Recent Advances in the Treatment of Industrial Wastewater from Different Celluloses in Continuous Systems

There are numerous studies on water care methods featured in various academic and research journals around the world. One research area is cellulose residue coupled with continuous systems to identify which are more efficient and easier to install. Investigations have included mathematical design models that provide methods for developing and commissioning industrial wastewater treatment plants, but nothing is provided on how to size and start these treatment systems. Therefore, the objective is to determine recent advances in the treatment of industrial wastewater from different celluloses in continuous systems. The dynamic behavior of the research results with cellulose biomasses was analyzed with the mass balance model and extra-particle and intraparticle dispersion, evaluating adsorption capacities, design variables, and removal constants, and making a size contribution for each cellulose analyzed using adsorption capacities. A mathematical model was also developed that feeds on cellulose reuse, determining new adsorption capacities and concluding that the implementation of cellulose waste treatment systems has a high feasibility due to low costs and high adsorption capacities. Furthermore, with the design equations, the companies themselves could design their systems for the treatment of water contaminated with heavy metals with cellulose.


Introduction
The world is experiencing a fearsome reality, which is the increasingly unavoidable scarcity of drinking water, often due to the irresponsibility of companies that do not have adequate treatment for their industrial wastewater [1][2][3]. The dumping of untreated heavy metals into different water bodies leads to a frightening reality due to its irreversible impacts in many cases [4][5][6][7]. Through research projects in the area of water treatment, compliance with the objectives of sustainable development could be achieved, such as clean water and sanitation, and indirectly the rest of these objectives [8][9][10].
A novel approach with reliable results is the development of treatment systems with residual cellulose biomass. This polymer can retain heavy metals due to cation exchange processes via chemisorption [11][12][13]. The unique hierarchical porous structure of cellulose is very conducive to fluid passage while absorbing small particles in the intercepted fluid [14].
One way to improve the removal of heavy metals from cellulose is through their chemical or physical modification to increase their affinity for contaminant molecules [15][16][17].
In both laboratory and pilot scale research, it is being concluded that through continuous systems, treatment systems could be installed to remove heavy metals from water, designing and developing mathematical models to adjust them to the established needs [18,19]. For example, the extra-particle diffusion equation could be adapted to the needs of contaminated wastewater treatment systems. In addition, this equation could be adapted to the needs in processing the final concentration of heavy metals, adapting it to the current discharge legislation [20][21][22][23][24].
Another model worthy of investigation is the intraparticle diffusion model that links microparticle densities and biomass density, relating them to establish the best design conditions [25][26][27][28][29]. To establish these treatment conditions, the design parameters of the system must be known, including density ratios, design flow rate, removal capacity, treatment biomass, breakpoint, and design volume. With this information, equations were developed to establish the initial conditions to achieve the heavy metal release targets [30,31]. Fixed bed column adsorption tests are used to establish the efficiency of biomass in pollutant removal, in a similar arrangement to that used in industry [32][33][34]. To optimize the treatment process, the use of chemical agents such as EDTA, HCl, NaOH, and HNO 3 is essential to reuse cellulose in the treatment of heavy metals, and therefore increase the adsorption capacity [35][36][37]. Cellulose can assimilate these chemical agents due to the presence of lignin in its biochemical structure, which helps to maintain its stringency in the processing process without being affected by it, allowing up to six times more recycling in heavy metal adsorption processes [38][39][40]. Traditional adsorbents have shortcomings, such as low adsorption capacity and low selectivity, so it is urgent to develop new adsorbents with high adsorption capacity, and which are renewable and without secondary contamination [41]. The adaptation of cellulose in treatment systems could be carried out through a fixed-bed column with PET plastic containers; this guarantees it has an economic advantage, being easy to implement and effective compared to other methods [9].
For this reason, the present review work aims to determine the recent advances in the treatment of industrial wastewater from different celluloses in continuous systems. The dynamic behavior of the results of the biomass research will be analyzed with the mass balance model and extra-particle and intraparticle diffusion, where adsorption capacities, design variables, and removal constants were evaluated and staging and sizing contributions were made for each cellulose analyzed for adsorption capacities. A mathematical model was also developed, where the elution of contaminant removal was fed to determine the new adsorption capacities, and conclude which is the chemical agent with the best performance in the reuse of cellulose. In addition, some system developments with cellulose biomass are shown, and the cost of these systems is analyzed.

