Technical Evaluation of the Influence of Inlet Flow Rate and Bed Height on a Packed Column Containing Residual Biomass During Computer-Aided Industrial Scale-Up

Abstract

This research seeks to model a packed bed with cocoa waste on an industrial scale using computer software and parametric evaluation to remove Pb(II) in solution. To achieve this, they developed multiple simulations of a packed bed using Aspen Adsorption software using different configurations of inlet flow rate and bed height through a parametric sensitivity study to evaluate the system performance using Langmuir as an isothermal model and the Linear Driving Force (LDF) model as a kinetic model. It was found that the efficiency of the adsorption process reached 99.7% for Pb(II) removal. On the other hand, the best simulation conditions considering efficiency, breakthrough time and saturation were a flow rate of 200 m³/day, a head of 5 m and an initial concentration of 1000 mg/L. This research exhibits a novel engineering perspective to anticipate the potential performance of packed bed with agro-industrial biomasses in the multiscale removal of Pb(II).

1. Introduction

Water is a vital natural resource essential for the survival of living organisms, economic growth, and human well-being. However, this resource has been in decline due to excessive use in various anthropogenic activities, which generate large volumes of wastewater loaded with multiple contaminants [1]. Water sources are affected by the presence of these pollutants originating from domestic sources, agricultural runoff, and industrial discharges, posing a risk to the health and integrity of living beings [2]. Among the various contaminants present in wastewater are heavy metals, also known as trace elements, which are classified as some of the most hazardous environmental toxins. Even at low concentrations, they represent a significant threat due to their toxicity, persistence, and bioaccumulative potential [3]. Lead (Pb(II)) metal ions are highly toxic to aquatic ecosystems and human health due to their non-biodegradable nature and their high persistence and accumulation in the environment. This heavy metal enters water bodies through various anthropogenic sources such as smelting processes, electroplating, and the discharge of industrial waste, among other activities. Pb(II) causes a range of health complications, including cardiovascular diseases, kidney failure, gastrointestinal disorders, and cognitive impairment, among others [4].

To remove heavy metals from wastewater discharged into aquatic ecosystems, various treatment techniques have been developed with the aim of eliminating these contaminants from water bodies. Among these are coagulation/flocculation processes, which use coagulants or flocculants that destabilize the contaminant particles in the water, thus facilitating their removal [5]. On the other hand, electrocoagulation is an innovative technique for water treatment, based on the use of coagulants in combination with the application of a direct current through sacrificial metal electrodes, usually made of iron or aluminum. This technique destabilizes colloidal particles and contaminants present in bodies of water [6]. One of these techniques is adsorption, a method that uses a surface phenomenon where the adsorbent is transferred to the adsorbate. It is also widely used because it is adaptable, low-cost, and easy to apply [7]. The adsorption mechanism first transports the molecules of the contaminants to be removed from the solution into the adsorbent boundary layer. Then, the diffusion of these species from the adsorbent boundary layer to the external surface of the adsorbent material occurs. Finally, the pollutants move to the interior of the porous matrix, where they attach to the available active sites, resulting in the effective retention of unwanted ions and molecules in the aqueous medium [8]. The adsorption can be divided between two main categories: chemical (chemisorption) and physical (physisorption). Chemisorption is defined by the chemical links formed by the adsorbed substance and the sorbent, which results in strong, specific, and generally irreversible interactions, as well as requiring a significant energy input [9].

The development of adsorbents based on lignocellulosic materials such as yam, cassava, corn, oil palm bagasse [10], coconut shells [11], and yam residues [12], among others, has been studied. The use of agro-industrial waste from cocoa (Theobroma cacao L.), such as husks, has been established as a sustainable alternative for the adsorption of contaminants in aqueous media. This material generates multiple by-products that stand out for their abundance, low cost, and availability in producing regions. Likewise, this material has a lignocellulosic matrix and a composition consisting of 19.82% cellulose, 9.45% hemicellulose, and 12.66% lignin, with functional groups capable of interacting with heavy metals and organic compounds [13].

These studies have highlighted the need to focus more attention on the research and development of biomass-based packed columns for potential industrial applications. Nevertheless, most studies related to adsorption are developed on a laboratory scale, which limits their direct application in real conditions. In response to this limitation, strategies have been implemented to predict the performance of adsorption systems on a larger scale, notably the use of computational tools that enable the simulation of experimental processes and thus facilitate their extrapolation to industrial contexts. Aspen Adsorption, a tool designed by AspenTech, is a simulation software focused on modelling adsorption processes in multiphase systems. This tool allows to virtually simulate the performance of adsorption columns under different operating conditions, enabling the prediction of efficiency in removing contaminants present in aqueous solutions. The use of this software not only contributes to understanding the physicochemical mechanisms that govern mass transfer and adsorbate-adsorbent interaction, but also provides fundamental support for the design, optimization, and scaling of adsorption-based water treatment technologies.

