Search Results (67)

Data-driven empirical models, including those based on reaction kinetics, are well-regarded for their ability to make accurate predictions and uncover underlying relationships. While such models have been extensively employed for microbial communities, their use in agricultural populations remains comparatively limited. In this study, researchers analyzed data from hydroponic lettuce cultivation experiments observing nitrogen-, phosphorus-, and potassium-limited growth. Dynamic μ models, which incorporated nutrient-fueled growth and maturity-based rate decay, were adapted to accommodate a variable nutrient supply, as would be expected for nutrient recovery efforts using domestic wastewater. To test these models, researchers analyzed multiple approaches, differing variations in analyses, and other agricultural models against observed biomass measurements. The resulting Dynamic μ biomass models showed significantly less error than all other tested models, were validated against three variable nutrient treatments, and were evaluated against expected wastewater concentrations. Wastewater-cultivated lettuce was predicted to grow between 20 and 72% of fresh mass compared to lettuce grown under ideal nutrient concentrations, and models identified 41.7 days to maximize dry biomass, with a final harvest time of 44.0 days to maximize fresh biomass. Finally, this research demonstrates the application of agricultural modeling for profit estimation and informing decisions on supplemental nutrient use, providing guidance for nutrient recovery from wastewater. Full article

Developing precision models to describe agricultural growth is a necessary step to promote sustainable agriculture and increase resource circulation. In this study, the researchers hydroponically cultivated Bibb lettuce (Lactuca sativa) across a variety of nitrogen, phosphorus, and potassium (NPK)-limited treatments and developed robust data-driven kinetic models observing nutrient uptake, biomass growth, and tissue composition based on all three primary macronutrients. The resulting Dynamic μ model is the first to integrate plant maturity’s impact on growth rate, significantly improving model accuracy across limiting nutrients, treatments, and developmental stages. This reduced error supports this simple expansion as a practical and necessary inclusion for agricultural kinetic modeling. Furthermore, analysis of nutrient uptake refines the ideal hydroponic nutrient balance for Bibb lettuce to 132, 35, and 174 mg L⁻¹ (N, P, and K, respectively), while qualitative cell yield analysis identifies minimum nutrient thresholds at approximately 26.2–41.7 mg-N L⁻¹, 3.7–5.6 mg-P L⁻¹, and 17.4–31.5 mg-K L⁻¹ to produce compositionally healthy lettuce. These findings evaluate reclaimed wastewater’s ability to offset the fertilizer burden for lettuce by 23–45%, 14–57%, and 3–23% for N, P, and K and guide the required minimum amount of wastewater pre-processing or nutrient supplements needed to completely fulfill hydroponic nutrient demands. Full article

Wastewater treatment plants (WWTPs) face increasing pressure to handle higher volumes of water due to climate change causing storm surges, which current infrastructure cannot handle. Aerobic granular sludge (AGS) is a promising alternative to activated sludge systems due to their improved settleability property, lowering the land footprint and improving efficiency. This research investigates the optimisation of a lab-scale sequencing batch reactor (SBR) into a continuous flow reactor through mathematical modelling, sensitivity analysis, and a computational fluid dynamic model. This is all applied for the future goal of scaling up the model designed to a full-scale continuous flow reactor. The mathematical model developed analyses microbial kinetics, COD degradation, and mixing flows using Reynolds and Froude numbers. To perform a sensitivity analysis, a Python code was developed to investigate the stability when influent concentrations and flow rates vary. Finally, CFD simulations on ANSYS Fluent evaluated the mixing within the reactor. An 82% COD removal efficiency was derived from the model and validated against the SBR data and other configurations. The sensitivity analysis highlighted the reactor’s inefficiency in handling high-concentration influents and fast flow rates. CFD simulations revealed good mixing within the reactor; however, they did show issues where biomass washout would be highly likely if applied in continuous flow operation. All of these results were taken under deep consideration to provide a new reactor configuration to be studied that may resolve all these downfalls. Full article