Analysis FTIR of Cellulose
Different investigations related to cellulose FTIR were analyzed, and the generic figure of heavy metal adsorption in cellulose was obtained. Figure 1 shows the characteristic spectra of a cellulose sample before and after the adsorption of heavy metals; for example, the hydroxyl groups (-OH) can be observed in the bands 3400 cm −1 and 580 cm −1 [42][43][44][45][46][47]. After the experimental process of adsorption of a heavy metal-light green spectrum, significant changes in its stretching levels were observed, displaying an important change in the hydroxyl group (OH) after the chemisorption process. Parts of the hydroxyl groups are lost in the characterization due to the presence in the cellulose of a heavy metal due to the strong vibrations of the O-HV [9]. FTIR spectra were used to show the binding of Cr (VI) ions in the -OH group, which contributed to the adsorption of this heavy metal in the biomass of E. crassipes. Other studies also found that -OH was involved in the adsorption process of different heavy metals, and in these investigations they modified cellulose in order to increase these groups, in order to increase the removal levels of these contaminants [48][49][50][51].

Analysis of Microphotographs of Cellulose
Representative microphotographs of cellulose were also obtained, where one of the biomass celluloses was shown. Figure 2 shows a characteristic image of the biomass of a cellulose sample, with a rough inhomogeneous porosity; these characteristics were also observed in [52].

Analysis of Microphotographs of Cellulose
Representative microphotographs of cellulose were also obtained, where one of the biomass celluloses was shown. Figure 2 shows a characteristic image of the biomass of a cellulose sample, with a rough inhomogeneous porosity; these characteristics were also observed in [52].
The analysis of cellulose samples was carried out in physicochemical characterizations through EDS (Energy Dispersive X-ray Spectroscopy). Table 1 shows the characterization and representative percentages of this sample, where it can be seen that carbon and oxygen were the representative elements of this biomass. Different characterizations are shown based on research by [53][54][55][56].     The analysis of cellulose samples was carried out in physicochemical characterizations through EDS (Energy Dispersive X-ray Spectroscopy). Table 1 shows the characterization and representative percentages of this sample, where it can be seen that carbon and oxygen were the representative elements of this biomass. Different characterizations are shown based on research by [53][54][55][56]. Figure 3 shows the microphotograph of cellulose with the location of each representative element in the photomicrograph. Figure 4 represents a micrograph of a general sample of cellulose, where the characteristic of its amounts of carbon and oxygen-representative elements of cellulose-and silicon, in small traces, can be observed and where cation exchange with heavy metals is possible. Table 1 shows the percentages obtained from the cellulose.     Figure 4 represents a micrograph of a general sample of cellulose, where the characteristic of its amounts of carbon and oxygen-representative elements of cellulose-and silicon, in small traces, can be observed and where cation exchange with heavy metals is possible. Table 1 shows the percentages obtained from the cellulose. Table 2 shows the percentages of these elements, but with an arithmetic average of the different heavy metals adsorbed from the research [9,18,20,[57][58][59][60][61].  Subsequently, after the adsorption treatment process of some heavy metals, the high levels of heavy metals were evident in the microphotograph, as can be seen in Figure 4.    Table 2 shows the percentages of these elements, but with an arithmetic average of the different heavy metals adsorbed from the research [9,18,20,[57][58][59][60][61]. Subsequently, after the adsorption treatment process of some heavy metals, the high levels of heavy metals were evident in the microphotograph, as can be seen in Figure 4. Figure 4 shows cellulose after a treatment process. Different colored dots representing the elements in the samples can be seen, with yellow dots showing a heavy metal, red dots representing carbon, and green dots being oxygen.