In this study, the main objective is to model an industrial-scale packed adsorption column using computational tools and parametric analysis to evaluate the removal of Pb(II) in aqueous solution using cocoa waste (Theobroma cacao L.) as an adsorbent material. This research is novel in that it uses widely available agro-industrial waste as a sustainable alternative for water decontamination, as well as applying computational simulations to predict the performance of large-scale adsorption systems. In this way, the objective is to provide quantitative information and technical criteria to facilitate the design and expansion of packed columns for the treatment of effluents contaminated with heavy metals. The selection of Pb(II) is based on its high toxicity and widespread presence in industrial process effluents, making it one of the priority heavy metals for removal studies. Various authors have pointed out that lignocellulosic residues such as cocoa shells have a notable affinity for different contaminants such as Pb(II) due to the presence of functional groups capable of forming stable complexes [14,15,16].

2. Materials and Methods

2.1. Parametric Sensitivity Study

To evaluate system performance in removing Pb(II) ions, Aspen Adsorption V10 software was used. In order to analyze the influence of operating conditions on process efficiency, a parametric sensitivity study was developed, in that the effect of varying critical system parameters was examined. Specifically, changes in bed height and feed flow rate were considered, while maintaining the initial Pb(II) concentration constant at 1000 mg/L [17,18], under operating conditions of 1 atm pressure and 30 °C temperature. Altering these variables allows the system’s performance to be analyzed under various operating conditions, making it possible to identify which factors have the greatest impact on adsorption efficiency. To establish the range of values for the parameters considered for the sensitivity study, a detailed review of multiple studies reported in the literature was conducted. This allowed us to identify different operating ranges and characteristic behaviours related to the variables studied, which were previously studied and adjusted [19,20].

Table 1. Adsorption column analysis parameters.

Analysis Factor	Unit	Range
Bed Height	m	3, 4, 5
Inlet Flow Rate	m3/day	100, 150, 200

shows the range of values for the parameters considered in the sensitivity study.

2.2. Parameters and Conditions Required for the Scale-Up of the Packed Bed Column to Industrial Scale

Aspen Adsorption requires specific parameters to model and simulate the adsorption column for the removal of Pb(II) from solution. These variables are essential to define the operating conditions during the simulation of the packed adsorption column using cocoa waste as the adsorbent for the removal of heavy metals from aqueous solutions. In order to establish the parameters required for the construction of the packed adsorption column for the removal of Pb(II), various studies reported in the literature were reviewed to identify the parameters required by the Aspen Adsorption software, including the apparent density of the biomaterial, the diameter of the column, the mass transfer coefficient, the void porosity, the total porosity, and the constant values for the isothermal model. Therefore, a study, analysis, and adjustments of these parameters were carried out for this simulation model [21,22].

Table 2. Values of the Factors Evaluated in the Parametric Sensitivity Analysis Study.

Parameters	Values	Unit
Bed Diameter	$1$	m
Bulk Density	0.0365	g/cm3
Mass Transfer Coefficient	1.88 × 10−7	m/s
Particle size	0.355	mm
Bed Porosity	0.67	m3 void/m3 bed
Total Void Porosity	0.4	m3 void/m3 bed
Langmuir Isotherm Parameters
b	3.18 × 10−5	-
qmax	4693.09	mg/g

presents the values for each of these parameters.

In order to simulate the packed column for Pb(II) adsorption, it is necessary to establish the appropriate thermodynamic package for the calculation of the physicochemical properties of the liquid phase. The precise definition of the physical properties of the process is essential for determining the characterization of the solution that interacts with the adsorbent material inside the adsorption column. These properties were calculated in this study using the ELECNRTL (Electrolyte Non-Random Two Liquid) thermodynamic model, which allows for an accurate representation of systems involving electrolytic solutions and thus ensures a more realistic description of the behaviour of the liquid phase during the adsorption process. This model accounts for molecular interactions between ionic and neutral species in aqueous solutions, enabling the estimation of properties such as fluid density, effective contaminant concentration (activity), viscosity, among others. These properties have a direct impact on key variables of the adsorption model, such as the mass transfer coefficient, and on the material balances within the column, as they allow the calculation of hydrodynamic parameters and the influence of certain factors on adsorbent performance and the breakthrough profile.

It is also necessary to configure various settings in Aspen Adsorption, such as the discretization method, the selected isotherm and kinetic models, among other conditions. The software includes several essential sections that must be properly defined to ensure accurate simulation settings.

Table 3. Configuration Sections for the Adsorption Column Simulation.

