1 Introduction

Advancements in water treatment approaches are of great advantage for developing and developed nations [1, 2]. Affordable water treatment methods can decrease disease burden, increasing productivity and lower energy costs [2,3,4]. Lowering energy costs is particularly important for improving access in energy- and water-scarce areas [5,6,7,8]. The connection between energy and water is crucial, as reducing the costs associated with both is of great importance.

One way to source energy is through the burning of fossil fuels, and the Fischer-Tropsch (F-T) process is a well-known method for producing liquid fossil fuels from gas [9]. However, this process generates large quantities of wastewater containing organic contaminants, known as gas-to-liquid (GTL) wastewater [10,11,12]. The conventional method for treating this wastewater involves aerobic treatment before discharge, but this approach is costly [11], especially when targeting low pollutant levels. The challenge in treating GTL wastewater lies in its complexity, as it consists of a variety of contaminants whose concentrations can vary significantly [13, 14], unlike synthesized wastewater where the concentrations are controlled and consistent. This variability makes it difficult to apply a one-size-fits-all treatment solution. Therefore, there is a need for more cost-effective polishing methods to reduce the energy costs associated with the F-T process.

Current literature extensively recommends adsorption using activated carbon as an affordable and effective technique for wastewater treatment [15,16,17,18]. While there is an abundance of lab-scale batch adsorption studies, continuous studies are comparatively few [19, 20]. Bridging the gap between batch and continuous studies is imperative for the progression of liquid adsorption research [21], especially when using actual industrial wastewater. Both methodologies play a pivotal role in the design of large-scale treatment columns [17]. Moreover, they contribute considerably to the identification of operational parameters influencing contaminant removal levels.

Recent studies have increasingly highlighted the viability of adsorption methods, particularly using activated carbon, as effective and affordable techniques for wastewater treatment. Activated carbon, known for its high surface area and porous structure, excels in adsorbing a range of organic and inorganic pollutants from wastewater [22,23,24]. Biological oxygen demand (BOD) and chemical oxygen demand (COD) are measures of the amount of oxygen required to oxidize organic and inorganic matter in a water sample and are critical parameters for assessing the level of contamination in water bodies [25, 26]. Organic and inorganic pollutants in the water adhere to the surface of the adsorbent, reducing the concentration of these contaminants and thereby lowering the COD [27]. Research has demonstrated the ability of activated carbon to significantly reduce BOD, COD and total suspended solids within optimal conditions of contact time and adsorbent mass. Moreover, it has been shown that activated carbon can achieve high adsorption uptake capacities for mixed pollutants, making it a potent option for treating complex wastewater streams [28,29,30,31].

Beyond experimental studies, simulations using tools such as ASPEN Adsorption have proven invaluable in optimizing adsorption processes [32,33,34,35]. For example, simulations have been used to predict breakthrough times and optimize operational parameters such as flow rate, initial contaminant concentration and bed height [36]. Studies comparing activated carbon with low-cost alternatives like bagasse fly ash and rice husk fly ash have shown that while activated carbon remains the most effective, alternatives can provide significant cost savings with reasonable efficiency [37]. These simulation studies bridge the gap between batch and continuous processes, offering a comprehensive understanding of adsorption dynamics and facilitating the design of large-scale treatment systems. However, it’s essential to validate simulation results against real-life experiments due to potential discrepancies between simulated and actual data. This validation ensures the reliability of simulation tools for decision-making in wastewater treatment.

While laboratory-scale batch studies are essential for understanding fundamental adsorption mechanisms and kinetics, integrating continuous flow simulations and optimization techniques is vital for the practical application of these findings in large-scale wastewater treatment. This holistic approach ensures that adsorption remains a versatile and economically feasible solution for managing industrial wastewater, including complex streams like GTL wastewater from the Fischer-Tropsch process.

