A mathematical model for bioremediation of hydrocarbon-contaminated soils

Citation: Martins, G.; Campos, S.; Ferreira, A.; Castro, R.; Duarte, M.S.; Cavaleiro, A.J. A Mathematical Model for Bioremediation of Hydrocarbon-Contaminated Soils. Appl. Sci. 2022,12, 11069. https:// doi.org/10.3390/app122111069 Academic Editors: Chang-Gu Lee and Seong-Jik Park Received: 29 September 2022 Accepted: 29 October 2022 Published: 1 November 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). applied sciences Article A Mathematical Model for Bioremediation of HydrocarbonContaminated Soils Gilberto Martins 1,2,* , Sara Campos 1, Ana Ferreira 1, Rita Castro 1,2 , Maria SaloméDuarte 1,2 and Ana J. Cavaleiro 1,2 1CEB—Centre of Biological Engineering, University of Minho, Campus de Gualtar, 4710-057 Braga, Portugal 2LABBELS—Associate Laboratory, Campus de Gualtar, 4710-057 Braga, Portugal *Correspondence: [email protected]; Tel.: +351-2536-01986 Featured Application: The developed mathematical model can be used as a decision-supporting tool for the definition of the best strategies for in situ bioremediation of contaminated sites. Abstract: Bioremediation of hydrocarbons in soil is a highly complex process, involving a multiplicity of physical, chemical and biological phenomena. Therefore, it is extremely difficult to control and boost the bioremediation of these systems after an oil spill. A mathematical model was developed to assist in the prediction and decision-making regarding the in situ bioremediation of hydrocarboncontaminated soils. The model considered the most relevant processes involved in the mass transfer and biodegradation of alkanes over time and along the depth of a flooded soil column. Aliphatic hydrocarbons were chosen since they are less water soluble than aromatics and account for 50–90% of the hydrocarbon fraction in several petroleum products. The effect of adding oxygen, nitrate, iron (III) or sulfate as electron acceptors was then simulated (bioremediation scenarios). Additionally, and to feed the model, batch assays were performed to obtain experimental data on hydrocarbon adsorption to soil particles (more than 60% of hydrocarbons tends to be adsorbed to soil particles), as well as hydrocarbon biodegradation rates in the presence of nitrate (0.114 d −1 ) and oxygen (0.587 d −1 ). The model indicates that saturated hydrocarbon removal occurs mainly with adsorption/desorption and transport processes in the upper layers of soil due to methanogenic biodegradation in deeper layers, since the other microbial processes are soon limited by the lack of electron acceptors. Simulation results show that higher initial electron acceptor concentrations led to higher hydrocarbon removal, confirming that the model is performing in accordance with the expected. Close to the surface (at 0.1 m depth), all scenarios predicted more than 83% hydrocarbon removal after two years of simulation. Soil re-aeration results in faster hydrocarbon removal (more than 20% after one year) and surfactants addition (around 15% after one year) may also accelerate soil bioremediation. With this model, the simultaneous contributions of the various physicochemical and biological processes are integrated, facilitating the simulation and comparison of different bioremediation scenarios. Therefore, it represents a useful support tool for the management of contaminated sites. Keywords: mathematical modelling; bioremediation; biostimulation; electron acceptors; hydrocarbons 1. Introduction Soil contamination constitutes a severe environmental problem. It is estimated to affect around 2.8 million sites in Europe [ 1 ], where mineral oils account for 22–24% of all the soil contamination incidents reported, and comprise 45% when considered together with BTEX and polyaromatic hydrocarbons [ 2 ]. The pollution of soils by petroleum hydrocarbons leads to ecological and health risks, due to their relatively low mobility and their toxic, mutagenic and carcinogenic effects [3,4]. The fate of petroleum hydrocarbons in soil is influenced by the physical and chemical properties of these compounds (e.g., solubility in water and affinity for the organic carbon in Appl. Sci. 2022,12, 11069. https://doi.org/10.3390/app122111069 https://www.mdpi.com/journal/applsci Appl. Sci. 2022,12, 11069 2 of 19 soil) as well as by the characteristics of the soil, such as particle size, porosity, organic matter content, permeability and surface area [ 3 , 5 ]. In general, soil acts as a sink for pollutants; thus, active cleaning operations must be performed to enable the recovery of contaminated soils within an acceptable timeframe [1]. To date, several physical and chemical remediation technologies are available (e.g., physical removal, soil washing and oxidation/reduction via chemical agents) [ 5 , 6 ]; however, there is an increasing willingness for the use of less aggressive and more eco-friendly techniques, such as bioremediation [ 7 , 8 ]. Critical factors in bioremediation are the availability of nutrients and electron acceptors (oxygen, nitrate, iron (III), sulfate) as well as the existence of microbial catabolic activity towards hydrocarbons [ 3 , 9 , 10 ]. Bioavailability of the contaminants also influences microbial activity, since the access of the microorganisms or their enzymes to the compounds can be hampered due to hydrocarbon interactions with the organic carbon content of the soil [ 3 ]. These aspects are particularly important when hydrocarbon contamination occurs in depth; for example, due to leaking underground storage tanks or pipelines. In permeable soils, the plume can penetrate to a significant depth, hindering the contamination removal and site decontamination [11]. Current knowledge of hydrocarbon biodegradation in soils is limited and requires further research. In addition, the selection and implementation of bioremediation approaches, as well as the prediction of the process outcomes, is highly complex. In this framework, mathematical modelling emerges as a promising tool, providing support for decision makers to effectively deal with the complexity of cleaning and restoring contaminated sites [ 12 , 13 ]. Over the years, mathematical modelling of hydrocarbon bioremediation has been performed, focused mainly on contaminated aquifers considering that relatively soluble hydrocarbon fractions will be transported from the contaminated soils to the water level, where further transport and biodegradation will occur [ 14 – 16 ]. Straight chain alkanes are less water soluble than other aliphatic and aromatic hydrocarbons and present a higher affinity for the organic carbon content of the soil. Moreover, saturated hydrocarbons account for 50–90% of the hydrocarbon fraction in several petroleum products (e.g., aviation gasoline, jet fuel, diesel fuel) [17]. As such, sequestration of this less soluble fraction of oil may occur in soils; its environmental fate is still not sufficiently studied. In soils, the majority of the developed models are designed for ex situ bioremediation [ 14 , 18 – 20 ]. In addition, only a few mathematical models couple mass transfer with Monod or first-order kinetics for hydrocarbon biodegradation [16,19,21–23], especially for less soluble hydrocarbons [16]. The aim of the present work was to develop a simple mathematical model to understand the processes involved in the decontamination of a saturated (flooded) soil column after an oil spill. This model can be used as a decision-supporting tool for the definition of the best strategies for in situ bioremediation of hydrocarbon-contaminated sites. The model specifically focused on the changes in alkanes concentration over time and at different depths. The effect of different electron acceptors (oxygen, nitrate, iron and sulphate) was also evaluated. Laboratory experiments were also carried out to gather important data to feed the model. 2. Materials and Methods 2.1. Mathematical Model Development and Implementation A mathematical model was developed comprising the description of transport and transformation of linear saturated petroleum hydrocarbons in a flooded soil column. The model assumed mass conservation for the chemical species, with mass partition between solid and liquid phases. Hydrocarbons in the liquid phase may be dissolved in the soil moisture or surrounded by other hydrocarbon molecules, forming a non-aqueous phase liquid (NAPL) [ 14 ]. In this model, these two possibilities were considered together, i.e., hydrocarbon concentration in the liquid phase refers to the mass of both dissolved and NAPL forms per unit of liquid volume. Both forms are considered to be available for microorganisms’ growth. In fact, other authors have already showed that microorganisms Appl. Sci. 2022,12, 11069 3 of 19 can directly access hydrocarbons in the NAPL phase and the hydrocarbon-water interphase and use it for growth [14]. The model was implemented in AQUASIM [ 24 ], a software for the analysis and simulation of aquatic systems, which allows to define the spatial configuration of the system as a set of compartments. Another advantage of AQUASIM is the fact that it allows the definition of new variables and processes at any time [ 25 ]. In the present case, we used the saturated soil column (with sorption and pore volume exchange) compartment [ 24 ]. Advective dispersive transport of substances present in the liquid phase was considered (first and second terms of Equation (1), respectively), as well as transformation (third term of Equation (1)) by adsorption/desorption and biodegradation processes [ 26 , 27 ]. Biodegradation was assumed to occur only in the liquid phase. ∂Cmob,i ∂t=−1 Aθ ∂ ∂x(QCmob,i)+1 Aθ ∂ ∂xAθE∂Cmob,i ∂x+rCmob,i(1) C mob,i— concentration of component iin the liquid phase; t—time; A—soil column cross-sectional area; θ —porosity; Q—water flow through the column, E—longitudinal dispersion coefficient; r—reaction term. The model is able to calculate phase concentrations and fluxes as a function of space (soil column depth) and time for the different components. In the present model, hydrocarbons biodegradation processes were based on the availability of