Brilliant Red HE-3B Dye Biosorption by Immobilized Residual Consortium Bacillus sp. Biomass: Fixed-Bed Column Studies

Abstract

Residual biomass from various industries represents an important source of valuable compounds, used as raw materials for the production of a wide range of new products and also in various treatment and valorization processes or/and sanitation services, thus responding to the principles of sustainable development, waste recovery, and a green and circular economy. The aim of this work is to make use of residual Bacillus sp. biomass (resulting from a process of removing fatty acids from municipal wastewater) immobilized in alginate that, although it results in large quantities from biotechnological processes, is not reported to be valorized in dye biosorption processes, except in few specific applications. The biosorption potential of residual Bacillus sp. biomass in the reactive Brilliant Red HE-3B textile dye removal from aqueous systems was studied in a fixed-bed column. The effects of various experimental operating parameters, such as bed depth (h), flow rate (F_v), were investigated, and the modeling of experimental data based on Thomas and Yoon–Nelson kinetic models was satisfactorily achieved. The obtained results reconfirm that the studied residual biomass can be also considered as a good biosorbent in dynamic operating system, and can be beneficially used in the treatment of wastewater containing small quantities of organic dyes.

1. Introduction

In recent years, water pollution has become a worrying phenomenon of global interest. It is obvious that the natural environment is deteriorating more and more and that ecological systems can no longer adapt to the pressure of anthropogenic factors [1,2,3]. In this context, there have been numerous methods and technologies developed over time for the depollution of environmental components, depending on the polluted matrix, the nature of the polluting species, and the subsequent use of the decontaminated element (water, air, soil) [4,5,6,7,8,9,10,11,12]. Each of these methods and techniques has a number of advantages and disadvantages, the main impediments sometimes being related to high or even prohibitive costs, the impossibility of achieving complete depollution in a single stage, the generation of by-products with polluting potential, and the production of waste, which must be included in a new process of recovery and treatment, respectively.

Some water/wastewater treatment specialists consider that the most efficient and economic method of removing organic pollutants from water/wastewater is the use of biological treatment processes, as well as combinations of inexpensive physicochemical processes to ensure the required degree of purification for residuals or resulting pollutants, or even complete disposal.

Attention in recent years has been focused on the use of various “living” techniques for treating contaminated environmental components, especially with organic pollutants, harnessing and developing known information from the self-purification processes of environmental components [13,14,15,16,17,18].

Biological treatment is a flexible process that can be easily adapted to a multitude of wastewaters, characterized by different concentrations and compositions in polluting compounds, and has a few advantages related to the chemical treatment processes linked with the lack of need for separation of colloids and dispersed solid particles before treatment, lower energy consumption, and the possibility of using open tanks/reactors, thus resulting in lower costs and no need for waste/gas treatment. Chemical treatment related to biological treatment has the advantages of low sludge production, mineralization of non-biodegradable compounds, and smaller reactor volumes. The combination of physical–chemical and biological treatment processes for increasing large amounts of residuals/pollutants to be eliminated from final treated water/wastewater are preferred.

Adsorption continues to be among the often applied methods to retain certain categories of organic or inorganic pollutants, due mainly to advantages that are difficult to neglect: equipment for applications is easy to design and operate under advantageous conditions, the possibility of using a wide range of adsorbent materials (well-known commercial adsorbents, or “low cost” ones), and application-dependent in terms of the type of pollutant and the required process conditions. One alternative to adsorption onto commercial adsorbents (activated carbon, silica gel, exchangeable resins) is the use of residual biomass or different (bio)adsorbents capable of replacing the above mentioned well-known commercial adsorbents [8,9,10,11,12,13,14,15]. In this context, a viable treatment technique with vast practical applications is biosorption, a separation method that is based on the formation of extracellular and intracellular bonds, interactions that are dependent on the nature of the chemical species, the structure of the biosorptive material, the microbial metabolism, and the transport process [14,15,17,19]. Usually, the amount of biosorbent required in wastewater treatment is very large in a static regime (aerated open biosorption tank) and convenient in a dynamic regime (fixed/packed bed reactor) and has caused biosorbents to be a nonselective adsorbent for a wide range of molecular and ionic species found in wastewater, and they can also be used under aggressive or severe conditions that are often required for performing high biosorption capacities.