In addition to the lack of liquid continuous studies, the literature is mostly utilizing synthesized wastewater, which was shown to behave differently from actual industrial plant wastewater [38]. Therefore, the novelty brought in this study is by using actual industrial GTL wastewater in continuous conditions using the adsorption technique. Furthermore, the novelty extends to use low cost activated carbon fiber (ACF) for treatment, as ACF is not commonly used for wastewater treatment. ACF offers the added benefit of being producible from textile waste fibers [39], thus contributing to waste reduction and material reusability [40]. Previous studies have demonstrated that ACF can be regenerated and reused [41], further suggesting its potential to be converted into an inert material suitable for safe disposal or use in construction [42]. This approach addresses a significant gap in existing research regarding the use of adsorption for treating GTL wastewater, particularly with activated carbon in fibrous form under continuous conditions. The objective in this work was addressed using a column analysis and reporting the parameters affecting the continuous process. The analysis further continued to understand the interactions within the column using the common continuous adsorption models available in the literature. To identify the best-performing model, the Akaike Information Criteria (AIC) was used for its ability to assess the quality of model fitting. The study also provided an insight into the validity of ASPEN Adsorption simulation environment using input data from batch experiments to study continuous wastewater treatment.

2 Materials and methods

2.1 Materials

The wastewater in this study was obtained from an industrial GTL plant and consisted of 76%, 7%, 14% and 3% of short-chain alcohol, long-chain alcohol, volatile fatty acids and other hydrocarbons, respectively. These components were qualitatively identified using gas chromatography-mass spectrometry (GC-MS) and quantified using a HAC-UV spectrometer with COD reagents [11, 12]. Prior to using the wastewater in the experimental setup, it is pre-treated through aeration at room temperature to remove volatile organic components. This process continued until the concentration of the raw GTL wastewater remained constant at 4000 to 6000 mg/L COD. After aeration, the wastewater was diluted to a concentration of 1000 mg/L COD. The activated carbon was obtained from Zhejiang Xingda, China, in a fibrous form. Characteristics and the competency of this adsorbent were investigated in a previous batch study by Yousef et al. [41], where it was proven to be effective.

2.2 Experimental setup

An acrylic bench-scale column, measuring 34 cm in length and 2 cm in outside diameter (Fig. 1 (3)), was utilized for the continuous experiments. Activated carbon fiber (ACF) was selected as the adsorbent due to its superior performance, as demonstrated in a previous study [41]. The column was packed with specified amounts of ACF as detailed in Table 1. It was fitted with beads at the bottom and sealed with a plug at the top (Fig. 1 (3)). GTL wastewater was pumped upward through the column using a peristaltic pump (Fig. 1 (2)) fitted with silicon tubing, and samples were collected at the top of the column (Fig. 1 (4)). The concentration of the samples was measured using a HAC-UV spectrometer and COD reagents. All experiments were conducted in replicates, with an average error margin of ± 5%.

Fig. 1
figure 1

Illustration of the experimental setup: (1) Feed Tank, (2) Pump, (3) Column and (4) collection Tank

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To portray the output of the experiments, a breakthrough curve was constructed. In dynamic conditions, breakthrough curves are used to understand the interactions between wastewater contaminants and the adsorbent in place [43]. This curve is valuable in determining the lifetime of the column and is widely used for column characterization. The shape of the curve depends on feed flow rate, adsorbent height, column diameter and adsorbent characteristics [19, 44]. The curve in this research consists of a normalized concentration on the y-axis plotted against time on the x-axis.

The conditions in this study were fixed except for packing mass and inlet flow rate. These parameters were varied as shown in Table 1 to study their effect on the column performance. The chosen packing mass and flow rate were determined by the constraints of the experimental setup. Specifically, flow rates below 5 mL/min resulted in obstruction, while flow rates above 10 mL/min caused non-uniform flow within the column, with some areas remaining empty and others experiencing flow. This variability in flow distribution limited the range of operable flow rates. Regarding the packing mass, 5 g was chosen based on a previous study conducted by El-Naas et al. [19], while the upper limit was determined by the maximum capacity that the experimental apparatus could hold.

Table 1 Varied continuous conditions at inlet concentration of 1000 mg COD/L
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2.3 Packed-bed models

To study the reliability of the available empirical approaches and the validity of the simulation approach, this study compared experimental output with modeling output for the experiments with packing mass of 5 g and a flow rate of 5 mL/min. For empirical modeling, Yoon-Nelson [45], El-Naas et al. [19], Thomas [46] and Adam-Bohart [47] formulas were used.