different electron acceptors (Figure 1). Appl. Sci. 2022, 12, x FOR PEER REVIEW 3 of 19 solid and liquid phases. Hydrocarbons in the liquid phase may be dissolved in the soil moisture or surrounded by other hydrocarbon molecules, forming a non-aqueous phase liquid (NAPL) [14]. In this model, these two possibilities were considered together, i.e., hydrocarbon concentration in the liquid phase refers to the mass of both dissolved and NAPL forms per unit of liquid volume. Both forms are considered to be available for microorganisms’ growth. In fact, other authors have already showed that microorganisms can directly access hydrocarbons in the NAPL phase and the hydrocarbon-water interphase and use it for growth [14]. The model was implemented in AQUASIM [24], a software for the analysis and simulation of aquatic systems, which allows to define the spatial configuration of the system as a set of compartments. Another advantage of AQUASIM is the fact that it allows the definition of new variables and processes at any time [25]. In the present case, we used the saturated soil column (with sorption and pore volume exchange) compartment [24]. Advective dispersive transport of substances present in the liquid phase was considered (first and second terms of Equation (1), respectively), as well as transformation (third term of Equation (1)) by adsorption/desorption and biodegradation processes [26,27]. Biodegradation was assumed to occur only in the liquid phase. 𝜕𝐶, 𝜕𝑡 =−1 𝐴 𝜃𝜕 𝜕𝑥𝑄𝐶,+1 𝐴 𝜃𝜕 𝜕𝑥 𝐴 𝜃𝐸𝜕𝐶, 𝜕𝑥 +𝑟𝐶, (1) C mob,i— concentration of component i in the liquid phase; t—time; A—soil column cross-sectional area; θ—porosity; Q—water flow through the column, E—longitudinal dispersion coefficient; r—reaction term. The model is able to calculate phase concentrations and fluxes as a function of space (soil column depth) and time for the different components. In the present model, hydrocarbons biodegradation processes were based on the availability of different electron acceptors (Figure 1). Figure 1. Schematic representation of hydrocarbon biodegradation processes considered in the mathematical model. Briefly, the presented mathematical model considered aerobic and anoxic biodegradation of total petroleum hydrocarbons (TPH), the latter occurring in the presence of iron (III), nitrate or sulfate as electron acceptors. Anaerobic biodegradation of hydrocarbons to methane, which occurs in the absence of any electron acceptor other than Figure 1. Schematic representation of hydrocarbon biodegradation processes considered in the mathematical model. Briefly, the presented mathematical model considered aerobic and anoxic biodegradation of total petroleum hydrocarbons (TPH), the latter occurring in the presence of iron (III), nitrate or sulfate as electron acceptors. Anaerobic biodegradation of hydrocarbons to methane, which occurs in the absence of any electron acceptor other than bicarbonate/CO 2 , was also considered. Hydrocarbon biodegradation to methane is generally performed by complex microbial communities, where close syntrophic relationships between bacteria and methanogenic archaea have been reported as essential [ 28 , 29 ]. Complete hydrocarbon degradation to methane is thermodynamically limited by the activity of the methanogens [ 29 ]. Moreover, within anaerobic microbial communities, methanogens are generally the most sensitive and slow-growing microorganisms [ 30 ]. Therefore, in this Appl. Sci. 2022,12, 11069 4 of 19 work, petroleum hydrocarbon biodegradation to methane was modelled in only one step, according with the reaction presented in Table S1, admitting that methanogenesis is the limiting step. The model also considered the adsorption/desorption of hydrocarbons, nitrate and sulfate to soil particles as transformation processes. The state variables and the processes rate equations of the developed model are given in Tables 1and 2, respectively. In Annex B of Supporting Information, the full AQUASIM system implementation of the present mathematical model can be consulted. Additionally, the executable file is available in DataRepositoriUM (https://doi.org/10.34622/datarepositorium/2BUM2J, accessed on 28 October 2022). Table 1. State variables. Variable Description Units CH4Methane concentration in the liquid phase mg/L Fe2+Iron(II) concentration in the liquid phase mg/L CNO− 3Nitrate concentration in the liquid phase mg/L O2Dissolved oxygen concentration mg/L CTPH Total petroleum hydrocarbon concentration in the liquid phase mg/L CSO2− 4Sulfate concentration in the liquid phase mg/L Fe(OH)3Amorphous iron (III) concentration g/kg SNO− 3Nitrate concentration in the solid phase g/kg STPH Total petroleum hydrocarbon concentration in the solid phase g/kg SSO2− 4Sulfate concentration in the solid phase g/kg Xaer Concentration of aerobic microorganisms g/kg Xdnb Concentration of denitrifying microorganisms g/kg Xirb Concentration of iron reducing microorganisms g/kg Xsrb Concentration of sulfate reducing microorganisms g/kg Xmet Concentration of methanogenic microorganisms g/kg Table 2. Processes rate equations. Process