Improving the performances of the biosorption process is also possible through the use of a new type of biosorptive material, resulting from the immobilization of non-living/living cells on inert support (e.g., sand, paper or textile fibers, polymers, activated carbon, etc.), in a stage of cultivation or in the in situ immobilization of biomass/living biosorbents on inert supports within a biosorption process reactor (by physical adsorption, chemosorption due to covalent bonding, reticulation, enhancement, cross-linking), or encapsulation/entrapment (with a polymeric matrix) of residual microorganisms or microbial biomass. Several microorganisms have demonstrated high biosorption capacities compared to conventional adsorbents (ion-exchanging resins and celluloses, activated charcoal, various polymeric materials). However, their use is limited due to mechanical–physical problems, which can be solved by immobilization, obtaining particles with good physico–chemical stability (higher mechanical resistance). Several aspects need to be taken into account when selecting an appropriate immobilization technique, as immobilization involves additional costs, the diffusion of a contaminant through a support that increases the time and decreases the efficiency of the process, and also decreases the capacity of biosorbent due to interactions between the support and all active site of the biosorbent [17,19,20,21,22].

Immobilization on different media/supports gives microorganisms improved properties, but especially improves their ease of handling and their ready application for effluent treatment through a biosorption process. Immobilization techniques can be divided into two groups [23,24,25,26]:

(1)

passive—based on the property of the microorganism film formation. The supporting materials are in contact with the cellular suspension of a tested micro-organism for a period of time (before sterilization and inoculation with the starting microorganism suspension), after which a microorganism film is formed on the supporting surface. This technique offers a number of advantages over other immobilization methods, including the ease of immobilization (natural catching/fixing), no need for the addition of chemicals, high rate of mass transfer in particles, and ease of the immobilization technique extension. However, this technique can only be applied to microorganisms with a natural tendency to attach or aggregate on a solid support.

(2)

active—based on gel capture/entrapment and chemical cross-linking (covalent binding to vector compounds and reticulation). Gel capture/entrapment is the most widely used technique for immobilizing microorganisms within a polymeric matrix, made using natural polysaccharides (chitosan, agar, carrageenan or alginates), proteins (gelatin, collagen), or synthetic polymers (acrylamide, photo-reticulated resins, polyurethanes). However, chemical entrapment or cross-linking has greater disadvantages when micro-organisms are intended for immobilization, because chemical interaction (covalent binding or reticulation-involving glutaraldehyde or photocrossable resins) causes damage to the cell surface, drastically reducing cell viability.

Considering this basic information, our paper presents experimental results of a biosorption process study performed in a fixed-bed column for the removal of Brilliant Red HE-3B (BRed) anionic dye from aqueous solutions (low concentrations of anionic dye, <10 mg/L). All experiments were carried out using dead/non-living residual Bacillus sp. biomass (resulting from a process of removing fatty acids from wastewater) immobilized in sodium alginate; thus, only physical–chemical interactions of the biosorbent can be considered to take place in the aqueous media for the studied anionic dye removal (not biological processes, such as bioaugmentation and bioconcentration). The information from only batch studies (static regime) [27] was not enough to completely design an effluent treatment system in a continuous operating regime, and, thus, biosorption-based treatment in a dynamic regime was obviously recommended to be performed.

Therefore, this new biosorption study will consider the following issues: (i) the determination of the principal operating parameters influencing the biosorption process and their optimum values. For a complete description of dye-immobilized biomass system behavior and performance, all outcomes in this fixed-bed column reactor study were compared with our results from batch studies (static regime), which were carried out for the biosorption mechanism determination, especially from the equilibrium biosorption isotherms and the estimation of biosorption capacity of residual Bacillus sp. biomass immobilized in alginate for BRed anionic dye; (ii) the modeling of the biosorption process using the experimental data from a dynamic regime processed for the determination of the most important kinetic biosorption parameters and the corresponding kinetic biosorption model using the Thomas and Yoon–Nelson models, especially for a fixed or packed bed reactor; and (iii) the design of a packed/fixed bed (column) reactor for a large industrial scale setup, especially through proposing the main sizes of the packed bed reactor, considering the basic characteristics of the residual biomass and the maximum biosorption capacity that is experimentally found and comparing it with the proposed sizes of the aerobic open biosorption tank working in a static regime.