Adsorption Mechanism
In cellulose, there are hydroxyl (OH) groups where the positive ions of heavy metals are accommodated. Figure 5 shows a representative figure of heavy metal adsorption on cellulose based on different investigations [46,62,63]. The properties of this biomass, such as its hydrophilic or hydrophobic character, elasticity, water absorbance, ionic exchange or adsorption capacity, and thermal resistance, help to incorporate chemical agents to optimize the adsorption or elution process [64,65].   Figure 5 shows a generic representation of cellulose adsorption mechanisms to heavy metals represented by Heavy Metal (HM + ) for every four glucose molecules ing the branching of the cellulose structure (n); these deductions have been obser [63][64][65][66][67][68][69][70][71]. Two molecules of the contaminant were attached due to chemisorption pro by the hydroxyl groups OH.
The use of Fe (III) iron chloride in vegetable cellulose has been used to treat o and inorganic contaminants. Fe (III) oxidizes the cellulose, forming iron hydr (FeOO), which is where the process of chromium diffusion by chemisorption takes  Figure 5 shows a generic representation of cellulose adsorption mechanisms towards heavy metals represented by Heavy Metal (HM + ) for every four glucose molecules forming the branching of the cellulose structure (n); these deductions have been observed in [63][64][65][66][67][68][69][70][71]. Two molecules of the contaminant were attached due to chemisorption provided by the hydroxyl groups OH. The use of Fe (III) iron chloride in vegetable cellulose has been used to treat organic and inorganic contaminants. Fe (III) oxidizes the cellulose, forming iron hydroxides (FeOO), which is where the process of chromium diffusion by chemisorption takes place, performing a series of cation exchanges [63]. The structure of cellulose with iron chloride [62] can be seen to react with the chromium structure (VI).
Upon reaction with cellulose, iron chloride FeCl 3 progressively oxidizes it, creating active sites for heavy metal adsorption [66]; chlorine reacts with the hydrogen-forming compounds of biomass (HCl). The Figure 6 show the process for reducing Cr (VI) to Cr (III).
The use of Fe (III) iron chloride in vegetable cellulose has been used to treat organi and inorganic contaminants. Fe (III) oxidizes the cellulose, forming iron hydroxide (FeOO), which is where the process of chromium diffusion by chemisorption takes place performing a series of cation exchanges [63]. The structure of cellulose with iron chlorid [62] can be seen to react with the chromium structure (VI).
Upon reaction with cellulose, iron chloride FeCl3 progressively oxidizes it, creatin active sites for heavy metal adsorption [66]; chlorine reacts with the hydrogen-formin compounds of biomass (HCl). The Figure 6 show the process for reducing Cr (VI) to C (III).   Figure 7 shows the reduced biomass, in which the Cr (VI) contaminant, in the form of Cr 2 O 7 dichromate, has a complex chemical structure. When it comes into contact with the biomass, reactions of (H + ) in the biomass with the oxygen in the Cr (VI) structure occur, reducing it to Cr (III) [72][73][74]. Cr 2 O 2 is chromium oxide. , x FOR PEER REVIEW 7 of 18 Figure 7 shows the reduced biomass, in which the Cr (VI) contaminant, in the form of Cr2O7 dichromate, has a complex chemical structure. When it comes into contact with the biomass, reactions of (H + ) in the biomass with the oxygen in the Cr (VI) structure occur, reducing it to Cr (III) [72][73][74]., Cr2O2 is chromium oxide.

Mass Balance in Treatment
A desorption-elution process is involved for the reuse of biomass, see Equation (1), and this equation was designed in [18].
where: Q = design flow (mL/min); Tbj = break time of use number j (Min); Ci = initial concentration (mg/mL); Co = final heavy metals concentration in the treated solution (mg/mL); V = volume of the system (mL); E = porosity; M = amount of biomass used (g); q T = total adsorption capacity of the biomass used (mg/g).

Extra-Particle Diffusion
Equation (2) is the balance when the treatment process begins, and K f can be obtained through this, which is the diffusion in the external liquid film.
Kl = Mass transfer coefficient in the liquid particle m/h; L: Length; Cs = Equilibrium concentration of pollutant.
Plotting this term, the natural logarithmic of initial and final concentration, with the volume and area of treated water in the experimental biotreatment process, will find the diffusion constant (k f ) of in the biomass.

