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Search String: (“fixed-bed” OR “column” OR “packed bed”) AND (“Cr(VI)” OR “hexavalent chromium” OR “chromium”) AND (“adsorption” OR “biosorption”) AND (“sawdust” OR “wood waste” OR “lignocellulosic” OR “biomass”)

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Table 1 summarizes key studies and their scope, highlighting the elements investigated in each. This systematic approach confirms that although individual elements (fixed-bed studies, real wastewater testing, model comparison, regeneration, speciation) have been reported separately, no prior study has combined all of them for Cordia africana sawdust. Specifically:

While individual elements have been reported separately, this study provides a comprehensive investigation combining multiple elements for Cordia africana sawdust. Based on the systematic review, the following specific contributions are identified:

Therefore, this study examined the dynamic adsorption performance of raw Cordia africana sawdust for Cr(VI) removal in a fixed-bed column system with the following specific objectives:

All results are reported as mean ± standard deviation (SD) from duplicate experiments, with the optimal run (Run 7) performed in triplicate. To support claims of significant effects, one-way analysis of variance (ANOVA) was performed using IBM SPSS Statistics (Version 26) to compare column performance parameters (t_b, q_e, MTZ) across flow rates (5, 8, 10 mL/min) and bed depths (6, 9, 12 cm). Tukey’s Honest Significant Difference (HSD) test was used for post-hoc multiple comparisons at α = 0.05. Confidence intervals (95%) were calculated for q_e, Thomas q₀, and Yoon-Nelson τ parameters. Uncertainty propagation for q_e was performed using the following equation:

where A represents the area under the breakthrough curve calculated by trapezoidal integration, and σ values are standard deviations from replicate experiments.

The operating pH of 5.5 was selected based on comprehensive preliminary batch optimization studies conducted on the same raw Cordia africana sawdust material. These studies investigated pH effects over the range 2-8 (Figure S1) and demonstrated maximum Cr(VI) removal efficiency (84.57 ± 2.1%) and adsorption capacity (1.99 ± 0.042 mg/g) at pH 5.5, with one-way ANOVA confirming a significant pH effect (F(6,14) = 32.4, p < 0.001). The selection of pH 5.5 over more acidic conditions (pH 2-3) represents a practical compromise considering:

While adsorption at pH 5.5 was significantly higher than at pH 3, 4, 7, and 8 (p < 0.05, Tukey’s test), it was not significantly different from pH 5 (p = 0.21) or pH 6 (p = 0.18). The PZC of the adsorbent (6.8) confirms that at pH 5.5, the surface carries a net positive charge, favoring electrostatic attraction with anionic Cr(VI) species (HCrO₄^-), which comprises approximately 94% of total Cr(VI) at this pH based on thermodynamic speciation calculations.

Preliminary Batch Optimization Data (pH Study): The full pH optimization data are presented in Table S1 and Figure S1. Briefly, the pH study covered the range 2-8 with 0.5 pH unit increments, using 0.2 g adsorbent, 50 mL solution (47 mg/L Cr(VI)), shaken at 150 rpm for 24 hours at 25°C. Maximum removal occurred at pH 5.5 (84.6%), with performance at pH 5.0 (82.1%) and pH 6.0 (80.3%) being statistically similar (p > 0.05).

The internal diameter was selected to maintain an appropriate column diameter-to-particle diameter ratio (>10) to minimize wall effects and ensure plug flow conditions [33]. Three bed heights—6 cm, 9 cm, and 12 cm—were tested to examine the effect of adsorbent depth on breakthrough behavior. The corresponding adsorbent masses were 7.63 ± 0.05 g, 11.44 ± 0.08 g, and 15.25 ± 0.10 g, respectively, based on the bulk density of the material (0.424 g/cm³).

To investigate different hydraulic conditions, the influent solution was introduced at flow rates of 5, 8, and 10 mL/min using a gravity flow system. These flow rates were chosen to provide a range of empty bed contact times (EBCT) from approximately 15 to 45 minutes, which are typical for fixed-bed adsorption systems [34]. Effluent samples were collected at 10-minute intervals for the first 60 minutes of each run to capture the initial breakthrough region (C/C₀ = 0.10-0.50), and thereafter at 20-minute intervals until column exhaustion (C/C₀ ≈ 0.95). This sampling frequency was selected to provide sufficient resolution for model fitting, particularly near the breakthrough point where the concentration gradient is steepest. For runs with very early breakthrough (e.g., Runs 2, 3, 6 with t_b ≤ 20 min), additional samples were collected at 5-minute intervals during the first 30 minutes. The total sampling duration ranged from 80 to 120 minutes depending on flow rate and bed depth. All experiments were conducted at pH 5.5.

Flow Configuration: Downflow gravity-fed system using a Mariotte siphon arrangement to maintain constant head (hydrostatic pressure: 45 ± 2 cm H₂O) throughout each experiment. Flow rate was controlled using a needle valve and verified gravimetrically every 15 minutes.

Bed Properties:

Bed Volumes:

Empty Bed Contact Time (EBCT): EBCT = Bed volume/Volumetric flow rate

Superficial Velocity (v_s): v_s = Q/(π × r²)

Reynolds Number (Re): Re = (ρ × vs × d_p)/μ

All Reynolds numbers are <1, confirming laminar flow and validating the plug-flow assumption for the fixed-bed column.