The Yoon-Nelson relationship assumes that the probability of molecules declining due to uptake of the contaminants in the water is proportional to the probability of contaminant adsorption and breakthrough. The formula is as described below:

$$\frac{{\rm{C}}}{{{{\rm{C}}_0} - {\rm{C}}}} = {\rm{exp}}\left[ {{{\rm{k}}_{{\rm{YN}}}}{\rm{}}\left( {{\rm{t}} - {\rm{\tau }}} \right)} \right]$$
(1)

Where kYN is the rate constant (1/min) and \(\:{\tau\:}\) (min) is the time when 50% of the breakthrough takes place.

El-Naas et al. developed an empirical formula for a continuous study of the adsorption of phenol from industrial refinery wastewater. This formula is a modification of the Yoon-Nelson formula, incorporating the Langmuir affinity constant. The purpose of the Langmuir affinity constant is to improve the fitting of adsorption systems that follow the Langmuir isotherm. The formula is described below:

$$\:\text{C}=\frac{{\text{C}}_{\text{o}}}{1+\text{e}\text{x}\text{p}[-\frac{{\text{k}}_{\text{e}}}{\text{b}}\left(\text{t}-\:{\tau\:}\right)]}$$
(2)

Where ke is the rate of adsorbent reduction (L/mg.min) and b is the Langmuir affinity constant that was found in a previous study using an isotherm analysis at 30 oC (0.0008 L/mg) [41].

Thomas model is based on the assumptions that there is negligible dispersion in the radial and axial directions and resulting in only plug flow. Kinetically, the model assumes a pseudo-second order reaction rate with constant column void, temperature, pressure and physical properties. Additionally, the model neglects external and intraparticle resistances in mass transfer. Based on these assumptions, the Thomas model is described by the following:

$$\:\frac{\text{C}}{{\text{C}}_{0}}=\frac{1}{1+\text{e}\text{x}\text{p}[\left(\frac{{\text{k}}_{\text{T}\text{h}\:}\text{M}\:{\text{q}}_{\text{e}}}{\text{Q}}\right)-\left({\text{k}}_{\text{T}\text{h}}{\text{C}}_{0}\:\text{t}\right)]}$$
(3)

Where kTh is Thomas rate constant (min/mg), qe is the equilibrium uptake of contaminant per the mass of adsorbent (mg/g), M is the packing mass (g) and Q is the flow rate in (cm3/min) [19, 46].

The Adams-Bohart formula is based on surface reaction theory, assuming that equilibrium is not instantaneous. This formula is commonly used to describe the initial part of the breakthrough curve by considering the proportionality of the rate of uptake to the remaining adsorption capacity. Based on quasi-chemical kinetic rate expression, the Adam-Bohart formula is as follows:

$$\:\frac{\text{C}}{{\text{C}}_{0}}=\text{e}\text{x}\text{p}\left[{\text{k}}_{\text{A}\text{B}}\left({\text{C}}_{0}\text{t}-{\text{N}}_{0}\frac{\text{Z}}{\text{v}}\right)\right]$$
(4)

Where C is concentration in (mg/g) at time t (min), C0 is the concentration at t = 0, kAB is the kinetic constant (min/mg), N0 is the maximum adsorption capacity per bed volume (mg/L), Z is bed depth (cm) and ν is the linear velocity (cm/min) that is calculated by dividing the flow rate in by the cross-sectional area of the flow [47, 48]. The above relationships were fitted using experimental column data by non-linear regression, employing the sum of squared errors (SSE) approach and setting the initial conditions at zero.

