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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Reactive Transport Modeling of Hydrogen Production from Serpentinization of Olivine

Hydrogen production from serpentinization of ultramafic rocks represents a promising natural pathway for generating carbon-free energy, yet its kinetics and controlling factors remain incompletely understood. A key challenge in advancing serpentinization research lies in the heterogeneity of porosity and permeability in rocks, which leads to nonuniform fluid velocity fields, as well as uncertainties in estimating reactive surface area and identifying appropriate mineral reaction equilibria. Additional complexities arise from the role of dissolved SiO 2 , Fe 2+ /Fe 3+ partitioning, and the limited effect of pH variations within the strongly alkaline regime on hydrogen yields. These challenges hinder straightforward extrapolation from laboratory tests to practical applications of hydrogen production from natural rocks. Here, in this work, we address these questions using a simulation-based reactive transport modeling framework calibrated against controlled laboratory experiments reported elsewhere. The model couples geochemical kinetics, multiphase flow, and mineralogical feedbacks, enabling systematic evaluation of how surface area, dissolved silica concentration, Fe redox state, temperature, and pressure govern serpentinization and H2 generation. We find that surface area exerts the strongest control on reaction rates and hydrogen yields, while Fe 2+ /Fe 3+ ratios act as secondary modulators. Elevated dissolved silica concentrations suppress hydrogen production but accelerate serpentine precipitation, whereas increasing pH beyond 12 within the strongly alkaline regime produces only marginal gains. Finally, we demonstrate that integrating targeted experiments with calibrated simulations offers a powerful and efficient approach for predicting hydrogen yields and assessing parameter trade-offs in industrial-scale applications. This integration can substantially reduce the experimental burden while improving predictive capability, thereby enhancing both the mechanistic understanding and the practical feasibility of hydrogen production from serpentinization.

08 HYDROGEN↗
DOE OSTI2026

Additional Data Focused on Phase 1 Geared Toward Computational Fluid Dynamics (CFD) validation

A new validation campaign was developed within the Offshore Code Comparison Collaboration, Continued, with Correlation and unCertainty (OC6) to better understand the complex interactions between components of a floating wind system (e.g., columns, pontoons, etc.) in a more generic sense, and to validate modeling approaches for a variety of floating designs. A set of cylinders based on the Offshore Code Comparison Collaboration Continuation (OC4)-DeepCwind semidesign were tested under wave loading, both individually and in different combinations (including the attachment of heave plates of different sizes). The cylinders were held rigid, and pressure sensors were used to measure the distributed loading on the structures, while load cells measured the total integrated hydrodynamic loads.

17 WIND ENERGY↗
DOE OSTI2024

Development of Segregated Thermal-Hydraulics Solvers in MOOSE

The simulation of fluid flows is an essential part of the design and analysis of nuclear systems. Algorithms able to simulate flows at different fidelity levels are available in the Multiphysics Object-Oriented Simulation Environment (MOOSE) and MOOSE-based applications such as Pronghorn \cite{novak2018pronghorn}, Pronghorn-Subchannel, RELAP-7, and SAM. Currently, significant effort is being invested in the development of coarse-mesh Computational Fluid Dynamics (CFD) capabilities within MOOSE and Pronghorn for the simulation of Generation IV nuclear reactors. Traditionally, the solution algorithms in MOOSE have relied on Newton or quasi-Newton methods (such as the preconditioned Jacobian-free Newton-Krylov method) where residuals and Jacobians (or approximations thereof) are constructed. Both Newton and quasi-Newton methods require the solution of a linear system at each nonlinear Newton iteration with the Jacobian as the system matrix. The Jacobian contains blocks originating from all variables in the problem (i.e., for thermal-hydraulics at least pressure, velocities, and temperature). Due to the formulation of the problem in a general multiphysics setting on unstructured mesh, creating a good preconditioner for the linear system can be challenging, thus many fluid applications have utilized direct solver-based methods such as LU factorization. However, with increasing system size and complexity in multi-dimensional problems, the direct solution of linear systems becomes computationally expensive both in execution time and and memory. For this reason, recent effort has focused on adapting segregated solution algorithms for CFD problems in MOOSE. These algorithms use fixed-point iteration between segregated systems whose assembly and preconditioning are easier those of the monolithic system. Initial results show that the segregated solution algorithm outperforms the monolithic approach in terms of memory usage and for large 3D problems in terms of CPU time as well.

