were mixed with the adequate amount of TiO2 and placed below the UV source for the corresponding period of time. After irradiation, the TiO2 powder was separated from the solutions using a centrifugal separator. The required UV path length that gives the intensity of the incident UV radiation was attained by changing the distance between the UV source and the sample under study.

### Chemical assays

The BL decolorization was checked by measuring the absorbance of the solution given by the lignin content at 280 nm (UV280) (Fig. 2). The correlation between COD and absorbance was determined at different dilution ratios in order to establish a calibration curve that validates the accuracy of decolorization efficiency calculations. The coefficient of determination (R2) was 0.97, in accordance with the literature reported values21. The efficacy of BL decolorization was calculated using the following equation:

$${{\eta (\% )}} = \frac{{\left[ {{\text{UV}}_{280} } \right]_{0} - \left[ {{\text{UV}}_{280} } \right]}}{{\left[ {{\text{UV}}_{{{280}}} } \right]_{0} }} \cdot 100$$
(1)

where $$\left[ {{\text{UV}}_{280} } \right]_{0}$$ and $$\left[ {{\text{UV}}_{280} } \right]$$ are the absorbance’s recorded before and after each experiment.

### Software and algorithm

The MINITAB package (Minitab Institute, USA) was chosen to implement the response surface method algorithm. In addition, the process was optimized with a second method represented by DE, an efficient metaheuristic approach, that was successfully used (simple or in combination with other approaches) for optimization and modelling of a wide range of systems: robot control59, water quality monitoring60, adsorption processes61. Examples of DE application in chemical engineering can be found in62. The DE based software used was developed in63 in combination with artificial neural networks (ANNs) and applied for predicting the liquid crystalline property of some organic compounds. Distinctively, in this work, the ANN is replaced by the model determined with MINITAB package and the DE variant (SADE) performs only the process optimization part.

DE is inspired from the Darwinian principle of evolution32 and it works with a population of potential solutions that it is evolved (through a series of steps that include mutation, crossover and selection) until a stop criterion is reached. In the first step, the potential solutions (which will be further referred as individuals) are initialized using a random based procedure. This population then undergoes a mutation procedure. DE has many mutation variants and, in this work, two differential terms combined with a randomly selected based vector was used. This combination is also known as the rand/2 version. Equation (2) describes the mutation equation used.

$$\omega_{i} = \alpha + F \cdot \left( {\beta + \gamma } \right)$$
(2)

where α is the base vector, F is the scaling factor (one of the control parameters of DE), and β, γ are the differential terms. The differential term is created by subtracting a randomly selected vector with another one.

After that, the features of the mutated and current individuals are combined to create a new population called trial. This is the crossover step and the variant used in this work is the binomial crossover.

In the next step, the trial and the current population undergo a one-to-one comparison where the best individuals are selected to form the next generation. The measure used to determine the best individuals is represented by the fitness function. For the current work, the fitness function represents the output of the regression model generated by Minitab software.

One of the main characteristics of the SADE version is represented by the use of self-adaptability to determine the values of the control parameters. In this manner, the difficult task of manually setting the optimal values for the control parameters is automatized. A simplified schema of approach used in this work is presented in Fig. 3.

## Results and discussion

### ACD vs PCD

Evidently, the basic principles of the BL decolorization methods selected for this study makes a comparison attempt to be rather impractical. Furthermore, the chosen parameters and their range of variation make the straightforward comparison between ACD and PCD quite difficult.

However, from the experimental data obtained on the samples with the dilution ratio (1:100) used for both methods (the experiments from 5 to 8 in Table 2) the superiority of ACD is clearly established. The results are comparable in one case only, for the experimental data set no. 8, when the values for the ACD and PCD parameters were set for minimum values. Evidently, in terms of decolorization efficiency, the ACD method exhibits better performances (83.08% vs. 36.63%).