2.4 Model comparison

Using R2, nonlinear regression approach – SSE and the AIC [19, 49, 50], the quality of each model fitting was determined. AIC is a method used for comparison of different models, where the lowest value yielded from the following formula is considered the best model:

$$\:\text{A}\text{I}\text{C}=2\text{p}+\text{N}\text{l}\text{n}\left(\frac{\text{S}\text{S}\text{E}}{\text{N}}\right)$$
(5)

Where p is the number of independent parameters in the tested model, N is the number of data points and for a small sample size (N/p < 40), the second order AIC (AICc) is defined as follows:

$$\:\text{A}\text{I}{\text{C}}_{\text{c}}=\text{A}\text{I}\text{C}+\left[\frac{2\text{p}\:\left(\text{p}+1\right)}{\text{N}-\text{p}-1}\right]$$
(6)

The following difference in the AIC between the model’s AICc and minimum AICc (AICcmin) from the tested models is used to find the Akaike weight (wi), where the highest value recommends the best model:

$$\:{\Delta\:}\text{A}\text{I}{\text{C}}_{\text{c}}=\text{A}\text{I}{\text{C}}_{\text{c}\left(\text{i}\right)}-\text{A}\text{I}{\text{C}}_{\text{c}\text{m}\text{i}\text{n}}$$
(7)
$$\:{\text{w}}_{\text{i}}=\frac{\text{e}\text{x}\text{p}(-\frac{1}{2}{\Delta\:}\text{A}\text{I}{\text{C}}_{\text{c}\left(\text{i}\right)})}{{\sum\:}_{\text{i}=1}\text{e}\text{x}\text{p}(-\frac{1}{2}{\Delta\:}\text{A}\text{I}{\text{C}}_{\text{c}\left(\text{i}\right)})}$$
(8)

2.5 Adsorption column simulation

The simulation of continuous adsorption in this study was performed using ASPEN Adsorption with input from batch experimental analysis [41] and contaminants were represented by 1-Octanol using the NRTL package. 1-Octanol was chosen due to the data availability in the literature on diffusion coefficient. The simulation was configured using the following assumptions (1) upwind differencing scheme-first order discretization model (UDS 1), (2) convection with estimated dispersion, (3) no pressure drop occurs within the column, (4) velocity remains constant throughout the column, (5) solid film assumption, (6) quadratic lumped resistance, (7) constant mass transfer coefficient, (8) Freundlich isotherm (best model – from experimental analysis) and (9) isothermal system. Sherwood number was used to calculate the mass transfer coefficient as follows:

$$\:\text{S}\text{h}=\frac{{\text{K}}_{\text{c}}\:{\text{D}}_{\text{p}}}{{\text{D}}_{\text{A}\text{B}}}=2+1.1\:\text{R}{\text{e}}^{0.6}\text{S}{\text{c}}^{\frac{1}{3}}$$
(9)

Given the low concentration of contaminants, DAB was assumed as 1-octanol’s diffusion coefficient into water (7.6 × 10− 10 m2/s [51]), Dp is the inner diameter of the column since the packing is fibrous and not shaped (0.0123 m), Re = Dpuρ/µ, u is the cross-sectional velocity (1.1 cm/min) with ρ and µ being density (997 kg/m3) and viscosity (0.001 kg/m.s2) respectively of water given the small fraction of contaminants and Sc = µ/ρDAB. Table 2 shows the input parameters used to specify the packed-bed characteristics in the simulation.

Table 2 Simulation Input for 5 g column with 5 mL/min flow rate
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3 Results and discussion

3.1 Effect of feed flowrate

The effect of flow rate on column performance is a critical aspect in adsorption studies, as demonstrated by numerous investigations [19, 54, 55]. The breakthrough curve shown in Fig. 2 from the experimental analysis, serve as a valuable tool for understanding the relationship between flow rate and contaminant uptake. Initially, at the onset of the adsorption process, it is evident that uptake occurs rapidly, indicating a highly instantaneous response. However, as time progresses, the rate of adsorption slows down. This phenomenon is particularly pronounced at higher flow rates. Under increased flow rates, contaminants from GTL wastewater tend to saturate the active sites of the adsorbent more rapidly. This accelerated saturation is expected due to the heightened availability of contaminants at the adsorbent’s sites, facilitating faster mass transfer. Notably, this suggests that mass transfer primarily occurs on a macroscopic scale initially, with the external portion of the adsorbent experiencing a greater influence from the flow rate compared to the internal portion. With time, however, internal diffusion becomes increasingly significant as the external portion of the adsorbent, particularly the macropores, becomes saturated. This shift towards internal diffusion is reflected in the slower uptake observed in Fig. 2. These observations are consistent with findings reported in the literature [19, 48, 54, 55], thereby corroborating this study’s conclusions. Importantly, the results suggest that ACF can withstand higher flow rates without a significant decrease in breakthrough levels compared to lower flow rates. However, it is crucial to note that flow rates exceeding 10 mL/min resulted in preferential flow paths within the column (channeling) due to the increased flow, prompting their exclusion from the study. This highlights the importance of carefully considering the flow rate to optimize column performance and prevent adverse effects such as channeling. Ultimately, the effect of flow rate on column performance is evident, with higher flow rates accelerating adsorption kinetics initially but potentially leading to channeling and reduced efficiency.