Channeling Diagnostics: Preliminary experiments with methylene blue dye tracer showed a uniform breakthrough front across the column cross-section, with no evidence of wall channeling or preferential flow paths. Bed compaction was <2% during operation (as measured by bed height observations).

The full factorial experimental design consisted of Table 2.

Each combination was run in duplicate (n = 2), providing 18 total experimental runs. The response variables measured were:

The factorial design enabled evaluation of:

The experimental setup is illustrated in Figure 1.

Raw tannery wastewater was freshly collected from the Batu Tannery effluent discharge point, located in Addis Ababa, Ethiopia. This factory processes raw hides and skins using conventional chrome tanning methods, generating wastewater with high chromium and other pollutant concentrations. Samples were collected in pre-cleaned high-density polyethylene containers and labeled with collection time, temperature, and initial pH.

To allow natural settling of large suspended particles, the wastewater was allowed to stand undisturbed for 12 hours at ambient temperature after collection. The clear upper layer was then carefully decanted, leaving the settled solids undisturbed. Subsequently, to remove smaller suspended particles and debris, the decanted sample was filtered first through a fine cloth (100 µm mesh) and then through a Whatman No. 42 filter paper to achieve a clarified effluent suitable for column studies. Any visible oil or grease floating on the surface was gently skimmed off. The sample was also refrigerated to help solidify residual oils, which were then removed by filtration through oil-absorbent pads. The pH of the filtered wastewater was measured with a calibrated pH meter and adjusted to pH 5.5 (the optimal operating condition) with 0.1 M HCl or 0.1 M NaOH. Finally, the pretreated wastewater was stored in clean glass bottles at 4°C to prevent biological activity and was used within four days to ensure sample integrity.

Important note on wastewater concentration: The raw wastewater characterization reflects the original, undiluted wastewater composition. After pretreatment (settling, filtration, pH adjustment), the Cr(VI) concentration remained approximately 35 mg/L—i.e., the wastewater was pretreated but not diluted. The synthetic solution was prepared at a reference concentration of 47 mg/L. Therefore, the comparison between synthetic and real wastewater (Section 3.5) represents a comparison at different initial Cr(VI) concentrations (47 mg/L vs. 35 mg/L), not a concentration-matched comparison. This difference should be considered when interpreting the reduced performance observed with real wastewater.

The authors acknowledge that this settling period may alter certain physicochemical properties of the wastewater. Specifically:

Potential changes during settling:

This settling step was necessary to prevent clogging of the fixed-bed column, as preliminary experiments showed that direct filtration of raw wastewater through the sawdust bed caused severe pressure drops and channeling within 2-3 hours of operation. The 12-hour settling period represents a practical compromise between preserving sample integrity and obtaining a treatable effluent. Readers should interpret the real wastewater results as performance for clarified, pre-treated tannery effluent rather than raw industrial discharge. All samples were stored in sealed containers at 4°C immediately after settling to minimize biological activity, and all column experiments were completed within 48 hours of collection to ensure sample consistency.

The real tannery wastewater was comprehensively characterized to determine its physicochemical properties before and after treatment. pH and temperature were measured on-site using a calibrated pH meter (Hanna Instruments HI98190) and thermometer. Electrical conductivity (EC) and total dissolved solids (TDS) were determined using a conductivity meter (Oakton CON 700) following standard procedures [37].

Total suspended solids (TSS) were measured by the gravimetric method after filtration through pre-weighed glass fiber filters (Whatman GF/C) and drying at 105°C to constant weight. Chemical oxygen demand (COD) was analyzed using the standard dichromate reflux method with mercuric sulfate added to eliminate chloride interference [38]. Sulfide, chloride, and sulfate concentrations were determined using standard titration and spectrophotometric methods according to APHA standard methods [37]. All analyses were performed in triplicate, and results are reported as mean ± standard deviation.

Heavy metals, including total chromium, Cr³⁺, Cr⁶⁺, Cu²⁺, Zn²⁺, Fe, Mn, and Cd, were quantified using Inductively Coupled Plasma Optical Emission Spectrometry (ICP-OES, PerkinElmer Optima 5300 DV). Hexavalent chromium (Cr⁶⁺) was specifically determined using the 1,5-diphenylcarbazide colorimetric method at 540 nm using a UV-Vis spectrophotometer (Shimadzu UV-1800), which provides selective determination of Cr(VI) in the presence of other metals [32]. The method detection limit for Cr(VI) was 0.005 mg/L, and calibration standards were prepared fresh for each analysis session (R² > 0.999 for all calibration curves).

Sample preservation: All wastewater samples were preserved according to standard methods [30]. For metal analysis, samples were acidified with concentrated HNO₃ to pH < 2 and stored in acid-washed polyethylene bottles at 4°C. For Cr(VI) analysis, samples were filtered immediately (0.45 µm) and analyzed within 24 hours without acidification to preserve chromium speciation.

Digestion procedure (EPA Method 3050B): For total metal analysis, 50 mL of homogenized sample was transferred to a digestion vessel with 5 mL concentrated HNO₃ and heated at 95°C for 15 minutes. After cooling, 2.5 mL of concentrated HNO₃ was added and the mixture was refluxed. The process was repeated until no brown fumes were visible. The digestate was filtered (Whatman No. 42), diluted to 50 mL with distilled water, and stored at 4°C before ICP-OES analysis.

Calibration standards: Multi-element standard solutions (1000 mg/L, Merck) were diluted to prepare calibration curves at 0.1, 0.5, 1.0, 5.0, 10.0, 25.0, and 50.0 mg/L for each target metal. Calibration curves were prepared fresh for each analysis session and exhibited R² > 0.999 for all elements.