2. Experimental Section

2.1. Materials

Biosorbent: The experiments were carried out using a mixture composed of equal fractions of the following strains: Bacillus subtilis, Bacillus megaterium, Bacillus licheniformis and Bacillus orto-liquefaciens, which was used for the removal of fats, oils, and grease (solid waste) FOGS from municipal wastewater, at 35 °C and 150 rpm, in an aerobic system for 96 h [27]. The residual Bacillus sp. biomass was immobilized in sodium alginate according to a protocol presented in our previous work [27].

Dye: Brilliant Red HE-3B (BRed) (C.I. Reactive Red 120) is a reactive anionic dye (MW = 1463 g/mol, λ_max = 530 nm) and its chemical structure shown in Figure 1, which was selected as the reference model for this biosorption study. A stock solution (with concentration of 548 mg dye/L) was prepared using the commercial dye product (solid, salt form of analytical reagent grade) and bidistilled water; the working solutions with established concentrations were prepared from the stock solution by proper dilution with bidistilled water.

2.2. Methods Used for Quantitative Determinations

The residual dye concentration in the aqueous samples was periodically collected and was spectrophotometrically determined by measuring the absorbance at the maximum dye wavelength of 530 nm (BRed dye) with a JK-VS-721N VIS spectrophotometer, using an established calibration curve (range of working solution concentrations was in the Lambert–Beer region).

The solution pH value was directly measured using a portable Hanna pH-meter, and pH adjustment (when needed) was performed with 1 N HCl solution. For the biosorption process study in the dynamic regime, the pH value was established for the batch biosorption system (static regime), meaning a pH = 3.0, which permitted to achieve a biosorption capacity of 81.968 mg of BRed dye/g of immobilized biomass [27]. The biosorption capacities of the tested biosorbent based on residual biomass immobilized in sodium alginate were evaluated by means of the amount of biosorbed dye (Equation (1)):

$$q=\frac{C_0-C_e}{m}\cdot V$$

(1)

where C₀ and C_e are the initial and equilibrium concentrations of dye in the aqueous solution (mg/L); m is the amount of biosorbent (g), and V is the volume of treated solution (L).

The behavior of the residual Bacillus sp. Biomass immobilized in alginate for Bred dye biosorption (dynamic regime) was analyzed, considering the shape of the obtained breakthrough curve for each selected flow rate. These curves are represented by the plotting of the dye concentration of effluent (C_t), or relative dye concentration of effluent (C_t/C₀) as a function that is dependent on biosorption time (t) or treated effluent volume (V_t). The study of the breakthrough curve can be considered an important step in the evaluation of treatment performance and the dynamic response of a fixed bed in a biosorption column [28]. Usually, when C_t approaches 90% of its initial concentration (C₀), the biosorbent is closed to its exhausted form, and can be considered as essentially exhausted (C_exh) [29], or as a “spent” biosorbent. The breakthrough concentration (C_b) was chosen arbitrarily, beginning with a low value (e.g., C_t value when it is about 10% of the initial concentration) or a legislative norm for the residual dye concentration in treated wastewater, i.e., the maximum admissible concentration of dye in treated effluent (M.A.C. = 1 mg dye/L), or another required value due to imposed industrial operating regulations/norms.

The total biosorption time (t_ads) is considered to be the contact time (biosorbent–dye solution) after which the biosorbent is exhausted (C_t = C₀), meaning that the analyzed samples have a residual dye concentration value equal to, or even higher than, the initial dye concentration.