Rate Equation 1Aerobic biodegradation r=umax,aerCTPH Ks, TPH +CTPH  O2 Ks,O2 +O2Xaer 2 Biodegradation coupled to denitrification r=umax,denCTPH Ks,TPH +CTPH CNO− 3 Ks,NO− 3+CNO− 3Ks,O2 Ks,O2 +O2Xdnb 3Biodegradation coupled to Fe(III) reduction r=umax,Fe(III)CTPH Ks,TPH +CTPH  Fe(OH) Ks, Fe(OH)+Fe(OH) Ks,O2 Ks,O2 +O2Xirb 4Biodegradation coupled to sulfate reduction r=umax,sulfCTPH Ks,TPH +CTPH CSO2− 4 Ks,SO2− 4 +CSO2− 4Ks,O2 Ks,O2 +O2Xsrb 5Biodegradation under methanogenic conditions r=umax,metCTPH Ks,TPH +CTPH  Ks,O2 Ks,O2 +O2Xmet 6Death of aerobic bacteria r=kdeath,X_aer ×Xaer 7Death of denitrifying microorganisms r=kdeath,X_anae ×Xdnb 8 Death of Fe(III)-reducing microorganisms r=kdeath,X_anae ×Xirb 9Death of sulfate-reducing microorganisms r=kdeath,X_anae ×Xsrb 10 Death of methanogenic microorganisms r=kdeath,X_anae ×Xmet 11 Adsorption of hydrocarbon r=k×Seq_freundlich_TPH −STPH 12 Adsorption of nitrate r=k×Seq_freundlich_NO3 −SNO− 3 13 Adsorption of sulfate r=k×Seq_freundlich_SO4 −SSO2− 4 14 Re-oxidation of Fe2+ r=kFeOx ×Fe2+×O2 Simplification assumptions were the following: (i) The model considered two phases: one solid, constituted by the soil particles, and another liquid with the water flowing through the soil column. Hydrocarbon might be adsorbed by the soil particles, be dissolved in the water, or float in the NAPL phase Appl. Sci. 2022,12, 11069 5 of 19 (due to its lower density in comparison with water, excess of hexadecane is considered to float, thus forming a free NAPL layer). For simplification, hydrocarbon concentration in the liquid phase refers to the mass of both dissolved and NAPL forms per unit of liquid volume and both are considered to be available for microorganisms growth; (ii) Soil temperature was kept constant and equal to 20 ◦C; (iii) Only values for alkanes were considered for all parameters and constants involved in the model processes; (iv) For processes of stoichiometric calculations, hexadecane was chosen as a model compound, as alkanes of intermediate chain length are major constituents of petroleum fuels [ 17 ]. Thus, processes rates and model parameters were defined following the reactions presented in Table S1; (v) Microorganisms do not use any other source of organic matter besides hydrocarbons for growth; (vi) The biomass of the hydrocarbon-degrading microorganisms follows growth kinetics according to the Monod equation; (vii) To guarantee that all soluble iron does not leave the soil column with the water flow, and due to the fast transformation process of Fe 2+ and its unstable nature in the environment [ 31 ], it was assumed to be a process for iron oxidation in the presence of O2. This process was considered a first order reaction for Fe2+ and O2(Table 3). Simplifications (ii) and (iii) make the results presented here specific to saturated hydrocarbons but the entire model design applies to any hydrocarbon or mixture of hydrocarbons by simply changing the values of parameters, constants and processes rates. In addition, the present model is considered a wet soil mainly composed of fine sand and/or pumices [ 32 ]. However, soil properties can be easily changed by assuming new values for soil porosity and soil density. Table 3. Initial conditions and input variables. Name Description Value Unit Reference ASoil column cross sectional area 1 m2 CCH4,in Input methane concentration 0 mg/L CFe (II),in Input iron(II) concentration 0 mg/L CNO3,in Input nitrate concentration 0 mg/L CNO3,ini Initial soluble nitrate concentration 10 mg/L [33] CO2,in Input concentration of dissolved oxygen 10 mg/L CO2,ini Initial concentration of dissolved oxygen 10 mg/L CTPH,in Input concentration of hydrocarbon 0 mg/L CSO4,in Input sulfate concentration 0 mg/L CSO4,ini Initial soluble sulfate concentration 10 mg/L [33] QPrecipitation water flowing through the soil column * L/d STPH,ini Initial TPH concentration 0.6 g/kg SFe (III),ini Initial amorphous iron(III) concentration 66.7 g/kg [34] SNO3,ini Initial nitrate concentration in the solid phase 0.3 g/kg [35] SSO4,ini Initial sulfate concentration in the solid phase 0.1 g/kg TTemperature 20 ◦C Xaer,ini Initial concentration of aerobic microorganisms 0.08 g/kg Xdnb,ini Initial concentration of denitrifying microorganisms 0.04 g/kg Xirb,ini Initial concentration of iron(III) reducing microorganisms 0.04 g/kg Xsrb,ini Initial concentration of sulfate reducing microorganisms 0.04 g/kg Xmet,ini Initial concentration of methanogenic microorganisms 0.02 g/kg * Values estimated based on the daily average precipitation for the city of Braga during one hydrological year. For the simulation of a real contamination, the model assumed an oil spill that resulted in a TPH concentration in the soil of 0.6 g/kg for an area of 1 m 2 and 2 m 2 soil column depth. In the model development, it was also considered the daily rainfall for the city of Braga (with an annual average of ~3.75 L/d) as an additional flow of water to the soil column (Q Appl. Sci. 2022,12, 11069 6 of 19 in Equation (1)). All input and initial variables are presented in Table 3. Stoichiometric and composition matrix are shown in supplementary material (Table S2). 