Intraparticle Diffusion
The calculation of ma ∂q/∂t of the adsorption capacity (q) is related to the particle density (dp), and (ks) is the internal mass transfer coefficient and (qs − q) [20].
where (Cs) is the maximum concentration of heavy metal in (mg/L) in the liquid, and (qs) is the concentration inside the biomass, practically its maximum capacity; the value of (qs) can be calculated using the following expressions, depending on the isotherm.
The term on the left-hand side represents the rate of accumulation of the metal in the constant volume solution, which decreases because the metal is adsorbed by the cellulose. The right side represents the speed with which the metal is diffused from within the solution to the outer surface of the biomass.

Modeling Process
By means of Equation (1) and with different bibliographic references, representative data were obtained to feed this equation, determining the capacities of each of these biomasses together with the new capacities, and determining the reuse power of the different solvents, as shown and summarized in Table 3. Cellulose has excellent biochemical characteristics for developing recycling processes through chemical elutions [75][76][77][78][79][80][81][82][83][84][85]. Applying Equation (1), an increase in adsorption capacity of over 100% is evidenced in all the processes.
Untreated cellulose does not have great capacity, so it must be improved with composite materials or chemical reagents [20]. However, this deficiency contrasts with its great capacity to resist elution via chemical agents [18].
For the EDTA eluent, satisfactory results were evidenced in terms of elutions and the recycling of the cellulosic biomass of E. crassipes when removing Cr (VI), reaching almost 150% of its original capacity. The eluents HCl and HNO 3 are also excellent chemical agents in the desorption process, since they achieve more than a 100% reusing of the biomass. Treatments using HCl elution represented an increase in capacities of 100%, but in all processes it acidified the cellulose, and this affected it in other adsorption processes. Elution with chemical agents is fundamental to the design of treatment systems with cellulosic biomass since, with this parameter, the removal of pollutants could be optimized [18].
Through Equation (2), the data corresponding to the investigations were linked to obtaining the extra-particle diffusion constants K f . The model establishes the input and output ratio of the pollutant as a function of the contact area, the volume of water to be treated, and the treatment time. All the models were adjusted from 500 mg/L to the 1 mg/L final quantity of the studied pollutant with a standard initial biomass of 70 g.
By obtaining K f , a treatment model of the amount of water that could be treated could be adjusted; for example, in [9], 0.20 cm/min K f was obtained with the biomass of E. crassipes. This system could treat 3.5 L of water. Table 4 shows a summary of the investigations.  [92] MXene and chitosan Cr (VI) 0.66 5.9 [89] Chitosan-modified magnetic carbon Cr (VI) 0.3 3.8 [85] Carboxymethylated Cellulose Pb (II) 1 14 [82] Cellulose/chitosan aerogel Cr (VI) 0.9 11 [83] Cellulose aerogels Cu (II) 1. 2 12 In the references of [20,86], ideal treatment yields were obtained, adjusting 11 and 10 L, respectively. FeO gradually oxidizes this biomass, negatively charging it, allowing heavy metal ions to form chelate complexes with the oxidized sites [64]. Using a biomass such as alginate, a treatment of about 7.2 L of contaminated water could be obtained, but with a modified biomass such as Cystoseria + Ca and chelating cellulose, better yields could be obtained; however, the production costs of these biomasses must be established on a larger scale. With cellulose aerogel biomass and cellulose carboxymethylate giving significant results due to the high adsorption capacity of the model, these biomasses can have great value in the treatment process in the fouling industry. Cellulose xanthate consists of transformation with carbon disulfide (CS 2 ), which is an alkaline biomass loaded with ions (OH − ) that allows the easy chemisorption of metal cations [18]. The incorporation of titanium oxide (TIO 2 ) increases the active sites in the biomass, such as hydroxyl groups (OH) and sites where heavy metals will lodge through cation exchange [89]. EDTA is a chemical agent that enhances the adsorption process of contaminants and is used as a chelating agent in industrial processes due to its high capacity to attract heavy metals through cation exchange [91][92][93]. Table 5 shows the intraparticle constants together with their isotherms. Rice bran Cr (VI) 0.035 Langmuir [95] MXene and chitosan Cr (VI) 0.02 Freunlinhchd [96] Chitosan-modified magnetic carbon Cr (VI) 0.03 Langmuir [85] Carboxymethylate Cellulose Pb (II) 0.08 Langmuir [82] Cellulose/chitosan aerogel Cr (VI) 0.075 Langmuir [84] Cellulose aerogels Cu (II) 0.08 Langmuir Equation (3), where K s is represented, is a function of capacity, particle diameter (which must be less than 0.212 mm) [9], biomass density, and microparticle density. Each of these parameters is considered for the best fit of the constant k s .
The adsorption capacity K s was 0.0198 s for E. crassipes biomass, this being the biomass with the lowest yields fed by the speed of adsorption capacities, but it did not have any chemical agent, and that could be important when creating a system with this biomass. Cellulose has a ratio between the adsorbent bed and particle density, which makes it ideal in its design to create treatment systems on a larger scale, unlike other types of biomasses, for example, bacterial cellulose [97], which has a very wide adsorbent bed, which prevents better performance; the same happens with chitosan [88,89].
Biomasses fitted to the Langmuir isotherm set monolayer conditions, such as chitosan, E. crassipes, alginate, and biochar, where the constants were adjusted to their best rates of contaminant adsorption capacity. Therefore, this isothermal model assumes that adsorption occurs at specific homogeneous sites on the cellulose [98][99][100][101].
The Langmuir model represents the experimental data of heavy metal adsorption on cellulose better than the other adsorption models [102][103][104][105][106]. The equilibrium experimental results with the Langmuir isotherm indicate that the cellulose biomass formed a monolayer cover and that the sites on the adsorbent surface were homogeneous, together with pseudosecond order kinetic experimental results. Biomasses fitted to the Langmuir isotherm set monolayer conditions, such as chitosan, E. crassipes, alginate, and biochar, where the constants were adjusted to their best rates of contaminant adsorption capacity. Therefore, this isothermal model assumes that adsorption occurs at specific homogeneous sites on the cellulose [98][99][100][101].