42 ENGINEERING↗
DOE OSTI2024

Development of Segregated Thermal-Hydraulics Solvers in MOOSE

The simulation of fluid flows is an essential part of the design and analysis of nuclear systems. Algorithms able to simulate flows at different fidelity levels are available in the Multiphysics Object-Oriented Simulation Environment (MOOSE) and MOOSE-based applications such as Pronghorn \cite{novak2018pronghorn}, Pronghorn-Subchannel, RELAP-7, and SAM. Currently, significant effort is being invested in the development of coarse-mesh Computational Fluid Dynamics (CFD) capabilities within MOOSE and Pronghorn for the simulation of Generation IV nuclear reactors. Traditionally, the solution algorithms in MOOSE have relied on Newton or quasi-Newton methods (such as the preconditioned Jacobian-free Newton-Krylov method) where residuals and Jacobians (or approximations thereof) are constructed. Both Newton and quasi-Newton methods require the solution of a linear system at each nonlinear Newton iteration with the Jacobian as the system matrix. The Jacobian contains blocks originating from all variables in the problem (i.e., for thermal-hydraulics at least pressure, velocities, and temperature). Due to the formulation of the problem in a general multiphysics setting on unstructured mesh, creating a good preconditioner for the linear system can be challenging, thus many fluid applications have utilized direct solver-based methods such as LU factorization. However, with increasing system size and complexity in multi-dimensional problems, the direct solution of linear systems becomes computationally expensive both in execution time and and memory. For this reason, recent effort has focused on adapting segregated solution algorithms for CFD problems in MOOSE. These algorithms use fixed-point iteration between segregated systems whose assembly and preconditioning are easier those of the monolithic system. Initial results show that the segregated solution algorithm outperforms the monolithic approach in terms of memory usage and for large 3D problems in terms of CPU time as well.

42 ENGINEERING↗
DOE OSTI2024

Investigation of a high-temperature combination heat pump for lower-cost electrification in multifamily buildings

The development of space and water heating combination heat pumps capable of generating water temperatures high enough for convective heat emitters will enable more cost-effective and equitable decarbonization solutions for electrifying multifamily buildings. Here, in this paper, multifamily building models and a charge-sensitive mechanistic cycle model of a combination heat pump are developed, and the system performance is predicted based on the models. Unlike other state-of-the-art residential heat pumping equipment, the modeled combination heat pump using an economized, fluid-injected variable-speed compressor can achieve higher temperature lifts of 40° - 85°C, with lower installation costs and complexity. The model predicted heating coefficient of performance (COP h ) is 2.1 at an ambient temperature of -15°C with a high-temperature lift of nearly 85°C, and a seasonal coefficient of performance in heating mode (SCOP h ) ranges from 2 - 4 for different locations. The system shows 30% - 90% lower CO 2 eq emissions over a condensing gas boiler and 9% - 13% lower projected installation costs than two separate space and water heat pumping appliances.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

StOKeDMD: Streaming Occupation kernel dynamic mode decomposition

Dynamic mode decomposition (DMD) has become a common technique for constructing surrogate models for dynamical systems from observed system states. The Occupation Kernel DMD (OKDMD) method proposed in (Rosenfeld et al., 2022) and (Rosenfeld et al., 2024) is a Liouville operator based method that builds surrogate models from system state trajectories. Here, this paper proposes an extension of OKDMD to the case when the system states are observed in a streaming fashion, i.e., only a small fraction of the state trajectory is available at a given time. The developed method, Streaming Occupation Kernel DMD (StOKeDMD), accommodates the streaming data input by leveraging properties of specific choices of kernel functions and occupation kernels. We apply the StoKeDMD method as a compression method for streaming data, analyze the memory complexity, and demonstrate the performance of StoKeDMD in the compression of streaming data generated from a Lorenz system and a fluid flow simulation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Unraveling Hydrogen Induced Geochemical Reaction Mechanisms through Coupled Geochemical Modeling and Machine Learning

