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At least 37 records · Page 2

Gas-Liquid Flow Modeling for Renewable Fuels Production

Aerobic/anaerobic and gas fermentation pathways have emerged as promising new technologies for the generation of renewable fuels/chemicals from biomass derived sugars, and mixtures of greenhouse/energy rich gas streams (CO2/CH4/H2/CO) via microbial action. Example pathways include sugars-to-ethanol conversion, biomethanation (CO2/H2 to CH4), biogas upgrading, CO fermentation and wet-waste conversion. Gas and liquid phase transport, mass-transfer, and mixing physics at large length scales can significantly affect microbial conversion rates, particularly when the microbial reaction requires a narrow set of conditions. These phenomena are difficult to study in small-scale bench-top reactors that are typically well-mixed. Predictive computational fluid dynamics (CFD) based simulations can therefore aid in the scale-up, design and optimization of these reactors. This work presents multiphase Euler-Euler CFD simulations of at-scale (~500 m3) bioreactors. Our mathematical model treats the gas and liquid as interpenetrating phases. This approach reduces the computational complexity of tracking individual gas bubbles that are several orders of magnitude smaller than reactor dimensions. We solve the Reynolds averaged Navier-Stokes (RANS) multiphase equations that account for phase and chemical species transport, interphase mass and momentum transfer and uses a phenomenological model for gas uptake by microbes. We use a customized solver derived from open-source CFD toolbox, OpenFOAM [1], to perform these simulations, which has been validated against small-scale reactors in our previous work [2]. There is currently a knowledge-gap regarding bubble-size distributions when using gas mixtures with vastly different properties, which can have a significant impact overall mass-transfer. For example, hydrogen bubbles are more buoyant compared to other relatively heavier gases (CO2/CH4/CO), resulting in a large distribution of residence times and bubble sizes. This work therefore develops a deeper understanding of bubble dynamics and interphase mass transfer in such heterogenous gas mixtures through well-resolved computational models. We use a population balance model (PBM) for bubble-size-distribution modeling that is validated against small-scale experiments in our solver with an uncertainty quantification study for bubble coalescence and break-up model parameters. Results pertaining to multiple simulations of gas-fermentation reactors are presented where gas mixtures with varying compositions of CO2/CH4/CO/H2 are imposed at the sparger boundaries. The spatio-temporal variations in bubble-size distribution and mass transfer coefficient are analyzed for varying superficial velocities and gas-compositions for varying sizes of bubble-column and airlift reactors. This work will also examine the performance of different reactor designs, viz. bubble column reactor, airlift reactor with an internal draft tube, and a stirred-tank reactor with Rushton impellers. Reactor mass-transfer coefficient, gas hold-up, and dissolved gas distribution are critically analyzed among reactors, and sensitivity studies pertaining to gas flow rates and reactor geometry will be presented. [1] Weller, H., Tabor, G., Jasak, H. and Fureby, C., A tensorial approach to computational continuum mechanics using object-oriented techniques, Computers in physics, 12, 6, 620--631, 1998. [2] Rahimi, M., Sitaraman, H., Humbird, D. and Stickel, J., Computational fluid dynamics study of full-scale aerobic bioreactors: Evaluation of gas-liquid mass transfer, oxygen uptake, and dynamic oxygen distribution, Chemical Engineering Research and Design, 139: 283-295.

BIOMASS FUELS↗

Expansion dynamics of femtosecond laser-induced plasmas: Influence of thermophysical plasma properties

This study investigates the expansion dynamics of femtosecond laser-induced plasmas, emphasizing the impact of plasma thermophysical properties and ambient gas composition. Through shadowgraphy experiments and multiphase computational fluid dynamics (CFD) simulations, the influence of parameters such as heat capacity, molecular weight, and thermal conductivity on plume morphology, shockwave evolution, and energy dissipation mechanisms is examined. A mixture multiphase model is implemented to capture the interaction between the plasma and the surrounding gas. Simulation results reveal that plasma expansion is strongly inertia-driven. Results show that differences in plasma properties and ambient conditions affect the shape and temperature distribution of the expanding plume. The early-stage dynamics are primarily dictated by pressure forces, whereas thermal and viscous effects play a growing role in the plume's behavior during later stages of expansion. The CFD findings show the necessity of accurate initial condition characterization, including crater geometry and plasma pressure and temperature, for reliable modeling of plasma evolution in laser ablation processes.