When it comes to PCD, it should be mentioned that, commonly, the method involves the use of additional chemical oxidants: Fenton’s reagent, hydrogen peroxide and other combinations that favours the formation of OH radicals and other short-lived radical species, which highly elevates the methods efficacy. However, no additional chemicals (reagents, pH regulators) were used during this study, since our goal was not necessary to compare two well-known methods but to use and apply classic and modern optimization techniques in order to find their optimal parameters. Therefore, no claim that one method is better than the other will conclude our work.

### Response surface method

A full second-order polynomial model was obtained by multiple regression technique for three parameters using the MINITAB package. For the ACD method, the regression equation in terms of actual factors (uncoded units) is presented below:

\begin{aligned} \eta_{{{\text{ACD}}}} \left( \% \right) = & 0.{2} + {2}.{833} \cdot {\text{AC}} + {1}.{59} \cdot {\text{Ct}} - 0.{124} \cdot {\text{Dil}} - 0.0{3}0{73} \cdot {\text{AC}}^{{2}} + 0.0{13}0 \cdot {\text{Ct}}^{{2}} \\ & \quad + 0.000{87} \cdot {\text{Dil}}^{{2}} - 0.0{143} \cdot {\text{AC}} \cdot {\text{Ct}} - 0.000{14} \cdot {\text{AC}} \cdot {\text{Dil}} - 0.00{478} \cdot {\text{Ct}} \cdot {\text{Dil}} \\ \end{aligned}
(3)

By setting one parameter at a constant value equal to the median value of the interval of variation, three dimensional plots were drawn (Fig. 4A,B,C). This allows the visualization of maximum and/or minimum points that leads to accurate identification of the optimal values and shows the influence of the selected parameters on the BL decolorization efficiency.

The response surface plots showing the evolution of the decolorization efficiency as a function of contact time and active carbon concentration at constant dilution ration 1:150 is displayed in Fig. 4A. As expected, the increase of Ct and AC have a substantial influence on efficiency, its maximum value (over 75%) being reached after 30 min at 40 g/L adsorbent concentration. Figure 4B shows the influence of dilution ratio and active carbon concentration on decolorization after 20 min of contact time. The maximum value of decolorization efficiency was reached at 1:200 Dil in presence of 40 g/L active carbon. When AC was held constant at 27.5 g/L the efficiency reached nearly 95% after 30 min and 1:200 Dil as presented in Fig. 4C.

The data presented in Table 3 represent the best five sets of Minitab optimization results. For all the optimization data provided in each case, two solutions were experimentally validated in order to confirm the results.

For the PCD method, the regression equations in terms of actual factors (uncoded units) is presented in Eq. (4). Figures 5A, 5B and 5C display the variation of BL decolorization efficiency for PCD as a function of two variables.

\begin{aligned} \eta_{{{\text{PCD}}}} \left( \% \right) = & {33}.0 - {16}.{3} \cdot {\text{TiO}}_{{2}} + 0.{6}00 \cdot {\text{It}} - {1}.{299} \cdot {\text{hUV}} + {4}.{3}0 \cdot {\text{TiO}}_{{2}}^{{2}} \\ & \quad - 0.00{292} \cdot {\text{It}}^{{2}} + 0.0{424} \cdot {\text{hUV}}^{{2}} - 0.000 \cdot {\text{TiO}}_{{2}} \cdot {\text{It}} \\ & \quad + 0.0{59} \cdot {\text{TiO}}_{{2}} \cdot {\text{hUV}} - 0.0{1468} \cdot {\text{It}} \cdot {\text{hUV}} \\ \end{aligned}
(4)

Figure 5A shows the response surface plots for decolorization efficiency as a function of irradiation time and TiO2 concentration at a constant UV path length of 15 cm. It can be noticed that the efficiency rises with the increase of It and it is higher at lower values of TiO2. The surface plot in Fig. 5B shows the influence of TiO2 concentration and UV path length after 37.5 min of irradiation. Once more, the efficiency is higher at lower values of TiO2 and tends to increase with the decrease of hUV. When TiO2 is held constant at 1.5 g/L (Fig. 5C), the efficiency grows with the increase of irradiation time and with the decrease of the UV path length.