2.2. Sensitivity Analysis A sensitivity analysis of the model parameters was carried out using the absolute– relative sensitivity function—Sens AR [ 25 ]. The Sens AR measures the absolute change in a state variable for a 100% change in a model parameter and does not depend on the parameter units [ 27 ]. The parameters are varied independently to assess how these changes affect the model results. The calculations were performed with AQUASIM for all model parameters present in Table S3. 2.3. Data Collection and Model Calibration Model parameters and boundary conditions were gathered from the literature and from a set of batch experiments described in Sections 2.3.1 and 2.3.2. With this approach, the developed model is assumed to be calibrated. Table S3 presents the values of all model parameters. 2.3.1. Solid–Liquid Partition Experiment Hydrocarbon adsorption to soil particles was assessed in batch assays, using serum bottles of 70 mL total volume. The assays were performed in quadruplicate. Hexadecane (C16:0) (ACROS ORGANICS, 99%) was chosen as a model compound due to its relative abundance in crude oil (up to 50% of the hydrocarbon fraction) [ 17 , 36 ] and its intermediate molecular weight (226.44 g/mol) [ 17 ]. Soil was collected from an agricultural site in Barcelos, Portugal, at approximately 1.5 m depth using hand augers. Soil samples were kept at 4 ◦ C, thoroughly homogenized through a 2 mm sieve and characterized. The soil presented a moisture of 2.5 ± 0.05% (w/w), an organic matter content of 0.28 ± 0.004%, pH of 5.2 ±0.2 (in water) and a silt loam texture from 25% clay, 65% silt and 8.5% sand. In each bottle, a 1:1 soil-water mixture was prepared [ 37 ] with 20 g of dry soil and 20 g of distilled water. Additionally, 100 µ L of sodium azide (0.2%, w/v) was used as a microbial activity inhibitor [ 38 ]. Different amounts of hexadecane (2.5, 5, 10, 25 and 50 mg ) were added with a glass syringe. These corresponded to the following concentrations, expressed relatively to the amount of soil added: 0.125 g/kg, 0.25 g/kg, 0.5 g/kg, 1.25 g/kg and 2.5 g/kg. Blank assays without hexadecane were also prepared. All bottles were closed with Viton rubber stoppers and were kept at 20 ◦ C, 200 rpm, for 7 days. This time period was defined based on preliminary tests carried out to guarantee that adsorption equilibrium was reached. Afterward, the liquid and solid phases were separated by decantation. The liquid phase was acidified at pH 2.0 with HCl and preserved at 4 ◦ C until further hydrocarbon analysis. The hexadecane present in the solid phase was immediately extracted and quantified. 2.3.2. Biodegradation Experiments Hydrocarbon biodegradation tests were carried out in batch experiments in the presence of oxygen or nitrate as electron acceptors. Sludge (17 ± 2 g/L of volatile solids, VS) from a full-scale treatment plant performing ex situ bioremediation of petroleumcontaminated groundwater, located in France, was used as inoculum. In each bottle, 10 mL of the inoculum was mixed with 35 mL of mineral bicarbonate-buffered culture medium supplemented with salts and vitamins (without reducing agent), prepared as described in [ 39 ]. The presence of a solid phase was accomplished by also adding to the bottles 20 g (dry sweight) of sediment from the reservoir of Alto Lindoso dam (Lima River, Portugal). The sediment presented an organic matter content of 5.5 ± 0.5% and a pH of 6.8. Nitrate, sulfate and phosphate concentrations in the sediment’s pore water were lower than the minimum values measurable by the used methods (i.e., 1 mg/L for nitrate, 40 mg/L for sulfate and 0.15 mg/L for phosphate). This sediment was used in the assays, instead of the soil used in the experiments described in Section 2.3.1, with the aim of guaranteeing Appl. Sci. 2022,12, 11069 7 of 19 and reinforcing the microbial hydrocarbon-degrading activity. Hydrocarbon-degrading microorganisms were expected, due to the presence of oil from the motors of boats in this dam. To have a complex hydrocarbon mixture, the concentrated oily fraction of a produced water (PW) was used as the hydrocarbon source. PW density was 0.75 g/cm 3 , with a total petroleum hydrocarbon (TPH) concentration of 202 g/L [40]. A PW mass equivalent to 50 mg TPH was added to each bottle, corresponding to a final TPH concentration of approximately 2.5 g/kg (expressed relatively to the dry weight of sediment). In the anoxic assays, nitrate (20 mmol/L final concentration) was added as an electron acceptor. Bottles (250 mL total volume) were closed with Viton rubber stoppers and aluminum crimp caps, pressurized with N 2 /CO 2 (80:20%, v/v) at 1.7 bar (final pressure), and incubated in the dark at 37 ◦ C on a horizontal shaker (110 rpm) for 90 days. In the aerobic assays (oxygen as electron acceptor), the tests were performed by adapting the Biochemical Oxygen Demand (BOD) Oxitop ® method [ 41 ]. Briefly, the amount of dissolved oxygen that is consumed during the aerobic biological oxidation is