Reverse osmosis (RO) desalination technology offers a promising solution for mitigating water scarcity. However, one of the major challenges faced by RO membranes is biofouling, which significantly increases the desalination costs. Traditional simulation models often overlook environmental variability and do not incorporate the effects of membrane-surface modifications. This paper develops a bacterial growth model for the prediction of seawater desalination performance, applicable to commercial RO membranes, which can be either uncoated or coated with iron nanoparticles (FeNPs or nZVI). FeNPs were selected due to their known antimicrobial properties and potential to mitigate biofilm formation. The native seawater bacterium Bacillus halotolerans MCC1 was used as a model biofouling bacterium. Growth kinetics were determined at different temperatures (from 26 to 50 °C) and pH values (from 4 to 10) to obtain growth parameters. Microbial growth on RO membranes was modeled using the Monod equation. The desalination performance was evaluated in terms of hydraulic resistance and permeate flux under clean and biofouled conditions. The model was validated using desalination data obtained at the laboratory scale. Bacteria grew faster at 42 °C and pH 10. The pH had a more significant effect than temperature on the bacterial growth rate. The FeNP-coated membranes exhibited lower resistance and maintained a higher long-term water flux than the commercial uncoated membrane. This modeling approach is useful for improving the monitoring of feed water parameters and assessing the operational conditions for minimum biofouling of RO membranes. In addition, it introduces a novel integration of environmental parameters and membrane coating effects, offering a predictive tool to support operational decisions for improved RO performance. Full article

Riboflavin is biosynthesized and excreted extracellularly by the novel yeast Hyphopichia wangnamkhiaoensis. The steady-state kinetics of cell growth, substrate consumption, and riboflavin production by H. wangnamkhiaoensis were studied in a chemostat continuous culture at different dilution rates. The unstructured Monod and Luedeking–Piret models were used to describe cell growth, substrate consumption, and riboflavin production, and crucial kinetic parameters were estimated. The experimental data fitted the proposed models well. The maximum specific growth rate, substrate affinity constant, maintenance energy coefficient, and maximum biomass yield values were 0.1378 h⁻¹, 0.4166 g of glucose L⁻¹, 0.1047 g of glucose g⁻¹ of biomass h⁻¹, and 0.172 g of biomass g⁻¹ of glucose, respectively. The maximum yield from glucose and volumetric and specific productivities of riboflavin were 0.7487 mg of riboflavin g⁻¹ of glucose, 0.5593 mg of riboflavin L⁻¹ h⁻¹, and 0.6547 mg of riboflavin g⁻¹ of biomass h⁻¹, respectively. The estimated growth-associated riboflavin production constant (4.88 mg of riboflavin g⁻¹ of biomass) was much higher than the non-growth-associated riboflavin production constant (0.0022 mg of riboflavin g⁻¹ of biomass h⁻¹), indicating that riboflavin production by H. wangnamkhiaoensis is a predominantly growth-associated process. The chemostat continuous culture offers a promising strategy for efficiently and sustainably producing riboflavin using H. wangnamkhiaoensis. Full article

Due to environmental pollution and the depletion of fossil fuels, there is growing interest in the development and use of biofuels as environmentally friendly alternatives. One of the most promising biofuels is biohydrogen, hydrogen produced through sustainable processes using microorganisms such as bacteria and algae. One of the most interesting bacteria for hydrogen production is Ralstonia eutropha H16, known for its ability to produce oxygen-tolerant hydrogenases. These enzymes play a crucial role in biohydrogen metabolism and production. The aim of this work was to determine the optimal conditions (reactor type and synthetic medium composition) for the cultivation of R. eutropha H16. The culture media contained different concentrations of fructose and glycerol (mono- or double-substrate cultivation) and the experiments were carried out in a batch reactor. The initial experiments were carried out with 4 g/L fructose or glycerol in the culture medium at pH 7, T = 30 °C, and 120 rpm. The mathematical model, consisting of the growth kinetics (described by the Monod’s model) and the corresponding mass balances, was proposed. The developed model was validated using two independent experiments with different initial substrate concentrations: 2 g/L glycerol and fructose in one medium and 4 g/L fructose and 1 g/L glycerol in the second. In order to propose the optimal cultivation procedure for future research, the mathematical model simulations were performed for different reactor types (batch, fed-batch, and continuous stirred tank reactors) and different initial substrate concentrations. The most successful experiment was the one with 4 g/L glycerol, where γ_X = 0.485 ± 0.001 g/L of biomass was achieved. Further calculations showed that the most biomass would be produced at higher glycerol concentrations (at γ_G = 6.358 g/L, γ_X = 1.311 g/L should be achieved after 200 h of cultivation) and when using a fed-batch reactor (γ_X = 0.944 g/L after 200 h of cultivation). Full article