Quality assurance/quality control (QA/QC): Method blanks, spike samples, and certified reference material (CRM-TMDW, High Purity Standards) were analyzed with each batch of 20 samples. The following QC criteria were applied:

ICP-OES operating conditions (PerkinElmer Optima 5300 DV): RF power: 1300 W, Plasma gas flow: 15 L/min Ar, Auxiliary gas flow: 0.2 L/min Ar, Nebulizer gas flow: 0.8 L/min Ar, View mode: Axial for trace metals, radial for major elements, Wavelengths (nm): Cr 267.716, Cu 324.754, Zn 213.857, Fe 238.204, Mn 257.610, Cd 228.802 and Integration time: 5-10 seconds per wavelength.

The total amount of chromium adsorbed by the column (M_a) was calculated from the area between the influent and effluent concentration curves up to the exhaustion time. This represents the cumulative mass of chromium retained by the adsorbent bed during column operation and was determined using the following equation [3,13,42]:

where M_a is the total amount of metal adsorbed (mg), Q is the volumetric flow rate (L/min), C₀ is the influent chromium concentration (mg/L), C_t is the effluent concentration at time t (mg/L), and t_e is the column exhaustion time (min). The integral was evaluated numerically using the trapezoidal rule based on experimental data [14,43].

The dynamic adsorption capacity (q_dyn) indicates the effective adsorption capacity of the adsorbent under flow conditions and was calculated by normalizing the total adsorbed metal with respect to the mass of adsorbent packed in the column [14,15,44]:

where q_dyn is the dynamic adsorption capacity (mg/g) and m is the mass of adsorbent in the column (g).

The overall removal efficiency (%) of the column was determined by comparing the total amount of chromium removed by the adsorbent to the total amount of chromium introduced into the column during the operating period [13,16,45]:

Bed utilization efficiency was used to evaluate the efficiency with which the adsorbent bed was utilized prior to breakthrough. It was calculated as the ratio of the amount of chromium adsorbed at breakthrough time (M_b) to the total amount adsorbed at exhaustion (M_a) [9,15,46]:

A higher bed utilization efficiency indicates more effective use of the adsorbent before breakthrough and reflects favorable mass transfer characteristics within the fixed-bed column.

For fixed-bed column adsorption, the efficiency is also determined using the mass transfer zone length (MTZ, cm) on the adsorbent layer where 10-90% of the influent concentration changes to effluent concentration, which is expressed as Equation (9) [17,47]:

where H is the bed depth (cm), additionally, the total amount of chromium entering the column (W_t, mg), the percentage removal (R, %) of the column, the total effluent volume (V_e, mL), and total breakthrough volume (V_b, mL) were estimated using Equations (10)-(13), respectively [18,48]:

The breakthrough curve analysis formed the basis for subsequent fixed-bed adsorption modeling using BDST, Thomas, and Yoon-Nelson models, enabling quantitative interpretation of column performance and comparison with previously reported studies [10,11,12,13,18,49].

The Bed Depth Service Time (BDST) model was applied to examine the relationship between bed height and breakthrough time, assuming that adsorption is controlled by surface reaction kinetics and that axial dispersion effects are negligible. The BDST model is particularly useful for preliminary column design and scale-up studies [20,52].

The BDST model, originally developed by Bohart and Adams [7], is expressed as:

where t_b is the breakthrough time (min), N₀ is the adsorption capacity per unit bed volume (mg/L), Z is the bed depth (cm), C₀ is the influent concentration (mg/L), C_b is the breakthrough concentration (mg/L), υ is the linear flow velocity (cm/min), and k_a is the kinetic constant of the BDST model (L/mg·min). Each term in the equation is dimensionally consistent, with both the slope and intercept contributions yielding time units.

A linear plot of breakthrough time (t_b) versus bed depth (Z) was used to determine N₀ from the slope and k_a from the intercept. A good linear fit indicates the applicability of the BDST model to the column system and validates its use for design purposes. Standard errors for N₀ and k_a were calculated from the regression analysis.

The Thomas model was used to describe the adsorption process assuming Langmuir kinetics, negligible axial dispersion, and constant adsorption-desorption rates [8]. This model is widely applied to estimate the maximum adsorption capacity of fixed-bed columns and evaluate the influence of flow rate and influent concentration [9,16,20,53].

The Thomas model equation is given as:

where k_Th is the Thomas rate constant (L/mg·min), q₀ is the maximum solid-phase concentration of the adsorbate (mg/g), m is the mass of adsorbent in the column (g), Q is the volumetric flow rate (L/min), C₀ is the influent concentration (mg/L), C_t is the effluent concentration at time t (mg/L), and t is the flow time (min).

The parameters k_Th and q₀ were obtained from the slope and intercept of the linear plot of ln[(C₀/C_t) - 1] versus time. Higher q₀ values indicate superior adsorption capacity of the adsorbent under dynamic conditions. Standard errors for k_Th and q₀ were calculated from the regression analysis.

The Yoon-Nelson model is a simplified probabilistic model based on the principle that the rate of decrease in the likelihood of adsorption is proportional to the probability of both adsorption and breakthrough occurring [9]. Unlike other models, it does not require detailed information on adsorbent characteristics, adsorption mechanisms, or physical properties of the adsorption bed [16,54].