2.3. Dynamic Biosorption Procedure

2.3.1. Dynamic Biosorption Working Methodology

Dynamic biosorption studies were performed using a glass column with an inner diameter of 1.5 cm and a length of 21 cm. The column was packed with known varying amounts of residual biomass, immobilized in sodium alginate (solid biosorbent) in the form of granules with a diameter of 0.5 mm (around 3.8–6.77 g) providing a height/depth of fixed/packed bed of 3.8–7.0 cm. A dye solution with a known concentration (usually 76.72 mg/L) was inserted at the top of the column using a feeding funnel to ensure a uniform and continuous flowing regime. The passing of the dye solution through the column was done gravitationally, and the treated effluent was collected at the bottom of the column (outlet) for further analysis and control. At specific time intervals (10 min), 5 mL-samples of treated effluent were taken from the column outlet and analyzed with a UV-vis digital spectrophotometer to measure the residual dye concentration in the analyzed sample. In order to evaluate the proposed dynamic adsorption models, all experiments had to be performed considering the following operating parameters:

(1)

The feeding temperature and pH were stabilized at 25 °C and 3.0 based on the best results found in the batch adsorption study (static regime) [27];

(2)

Three different flow rates (F_vi = 2.9, 4.5 and 7.3 mL/min) of dye-containing solutions with the same concentration were passed through the fixed/packed biosorbent bed in the column, corresponding to the mass of biosorbent (m) equal to 3.800, 4.074 and 6.770 g, respectively.

(3)

All experiments were stopped when saturation was achieved and after further control (at least three samplings after the saturation point had equal or higher values than the initial dye concentration in the collected treated samples).

2.3.2. Biosorption Design in the Fixed/Packed Bed Column

In order to design an installation with a biosorption column with a solid biosorbent fixed/packed in a bed, a series of required operating parameters were determined, i.e., the mean flow of treated effluent per mass of biosorbent (b_i), to determine the optimal volume of treated effluent (V_opt), the biosorption time (t_ri) to the maximum admissible concentration of dye in the treated effluent (i.e., M.A.C. = 1 mg dye/L), and the size of a proposed biosorption tank or reactor (i.e., the height of fixed/packed bed (H_ads), the interior/inner diameter (D_R) and the height (H_R) of the biosorption reactor) working with granules of immobilized residual Bacillus sp. biomass.

Thus, the mean flow of treated effluent per mass of biosorbent, b_i, was calculated as per Equation (2) [30]:

$$b_i=\frac{V_n+n_i\cdot v}{m\cdot t_{ni}}(\mathrm{mL}/\mathrm{g}·\min )$$

(2)

where V_n is the treated effluent volume that passes through the packed bed, collected at the bottom of the column (mL); n_i is the number of samples periodically analyzed for residual dye content; v is the volume of each analyzed sample (v = 5 mL); m is the immobilized biosorbent mass (g), and t_ni is the total biosorption time until the maximum value of residual dye concentration in the treated effluent is reached (equal to or greater than the initial dye concentration in the aqueous solution) (min).

For each series of experiments performed at a certain effluent flow rate (F_vi), the biosorption time (t_ri) after which the treated effluent (passed through the packed biosorbent bed) has a residual dye concentration equal to the maximum admissible limit (M.A.C.) (M.A.C. = 1 mg dye/L) was established from a graphical representation of the residual dye concentration variations (mg of dye /L of solution) as a function of biosorption time (min) (i.e., C_i,dye = f(t_i)). Moreover, the optimal volume (V_opt) of treated effluent per biosorbent mass needed to be determined from the graphical representation of V_i = f(b_i), where V_i is the volume of the treated effluent with a certain flow rate (F_vi) passed through the mass (m_i) of fixed/packed biosorbent bed until the maximum admissible concentration of residual dye is attained (M.A.C.= 1 mg dye/L) (mL), and is calculated follwing Equation (3) (mL/g). b_i represents the mean effluent flow rate per immobilized biosorbent mass (mL/g.min) calculated using Equation (2) [30].

V_i = b_i × t_ri (mL/g)

(3)

Three values for V_i and b_i were calculated for each treated effluent flow rate (F_vi = 2.9, 4.5, and 7.3 mL/min) and were plotted; the optimal treated effluent volume per mass of fixed/packed biosorbent bed (V_opt) until the maximum admissible BRed dye concentration in the treated effluent were reached (dynamic regime, M.A.C. = 1 mg dye/L) was determined as the inflexion point of the graphical representation.