Underground hydrogen storage (UHS) provides a promising large-scale, long-term energy storage solution. A reasonable recovery of stored hydrogen is critical for a successful storage scheme. However, in subsurface reservoirs hydrogen is subject to active geochemical reactions that might result in hydrogen loss. In this study, we implemented a geochemical modeling approach coupled with an unsupervised machine learning technique called non-negative matrix factorization (NMF) to unravel the complex brine-rock-H 2 geochemical processes responsible for hydrogen losses, with particular focus on sulfate reduction reactions. NMF is applied to modeled mineral evolution and fluid component profiles to retrieve profiles that can be interpreted to more easily assess competing processes. NMF decouples simulated competing equilibrium reactions. This facilitates separation of overlapping reaction profiles from redox processes, dissolution fronts, and secondary precipitation while considering the effects of simulation parameters such as salinity, temperature, and total H 2 pressure. NMF successfully discriminates these competing effects in nonlinear ways, allowing robust interpretation. In addition, NMF reveals subtle coupled mineral associations and reaction fronts that are invisible to conventional model analysis. This integrated approach strengthens the conceptual understanding of complex nonlinear hydrogen-brine-rock interactions and advances geochemical research on UHS systems to resolve complexities in modeled geochemical systems without the need for direct experiments or prior knowledge. Furthermore, this study highlights the efficacy of combining geochemical modeling with machine learning techniques to enhance the interpretability of the intricate geochemical simulation output through deciphering the overlapping reaction path that cannot be achieved only using conventional analysis of geochemical models alone.

08 HYDROGEN↗
DOE OSTI2025

Scalability analysis of heavy-duty gas turbines using data-driven machine learning

With the increasing integration of variable renewable energy sources into power systems, the role of flexible power generation technologies like gas turbines (GT) in rapid grid balancing remains crucial. This sustained importance underscores the need for scaled and precise modeling of GT to ensure effective integration within evolving energy frameworks. While physics-driven GT models integrate thermodynamics, fluid dynamics, and combustion principles, they often rely on approximate mathematical representations to accommodate scaling that may not capture the actual complex dynamics for GTs and inertial effects associated to GTs with different ratings. In this study, a data-driven model is proposed using machine learning (ML) techniques to conduct GT scalability analysis and performance evaluation with high accuracy. The ML model, trained on data from various operating conditions and performance parameters, aims to uncover intricate relationships and patterns, resembling GT characteristics at different scales (ratings). The model is developed to capture complex system interaction and to adapt to changing operational scenarios at different capacities, providing valuable insights of power system dynamics. In this study, the real-time digital simulator platform was employed to generate training data for the ML model and assess its dynamic characteristics. The ultimate objective was to develop a detailed modeling framework based on governing equations and data-driven ML capable of predicting key performance indicators, in thermal systems such as GTs, including power output, speed, fuel consumption, and exhaust temperature under diverse operating conditions at different scales. The developed ML framework demonstrated high accuracy, with mean relative errors for GT power prediction, reference speed, exhaust temperature, and compressor pressure ratio (CPR) parameters consistently below 0.1% across typical load fluctuation scenarios. Maximum deviations were limited to approximately 0.5 K for exhaust temperature and 0.009 for CPR, underscoring the model’s ability to replicating dynamic GT behavior with high precision. The adaptability of the ML model enables its application across diverse operational conditions and its extension to other thermal systems. By leveraging advanced ML techniques, this study presents a robust and scalable modeling framework that enhances GT simulation precision, facilitating improved integration into evolving power systems.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Development of a Method for Shape Optimization for a Gas Turbine Fuel Injector Design Using Metal-Additive Manufacturing