The Yoon-Nelson equation is expressed as:

where k_YN is the Yoon-Nelson rate constant (min^-1), and τ is the time required for 50% breakthrough (min).

A linear plot of ln[C_t/(C₀ - C_t)] versus time was used to determine k_YN from the slope and τ from the intercept. The parameter τ provides a direct estimate of the column service time and is particularly useful for comparing breakthrough behavior under different operating conditions. Standard errors for k_YN and τ were calculated from the regression analysis.

Together, these models provided complementary insights into the fixed-bed adsorption behavior and were used to validate experimental observations and support column performance evaluation for potential scale-up applications.

In addition to R², model performance was evaluated using:

Root Mean Square Error (RMSE):

Mean Absolute Error (MAE):

Normalized Root Mean Square Error (NRMSE):

Coefficient of Determination (R²):

Model comparisons were made using Akaike Information Criterion (AIC) to account for model complexity:

where n is the number of data points, RSS is the residual sum of squares, and k is the number of model parameters.

While keeping constant bed depths (6, 9, and 12 cm), the effect of influent flow rate on Cr(VI) adsorption onto raw Cordia africana sawdust was evaluated at three different flow rates (5, 8, and 10 mL/min). All experiments were performed in triplicate, and the results presented in Table 3 represent mean values with standard deviations. As shown in Figure 6, the breakthrough curves clearly demonstrated that increasing the flow rate significantly affected column performance, with steeper curves and earlier breakthrough at higher flow rates.

At the lowest flow rate (5 mL/min), the breakthrough time (C/C₀ = 0.10) was longest for all bed depths, and the exhaustion time (C/C₀ ≈ 0.95) was significantly delayed. For example, at a bed depth of 12 cm (Run 7), breakthrough occurred at approximately 50.0 min at 5 mL/min, whereas it shifted earlier to 35.0 min at 8 mL/min (Run 8) and further decreased to 36.0 min at 10 mL/min (Run 9). A similar trend was observed at 6 cm and 9 cm bed heights. This behavior is attributed to the increase in flow rate, which allows more influent to pass through the column, which exposes more Cr(VI) ions to the active sites of the adsorbent but with insufficient contact time for complete adsorption [9,19,55].

As the flow rate increased from 5 to 10 mL/min at 12 cm bed depth, the following effects were consistently observed across all bed depths:

Critical Distinction Between Service Time and Exhaustion Capacity: A careful interpretation of these results is necessary. While lower flow rates (5 mL/min) provided longer breakthrough times (50.0 min vs. 36.0 min at 10 mL/min), the calculated q_e values were lower at 5 mL/min (1.34 mg/g) than at 10 mL/min (1.78 mg/g). This apparent paradox arises because q_e is calculated at exhaustion (C/C₀ ≈ 0.95), which occurs earlier at higher flow rates. At 10 mL/min, the column saturates more rapidly (80 min vs. 120 min at 5 mL/min), so the breakthrough curve integrates to a higher qe value because the effluent concentration reaches the influent concentration faster, leaving less bed capacity unused. At lower flow rates, the extended exhaustion time means the bed operates for a longer period, but the gradual saturation profile results in a lower calculated q_e when normalized by adsorbent mass.

Therefore, q_e should be interpreted as a reflection of the integration limits rather than a measure of adsorbent efficiency. The more relevant metric for practical applications is breakthrough capacity (q_b) and bed utilization efficiency at breakthrough (q_b/q_e × 100%), which was higher at 5 mL/min (Run 7: q_b = 0.56 mg/g, utilization = 41.8%) than at 10 mL/min (Run 9: q_b = 0.80 mg/g, utilization = 44.9%). This indicates that at lower flow rates, a greater proportion of the bed capacity is utilized before breakthrough occurs.

The earlier breakthrough at higher flow rates is attributed to reduced contact time between Cr(VI) ions and available adsorption sites within the packed bed [21,22,56]. The shorter residence time limits intraparticle diffusion and reduces effective mass transfer, causing faster column saturation [21,22,57]. Conversely, at lower flow rates, longer residence time enhances external mass transfer and intraparticle diffusion, allowing more efficient utilization of active sites [21,23,51].

Statistical Significance: Two-way ANOVA results (Table 4) confirmed that the effects of flow rate and bed depth on breakthrough time were significant (p < 0.01 for both factors), with no significant interaction between factors (p = 0.087). Tukey’s HSD post-hoc analysis revealed that the 5 mL/min flow rate produced significantly longer breakthrough times compared to both 8 mL/min (p = 0.008) and 10 mL/min (p = 0.003) at 12 cm bed depth. However, differences in q_e between 5 mL/min and 10 mL/min at 12 cm bed depth were not statistically significant (p = 0.087), indicating that the apparent increase in q_e at higher flow rates should be interpreted with caution. The interaction between flow rate and bed depth was not significant for any response variable (p > 0.05 for all).

Overall, the results demonstrate that lower flow rates (5 mL/min) improve column service time and bed utilization efficiency. In contrast, higher flow rates (10 mL/min) accelerate column saturation and yield higher q_e values due to faster exhaustion. For practical applications prioritizing effluent quality and extended operation between regenerations, lower flow rates are preferred.

The effect of column depth on Cr(VI) adsorption was investigated by varying the packed bed height (6, 9, and 12 cm) while maintaining constant flow rates (5, 8, and 10 mL/min). The breakthrough data presented in Table 3 and Figure 7 clearly demonstrate that increasing the bed height significantly enhances column performance, elayed breakthrough and extended service life.