If the bulk density of biosorbent (ρ_ads) and V_opt for a certain estimated flow rate of the real effluent are known (e.g., F_vi = 20 L/h for the treated dye-containing effluent of a cotton fabrics’ manufacturing company), the main sizes of the biosorption (column) reactor can be calculated with the help of the biosorbent mass (M_ads), biosorbent volume in the column packed bed (V_ads), working flow rate (F_vi), biosorption time (t_ni), uniformity distribution coefficient (β) of biosorbent in the packed bed, and the estimated free space above the packed bed of biosorbent (λ), mainly considering the relations summarized in

Table 1. Relations used in the experimental design of the biosorption (column) reactor.

Biosorbent Mass, [kg]	Biosorbent Volume, [m3]	Internal Diameter of Biosorption (Column) Reactor, [m]	Height of Packed Bed, [m]	Height of Biosorption (Column) Reactor, [m]
$M_{ads}=\frac{F_v{}_i\cdot t_{ni}}{V_{opt}}$	$V_{ads}=\frac{M_{ads}}{{\rho }_{ads}}$	$D_R=\sqrt[3]{\frac{4\cdot M_{ads}}{\beta \cdot \pi \cdot {\rho }_{ads}}}$	$H_{ads}=\beta \cdot D_R$ β = 1–3	$H_R=\lambda \cdot H_{ads}$ (λ = 1–3)

[30,31].

2.4. Modeling of Experimental Biosorption Data in Dynamic Regime

In order to evaluate some characteristic biosorption parameters in a dynamic biosorption system, the experimental data were processed using two of the most well-known models from the scientific literature, i.e., the Thomas and Yoon–Nelson kinetic models [27,32,33,34]. These selected models were applied for the investigated biosorption system; the removal BRed dye using a fixed/packed bed of immobilized residual biomass operating in a continuous dynamic regime.

One of the most used sorption models in packed-bed column studies is considered to be the Thomas model, which assumes the Langmuir kinetics of biosorption–desorption without axial dispersion, and the hypothesis of the rate driving force corresponding to second-order reversible reaction kinetics [28]. The Thomas model does not rely on resistance to internal and external mass transfer, and does not consider the axial dispersion phenomenon [35], and is characterized as in Equation (4):

$$ln(\frac{C_0}{C_t}-1)=\frac{k_T\cdot q_{0\left(T\right)}\cdot m}{F_V}-\frac{K_T\cdot C_0}{F_V}\cdot V_t$$

(4)

where C₀ and C_t are the dye concentration at the initial moment (t = 0) and time t (mg/L); k_T is the Thomas constant (L/min^.mg); F_v is the effluent flow rate (L/min); q_0(T) is the maximum adsorptive capacity (mg/g); m is the weighted adsorbent mass (g) and V_t is the treated effluent volume at time t (L). The linear model corresponds to the graphical representation of ln(C₀/C_t − 1) versus V_t.

A simpler kinetic model was proposed by Yoon–Nelson [32]. This model assumed that the dye amount adsorbed in a packed bed is half of the total initial dye amount passing through the packed bed a within t_1/2 period [36], and the decrease in the adsorption rate for each adsorbed species is proportional to the probability of adsorbate breakthrough onto the adsorbent bed [37], according to Equation (5):

$$ln(\frac{C_t^{}}{C_0-C_t})=k_{YN}\cdot t-t_{1/2}\cdot k_{YN}$$

(5)

where k_YN is the Yoon–Nelson rate constant (min⁻¹); t_1/2 is the time required for 50% dye breakthrough; and t is the biosorption time (min). The linear model corresponds to the graphical representation of ln[C_t/(C₀ − C_t)] versus t.

The specific biosorption parameters of these two models are determined from the slope and intercepts of the characteristic graphical representations of their linearized forms, considering the specific theoretical assumptions for each one. For comparison of the experimental and calculated data with the proposed dynamic models, linear regression coefficients (R²) were used and their values must be close to unity for the best data accordance/agreement.