Adjoint shape optimization has enabled physics-based optimal designs for aerodynamic surfaces. Additive manufacturing (AM) makes it possible to manufacture complex shapes. However, there has been a gap between optimal and manufacturable surfaces due to the inherent limitations of commercial computational fluid dynamics (CFD) codes to implement geometric constraints during adjoint computation. In such cases, the design sensitivities are exported and used to perform constrained shape modifications using parametric information stored in computer aided design (CAD) files to satisfy manufacturability constraints. However, modifying the design using adjoint methods in CFD solvers and performing constrained shape modification in CAD can lead to inconsistencies due to different shape parameterization schemes. This paper describes a method to enable the simultaneous optimization of the fluid domain and impose AM manufacturability constraints, resolving one of the key issues of geometry definition for isogeometric analysis. Similar to a grid convergence study, the proposed method verifies the consistencies between shape parameterization techniques present within commercial CAD and CFD software during mesh movement as a part of the adjoint shape optimization routine. By identifying the appropriate parameters essential to a shape optimization study, the error metric between the different parameterization techniques converges to demonstrate sufficient consistencies for justifiable exchange of data between CAD and CFD. For the identified shape optimization parameters, the error metric to measure the deviation between the two parameterization schemes lies within the AM laser-powder bed fusion (L-PBF) process tolerance. Additionally, comparison for subsequent objective function calculations between iterations of the optimization loop showed acceptable differences within 1% variation between the modified geometries obtained using the two parameterization schemes. This method provides justification for the use of multiphysics guided adjoint design sensitivities computed in CFD software to perform shape modifications in CAD to incorporate AM manufacturability constraints during the shape optimization loop such that optimal designs are also additively manufacturable.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2025

In situ Raman investigation of Dy complexation in Cl-bearing aqueous solutions at 20–300 °C

Raman spectroscopy provides a versatile tool for in situ characterization of aqueous rare earth elements (REE) speciation at the molecular level. Complexation of REE with ligands such as Cl – and OH – is of particular interest for understanding the mobility of REE in NaCl-bearing hydrothermal fluids responsible for enriching REE to economic levels in nature. Raman spectroscopic studies of REE speciation in Cl-bearing aqueous fluids are primarily conducted at ambient temperature, whereas natural systems indicate temperatures of >100–600 °C. In this study, the speciation of Dy in acidic chloride-bearing hydrothermal solutions was investigated using confocal Raman spectroscopy with a new capillary Raman heating stage at 20–300 °C. Background solutions (pure water, NaCl-solutions) and solutions with 0.14–1.8 mol kg –1 dissolved DyCl 3 were sealed in quartz capillary cells. Comparison of the spectra for Dy chloride solutions with those for background solutions and the spectra for reference Dy-bearing solids was used to identify Raman bands specific to Dy–O and Dy–Cl bonds. The Raman band for the Dy–O stretching mode of hydrated Dy 3+ aqua ions was measured at 365–384 cm –1 and a Raman band for the Dy–Cl stretching modes of Dy chloride complexes was measured near 240 cm –1 . The Dy–O band decreases systematically with temperature, whereas the Dy–Cl band systematically increases, indicating a systematic increase in the stability of Dy chloride complexes with temperature. Here, this study provides the framework for expanding the use of in situ Raman spectroscopy to investigate the speciation of REE in aqueous solutions to hydrothermal conditions.

58 GEOSCIENCES↗
DOE OSTI2024

PYSIMFRAC: A Python library for synthetic fracture generation and analysis

In this paper, we introduce PYSIMFRAC, an open-source python library for generating 3-D synthetic fracture realizations, integrating with fluid simulators, and performing analysis. PYSIMFRAC allows the user to specify one of three fracture generation techniques (Box, Gaussian, or Spectral) and perform statistical analysis including the autocorrelation, moments, and probability density functions of the fracture surfaces and aperture. This analysis and accessibility of a python library allows the user to create realistic fracture realizations and vary properties of interest. In addition, PYSIMFRAC includes integration examples to two different pore-scale simulators and the discrete fracture network simulator, dfnWorks. The capabilities developed in this work provides opportunity for quick and smooth adoption and implementation by the wider scientific community for accurate characterization of fluid transport in geologic media. We present PYSIMFRAC along with integration examples and discuss the ability to extend PYSIMFRAC from a single complex fracture to complex fracture networks.