Fig. 2
figure 2

Breakthrough curves at different flow rates (a) ACF packing mass = 5 g and (b) ACF packing mass = 10 g

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3.2 Effect of packing mass

In addition to examining the feed flow rate, this study investigated the effect of adsorbent mass on the duration of column saturation. This characterization is crucial for process design as it determines the number of columns required to ensure uninterrupted flow [56]. The breakthrough curves illustrated in Fig. 3 demonstrate that breakthrough occurs at a slower rate with a higher packing mass, regardless of the applied flow rate. The observed slower breakthrough rate with a higher packing mass can be attributed to the increased availability of active sites on the adsorbent. With a lower mass, fewer active sites are available over time, leading to faster saturation. In contrast, doubling the packing mass increases the uptake capacity by a factor of 1.25, owing to the increased surface area and the presence of more active sites. Consequently, this results in a longer time to reach breakthrough. Given that slow exhaustion of the adsorption bed is desirable for uninterrupted flow, a higher packing mass is preferred for GTL wastewater treatment. This finding is corroborated by similar observations in studies where the packing mass was varied [19, 48, 55].

Fig. 3
figure 3

Breakthrough curves at different packing mass (a) flow rate = 5 mL/min and (b) flow rate = 10 mL/min

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3.3 Interactions within continuous column

To understand the interactions within a column, common models available in the literature were used, as described in the methods section. The Yoon-Nelson model was developed to address the adsorption of volatile contaminants by predicting their breakthrough curve on the adsorbent [57]. kYN and τ of the Yoon-Nelson model were fitted. As observed in Table 3 and Fig. 4, the model represents the experimental data well, indicating that adsorption occurs on a molecular level and that the rate of mass transfer is governed by internal mass transfer, as adsorption is dependent on the number of available active sites. The kYN constant increased as the flow rate increased, which can be attributed to the increased concentration gradient across the bed. The τ value (time needed to reach 50% adsorption) increased with packing mass due to the increased number of active sites when the packing mass was doubled [58].

Table 3 Yoon-Nelson model parameters at different conditions
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Fig. 4
figure 4

Yoon-Nelson fitting of experimental data for GTL wastewater at packing mass = 5 g and flow rate = 5 mL/min

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In comparison to experimental data, τ rom the Yoon-Nelson model deviated within a 2 − 15% range, showcasing an acceptable margin of error. Due to the model’s adequacy, this work also considered the El-Naas et al. model, which is an extension of the Yoon-Nelson model. This model considers adsorption affinity and was shown to provide a better fit to the experimental data [19]. Table 4 demonstrates this enhancement, attributed to the model’s consideration of the molecules’ likelihood of being adsorbed based on the probability of the available active sites. Overall, τ decreased with an increased flow rate, which was due to the faster uptake, thereby lowering the time needed for 50% breakthrough (τ). This was not observed with the Yoon-Nelson model, as τ fluctuated at a packing mass of 5 g. This highlights the superior representation of the experimental data by the El-Naas et al. modification, as the physically found τ is in line with its definition. Figure 5 presents the comparison of experimental data against the El-Naas et al. model at 5 g and 5 mL/min.