In this work, kinetic models are assessed to describe bacterial cellulose (BC) production, substrate consumption, and biomass growth by K. xylinus in a batch-stirred tank bioreactor, under 700 rpm and 500 rpm agitation rates. The kinetic models commonly used for Acetobacter or Gluconacetobacter were fitted to published data and compared using the Akaike Information Criterion (AIC). A stepwise fitting procedure was proposed for model selection to reduce computation effort, including a first calibration in which only the biomass and substrate were simulated, a selection of the three most effective models in terms of AIC, and a calibration of the three selected models with the simulation of biomass, substrate, and product. Also, an uncoupled product equation involving a modified Monod substrate function is proposed for a 500 rpm agitation rate, leading to an improved prediction of BC productivity. The M2c and M1c models were the most efficient for biomass growth and substrate consumption for the combined AIC, under 700 rpm and 500 rpm agitation rates, respectively. The average coefficients of determination for biomass, substrate, and product predictions were 0.981, 0.994, and 0.946 for the 700 rpm agitation rate, and 0.984, 0.991, and 0.847 for the 500 rpm agitation rate. It is shown that the prediction of BC productivity is improved through the proposed substrate function, whereas the computation effort is reduced through the proposed model fitting procedure. Full article

This work focused on demonstrating the use of dynamic time warping (DTW) as a metric for the elementary effects computation in Morris-based global sensitivity analysis (GSA) of model parameters in multivariate dynamical systems. One of the challenges of GSA on multivariate time-dependent dynamics is the modeling of parameter perturbation effects propagated to all model outputs while capturing time-dependent patterns. The study establishes and demonstrates the use of DTW as a metric of elementary effects across the time domain and the multivariate output domain, which are all aggregated together via the DTW cost function into a single metric value. Unlike the commonly studied coefficient-based functional approximation and covariance decomposition methods, this new DTW-based Morris GSA algorithm implements curve alignment via dynamic programing for cost computation in every parameter perturbation trajectory, which captures the essence of “elementary effect” in the original Morris formulation. This new algorithm eliminates approximations and assumptions about the model outputs while achieving the objective of capturing perturbations across time and the array of model outputs. The technique was demonstrated using an ordinary differential equation (ODE) system of mixed-order adsorption kinetics, Monod-type microbial kinetics, and the Lorenz attractor for chaotic solutions. DTW as a Morris-based GSA metric enables the modeling of parameter sensitivity effects on the entire array of model output variables evolving in the time domain, resulting in parameter rankings attributed to the entire model dynamics. Full article

Global fertilizer production and mismanagement significantly contribute to many harmful environmental impacts, revealing the need for a greater understanding of crop growth and nutrient uptake, which can be used to optimize fertilizer management. This study experimentally adapts first-principles microbial modeling techniques to the hydroponic cultivation of Bibb lettuce (Lactuca sativa) under nitrogen-limited conditions. Monod and Michaelis–Menten’s approaches are applied to predict biomass productivity and nutrient uptake and to evaluate the feasibility of reclaimed wastewater as a nutrient source of nitrogen. Experimental and modeling results reveal significantly different kinetic saturation constants ($K_s$ = 1.331 and $K_m$ = 17.887 mg L⁻¹) and a corresponding cell yield strongly dependent on nutrient concentration, producing visually and compositionally distinct tissue between treatments receiving $\le$26.2 and $\ge$41.7 $\mathrm{m}{\mathrm{g}}_{\mathrm{N}}$ L⁻¹. The resulting Monod model overestimates dry mass predictions during low nutrient conditions, and the collective results support the development of a dynamic Monod curve that is temporally dependent during the plants’ lifecycle. Despite this shortcoming, these results support the feasibility of reclaiming nitrogen from wastewater in hydroponic agriculture, expecting to produce lesser biomass lettuce exhibiting healthy tissue. Furthermore, this study provides a mathematical foundation for agricultural simulations and nutrient management. Full article