58 GEOSCIENCES↗
DOE OSTI2024

Mild-Temperature Supercritical Water Confined in Hydrophobic Metal–Organic Frameworks

Fluids under extreme confinement show characteristics significantly different from those of their bulk counterpart. This work focuses on water confined within the complex cavities of highly hydrophobic metal–organic frameworks (MOFs) at high pressures. A combination of high-pressure intrusion–extrusion experiments with molecular dynamic simulations and synchrotron data reveals that supercritical transition for MOF-confined water takes place at a much lower temperature than in bulk water, ~250 K below the reference values. This large shifting of the critical temperature (T c ) is attributed to the very large density of confined water vapor in the peculiar geometry and chemistry of the cavities of Cu 2 tebpz (tebpz = 3,3',5,5'-tetraethyl-4,4'-bipyrazolate) hydrophobic MOF. This is the first time the shift of Tc is investigated for water confined within highly hydrophobic nanoporous materials, which explains why such a large reduction of the critical temperature was never reported before, neither experimentally nor computationally.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Forecasting fluid-injection induced seismicity to choose the best injection strategy for safety and efficiency

Induced seismicity poses a challenge to the development of Enhanced Geothermal Systems (EGS). Improving monitoring and forecasting techniques is essential to mitigate induced seismicity and thereby fostering a positive perception of EGS projects among local authorities and population. Induced seismicity is the result of complex and coupled thermo-hydro-mechanical-chemical mechanisms. Injection flux and pressure are crucial controlling parameters for both hydraulic stimulation and circulation protocols. We develop a methodology combining a hydro-mechanical model with a seismicity rate model to estimate the magnitude and frequency of mainshocks and aftershocks induced by fluid injection. We apply the methodology to the case of the Basel EGS (2006, Switzerland) to compare the effects of progressive, cyclic and constant injections on the mechanical response of discrete faults. Results from the coupled hydro-mechanical models show that the pore pressure diffusion and consequent enhancement of fault permeability are limited to the vicinity of the injection well during cyclic injection. Additionally, constant injection induces seismicity from the start of the injection but enhances the permeability of most of the faults within a shorter duration, inducing less post-injection seismicity. The methodology can be adapted to any numerical model and allows new projects to be developed by anticipating the safest injection protocol. This article is part of the theme issue ‘Induced seismicity in coupled subsurface systems’.

58 GEOSCIENCES↗
DOE OSTI2024

Abstract for CRADA between National Energy Technology Laboratory and Shell International Exploration & Production, Inc

Introducing CO₂ into geothermal systems as a working fluid in reservoirs can enhance geothermal conductivity, production, and pressure maintenance. A cross-disciplinary interaction of geothermal reservoir stimulation and CO₂ utilization satisfies renewable energy demands and operations that support sustainable energy infrastructure. Challenges to implementing CO₂-stimulated geothermal enhancement (CS-GE) include (1) accurately characterizing and imaging CO₂-stimulated geothermal reservoirs; (2) quantitatively inferring CS-GE evolution under current and future engineered conditions for cost effective operations; and (3) monitoring resources by improving observational methods to advance the understanding of complex geothermal systems for sweep efficiency and, ultimately, cost effectiveness. NETL and Shell will collaborate under this CRADA to develop software to image key features, including CO₂-stimulated fracture imaging, CO₂ fluid sweep imaging and heat transfer and exchange imaging by leveraging available datasets and applying advanced Artificial Intelligence/Machine Learning (AI/ML), multi-level data analytics and data/information fusion to better understand the comprehensive mechanisms of CO₂-stimulated geothermal systems.

15 GEOTHERMAL ENERGY↗
DOE OSTI2024

Vidyut3d: A Non-Equilibrium Plasma Modeling Tool [SWR-24-101]

Vidyut3d is a massively-parallel plasma-fluid solver for low-temperature plasmas (LTPs) that supports both local field (LFA) and local mean energy (LMEA) approximations, as well as complex gas and surface-phase chemistry. The solver supports 2D and 3D domains, and uses AMReX's adaptive mesh refinement capabilities to increase the grid resolution around complex structures (e.g. streamer heads and sheaths) while maintaining a tractable problem size. Vidyut specializes in simulating various types of gas-phase discharges, as well as plasma/surface interactions and surface chemistry (e.g. for plasma-mediated catalysis applications). The solver also supports hybrid CPU/GPU parallelization strategies, and has demonstrated excellent scaling on various HPC architectures for problem sizes consisting of O(100 M) control volumes.