Sections	Description
General	This section defines the discretization method required to perform the simulations of the adsorption bed. In the present study, the first-order Upwind Differentiation Scheme (UDS1) was used as a method for solving mass transport equations [23]. This method is described using Equation (1):
	${\displaystyle \frac{\delta {\mathsf{\Gamma }}_i}{\delta z}}={\displaystyle \frac{{\mathsf{\Gamma }}_i-{\mathsf{\Gamma }}_{i-1}}{\mathsf{\Delta }z}}$	(1)
	Additionally, a total number of 10 nodes was defined.
Mass/Momentum Balance	This section establishes the hypotheses related to axial dispersion, pressure drop, and velocity in the column. For this study, it was established that there is no pressure drop, the velocity is constant, and there is only convection, indicating that solute transport occurs solely through fluid flow.
Kinetic Model	This section defines the kinetic model employed to describe the velocity of the adsorption process. In this investigation, the linear driving force (LDF) model was selected, a kinetic model used in the simulation of liquid phase processes due to its balance between computational simplicity and the ability to capture intraparticular mass transfer resistance, which considers that mass transfer is governed by the concentration gradient between the liquid phase and the adsorbed surface [24]. It is represented by Equation (2):
	${\displaystyle \frac{\partial w_k}{{\partial }_t}}=MT{C}_{sk}\left(w_k^{\ast }-w_k\right)$	(2)
Isotherm Model	This section describes the isothermal model utilized to describe the interactions that occur in the process. In this case, the Langmuir isotherm model was selected, an isothermal model widely used in batch or continuous heavy metal adsorption studies, which assumes that interactions occur on solid surfaces and is particularly relevant when the system under study forms a monomolecular layer [25,26]. This model is described using Equation (3):
	$q_e={\displaystyle \frac{q_{max}b{C}_e}{1+b{C}_e}}$	(3)
Energy Balance	This section establishes the energy balance of the system. For this case, isothermal operating conditions are assumed, meaning that the system temperature remains constant throughout the entire process.

presents the different sections to be configured along with the conditions established for each.

3. Results and Discussion

3.1. Data Obtained from Adsorption Bed Simulations for the Removal of Pb(II)

Multiple simulations of the Pb(II) adsorption bed were performed on an industrial scale using Aspen Adsorption software and different inlet flow rates and bed heights. The results obtained include the breakthrough time (B.T), which indicates the point at which the adsorbent biomaterial begins to lose its contaminant retention capacity; the saturation time (S.T), corresponding to when the adsorbent reaches its maximum adsorption capacity; and the process efficiency, which reflects how effective the material used is in carrying out the adsorption process. The simulations were conducted using the Langmuir isothermal model combined with the LDF kinetic model.

Table 4. Results of the Langmuir-LDF Model Evaluation.

Bed Height (m)	Inlet Flow Rate (m3/day)	B.T (min)	S.T (min)	Efficiency (1 − Cf/Co) × 100
3	200	440	1379	99.7
	150	587	1913	99.6
	100	883	2224	99.5
4	200	587	1913	99.6
	150	784	2110	99.5
	100	1176	2992	99.4
5	200	735	2642	99.4
	150	981	2883	99.2
	100	1474	3783	98.8

shows the results obtained from the simulations.

3.2. Parametric Sensitivity Analysis

3.2.1. Influence of Inlet Flow Rate on the Adsorption Process

Simulations were performed with flow rates of 100, 150, and 200 m³/day, considering the initial concentration (1000 mg/L) and the fixed bed height (5 m) as constants. Figure 1 shows the breakthrough curves generated from the Langmuir model coupled with LDF kinetic model. These curves indicate the evolution of the adsorption process over time, allowing fundamental parameters of bed performance to be identified: B.T, S.T, and efficiency.

These results show a significant increase in both breakthrough time (B.T.) and saturation time (S.T.) as flow rate decreases. This performance is attributable to the fact that, at lower flow rates, fluid stays in contact with the adsorbent bed longer, favouring greater diffusion of Pb(II) ions toward the active surface of the material and, consequently, more efficient use of the adsorption sites. On the contrary, at high flow rates, the reduction in residence time limits the equilibrium between the liquid and solid phases, causing faster saturation of the column. These results confirm that controlling the inlet flow rate is a determining factor in optimizing the removal capacity and useful life of the adsorption column [27].

This behaviour can be seen in the data presented in Table 3. At an inlet flow rate of 200 m³/day, the B.T. and S.T. values were 735 min and 2642 min, respectively. When the flow rate was reduced to 150 m³/day, an increase in B.T. and S.T. was recorded, reaching 981 min and 2883 min, respectively. Similarly, further reducing the flow rate to 100 m³/day led to an additional increase in these times, yielding 1474 min for B.T. and 3783 min for S.T. These values show the operational performance and useful life of the adsorbent column: high B.T. values mean a delay in the advance of Pb(II), which shows better performance. On the other hand, high S.T. values mean a higher adsorption capacity of the bioadsorbents before it needs to be regenerated or replaced. Therefore, as the flow rate decreases, better B.T. and S.T. values are obtained.