At the optimum flow rate of 5 mL/min, breakthrough occurred earliest at 6 cm (approximately 30 min, Run 1), was delayed at 9 cm (approximately 30 min, Run 4), and was longest at 12 cm (approximately 50 min, Run 7). The deeper bed provided several advantages:

As a result, total chromium uptake and treated volume before breakthrough increased substantially with bed height. At 5 mL/min, the volume treated before breakthrough increased from 150 mL at 6 cm to 250 mL at 12 cm (Table 3). Dynamic adsorption capacity at breakthrough (q_b) showed improvement with increasing bed depth, with the 12 cm bed achieving more gradual saturation and better utilization of the adsorbent bed.

The improved performance with increasing bed depth can be attributed to several factors. First, the longer bed provides more time for Cr(VI) ions to diffuse from the bulk solution to the adsorbent surface and into the internal pore structure [25,58]. Second, the greater adsorbent mass provides a larger number of binding sites, delaying saturation. Third, axial dispersion effects become less significant relative to the bed length, promoting more plug-like flow conditions [32].

The mass transfer zone length (MTZ) increased with bed depth at all flow rates, as shown in Table 2. For example, at 5 mL/min, MTZ increased from 3.75 cm at 6 cm bed depth to 7.0 cm at 12 cm bed depth. This indicates that while deeper beds provide longer service times, they also contain a larger zone of partial saturation at breakthrough, which must be considered in design calculations [59].

Overall, increasing the column depth from 6 to 12 cm significantly improved chromium removal performance, delayed breakthrough, and enhanced bed utilization efficiency. These findings confirm that bed height is a critical design parameter in fixed-bed adsorption systems, directly influencing mass transfer behavior, adsorbent utilization, and column lifetime [21,22,23,24,25,60].

The Thomas model was applied to describe the dynamic behavior of Cr(VI) adsorption in the fixed-bed column packed with raw Cordia africana sawdust. The model showed good agreement with the experimental breakthrough data, as indicated by high R² values (>0.98) across all operating conditions (Table 6). This suggests that the adsorption process followed second-order reversible reaction kinetics and that external and internal diffusion limitations were not dominant under the studied conditions [8,19,62].

Figure 9a (Thomas plot at constant bed depth of 9 cm) shows the relationship of ln[(C₀/C_t) - 1] versus time for flow rates of 5, 8, and 10 mL/min. The approximately linear relationships confirm that the Thomas model adequately describes the dynamic adsorption behavior of Cr(VI) under the studied conditions. The high R² values (0.984-0.993) obtained across all experimental runs indicate that the model assumptions are valid for this adsorbent-adsorbate system.

As the flow rate increased from 5 to 10 mL/min at a constant bed depth, the slope of the plot became steeper, indicating an increase in the Thomas rate constant (k_Th). At 9 cm bed depth, k_Th increased from 1.06 × 10^-4 to 2.41 × 10^-4 L/mg·min as flow rate increased from 5 to 10 mL/min (Table 6). This increase in k_Th is associated with faster mass transfer due to higher hydraulic loading and reduced external film resistance at higher flow velocities [63]. However, despite the higher rate constant, breakthrough occurred earlier at higher flow rates because the contact time between chromium ions and the adsorbent surface decreased, limiting the extent of adsorption.

At the lower flow rate (5 mL/min), the curve shifted toward longer time, indicating prolonged breakthrough time and improved column utilization. The Thomas adsorption capacity (q₀) increased with decreasing flow rate, with better performance observed at lower flow rates across all bed depths (Table 6).

Figure 9b (Thomas plot at constant flow rate of 8 mL/min) presents the relationship of ln[(C₀/C_t) - 1] versus time for bed depths of 6, 9, and 12 cm. The graph clearly shows that increasing the bed depth from 6 to 12 cm resulted in a noticeable upward shift and extension of the linear region toward longer times. At 8 mL/min, the ln[(C₀/C_t) - 1] values at 50 min were approximately 0.1 for 6 cm, while the 12 cm bed maintained higher values for extended operation. The deeper bed exhibited a more extended linear region, indicating improved adsorption performance and delayed breakthrough.

The increase in bed height provides a larger adsorbent mass and more active sites, thereby increasing adsorption capacity. As shown in Table 4, q₀ increased from 1.32 mg/g at 6 cm to 1.98 mg/g at 12 cm for 8 mL/min. At 5 mL/min, q₀ increased from 1.91 mg/g at 6 cm to 1.51 mg/g at 12 cm (Run 7), demonstrating that deeper beds generally provide greater total adsorption capacity.

The extended residence time in deeper beds enhances solute-adsorbent interaction, allowing more chromium ions to diffuse into the internal pore structure of the sawdust particles [64]. In contrast, the shallow bed (6 cm) reached breakthrough much earlier due to limited adsorption sites and shorter contact time, as reflected in the rapid decline of ln[(C₀/C_t) - 1] values after 40-50 minutes. This confirms that bed depth strongly influences column service time and overall adsorption efficiency [9,26,65].

The Thomas rate constant (k_Th) generally decreased with increasing bed depth at constant flow rate. For 8 mL/min, k_Th decreased from 2.23 × 10^-4 L/mg·min at 6 cm to 1.86 × 10^-4 L/mg·min at 12 cm. This decrease reflects the longer path length and greater resistance to mass transfer in deeper beds, although the overall adsorption capacity increases due to greater adsorbent mass [66].