CFD modeling↗

Modeling and simulation of multiphase flows

Multiphase flow can be found in a wide range of natural and industrial systems, such as sediment flow in rivers and coasts to pipeline transport, and reactors of all types. Computational fluid dynamics (CFD) modeling provides a rigorous physics-based method to visualize and quantify these flows and to assess their influence on their surroundings. This presentation will highlight computational research on two varied technologies in the energy sector: carbon capture and wellbore acoustics.

acoustic analysis↗

Investigating biomass composition and size effects on fast pyrolysis using global sensitivity analysis and CFD simulations

It is notoriously difficult to build an accurate universal model for biomass pyrolysis due to its sensitivity to a wide number of critical material attributes such as chemical species and physical sizes. In this work, a biomass pyrolysis kinetics with 32 heterogeneous reactions and 59 species was implemented in an open-source multiphase computational fluid dynamics (CFD) software MFiX and validated against two different experimental pyrolysis data sets that provided detailed data describing chemical component yields. The reaction scheme was then used to build a surrogate model and assess the sensitivity of pyrolysis yields to feedstock compositions. The sensitivity analysis determined that the yield of bio-char showed a strong positive sensitivity to the carbon-rich lignin and tannin pseudo-species in the reaction scheme while the bio-oil and bio-gas were correlated to oxygen-rich lignin pseudo-species. The reaction scheme was then integrated into a coarse-grained discrete element model to simulate fast pyrolysis in a bubbling fluidized bed over a range of feedstock particle sizes. The reactor simulations showed further sensitivity to particle size and hydrodynamics. Notably, particles under 0.5 mm have small heat transfer limitations but left the reactor before completely converting and thus reduced the bio-oil yield. Results from this study can be used to guide future development of highly accurate models for fast pyrolysis reactors with a variety of feedstock properties and operating conditions.

09 BIOMASS FUELS↗

Theoretical Review of the MFIX Fluid and Two-Fluid Models

MFIX (Multiphase Flow with Interphase eXchanges) is a general purpose code that can be used for describing the hydrodynamics, chemical reactions, and heat transfer of dense or dilute multiphase fluid flows. MFIX calculations give detailed information on pressure, temperature, composition, and velocity distributions in the defined system. This report provides an overview of MFIX’s expressions for single phase flow and continuous dispersed multiphase flow (i.e., the two-fluid model). In addition to the two fluid model (MFIX-TFM), MFIX contains a discrete element model (MFIX-DEM) and a multi-phase particle in cell model (MFIX-PIC) that are not reviewed within this document.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The Onset of Nucleate Boiling Prediction in a Mini Channel with the Eulerian Multiphase Flow

The prediction of boiling incipience is a critical issue for a reactor. Vapor lock causes operating instability and undesirable temperature rise, especially for small channels. This study uses the Eulerian multiphase flow boiling model to predict the onset of nucleate boiling in a millimeter scale rectangular channel. Two wall boiling models, namely the RPI (Rensselaer Polytechnic Institute) and the non-equilibrium sub cooled model are applied. Computational fluid dynamics is employed for this study to investigate the impact of operating conditions like liquid flow rate, operating pressure, heat flux, velocity profile, turbulence model, and inlet liquid temperature. Here, the effect of fundamental boiling parameters on the surface wall temperature and vapor volume fraction is also studied. The parameters under consideration are the bubble departure diameter, bubble departure frequency, nucleate site density, quenching time period, and interface heat transfer coefficients. A series of CFD calculations is conducted by varying the considered variables systematically in a wide range of flow conditions covering laminar, transition, and turbulent flows. The sub-component heat fluxes like the liquid convective, the vapor convective, the evaporative, and the quenching terms are monitored to infer the boiling dynamics in the transition region from the single-phase flow to the nucleate boiling zone. It is found that the CFD approach to detecting the boiling incipience point agrees reasonably with available experimental data. However, its limitations, like inaccuracy for lower flow rates and early transition to boiling flow, are also noticed due to the nature of the considered RPI model.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

A reacting multiphase computational flow model for 2,3-butanediol synthesis in industrial-scale bioreactors

The microbe, Zymomonas mobilis, can efficiently convert sugars to 2,3 butanediol (BDO), an important intermediate for downstream chemical products, only in a well-controlled microaerated environment. However, controlling oxygen distribution in industrial-scale bioreactors is challenging, and at-scale BDO production is hard to optimize using traditional engineering methods. This study takes a step towards addressing this problem through a computational model for reacting multiphase flows in large-scale bioreactors. A phenomenological metabolic model was first developed and validated against experiments, and then it was coupled to a multiphase computational fluid dynamics (CFD) solver using a subcycling algorithm for simulating long conversion times (~30 hours). Large-scale (~500 m 3 ) bubble column simulations using this coupled approach demonstrated a 25% improvement in BDO yield with low sparging rates (0.002 m/s) and low height-to-diameter ratio (0.875) compared to a baseline bubble column (35 m height, 5 m diameter) with a superficial gas velocity of 0.06 m/s.

09 BIOMASS FUELS↗

The influence of random packed column parameters on the liquid holdup and interfacial area

Abstract Carbon dioxide capture via solvent absorption in packed columns has emerged as a potential technology to mitigate coal‐fired power plant CO 2 emissions. Parameters, including packing types, solvent properties, and operating conditions, could potentially affect the packed column CO 2 capture efficiency. To understand the importance of those parameters and help packed column optimization, a design of experiments (DoEs) method was proposed to generate input parameter matrix. Combined with multiphase computational fluid dynamics (CFD), the random packed column parameter influence on the liquid holdup and interfacial area can be efficiently investigated. Surrogate‐based sensitivity analysis shows that the solvent flow rate and contact angle are key factors dictating liquid holdup and interfacial area. On the other hand, solvent viscosity has a marginal impact on the interfacial area. The sensitivity scores were calculated for each input parameter to guide the selection of dimensionless numbers for the liquid holdup and interfacial area correlation development.