3.2.2. Influence of Bed Height on the Adsorption Process

In this study, we looked at how the height of the adsorption bed affected the process, testing heights of 3, 4, and 5 m, while maintaining a constant initial concentration of Pb(II) (1000 mg/L) and feed flow rate (200 m³/day). Figure 2 shows the breakthrough curves generated using the Langmuir isothermal model, coupled with the LDF kinetic model. These curves indicate the evolution of the adsorption process over time, allowing fundamental parameters of bed performance to be identified: B.T, S.T, and efficiency.

The results show a clear trend: as the bed height increases, there is a prolongation in both the breakthrough time (B.T.) and the saturation time (S.T.). This is due to the greater amount of biomass available in contact with the liquid phase, the higher number of active sites for adsorption, and, consequently, the improved total contaminant removal capacity. Practically speaking, this means that a higher bed favours a longer service time before the effluent reaches critical concentrations of Pb(II) [28,29].

The simulation data confirmed this trend for Pb(II) removal. As shown in Table 3, with a bed height of 3 m, B.T. and S.T. were 440 min and 1379 min, respectively. Increasing the bed height to 4 m resulted in values of 587 min for B.T. and 1913 min for S.T. Similarly, raising the bed height to 5 m further increased these times to 735 min for B.T. and 2642 min for S.T. These values show the operational performance and useful life of the adsorbent column: high B.T. values mean a delay in the advance of Pb(II), which shows better performance. On the other hand, high S.T. values mean a higher adsorption capacity of the bioadsorbent before it needs to be regenerated or replaced. Therefore, as the height of the bed increases, there is an increase in the values of B.T. and S.T.

3.3. Report on the Use of Different Simulators to Scale Packed Adsorption Columns for the Removal of Pb(II)

The results obtained from the simulation of the packed column with cocoa residues on an industrial scale demonstrated the promising performance of this adsorption system for the removal of Pb(II) in solution. In this study, the Langmuir isothermal model was combined with LDF kinetic model. Operating conditions for the bed were established, and different values were used for the inlet flow rate and bed height. Different authors have implemented simulators to predict the behaviour of packed adsorption columns for Pb(II) removal using different types of adsorbent materials such as activated carbons [30], olive tree pruning [31], among others. These studies demonstrate the advantages of implementing computational tools such as Aspen Adsorption to analyze the dynamic behaviour of systems, adjust parameters, reduce costs and time associated with experimentation, among other factors, facilitating the design, validation, and subsequent scaling of adsorption processes. Likewise, the potential of agro-industrial materials as adsorbents for the removal of Pb(II) is observed, such as Theobroma cacao L., which presented high removal values and high breakage and saturation times under industrial conditions, highlighting its potential as a sustainable adsorbent.

3.4. Limitations of the Established Assumptions

It was assumed that the adsorption process took place under isothermal conditions and without pressure drop in the column. This simplified the process, facilitating numerical resolution and allowing focus on analyzing the behaviour of the adsorbent. Likewise, the mass transfer coefficient was used as a fixed value, established by values reported in the literature. This parameter was kept constant to focus the sensitivity analysis on the variables of bed height and operating flow rate, allowing for a clearer evaluation of their influence on the adsorption process. Although these assumptions cannot express certain situations on an industrial scale, they allow for a solid and controlled understanding of the system’s performance.

4. Conclusions

The study offers a novel approach to modelling and simulating adsorption beds at an industrial scale, utilizing agro-industrial residues from Theobroma cacao L. as an adsorbent for the removal of Pb(II) in aqueous solutions. The results derived from computational simulations provide quantitative information of great relevance for the progression of adsorption processes in industry applications. Parametric sensitivity analysis showed the decisive role of operational variables, such as bed height and inlet flow rate, in system efficiency. It was observed that a larger bed increases breakthrough and saturation times, although with a decrease in adsorption efficiency, while increasing the inlet flow rate improves this efficiency but reduces the operating times of the biomaterial. Such findings are providing a solid technical basis for the design and optimization of industrial effluent treatment systems, enabling the prediction of their performance and the anticipation of process behaviour prior to implementation. Finally, it is recommended that future studies integrate economic assessments and techno-economic resilience analyses to determine the viability and sustainability of optimal adsorption column configurations in real-world application scenarios. Similarly, there are plans to develop a pilot-scale laboratory test to experimentally validate the reliability of the results obtained with the Aspen Adsorption software, thus reinforcing the robustness and applicability of this tool for modelling packed adsorption columns.