Overall, the Thomas model adequately predicted breakthrough behavior and can be reliably used for the design and scale-up of the fixed-bed adsorption system for Cr(VI) removal using raw Cordia africana sawdust [8,19].

The Yoon-Nelson model was also applied to analyze the breakthrough data. This model assumes that the rate of decrease in the probability of adsorption is proportional to both the probability of adsorption and the probability of adsorbate breakthrough, providing a simple but effective representation of breakthrough behavior without requiring detailed information about the adsorbent characteristics or the adsorption system [9,16,67]. The experimental results showed good agreement with the model predictions, as reflected by high R² values (0.984-0.993) across all experimental conditions (Table 6).

Figure 10a presents the Yoon-Nelson plot of ln[C_t/(C₀ - C_t)] versus time at a constant bed depth of 9 cm for all flow rates (5, 8, and 10 mL/min). The good linear relationships confirm the applicability of the Yoon-Nelson model for describing breakthrough behavior in this system. The high correlation coefficients (R² = 0.984-0.993) indicate that the model effectively captures the dynamics of Cr(VI) adsorption onto raw Cordia africana sawdust.

As the flow rate increased from 5 to 10 mL/min at constant bed depth, the lines shifted upward and became steeper, indicating a higher Yoon-Nelson rate constant (k_YN) and a shorter time required to reach 50% breakthrough (τ). At 9 cm bed depth, k_YN increased from 0.00498 min^-1 to 0.0113 min^-1 as flow rate increased from 5 to 10 mL/min (Table 6), while τ decreased correspondingly from 48.2 min to 22.8 min. This behavior reflects the faster saturation of the adsorption bed at higher hydraulic loading rates due to reduced contact time [34,68].

At the lower flow rate (5 mL/min), the breakthrough time was substantially delayed (τ = 52.0 min at 12 cm bed depth, Run 7), reflecting better column performance due to longer interaction time between Cr(VI) and the raw sawdust adsorbent. The longer residence time at lower flow rates allows chromium ions to penetrate deeper into the porous structure of the adsorbent and access more active sites before breakthrough occurs [69].

The Yoon-Nelson rate constant (k_YN) increased at higher flow rates across all bed depths, indicating faster saturation of the adsorption bed [34]. For example, at 12 cm bed depth, k_YN increased from 0.00573 min^-1 to 0.0107 min^-1 as flow rate increased from 5 to 10 mL/min (Runs 7, 8, and 9). This trend is consistent with the Thomas model results and confirms that higher flow rates accelerate column saturation.

Figure 10b (Yoon-Nelson plot at constant flow rate of 8 mL/min) presents the relationship of ln[C_t/(C₀ - C_t)] versus time for bed depths of 6, 9, and 12 cm. The graph clearly shows that increasing the bed depth from 6 to 12 cm resulted in a noticeable upward shift and extension of the linear region toward longer times. The deepest bed (12 cm) exhibited the most gradual increase in ln[C_t/(C₀ - C_t)] values, maintaining lower values for extended operation periods before reaching the 50% breakthrough point (where ln[C_t/(C₀ - C_t)] = 0).

At constant flow rate (8 mL/min), increasing the bed depth from 6 to 12 cm substantially increased the time required to reach 50% breakthrough (τ). From Table 4, τ increased from 13.8 min at 6 cm (Run 2) to 36.5 min at 12 cm (Run 8). The deeper bed showed a clear shift toward longer operation time before saturation, indicating enhanced service life and improved adsorption performance.

The deeper bed provided a wider mass transfer zone and greater chromium removal efficiency, as reflected in the higher τ values [64]. The shallow bed (6 cm) exhibited faster breakthrough and a steeper slope in the Yoon-Nelson plot, as seen in the rapid increase of ln[C_t/(C₀ - C_t)] values from approximately -2.9 at 10 min to positive values by 50-60 min. This reflects quicker saturation of available adsorption sites due to the limited adsorbent mass and shorter contact time.

The good linearity of the plots across all experimental conditions further confirms that the Yoon-Nelson model reliably predicts dynamic adsorption behavior in the fixed-bed system. The model’s simplicity and minimal data requirements make it particularly suitable for practical applications and performance prediction in industrial settings where detailed adsorbent characterization may not be available [29].

The consistency between experimental data and model predictions demonstrates that the Yoon-Nelson model effectively describes the adsorption dynamics of Cr(VI) onto raw sawdust. The τ values obtained from the model match the experimentally observed 50% breakthrough times, validating the model’s predictive capability.

The Bed Depth Service Time (BDST) model was applied to examine the relationship between bed depth and service time at different breakthrough levels. At a constant flow rate of 8 mL/min, Figure 11 shows the relationship between service time and bed depth for chromium adsorption at breakthrough levels of 10%, 20%, 30%, 40%, and 50% s. The linear relationships observed at all breakthrough levels, with correlation coefficients ranging from R² = 0.965 to 0.994 (Table 7), confirm the applicability of the BDST model to this adsorption system.

The results show that the adsorption capacity per unit bed volume (N₀) increases gradually as the breakthrough percentage increases from 10% to 50%. N₀ increased from 1252 mg/L at 10% breakthrough to 2132 mg/L at 50% breakthrough, representing an increase of approximately 70% over the range studied. This behavior indicates that the column can utilize more of its adsorption capacity when higher breakthrough levels are allowed, as a greater portion of the adsorbent bed becomes saturated before the column is considered exhausted [7,19,33,70]. At lower breakthrough levels (e.g., 10%), the column is stopped early, leaving a significant portion of the adsorbent capacity unused.