Sitaraman, Hariswaran↗
DOE OSTI2024

Revealing complex subsurface dynamics with continuous seismic monitoring: Observations using distributed acoustic sensing and surface orbital vibrators during hydraulic fracturing

Understanding hydraulic fracturing is crucial to improving the stimulation of unconventional reservoirs and increasing fluid production. This study develops a novel seismic monitoring technology using distributed acoustic sensing (DAS) and surface orbital vibrators (SOV) to capture fracture seismic response and mechanical properties at high temporal intervals. We analyze continuous time-lapse vertical seismic profiling (VSP) data acquired every hour during the first nine days of treatment of an unconventional reservoir in the Austin Chalk/Eagle Field Laboratory. The VSP data contain clear seismic signals scattered from the activated fractures. The spatiotemporal changes of the fracture reflectivity revealed by the SOV/DAS data correlate well with the observations of fracture locations inferred from low-frequency DAS data. These results capture the fracture opening and closure processes, as well as highlight potential prestage activations of the fractures due to hydraulic connectivity with preexisting fracture systems. Therefore, analysis of the presented data set provides a unique opportunity to understand fracture initiation and subsequent evolution, not only in the context of unconventional resources but also in enhanced geothermal systems.

Correa, Julia↗
DOE OSTI2025

Multimode turbulent flow measurements using magnetic resonance imaging- and laser-based techniques and computational fluid dynamics simulations

We studied the flow field characteristics of a turbulent flow over a regularized cube array with a perpendicular injection flow through the floor between the second and third cubical elements, representing the complex flow interactions of a 3D jet and the wake flows behind cubical obstacles. Four different experimental measurements were performed: two magnetic resonance imaging-based measurements for three-dimensional three-component velocity (MRV) and concentration (MRC) and two laser-based techniques, particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF), for two-dimensional two-component velocity and concentration measurement, respectively. The mainstream Reynolds number is Re = 15 000⁠, based on the primary inlet velocity U m and channel height D H ⁠, whereas the injector Reynolds number is Re j = 3400⁠, based on the injector velocity U j and the injector's exit width D j ⁠. Numerical simulations were performed for the studied flow configuration of turbulent flow over a regularized cube array using Reynolds-averaged Navier–Stokes (RANS) and large-eddy simulation (LES) approaches. Results obtained from experimental measurements—including MRV, MRC, PIV, and PLIF—as well as RANS and LES simulations are discussed and compared along several horizontal and vertical planes of the studied configuration. In addition, 3D turbulent flow structures, such as leading-edge vortex, horseshoe vortex, and jet shear-layer vortex, and the isosurfaces of scalar concentration successfully revealed by MRV and MRC techniques were found to be in very good agreement with those 3D features extracted from RANS and LES simulations. In conclusion, the high-resolution experimental and numerical database obtained from this study could be useful for validation and verification of numerical codes.

Computational fluid dynamics↗
DOE OSTI2025

CFD Simulation of Aerobic Gas Fermentation to Enable Commercial Conversion of CO 2 into Aquaculture and Animal Feed: Cooperative Research and Development (Final Report)

NovoNutrients’ fermentation technology uses energy from hydrogen to transform industrial CO2 emissions into premium animal feed ingredients and other valuable products. A single NovoNutrients’ commercial manufacturing plant will capture and convert over 200,000 tons/yr of CO2 into over 100,000 tons/yr of high-protein feed. Key to the rapid and widespread deployment of the technology is maximization of its productivity and energy efficiency. Robust, physically based computational models of the technology will significantly increase productivity and efficiency, accelerating NovoNutrients’ technology to manufacturing scale. NREL has unique capabilities for creating and running such computational models. NREL's existing aerobic bioreaction computational fluid dynamics (CFD) models will be adapted to NovoNutrients’ gas fermentation (CO2, H2, O2) technology. The multiphysics CFD simulations require thousands of high-performance computing (HPC) node hours to simulate the complex geometries and contents of NovoNutrients’ industrial bioreactors. The experimentally validated CFD models were used to identify optimally efficient and productive bioreactor designs and operating conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