3. Results and Discussion

3.1. Breakthrough Curves

The breakthrough curve for the removal of BRed dye by a column loaded with a packed bed of residual Bacillus sp. biomass immobilized in alginate, represented in axial coordinates, showing dye concentration of effluent (C_t, mg/L), or relative dye concentration of effluent (C_t/C₀) versus biosorption time (t, min), is presented in Figure 2. It is known that the shapes of curves offer preliminary information on the nature of a studied biosorption process as well as the loading behavior of the dye in the biosorbent packed bed of the tested column. Additionally, some characteristic parameters of the biosorption process are presented in

Table 2. Characteristic parameters of the breakthrough curves.

Parameter	Significance and Characteristics	Experimental Values For Each Tested Flowrate (Fv), (mL/min)
		2.9	4.5	7.3
Biosorbent packed bed height—h (cm)	Height in column of each added immobilized biosorbent amount bed	4.0	7.0	3.8
Breakthrough time—tb (min)	Time required for attaining the breakthrough point, when the dye concentration has the value of 0.1 C0 (Cb)	7.0	4.0	1.5
Saturation time—ts (min)	Time required for attaining the saturation point, where dye concentration has a value of 0.9 C0 (Cs)	55.0	32.5	16.5
Length of mass transfer zone—L(MTZ) (cm)	$L(MTZ)=h\cdot \left(1-\frac{t_b}{t_S}\right)$ where h—the height of biosorbent bed (cm)	3.49	6.138	3.45
Breakthrough volume—Vb (mL)	Volume of treated effluent at breakthrough point, calculated as Vb = Fv × tb, where Fv is the flow rate (mL/min)	20.3	18.0	10.95
Saturation volume—Vs (mL)	Volume of treated effluent at saturation point, calculated as VS = Fv . tS, where Fv is the flow rate (mL/min)	159.5	146.25	120.45
Breakthrough capacity—qb (mg/g)	Amount of BRed dye retained per immobilized biosorbent mass at breakthrough point. $q_b=\frac{(C_0-C_b)\cdot V_b}{m}$ where m—adsorbent mass, g.	7.293 × 10−3	3.89 × 10−3	4.2 × 10−3
Saturation capacity—qS (mg/g)	Amount of BRed dye retained per immobilized biosorbent mass at saturation point $q_S=\frac{(C_0-C_S)\cdot V_S}{m}$ where m—adsorbent mass, g.	57.307	34.81	46.17
Rate of exhaustion—RAE (g/L)	Amount of exhausted immobilized biosorbent(g) per volume of treated effluent at the breakthrough point (L) $R_{AE}(g/L)=\frac{massofexhaustedadsorbent}{volumeofworkingsolution}$	0.2114	0.556	0.208

, which were determined from the slope and intercepts of the breakthrough curves in Figure 2.

From Figure 2, it can be observed that an increase in flow rate (F_v) leads to a decrease in breakthrough time (t_b), which suggests that biosorbent saturation is achieved much faster. This finding is also confirmed by the value of the penetration time (t_b) (Table 2), which is reduced with the increase of the treated effluent flow rate value, and also by the volume of the treated effluent, until the penetration point (breakthrough), which decreases from 909 mL (F_v = 2.9 mL/min) to 575 mL (F_v = 4.5 mL/min). A similar behavior is recorded for saturation time (t_s) and saturation volume (V_s), respectively; thus, the saturation time (t_s) is reduced from 55 min (F_v = 2.9 mL/min) to 16.5 min (F_v = 7.3 mL/min), and the breakthrough volume (V_b) decreases from 20.3 mL (F_v = 2.9 mL/min) to 10.95 mL (F_v = 7.3 mL/min).

All obtained data suggest that the biosorption of the BRed dye onto the granular biosorbent based on residual Bacillus sp. biomass immobilized on the alginate placed in a vertical column reactor depends on the flow rate (F_v), the height of the biosorbent fixed/packed bed (h) and the dye concentration (C_t) in the effluent passing through the fixed bed column.