The BDST rate constant (k_a) decreases at higher breakthrough levels, from 0.00936 L/mg·min at 10% breakthrough to 0.00089 ± 0.00015 L/mg·min at 50% breakthrough (Table 7). This trend suggests a reduction in the overall adsorption driving force and mass transfer rate as the column approaches saturation [7,19,33,71]. At early stages of operation (low breakthrough percentages), the concentration gradient between the influent solution and the adsorbent surface is high, promoting faster adsorption kinetics. However, as active sites become occupied and the column approaches higher breakthrough levels, the adsorption rate slows down dramatically, reflected in the decreasing k_a values.

Interpretation of k_a at 50% breakthrough: The low k_a value at 50% breakthrough (0.00089 ± 0.00015 L/mg·min) indicates that the intercept of the BDST plot is very small (1.8 ± 0.8 min). Regression analysis revealed that the intercept is not significantly different from zero (p = 0.067), meaning the BDST plot passes very close to the origin at this breakthrough level. This is physically reasonable because at 50% breakthrough, the column is approximately half-saturated, and the adsorption driving force is substantially reduced. However, the uncertainty in k_a at 50% breakthrough (±0.00015 L/mg·min) represents approximately 17% relative standard error, suggesting that the parameter estimate is less reliable at this breakthrough level. The authors acknowledge that k_a values approaching zero at high breakthrough levels should be interpreted qualitatively as an indicator of reduced driving force rather than as a precise kinetic constant. Mechanistic validation (e.g., through independent mass transfer experiments) would be required to confirm whether k_a truly approaches zero or whether this reflects a regression artifact.

The high correlation coefficients (R² > 0.96) across all breakthrough levels confirm the strong agreement between the experimental data and the BDST model predictions. Notably, the best linearity is observed at higher breakthrough percentages (40-50%), with R² values of 0.993 and 0.994, respectively. This indicates that the BDST model provides more accurate predictions as the column approaches saturation, which is useful for understanding total bed capacity. However, for design purposes, lower breakthrough levels (10-20%) are typically more relevant for meeting regulatory effluent limits [72].

The BDST model parameters presented in Table 4 can be used to predict column performance at different bed depths without conducting additional experiments, making it a valuable tool for scale-up. For example, using the parameters obtained at 8 mL/min, the service time at any bed depth for a given breakthrough level can be calculated using the BDST equation:

where the intercept term incorporates the natural logarithm of the breakthrough ratio, this capability is particularly useful for designing full-scale treatment systems based on laboratory-scale experimental data [69].

BDST regression details (50% breakthrough):

The trend of decreasing k_a with increasing breakthrough level is consistent with the progressive saturation of adsorption sites. At early stages (10% breakthrough), the concentration gradient between the influent and the adsorbent surface is high, promoting faster adsorption kinetics. As the column approaches higher breakthrough levels, active sites become occupied, the driving force decreases, and the adsorption rate slows dramatically, reflected in the decreasing k_a values.

All three models showed excellent fit with R² > 0.98 and low error metrics as shown in Table 8. The BDST model exhibited the lowest RMSE (1.68 mg/L) and AIC (39.8), indicating slightly better performance for the 50% breakthrough level. Residual analysis confirmed random distribution with no systematic trends, and Shapiro-Wilk tests (p > 0.05) indicated normally distributed residuals for all models. However, the differences in RMSE (1.68-1.84 mg/L) represent less than 4% of the influent concentration (47 mg/L), suggesting that all three models are practically equivalent for describing breakthrough behavior under the studied conditions.

Model Selection Guidance: For design purposes (predicting breakthrough at low C/C₀ ratios), the Thomas and Yoon-Nelson models are more appropriate as they directly model the entire breakthrough curve. The BDST model is most useful for scale-up and for determining the required bed depth for a desired service time at a given breakthrough level. The choice of model should be guided by the specific application: BDST for preliminary design, Thomas for capacity estimation, and Yoon-Nelson for service time prediction.

Model Assumption Verification: The Thomas and BDST models carry specific assumptions that were not independently verified in this study:

Thomas Model Assumptions:

BDST Model Assumptions:

The high R² values (0.984-0.993) indicate the models provide good mathematical descriptions of the breakthrough curves. However, the agreement between model and data should not be interpreted as proof that the underlying mechanisms (Langmuir kinetics, surface reaction control, negligible dispersion) are physically correct. Independent experiments (e.g., tracer studies for axial dispersion, diffusion coefficient measurements, intraparticle diffusion studies) would be required to validate the mechanistic assumptions. The authors recommend such studies for future investigations.

Model Validation Limitations: While the three models showed excellent fit to experimental data (R² > 0.98, RMSE < 1.84 mg/L), the following limitations should be acknowledged:

Therefore, high R² values should be interpreted as indicating good descriptive capability for the experimental data rather than definitive proof that the underlying model assumptions are physically correct. Future studies should employ cross-validation with independent datasets, incorporate additional bed-depth values for BDST analysis, and consider nonlinear fitting approaches.