Table 4 El-Naas et al. model parameters at different conditions
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Fig. 5
figure 5

El-Naas et al. fitting of experimental data for GTL wastewater at packing mass = 5 g and flow rate = 5 mL/min

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The Thomas model was applied to fit all the experimental data, resulting in the fitting parameters kTh and qe shown in Table 5, where Fig. 6 illustrates these results. From Table 5, it is evident that the kTh constant increased with flow rate and this is due to the increased driving force that increased the adsorption rate. In terms of the equilibrium uptake qe, the values were underestimated compared to the actual value of 322.3 mg/g determined by the Langmuir model in a study by Yousef et al. [41]. This observation aligns with similar findings reported by Ang et al. [57] The limitations of the Thomas model can be attributed to the underlying assumptions, particularly the negligible radial and axial dispersion. Ignoring dispersion effects can result in an overestimation of the adsorption capacity of the column, as radial and axial dispersion can lead to a broader concentration profile along the column, reducing the effective concentration gradient driving the adsorption process [59,60,61]. This was tested and confirmed using ASPEN Adsorption software, which failed to replicate experimental breakthrough profiles when dispersion was neglected. Additionally, the Thomas model assumes that the adsorbent system follows the Langmuir isotherm. However, previous isotherm studies [41] have demonstrated that the system is better described by the Freundlich model. This discrepancy contributes to the model’s inadequacy in accurately predicting the adsorption behavior observed in the experiments.

Table 5 Thomas model parameters at different conditions
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Fig. 6
figure 6

Thomas fitting of experimental data for GTL wastewater at packing mass = 5 g and flow rate = 5 mL/min

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The Adams-Bohart model is known to be applicable for fitting the initial part of breakthrough curves [19]. As observed in Figs. 2 and 3, breakthrough occurs at a very fast rate, making it challenging to collect concentration measurements at the initial stages of the experiment. Given this, the kinetic kAB in Table 6 was observed to increase with increasing flow rate, while no significant change was noted with the variation in packing mass (bed height). For the maximum adsorption capacity N0, the parameter increased with bed height, which is expected as increased bed height allows for more uptake per bed volume. This was observed in the analysis of the bed height effect at the beginning of this study This indicates that the rate of mass transfer is not dominated by external mass transfer, aligning with the findings from the Yoon-Nelson model, which suggests the system is governed by internal mass transfer. Relative to flow rate, N0 fluctuated and did not show a clear trend, indicating that the maximum uptake per wastewater volume is independent of packing mass. Figure 7 presents a plot of the Adams-Bohart model fitting against experimental data at a packing mass of 5 g and a flow rate of 5 mL/min.

Table 6 Adams-Bohart model parameters at different conditions
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Fig. 7
figure 7

Adams-Bohart fitting of experimental data for GTL wastewater at packing mass = 5 g and flow rate = 5 mL/min

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3.4 Comparison of models

The kinetics of GTL wastewater contaminant adsorption in all examined models were significantly influenced by the concentration gradient across the bed. These kinetic parameters suggest that minimal mass transfer resistance occurs, elucidating the sharp and instantaneous breakthrough observed in the adsorption system [62]. Furthermore, the shape of the breakthrough curve is attributed to the internal adsorption pathway within the column.

To determine the model that best describes the GTL wastewater/ACF system, SSE and R2 values for experimental conditions of 5 g and 5 mL/min are presented in Table 7. Despite the close values observed, an additional metric is necessary to select the optimal model. Hence, the AIC method is employed, given its basis on maximum likelihood theory and superior fit demonstrated in previous studies [20, 65, 52,53]. Analysis of the table reveals that the El-Naas et al. and Yoon-Nelson models exhibit the best fit for the experimental data across all considered conditions in this study. This finding suggests that the adsorption mechanism within the column is molecular-based and occurs internally. Although promising results were shown using the El-Naas et al. and Yoon-Nelson models, limitations arise when using these models. The Yoon-Nelson model can only be applied to a single component, assumes a constant flow rate and a fixed bed height [66]. Similarly, the El-Naas model, being an extension of the Yoon-Nelson model, shares these limitations. In situations where these parameters change during adsorption, such changes will not be reflected in the model’s output. Therefore, it is recommended to consider models that account for varying parameters, such as ASPEN Adsorption, which provides a more comprehensive and accurate representation of the adsorption process.