3.2. Experimental Biosorption Data Modeling in a Dynamic Regime

The graphical representations of linearized equations of the Thomas and Yoon–Nelson kinetic models are illustrated in Figure 3, and the values obtained for the characteristic biosorption parameters of each model are systematized in

Table 3. Thomas and Yoon–Nelson models applied for BRed dye—residual Bacillus sp. biomass immobilized in an alginate biosorption system in a dynamic regime.

Model	Fv, Initial Flow Rate (mL/min)	kT (L/min mg)	q0(T) (mg/g)	R2	kYN (min−1)	t1/2 (min)	q0(YN) (mg/g)	R2	q0(Langmuir) * (mg/g)
Thomas	2.9 4.5 * 7.3	1.722 × 10−4 5.126 × 10−4 2.614 × 10−3	38.05	0.824 0.938 0.891					588.235 * [27]
Yoon–Nelson	2.9 4.5 7.3 *				0.0133 0.0393 0.179	11.166	34.742	0.875 0.938 0.947

(*) Note: For other flow rates, the experimental data are difficult to process and can lead to inadequate results.

.

The data presented in Table 3, in association with the graphical representations from Figure 3, underline some findings about the studied biosorption kinetics in the fixed/packed bed (column) reactor (dynamic regime):

• Because the plot ln[(C₀/C_t) − 1] versus V gives a straight line (Figure 3a) and the R² is lower than 0.938 (equal for F_v = 4.5 mL/min), the viable suggestion is that the Thomas kinetic model is relatively well fitted for modeling of kinetic data, especially for F_v ≥ 4.5 mL/min and the maximum biosorption capacity is of 38.05 mg/g.
• The linearity of plots ln[C_t/(C₀ − C_t)] versus t for all three tested flow rates and the high values of the correlation coefficient, R² (e.g., 0.947 for F_v = 7.3 mL/min), suggest that the biosorption kinetic of BRed dye onto residual biomass follows the Yoon-Nelson kinetic model, and the maximum biosorption capacity is of around 34.742 mg/g.
• Both kinetic models (Thomson and Yoon-Nelson) can be used to describe to biosorption kinetics of BRed anionic dye onto immobilised residual biomass when is working with flow rates higher than 4.5 mL/min.

As pointed out in the previous static study [27], the results show that the biosorption process of reactive BRed anionic dye by the immobilised residual biomass as biosorbent, is a physico-chemical process (based on competitive hydrogen bonding, π-π interactions, electrostatic interactions, ion-exchanges, covalent (coordinative) bonding, hydrophobic interactions) that proceeds properly at acidic pH, moderate dye concentrations in aqueous solution and ambient temperature (20–25 °C).

3.3. Biosorption Design in the Fixed/Packed Bed (Column) Reactor

The appropriate selection of the sizes of the fixed/packed bed in a biosorption (column) reactor influences the efficiency of the retention of reactive BRed anionic dye from the treated effluent, the biosorption operating time, the volume of treated effluent and the possibility of using relatively reasonable amounts of biosorbent for the retention of persistent organic pollutants such as organic dyes. This is why it is necessary to obtain experimental data to be properly processed for the determination of the sizes of the biosorption (column) reactor (e.g., for a large industrial setup scale application).

Based on the previously obtained experimental data, the following two operating parameters necessary for the design of the biosorption step in an industrial effluent treatment station (

Table 4. V_i vs. b_i variation and optimal volume (V_opt) determination.

Parameter	Significance and Characteristics	Experimental Values for Each Tested Flow Rate (Fv), (mL/min)
		2.9	4.5	7.3
Mean flow rate per immobilized biosorbent mass, bi (mL/g.min)	$b_i=\frac{V_n+n_i\cdot v}{m\cdot t_{ni}}$ where Vn is the treated effluent volume passing through the packed bed of immobilized biosorbent (mL); ni is the number of analyzed samples; v is the volume of analyzed sample (v = 5 mL); m is the biosorbent mass (g) and tni is the total biosorption time (min).	1.8757	0.6396	1.1248
Mean volume of treated effluent passing through the packed bed of biosorbent (mL) per immobilized biosorbent mass (g), Vi (mL/g)	$V_i=b_i\cdot t_{ri}$ The biosorption time until maximum admissible concentration of residual dye in the treated effluent (tri, (min)): 10, 7.86 and 5.652 min.	10.149	5.027	11.248