The real wastewater used in column experiments had an initial Cr(VI) concentration of 35.00 ± 0.74 mg/L after pretreatment (settling, filtration, oil removal, pH adjustment to 5.5). The synthetic solution was prepared at 47 mg/L as a reference concentration. Therefore, the breakthrough curve comparison (Figure 13) is not a concentration-matched comparison; it compares breakthrough curves at different influent concentrations (47 mg/L synthetic vs. 35 mg/L real wastewater). This difference is acknowledged as a limitation of the study.

Figure 13 presents a comparison of breakthrough curves for a synthetic Cr(VI) solution (47 mg/L) and real tannery wastewater (35 mg/L) under identical operating conditions (12 cm bed height, 5 mL/min flow rate, pH 5.5). The data points are plotted with clear markers and error bars representing standard deviations from duplicate experiments.

From the figure, several important observations can be made:

This behavior is expected and consistent with the complex composition of real tannery wastewater. The presence of competing metal ions (Cu²⁺, Zn²⁺, Fe²⁺/Fe³⁺) and anions (sulfates, chlorides) creates competition for the available adsorption sites on the sawdust surface [61]. These competing species may bind to the same functional groups (hydroxyl, carboxyl, phenolic) responsible for Cr(VI) uptake, thereby reducing the effective capacity for chromium removal.

The total dynamic adsorption capacity of raw Cordia africana sawdust was substantially higher for the synthetic chromium solution (1.78 ± 0.06 mg/g at 47 mg/L) than for real tannery wastewater (1.51 ± 0.28 mg/g at 35 mg/L) under identical operating conditions. This represents an approximately 15% reduction in dynamic capacity, which is comparable to or better than reductions reported for other adsorbents when transitioning from synthetic to real wastewater matrices [77].

The observed reduction in dynamic capacity from 1.78 mg/g (synthetic, 47 mg/L) to 1.51 mg/g (real wastewater, 35 mg/L) represents a 15.2% decrease. To estimate the contribution of the concentration difference versus matrix effects, the following analysis is provided:

Using the Thomas model q₀ values (which account for concentration effects) at 12 cm bed depth and 5 mL/min, the predicted capacity at 35 mg/L (assuming no matrix effects) would be approximately 1.62 mg/g based on the relationship between q₀ and C₀ observed in this study. The actual observed capacity in real wastewater was 1.51 mg/g, suggesting that:

This estimation assumes linear scaling and should be interpreted cautiously. Matrix effects (Cu²⁺, Zn²⁺, Fe³⁺ competition; high TDS; elevated COD) likely contributed significantly to the reduced performance, but the concentration difference is a confounding variable that cannot be isolated from the current dataset.

The comparison between synthetic (47 mg/L) and real wastewater (35 mg/L) is complicated by the different influent concentrations. The approximately 15% reduction in dynamic capacity cannot be attributed solely to matrix effects; the lower influent concentration of the real wastewater also contributes to the observed difference. Future studies should conduct concentration-matched experiments (e.g., diluting or spiking real wastewater to 47 mg/L Cr(VI)) to isolate matrix effects from concentration effects.

Direct material and preparation costs are presented in Table 13 below and cost comparison for alternative adsorbents in the Ethiopian market is presented in Table 14.

Base Case (No Regeneration):

Based on dynamic capacity of 1.78 mg/g under optimal conditions (Run 9: 12 cm bed depth, 10 mL/min flow rate, 47 mg/L Cr(VI)):

With Three-Cycle Reuse (76% Capacity Retention):

The complete cost Breakdown to treat 1000 L of wastewater is presented in Table 15 below.

Spent adsorbent containing 1.78 mg/g chromium would require disposal as hazardous waste in many jurisdictions. Several options exist, the options and their costs are presented in Table 16.

Table 17 presents the comparison of adsorption with Cordial africana sawdust with other conventional technologies.

Important caveat: The raw sawdust cost appears competitive with activated carbon and chemical precipitation. However, the substantially lower capacity (1.78 mg/g vs. 50-200 mg/g for activated carbon) means raw sawdust requires much more adsorbent mass per volume treated. This makes it less attractive for high-concentration Cr(VI) wastewater but potentially viable for polishing applications where Cr(VI) concentrations are low (<20 mg/L) and the cost of adsorbent replacement is acceptable.

Worst-Case Scenario (High Concentration, Low Efficiency):

Break-Even Concentration Analysis:

At $0.15/kg adsorbent, $0.30/kg disposal cost, and assuming 50% of cost is material and 50% is other operating costs:

Break-even with activated carbon ($10/1000 L total cost):

Interpretation: Raw Cordia africana sawdust becomes economically competitive with activated carbon at Cr(VI) concentrations below approximately 50-60 mg/L. At higher concentrations, the high adsorbent mass requirement makes it less economically attractive than higher-capacity adsorbents.

Table 18 presents the omitted cost during analysis.

Acknowledged limitation: This techno-economic analysis is based on laboratory-scale data and Ethiopian local prices. The relatively low dynamic capacity (1.78 mg/g) suggests that raw Cordia africana sawdust may be more suitable for low-concentration Cr(VI) polishing applications or as an emergency treatment option rather than as a primary treatment for moderate-to-high Cr(VI) concentrations (>50 mg/L). Scale-up to industrial applications would require site-specific cost assessments for capital equipment, labor, energy, transportation, and regulatory compliance. Chemical modification or activation should be explored to improve capacity while maintaining cost-effectiveness.

The economic conclusions should therefore be interpreted as preliminary screening estimates rather than definitive treatment costs. Pilot-scale studies and detailed engineering analysis would be required to establish realistic cost estimates for full-scale implementation.