quantified by measuring the negative pressure values generated in the headspace of the bottles. The measuring units (heads) automatically record the pressure values once a day, which are converted into digits and showed in a display. Whenever the Oxitop ® value did not increase by about 5% from the previous value, the bottle was opened, replenishing the available oxygen, and the NaOH pellet (which removes from the headspace the CO 2 released during microbial oxidation) was replaced by a new one. The aerobic assays were incubated in the dark, at 30 ◦C for 90 days with agitation. All the assays were made in duplicate. Throughout the incubation time, NO 3− concentration were periodically measured in the anoxic assays. In the aerobic tests, Oxitop ® values were regularly recorded and the cumulative oxygen consumption was calculated by the sum of the Oxitop ® value after multiplication by the corresponding conversion factor. 2.3.3. Analytical Methods The water and organic matter content in the soil and sediment samples were determined with gravimetry [ 42 ] through drying the samples at 105 ◦ C for 24 h and subsequent ignition at 550 ◦ C for 2 h. Volatile solids were determined according to the Standard Methods [ 43 ]. Soil texture was evaluated by separating the relative proportions of sand, silt and clay using grading sieves. Nitrate, sulfate and phosphate concentrations were determined using spectrophotometric measurement kits (HACH-LANGE, Germany): LCK 339, range 1–60 mg/L for nitrate; LCK 153, range 40–150 mg/L for sulfate; LCK 349, range 0.15–4.50 mg/L for phosphate. DR2800 spectrophotometer (HACH-LANGE, Düsseldorf, Germany) was used in these analyses. The pH was measured with an inoLab ® pH 7110 bench meter (WTW, Weilheim, Germany). Hexadecane was quantified in solid and liquid phases. Quantification in solid phase was performed by extracting the hydrocarbon with a mixture of hexane and acetone (1:1) in closed Schott flasks at room temperature for 4 h at 180 rpm [ 44 ]. Hexadecane in liquid samples was sequentially extracted three times with hexane, using separatory funnels [ 45 ]. All the extracts were cleaned using Sep-Pak Florisil ® cartridges (Waters, Milford, MA, USA) and evaporated in TurboVap ® LV (Biotage, Uppsala, Sweden). Hexadecane concentration was quantified by gas chromatography (GC) in a Varian 4000 GC/MS equipped with a BRUKER BR-1ms column. The injector temperature was set at 250 ◦ C. The temperature of the oven started at 60 ◦ C for 1 min, and then increased up to 170 ◦ C through a temperature ramp of 8 ◦ C/min, holding then at 170 ◦ C for 1 min. Airflow rate was 1 mL/min and the flame ionization detector (FID) temperature was 315 ◦C [46]. 2.4. Model Simulation and Hypothetical Bioremediation Scenarios Five bioremediation scenarios were developed and compared with the baseline scenario (i.e., the scenario keeping the initial conditions and mimicking the natural attenuation) in order to understand the effect of the different electron acceptors in the biodegradation of Appl. Sci. 2022,12, 11069 8 of 19 saturated hydrocarbons and to demonstrate that the developed model provided a coherent response to external perturbations. The first scenario considered a re-aeration process ( r=KLa(O2,sat −O2 ) with an oxygen mass transfer coefficient ( KLa = 1 d −1 [ 47 ]) in order to increase the dissolved oxygen concentration in the soil column. This scenario foresees that oxygen will be flushed into the soil column. In the second, third and fourth scenarios, initial concentrations of nitrate, sulfate or iron (III) that were 100 times higher than in the baseline scenario were simulated (i.e., 1000 mg/L for nitrate or sulfate and 6.6 kg/kg for iron). The fifth scenario considered the use of the adsorbed TPH by microorganisms at a rate of approximately 10% of the biodegradation rate that occurs in the liquid phase. This scenario was coded as 10%_STPH and could reflect, for example, the addition of surfactants to contaminated soil. 3. Results 3.1. Solid-Liquid Partition Experiment In this experiment, the aqueous and non-aqueous liquids were not separated; as such, the amount of hexadecane retrieved from the liquid phase accounts for the dissolved and NAPL forms of this compound. Considering the physical-chemical properties of hexadecane, i.e., low water solubility (9.0 × 10 −4 mg/L at 20 ◦ C), low vapour pressure ( 1.9 ×10−1Pa at 20 ◦ C) and predicted log Kow = 8.6 and Koc = 2.9 × 10 3 L/kg [ 48 ], adsorption to the organic carbon in soil can be mainly expected to occur. The mass of hexadecane recovered from the solid and liquid (aqueous and nonaqueous) phases, relativel to the different amounts added, are shown in supplementary material (Figure S1). More than 61% of the hexadecane added was retrieved from the solid phase, while only 1 to 4% was quantified in the liquid phase (Table 4), showing that this compound mostly adsorbed soil particles for all the concentrations tested. Total hexadecane recovery, calculated by the sum of the mass obtained from both solid and liquid phases, ranged from 64% to 