), meaning the mean flow rate of the treated effluent passing through the immobilized biosorbent fixed/packed bed (b_i) and the mean volume of the treated effluent passing through the immobilized biosorbent fixed/packed bed till the maximum admissible concentration attaining of residual dye in the treated effluent (V_i), were determined accordingly. The graphical representation (Figure 4) of these operating parameters will allow to determine the optimal volume (V_opt) of treated effluent which passes through the fixed/packed bed of immobilised residual biosorbent until imposed norms for the residual dye concentration in the treated effluent (M.A.C.).

The optimal volume of treated effluent passing through the immobilized biosorbent mass (V_opt) was found to be 11.248 mL/g or 11.248^.10³ m³/kg. In addition, the bulk density of immobilized residual biomass was considered to be of 576.65 kg/m³. The sizes of the biosorption (column) reactors were calculated using the relations from Table 1, considering the uniformity distribution coefficient of biosorbent in packed/fixed bed of β = 1.5 and the free space above the packed bed of λ = 2.

The relationships from Table 1 ensure an appropriate design of the biosorption (column) reactor according to the effluent flow rate to be treated and also the imposed constructive and experimental characteristics and operational restrictions. Thus, for a regular industrial effluent flow rate (i.e., textile effluent of a textile fabrics manufacturing company) of 50 m³/day (or 2.083 m³/h), the sizes of a biosorption (column) reactor working in a dynamic regime and of a static biosorption tank have been determined for comparison, taking into account a biosorption time of at least one day, and these data correspond to the values mentioned below:

Biosorption (column) reactor (dynamic regime) characterized by Vads = 17.251 m3; Mads = 9945.7 kg	DR = 1.671 m	Hads = 2.507 m HR = 3.76 m Efficiency: low–satisfactory, qmax = (34.742–38.05) mg/g
Radial biosorption tank/reactor (static regime) characterized by VR = min 52.783 m3; variable biosorbent amounts can be used	DR = 4.10 m	HR = 4 m (with aeration by air dispersion); Huseful = 3.6 m Efficiency: moderate–high, qmax = 588.235 mg/g [27]

The sizes determined for biosorption reactors working in the static or dynamic regimes are feasible and are able to be applied to a large-scale setup in the biosorption treatment step of industrial dye-containing effluents resulting from textile finishing processes, or different chemicals synthesis industries with good removal results, thus the legal requirements of the final effluent discharges can be well controlled and respected.

4. Conclusions

The experimental results confirmed that the studied residual biomass, immobilized in alginate, can be considered a very effective biosorbent in a static operating regime, but not for dynamic operating systems, especially when the intention is treat industrial effluents containing organic dyes.

The biosorption time until the regeneration of the “spent” biosorbent in the dynamic operating regime (working in a biosorption column reactor) is very low (10–15 min, or no more than 30 min), and thus better results were achieved in the static regime, which permitted the use of various amounts of immobilized biosorbent without additional problems, as shown in our previous data.

All the determined operating parameters were found to be better in the static regime (aerobic open biosorption tank) compared to the dynamic regime (fixed/packed bed reactor) for a temperature of 20 °C, pH = 3 and low dye concentrations in aqueous solutions (<10 mg dye/L). The optimum volume of dye-containing effluent passing through the immobilized biomass is not very high (only 11.248 mL/g) and the maximum biosorption capacity of immobilized residual Bacillus sp. consortia biomass for reactive BRed anionic dye varied in the range of 34.742–38.05 mg/g in the dynamic regime relative to the value of around 588.235 mg/g in the static regime.

The obtained results reconfirmed that the studied residual biomass immobilized in alginate can be considered as a good aspirant of biosorbent in an open tank with agitation by aeration (air bubbling or dissolved air dispersion) applied for the treatment of different effluents containing organic dyes in a static regime. If the open biosorption tank volume is restricted due to space limitations, a fixed/packed bed reactor can be a viable solution to retain anionic dyes from industrial effluents by biosorption onto immobilized residual biomass.