Table 7 A comparison between the models used in this study at packing mass = 5 g and flow rate = 5 mL/min
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3.5 Adsorption simulation

The integration of computational tools, such as ASPEN Adsorption, offers a viable approach to address the challenges associated with conducting continuous analysis within batch studies, particularly when experimental means are impractical or inaccessible. While ASPEN Adsorption has garnered widespread recognition for its utility in gas adsorption studies, its application to liquid adsorption has been relatively underexplored in the literature. To fill this gap, this study evaluated the software’s efficacy in simulating liquid adsorption processes and comparing its performance against experimental data. Conditions of 5 g and 5 mL/min, served as a basis for comparison between the simulated and experimental data, with the results as illustrated in Fig. 8. Notably, the findings revealed a notable agreement between the experimental and simulation results, indicative of ASPEN Adsorption’s capability to accurately replicate the dynamic behavior of liquid adsorption systems.

While these empirical models provide valuable insights by fitting specific data points, they have certain limitations, including a lack of comprehensive analysis of the system’s behavior under varying conditions. In contrast, ASPEN Adsorption incorporates detailed thermodynamic and kinetic parameters [36, 65], allowing for a more wholistic and accurate simulation of the adsorption process. Moreover, when compared to alternative models, ASPEN Adsorption demonstrated a smoother breakthrough profile that closely mirrored experimental observations, highlighting its reliability for simulating continuous analysis using output from batch investigations. Nevertheless, improvements could be made to the model by measuring specific contaminant isotherm parameters, diffusion coefficient, and mass transfer constant to see whether this enhances the output of ASPEN Adsorption.

The implications of these findings extend beyond the confines of this study, particularly within the field of wastewater treatment research. By enabling the assessment of operating conditions and the characterization of proposed adsorbent systems, the integration of ASPEN Adsorption in batch studies holds significant promise for expediting large-scale analysis and streamlining the preliminary design phase of wastewater treatment pilot plants [66].

Fig. 8
figure 8

ASPEN Adsorption breakthrough profile against experimental data for GTL wastewater at packing mass = 5 g and flow rate = 5 mL/min

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4 Conclusions

This study evaluated the adsorption performance of a packed-bed column for the removal of pollutants from GTL wastewater under various conditions. ACF demonstrated superior performance in adsorbing organic contaminants across different conditions, with optimal breakthrough curves observed at lower flow rates and higher packing masses. To model the packed-bed column and understand the adsorption mechanism, four models (Yoon-Nelson, El-Naas et al., Thomas, and Adams-Bohart) were employed alongside ASPEN Adsorption simulation. Among these models, El-Naas et al. and Yoon-Nelson exhibited the best fit relative to experimental data, with approximately 86.5% R2, 10,767 SEE, and 0.33 AIC wi for 5 g packing mass and 5 mL/min flow rate. The fitting of these models indicated that adsorption is governed by internal diffusion, as these models assume internal adsorption. Furthermore, the ASPEN Adsorption simulation environment proved valuable in numerically addressing continuous studies, with breakthrough profiles in agreement with experimental data, validating its reliability for simulating GTL wastewater adsorption systems. This novel approach reduces the number of experiments needed, providing insights into contaminant behavior under different conditions and aiding in large-scale design. Additionally, the novelty of this study lies in the use of actual industrial GTL wastewater and activated carbon in the form of fiber, further contributing to the advancement of wastewater treatment research.

Based on the findings of this study, it is recommended to employ the ASPEN Adsorption tool to investigate the behavior of actual industrial wastewater using batch input parameters. For complex industrial wastewaters like GTL wastewater, obtaining contaminant specific batch parameters and incorporating them into ASPEN Adsorption is advisable. The results from ASPEN Adsorption can then serve as a preliminary guide for designing continuous columns for wastewater treatment. This approach enhances the accuracy of simulations and facilitates the efficient design of large-scale treatment systems, thereby optimizing the overall wastewater treatment process. The breakthrough curves obtained offer crucial information about ACF’s adsorption capacity and saturation behavior, informing the design of larger columns by optimizing bed height, flow rate and adsorbent quantity.

While the validation of results through ASPEN Adsorption simulation provides a reliable foundation for scaling up, challenges remain in maintaining uniform flow distribution within larger industrial-scale columns. Future research should focus on addressing these scale-up issues, particularly investigating methods to ensure even flow and adequate contact time.