109% (Table 4). Table 4. Hexadecane recovery (%) from the solid and liquid phases and total recovery in the partition experiments. Mass Added (mg) Recovery from Solid Phase (%) Recovery from Liquid Phase (%) Total Recovery (%) 2.5 77.5 ±28.0 1.6 ±0.4 79.1 ±28.0 5 107.6 ±0.7 1.3 ±0.8 108.9 ±1.0 10 71.7 ±2.8 4.2 ±0.4 75.9 ±2.8 25 61.1 ±2.0 2.7 ±0.4 63.9 ±2.0 50 69.6 ±5.2 2.4 ±0.2 71.9 ±5.2 In Figure 2, the distribution of hexadecane concentration between solid and liquid matrices is presented, highlighting once more the tendency of hexadecane for partitioning into the soil. The experimental results were adjusted to a Freundlich isotherm (Equation (2)) [ 49 ]. This equation is used here to describe the distribution of hexadecane in the soil (solid phase) versus in the liquid (aqueous and nonaqueous) phase. In this experiment, S=KfC1 n(2) where Sis the hexadecane concentration adsorbed on the solid phase (g/kg), Cis the remained hexadecane concentration in the liquid (aqueous and nonaqueous phase) (g/L) and K f and n are constants, specific for the adsorbate and adsorbent at a given temperature. The obtained parameters were: K f = 0.004355 L/kg and n= 0.6712, with a R 2 of 0.97. This correlation coefficient is satisfactory, suggesting that the Freundlich model can adequately describe hexadecane sorption characteristics. Appl. Sci. 2022,12, 11069 9 of 19 Appl. Sci. 2022, 12, x FOR PEER REVIEW 9 of 19 2.5 77.5 ± 28.0 1.6 ± 0.4 79.1 ± 28.0 5 107.6 ± 0.7 1.3 ± 0.8 108.9 ± 1.0 10 71.7 ± 2.8 4.2 ± 0.4 75.9 ± 2.8 25 61.1 ± 2.0 2.7 ± 0.4 63.9 ± 2.0 50 69.6 ± 5.2 2.4 ± 0.2 71.9 ± 5.2 In Figure 2, the distribution of hexadecane concentration between solid and liquid matrices is presented, highlighting once more the tendency of hexadecane for partitioning into the soil. The experimental results were adjusted to a Freundlich isotherm (Equation (2)) [49]. This equation is used here to describe the distribution of hexadecane in the soil (solid phase) versus in the liquid (aqueous and nonaqueous) phase. In this experiment, 𝑆=𝐾 𝐶  (2) where S is the hexadecane concentration adsorbed on the solid phase (g/kg), C is the remained hexadecane concentration in the liquid (aqueous and nonaqueous phase) (g/L) and K f and n are constants, specific for the adsorbate and adsorbent at a given temperature. The obtained parameters were: K f = 0.004355 L/kg and n = 0.6712, with a R 2 of 0.97. This correlation coefficient is satisfactory, suggesting that the Freundlich model can adequately describe hexadecane sorption characteristics. Figure 2. Hexadecane partition between solid and liquid (aqueous and non-aqueous) phases. The results presented are the average and standard deviation for quadruplicate assays. The ratio between the concentration of hexadecane adsorbed in soil and remaining in the liquid phase increases with the increase of hexadecane concentration, resulting in a convex curve (Figure 2). Therefore, for higher initial hexadecane concentrations, this compound will tend to adsorb more in soil and remain less in the liquid phase. This can possibly relate to the fact that at higher hexadecane concentrations, the surface of the soil particles may become covered by this compound, which potentially facilitates additional adsorption. Since in Figure 2 a plateau was not reached, the sorption capacity of the soil was not limited under the range of concentrations studied. 3.2. Biodegradation Assays In the hydrocarbon biodegradation assays, a rapid increase of the Oxitop values (i.e., a fast oxygen consumption) and a decrease of NO 3− concentrations were verified in the aerobic and anoxic assays, respectively, during the first 30–40 days of incubation (data not shown). This was probably due to the oxidation of more biodegradable substrates from Figure 2. Hexadecane partition between solid and liquid (aqueous and non-aqueous) phases. The results presented are the average and standard deviation for quadruplicate assays. The ratio between the concentration of hexadecane adsorbed in soil and remaining in the liquid phase increases with the increase of hexadecane concentration, resulting in a convex curve (Figure 2). Therefore, for higher initial hexadecane concentrations, this compound will tend to adsorb more in soil and remain less in the liquid phase. This can possibly relate to the fact that at higher hexadecane concentrations, the surface of the soil particles may become covered by this compound, which potentially facilitates additional adsorption. Since in Figure 2a plateau was not reached, the sorption capacity of the soil was not limited under the range of concentrations studied. 