Design of System with the Cellulose
The Langmuir model represents the experimental data of heavy metal adsorption on cellulose better than the other adsorption models [102][103][104][105][106]. The equilibrium experimental results with the Langmuir isotherm indicate that the cellulose biomass formed a monolayer cover and that the sites on the adsorbent surface were homogeneous, together with pseudo-second order kinetic experimental results.  The treatment systems could be built with recycled PET bottles (400 and 1000 mL) (See Figure 9). Capsules or compartments were built to house the cellulose, with openings in the caps at the bottom of each capsule to allow the flow of treated water to the next capsule, as shown in Figure 9; the two processes would be used in parallel, dividing the flow into two, with three cellulose compartments each. Fixed bed column adsorption tests The treatment systems could be built with recycled PET bottles (400 and 1000 mL) (See Figure 9). Capsules or compartments were built to house the cellulose, with openings in the caps at the bottom of each capsule to allow the flow of treated water to the next capsule, as shown in Figure 9; the two processes would be used in parallel, dividing the flow into two, with three cellulose compartments each. Fixed bed column adsorption tests can be used to establish the efficiency of biomass in pollutant removal, in a similar arrangement to that used in industry [32][33][34].

Design of System with the Cellulose
Polymers 2023, 15, x FOR PEER REVIEW can be used to establish the efficiency of biomass in pollutant removal, in a si rangement to that used in industry [32][33][34]. The dry, shredded biomass was passed through a 60-mesh screen, allowing 0 diameter particles to pass through. The flow must be guaranteed in the upper conserving the system flow, and the system must have a manual flow control [9] With the biomass of E. crassipes modified with iron chloride, a serial system veloped to treat water contaminated with Cr (VI) with an adsorption capacity of [20]; with the same biomass but modified with cellulose xanthate, a parallel t system was being developed [18]. With cellulose aerogels [84], it was possible to a treatment system with EDTA elutions due to their high adsorption capacity of a mg/g [81].