Simultaneous nitrification and autotrophic denitrification (SNAD) has received attention as an efficient biological nitrogen removal alternative. However, SNAD using elemental sulfur (S⁰) has scarcely been studied. Thus, the main objective of this research was to study the behavior of a simultaneous nitrification–autotrophic denitrification operation in a sequential batch reactor (SNAD-SBR) at a lab scale using S⁰ as an electron donor, including its kinetics. Two-scale reactors were operated at lab scales in cycles for 155 days with an increasing nitrogen loading rate (NLR: 0.0296 to 0.0511 kg N-NH₄⁺/m³/d) at 31 °C. As a result, simultaneous nitrification–autotrophic denitrification using S⁰ as an electron donor was performed successfully, with nitrification efficiency of 98.63% and denitrification efficiency of 44.9%, with autotrophic denitrification as the limiting phase. The kinetic model adjusted for ammonium-oxidizing bacteria (AOB) was the Monod-type kinetic model (µmax = 0.791 d⁻¹), while, for nitrite-oxidizing bacteria (NOB), the Haldane-type model was employed (µmax = 0.822 d⁻¹). For denitrifying microorganisms, the kinetic model was adjusted by a half order (k_1/2v = 0.2054 mg^1/2/L^1/2/h). Thus, we concluded that SNAD could be feasible using S⁰ as an electron donor, with kinetic behavior similar to that of other processes. Full article

In this work, the feasibility of uncontrolled pH acidogenic fermentation of industrial organic effluent from corn-bioethanol production was studied and modelled by using a Monod-based mathematical model. In order to do that, several tests were carried out at different initial pH values, ranging from 4 to 6. The experimental data showed a pH reduction during the fermentation process due to the generation of short-chain acids. When starting at initial pH of 5.0 and 6.0, the substrates were fully fermented reaching final pH s over 4 units in both cases and a final undissociated fatty acid concentration of about 80 (mmol·L⁻¹) in both cases. Regarding fermentation at an initial pH of 4, the pH decreased to 3.5 units, and the organic substrates were not fully fermented due to the stoppage of the fermentation. The stoppage was caused by the very acidic pH conditions. The biomass showed an uncoupled growth as the operating conditions became more acidic, and, finally, the biomass growth was zero. Regarding the generation of fermentation products, in general terms, the highest economical value of products was obtained when fermenting at an initial pH of 5. More specifically, acetic acid was the acid that presented the highest yield at an initial pH value of 4. Butyric yield showed the highest values at initial pH values of 5 and 6. The highest H₂ yield (1.1 mol H₂·mol⁻¹ dextrose) was achieved at an initial pH value of 5. Finally, the experimental data were modelled using a Monod-based model. From this model, the value of the main kinetics and stoichiometric parameters were determined. Full article

The high chemical oxygen demand (COD) and biochemical oxygen demand (BOD) levels in palm oil mill effluent (POME) wastewater make it an environmental contaminant. Moreover, conventional POME wastewater treatment approaches pose economic and environmental risks. The present study employed an ultrasonic membrane anaerobic system (UMAS) to treat POME. Resultantly, six steady states were procured when a kinetic assessment involving 11,800–21,700 mg·L⁻¹ of mixed liquor suspended solids (MLSS) and 9800–16,800 mg·L⁻¹ of mixed liquor volatile suspended solids (MLVSS) was conducted. The POME treatment kinetics were explained with kinetic equations derived by Monod, Contois and Chen and Hashimoto for organic at loading rates within the 1–11 kg·COD·m⁻³·d⁻¹ range. The UMAS proposed successfully removed 96.6–98.4% COD with a 7.5 day hydraulic retention time. The Y value was 0.67 g·VSS/g·COD, while the specific micro-organism decay rate, b was 0.24 day⁻¹. Methane (CH₄) gas production ranged from 0.24 to 0.59 litres per gram of COD daily. Once the initial steady state was achieved, the incoming COD concentrations increased to 88,100 mg·L⁻¹. The three kinetic models recorded a minimum calculated solids retention time of 12.1 days with maximum substrate utilization rate, K values ranging from 0.340 to 0.527 COD·g⁻¹·VSS·d⁻¹ and maximum specific growth rate, µ_max from 0.248 to 0.474 d⁻¹. Furthermore, the solids retention time (SRT) was reduced from 500 to 12.1 days, resulting in a 98.4% COD level reduction to 1400 mg·L⁻¹. Full article