3.2. Biodegradation Assays In the hydrocarbon biodegradation assays, a rapid increase of the Oxitop values (i.e., a fast oxygen consumption) and a decrease of NO 3− concentrations were verified in the aerobic and anoxic assays, respectively, during the first 30–40 days of incubation (data not shown). This was probably due to the oxidation of more biodegradable substrates from the sediment and inoculum sludge. The same inoculum already showed similar behavior in previous experiments [ 50 ]. Therefore, this initial period was not considered for the calculation of the hydrocarbon biodegradation rates. From day 32 and until the end of the test, the oxygen consumed increased gradually in the aerobic assays (Figure 3A), while in the anoxic tests NO 3− concentrations decreased consistently after the first 40 days of incubation (Figure 3B), pointing to the occurrence of aerobic and denitrifying hydrocarbon biodegradation activity. From the curves slope, the corresponding biodegradation rates were obtained and are depicted in the Figure 3. For the calculation of biodegradation rates, the stoichiometry of the chemical reactions presented in Table S1 was considered. Regarding the biodegradation rate in the presence of oxygen, a wide range of values have been reported by several authors, depending on the substrate and experimental conditions applied. For example, aerobic biodegradation rate of diesel could range from 0.074 d −1 to 0.35 d −1 [ 14 ], while other studies present values ranging from 0.587 d −1 to 4.75 d −1 for petroleum hydrocarbons and diesel [ 7 , 51 ]. The value obtained in this work is in line with those from the literature. Regarding the values in the presence of nitrate, Roy and Greer [ 52 ] reported a higher rate (0.91 d −1 ) for hexadecane mineralisation in the presence of NaNO3, while Bregnard et al. [53] reported values around 0.14 to 0.35 d−1. Appl. Sci. 2022,12, 11069 16 of 19 Physicochemical parameters such as porosity, soil density and adsorption isothermal parameters presented high sensitivity, thus requiring careful definition and, if needed, further investigation for real case implementation of the model. For practical purposes, this model can be used as a support tool for the management of contaminated sites, since it allows the simulation and comparison of different bioremediation strategies, namely the addition of different electron acceptors, including soil re-aeration (that can stimulate a specific microbial group, relative to the others) or surfactants addition (that may also accelerate soil bioremediation by increasing hydrocarbons bioavailability), among others. Different bioremediation scenarios were simulated and pointed to natural attenuation or soil re-aeration being the best strategies under the simulated conditions. The addition of surfactants will also accelerate soil bioremediation. Finally, this study demonstrates that a mathematical model capable of responding to environmental perturbation can work as a decision-supporting tool for the proper design of soil bioremediation strategies tackling petroleum hydrocarbon contamination. Supplementary Materials: The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/app122111069/s1, Table S1. Stoichiometry of the main processes involved in hexadecane biodegradation; Table S2. Stoichiometric (Petersen) and composition matrix for the bioremediation model; Table S3. Values of model parameters and constants; Table S4. Values of absolute-relative sensitivity (Sens AR) of model parameters on TPH concentration in the liquid and solid phases (expressed as mg/L and g/kg, respectively); Figure S1. Hexadecane mass recovered from solid (a) and liquid (b) phases, relatively to the mass added in the solid-liquid partition experiments; Figure S2. Variation of dissolved oxygen (A) and aerobic biomass (B) concentrations in depth; Figure S3. Variation of nitrate, sulfate and Fe (III) over time, and denitrifying, sulfate reducing and iron reducing bacteria in depth; Figure S4. Variation of methane concentration over time (A), and of methanogenic biomass concentration in depth (B). References [ 60 – 63 ] are cited in the supplementary materials. Author Contributions: G.M.: Conceptualization, Investigation, Methodology, Data curation, Software, Formal analysis, Writing—original draft, Writing—review and editing. S.C.: Investigation, Software, Visualization. A.F.: Investigation, Software, Visualization. R.C.: Conceptualization, Investigation, Visualization, Writing—review and editing. M.S.D.: Conceptualization, Investigation, Visualization, Writing—review and editing. A.J.C.: Conceptualization, Investigation, Methodology, Data curation, Software, Formal analysis, Funding acquisition, Writing—original draft, Writing—review and editing, Writing—review and editing. All authors have read and agreed to the published version of the manuscript. Funding: This study was supported by the Portuguese Foundation for Science and Technology (FCT) under the scope of project MORE (PTDC/AAG-TEC/3500/2014; POCI-01-0145-FEDER-016575), the strategic funding of UIDB/04469/2020 unit and by LABBELS—Associate Laboratory in Biotechnology, Bioengineering and Microelectromechanical Systems, LA/P/0029/2020. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The AQUASIM executable file is available in DataRepositoriUM (https: //doi.org/10.34622/datarepositorium/2BUM2J, accessed on 15 September 2022). Conflicts of Interest: The authors declare no conflict of interest. References 1. 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