Perspectives in Cost of Implementation
Another important aspect for evaluating the process is the cost of the adsor terials; consequently, this section shows the estimated cost involved in obtaining The characterization of the costs of the treatment systems through cellulose w orated on through unit costs of production of 1 kg, which were considered fo crushing, chemical reagents, and logistics for obtaining cellulose. The ratio with sorption capacity (mg/g) gives the (g HM + /USD) dollar spent, relating cost to ad capacity. Table 6 shows costs related to treatment systems.
The dry, shredded biomass was passed through a 60-mesh screen, allowing 0.212 mm diameter particles to pass through. The flow must be guaranteed in the upper capsule, conserving the system flow, and the system must have a manual flow control [9].
With the biomass of E. crassipes modified with iron chloride, a serial system was developed to treat water contaminated with Cr (VI) with an adsorption capacity of 18 mg/g [20]; with the same biomass but modified with cellulose xanthate, a parallel treatment system was being developed [18]. With cellulose aerogels [84], it was possible to develop a treatment system with EDTA elutions due to their high adsorption capacity of about 300 mg/g [81].

Perspectives in Cost of Implementation
Another important aspect for evaluating the process is the cost of the adsorbent materials; consequently, this section shows the estimated cost involved in obtaining them.
The characterization of the costs of the treatment systems through cellulose was elaborated on through unit costs of production of 1 kg, which were considered for drying, crushing, chemical reagents, and logistics for obtaining cellulose. The ratio with the adsorption capacity (mg/g) gives the (g HM + /USD) dollar spent, relating cost to adsorption capacity. Table 6 shows costs related to treatment systems.
One way to reflect the sustainability of a project is to link benefits and costs to obtain a monetary indicator [106]. Cost vs. benefit explicitly or implicitly involves cost versus total possible benefits to select the best or most cost-effective option [107]. The benefit of this project is represented through the adsorption capacity of Cr (VI) by each of the evaluated biomasses. To establish feasibility in the development of a processing and treatment system, for example, the biomass of E. crassipes and its chemical modifications have excellent indicators. The best indicator is cellulose aerogels at 15 g HV + /USD, given the efficiency of this biomass in adsorption capacity. Cellulose clay had a value of 12.7, which is an important indicator. A suitable criterion for selecting cellulosic biomass is the geographic status; for example, in wetlands where E. crassipes or other plants grow, it can be decided to develop treatment systems with this biomass. On coasts, the alternatives could be marine, such as algae, but if their effluents have very large loads of heavy metals, specialized biomass such as clay-cellulose composites and cellulose aerogels could be used. Studies have revealed that cellulose waste has the potential to remove heavy metal ions in polluted water. Coupled with the adsorption capacity and costs associated with its development, this material was found to be efficient, capable of treating about 11 g of heavy metal per dollar g HM + /(USD), taking into account the replacements in the elutions.

Conclusions
Through the bibliographic review, it was established that the cellulose adsorption mechanism is reinforced by a microparticle-contaminant relationship, and this can be achieved through a particle diameter of less than 0.212 mm.
An adjustment process of several parameters established in the different cellulose investigations for the removal of heavy metals has been developed, finding new adsorption capacities that have not been considered, due to studies of regeneration and reuse of cellulose adsorbents, where it was evidenced that the adsorption capacity increased considerably due to the ability of this polysaccharide to tolerate chemical reagents.
To calibrate, adjust and model a wastewater treatment system contaminated with heavy metals in continuous processes, it is ideal for due regulatory compliance to use the extra-particle diffusion model, since this function of concentrations required initial and final pollutants, together with the contact area of the biomass and the volume to be treated, in which several processes were suggested and the different extra-particle diffusion constants were calibrated.
Using the adsorption capacity and mass balance modeling equations, it was determined that cellulose, with a more compact density, has ideal diffusion constants in the design of industrial wastewater treatment systems contaminated with heavy metals in flow systems, whether continuous, in series or in parallel.
Through a cost-benefit analysis, where the unit cost of different investigations used and the adsorption capacities were considered, it was determined that cellulose has highly viable indicators when developing treatment systems.
Future studies should be carried out on a larger scale with a view to the industrial applications of this biomass, since in addition to its good adsorption capacity, it presents several advantages such as low cost.