The best five sets of results for the Minitab optimization are presented in Table 4.

### Differential evolution

In order to determine the optimal configuration of parameters leading to the maximization ηPCD, (%) for both PCD and ACD approaches, DE in combination with the regression equations generated by Minitab (Eqs. 3, 4) was applied. The control parameters values were automatically adjusted by the software using a self-adaptive procedure63. The settings used for DE optimization were: number of individuals in the population = 30, number of iterations = 50. These values were selected based on the author’s expertise and practical aspects. The parameters included into the optimization process are the same as the process parameters considered in the modelling phase: AC, Ct, Dil (for ACD) and TiO2, It, hUV (for PCD).

For both PCD and ACD, the DE based optimization procedure was applied in three cases: (i) the limits of the operating conditions were the same as in the experimental data (Case 1); (ii) the limits were extended to ± 20% (extrapolation) (Case 2); and (iii) the quantity of active reagents added was limited (1–20 g/L activated carbon for ACD and 0.4–1 g/L TiO2 for PCD) (Case 3). Tables 5 and 6 list five solutions obtained in each of these three cases. It is worth mentioning that, due to the stochastic nature of the DE base algorithm, at each run, different solutions can be obtained. Therefore, DE is not limited by a pre-specified number of solutions and can provide various configurations that lead to very similar results.

As it can be observed from the experimental validation, there is an acceptable error between the predictions and the actual values. In addition, compared with the solutions provided by the RSM approach, DE is able to find optimal values in a wide range of combinations. For example, for the ACD process, in Case 1, the process efficiency varies between 99.97 and 100%, while the values for the identified parameters varies between [7.29, 31.27] for AC, [41, 52.42] for Ct and [104.08, 169.59] for Dil. This implies that the efficiency function is multimodal and that that there are multiple combinations for the parameters values that lead to the same result. Taking into consideration the economic aspect, the process optimization can be transformed from a single-objective (maximum efficiency) to a multi-objective problem (highest efficiency with the minimum of resources consumed).

A literature analysis regarding similar strategies for decolorization using active carbon (Table 7) and TiO2 (Table 8) indicate that the obtained results are similar with other studies. However, the BL decolorization efficiency is strongly influenced by: (i) the black liquor source and/or the preparation methods; (ii) the source and preparation methods used for the materials (active carbon or TiO2); (iii) the scheme used for decolorization treatment (e.g., UV-Fenton-TiO2, free TiO2/UV, enzyme-AC).

As it can be observed from Table 7, in case of activated carbon, the efficiency obtained in this work is comparable with more complex strategies that include immobilized enzymes and combined physiochemical treatment. On the other hand, for TiO2, the obtained degradation efficiency is lower compared with the works where TiO2, Degussa was used. However, compared with TiO2 Degussa, the TiO2 used in this work is approximately 40 times cheaper.

## Conclusions

In this work, the active carbon decolorization and TiO2 promoted photochemical decolorization of black liquor obtained from laboratory pulping of corn stalks was studied using experimental combined with Design of Experiments, Response Surface Methodology and Differential Evolution algorithm. The optimization simulations for both processes were experimentally validated, the obtained errors being in an acceptable interval (< 5%). Compared with RSM, the DE based approach is more flexible (allows a wide range for parameter limits) and it is better at exploring the search space, being able to determine multiple combinations of solutions leading to similar outputs. Moreover, for active carbon, an improvement from 81.27% to 100% and for TiO2/UV decolorization from 36.63% to 46.83% was obtained, proving that the application of state-of-the-art computational approaches can lead to significant improvements and that they can be efficiently used raise performance of various decolorization processes. The mechanisms and kinetics of active carbon absorption and of TiO2/UV photochemical degradation and/or mineralization (considering the optimal conditions identified in this study) represents the subject of a future work that will include a detailed HPLC analysis of black liquor before and after decolorization.