This work studied the effect of cellulose nanocrystal (NCC) content on the biodegradation kinetics of PLA-based multiscale cellulosic biocomposites (PLAMCBs). To facilitate biodegradation, the materials were subjected to thermo-oxidation before composting. Biodegradation was carried out for 180 days under controlled thermophilic composting conditions according to the ASTM D 5338 standard. A first-order model based on Monod’s kinetics under limiting substrate conditions was used to study the effect of cellulose nanocrystal (NCC) content on the biodegradation kinetics of multiscale composite materials. It was found that thermo-oxidation at 70 °C for 160 h increased the biodegradability of PLA. Also, it was found that the incorporation of cellulosic fibrous reinforcements increased the biodegradability of PLA by promoting hydrolysis during the first stage of composting. Likewise, it was found that partial substitution of micro cellulose (MFC) by cellulose nanocrystals (NCCs) increased the biodegradability of the biocomposite. This increase was more evident as the NCC content increased, which was attributed to the fact that the incorporation of cellulose nanocrystals facilitated the entry of water into the material and therefore promoted the hydrolytic degradation of the most recalcitrant fraction of PLA from the bulk and not only by surface erosion. Full article

An attractive application of crude glycerol is in the generation of biomethane by means of anaerobic co-digestion. Thus, the objective of this work was to evaluate the potential of neural networks and fuzzy logic to predict the production of biomethane from the anaerobic co-digestion of glycerol and/or sugarcane molasses. Firstly, a reactor model was implemented using Scilab (v. 6.1.1), considering the Monod two-substrate with an intermediate (M2SI) kinetic model proposed by Rakmak et al. (Rakmak, N.; Noynoo, L.; Jijai, S.; Siripatana, C. Lecture Notes in Applied Mathematics and Applied Science in Engineering. Melaka, Malaysia, p. 11–20, 2019), to generate a database for subsequent fitting and evaluation of neural and fuzzy models. The neural network package of Matlab was used. Fuzzy modeling was applied using the Takagi–Sugeno approach available in the ANFIS package of Matlab. The biomethane production data simulated using Scilab were considered in neural network modeling and validation, firstly employing a “generic” network applicable to all eight scenarios, providing a very good fit (R² > 0.99). Excellent performance was also observed for specific artificial neural networks (one for each condition, again by using validation data generated by the M2SI model). The parameters of the M2SI model for the eight different conditions were also mapped using a neural network, as a function of the organic material composition, providing a fit with R² > 0.99 when using 25 neurons. In the case of fuzzy logic, an RMSE (Root Mean Squared Error) of 18.88 mL of methane was obtained with 216 rules, which was a value lower than 0.5% of the order of magnitude of the accumulated methane. It could be concluded from the results that fuzzy logic and artificial neural networks offer excellent ability to predict methane production, as well as to parameterize the M2SI kinetic model (using neural networks). Full article

A downflow hanging sponge (DHS) unit was established for treating synthetic domestic wastewater (SDW) for over 100 days of continuous feed. The DHS system was operated at a chemical oxygen demand (COD) concentration of 531.62 ± 93.6 mg/L, and different hydraulic retention times (HRTs) = 6.0–2.0 h to determine the system kinetics. The substrate removal kinetics of the DHS reactor was calculated using modified Stover–Kincannon, Monod, Grau’s second-order and first-order models. The Monod model has the following decay coefficient (K_d), yield coefficient (Y), and maximum specific growth rate of bacteria (μ_max) that were, respectively, 0.0025 1/d, 0.1337 gVSS/gCOD, and 0.0364 1/d. Maximum substrate utilization rate (U_max) and saturation value constant (K_B) for the modified Stover–Kincannon model were determined to be, respectively, 15.46 and 14.45 g/L/d. While the kinetic coefficient for the second-order model ranged was 0.516–0.641 1/d versus 27.627 1/d for the first-order model, the constants of the Grau second-order model (a and b) were estimated as 0.0366 and 0.9215. The Grau second-order and modified Stover–Kincannon models showed an R² value of 0.995, making them the most convenient for the experimental results. The results indicated that these models could be used to predict the DHS reactor behavior at different scales. Full article