42 ENGINEERING↗

MFIX DEM Enhancement for Industry-Relevant Flows (Final Report)

The overall goal of this two-phase project is to implement performance improvements of the Multiphase Flow with Interphase Exchanges (MFIX) Discrete Element Model (DEM) code that enable a transformative shift for industrial use. Prior to this effort, the largest simulations performed using MFIX are O(10 7 ) particles. This falls short of the O(10 9 ) particle simulations that must be completed on a timescale of days or weeks (vs. months or years) to enable simulations with physically-relevant domain sizes to be incorporated into industrial design cycles within five years. This was accomplished by tailoring best-in-class practices to bear on the unique challenges posed by the MFIX-DEM algorithm and code base. Scientific simulations (e.g., in cosmology, turbulent combustion) routinely use massively parallel computing to update far more particles in short wall clock times. Results from Phase 1 (1.5 years in duration) indicated significant gains in speed were possible for a wide range of benchmark cases. Moreover, a survey sent to >35 companies indicates that the timing is ideal for such an enhanced tool, with >80% of the respondents indicating that DEM is already value-added or will be within the next 5 years, and >70% of the respondents indicating that improved speed is the top computational priority. In Phase 2 (3.5 years in duration), the two major barriers that hinder industry from effectively using multiphase Computational Fluid Dynamics (CFD) to cut costs and improve performance, namely computational overhead and confidence in predictions, continued to be addressed. Regarding the former, the results from Phase 1 to guide the effort, with enhancements focused on an improved time-stepping algorithm and particle sorting. Four target problems of 1 billion particles each and increasing complexity were identified: homogeneous cooling, tumbler with continuous particle size distribution, discharge from a rectangular hopper and a cylindrical riser. Each of these were successfully simulated for relevant time scales (on order of seconds) using less than 24 hours of wall clock time. These represent the first 1-billion particle DEM simulations performed with MFIX, namely using the MFIX-Exa code. This code is currently under development at NETL in collaboration with Lawrence Berkeley National Laboratory. Regarding the second barrier on predictive uncertainty, experiments from Phase 1 (interacting nozzles - hydrodynamics only) and Phase 2 (very small-scale segregation experiments) were used to demonstrate the ability of two simplified approaches to uncertainty quantification (UQ). By limiting the number of particles, UQ based on the simplified treatment was compared to standard UQ, which was shown to have much higher computational demands. Experiments were also performed on a pilot-scale stripper unit to provide validation data for future CFD-DEM simulations and UQ.

20 FOSSIL-FUELED POWER PLANTS↗

Niowave Neutron Source Converter: Lead-Bismuth-Eutectic (LBE) Windowless Target Design and Evaluation

Los Alamos National Laboratory (LANL) is working with Niowave on the design and evaluation of their lead-bismuth-eutectic (LBE) windowless target (i.e., neutron source converter). Niowave plans to use 200 kW electron beam at 40 MeV beam energy to produce neutrons by photonuclear reaction with LBE. Then, the neutrons undergo fission at the surrounding uranium target assembly (UTA) to produce Molybdenum 99 (Mo-99) as a fission product, which eventually decays to Technetium-99 (Tc-99m). Tc-99m is one of important radioisotopes that is used for medical diagnostics. LANL conducted 3D multiphysics analysis for the Niowave neutron converter design and provided design assessment in thermohydraulic aspects. LANL conducted radiation transport calculations using Monte-Carlo N-Particle (MCNP) code with unstructured meshing scheme. The 3D volumetric heating profiles in the LBE and Stainless-Steel (SS) housing were imported into multiphase computational fluid dynamics (CFD) to obtain 3D temperature profiles of LBE and SS through conjugate heat transfer (CHT) analysis. The key findings are: LBE film thickness at the center of the beam is approximately 1.6 cm with a maximum LBE velocity of approximately 1.8 m/s, which is below a 2 m/s limit to avoid erosion issues on supporting structures; Heat deposition in the LBE peaks at ~1 cm depth from the LBE free-surface because of the forward interactions of electron, photon, and neutron with LBE; LBE maximum temperature is ~360 °C, which is below LBE evaporation initiative temperature, ~450 °C; LBE-SS interface temperature is ~350 °C, which is below the safety thermal limit to prevent severe corrosion on SS. The results indicate that Niowave’s neutron converter design satisfies both hydraulic and thermal criteria for safe operation. By virtue of such computational analysis, Niowave can move toward establishing an experimental setup to experimentally test their LBE neutron converter. The following sections describe the detailed work done by LANL.

43 PARTICLE ACCELERATORS↗

MFiX: Fractional-Step Method Implementation

A comprehensive, multiphase computational fluid dynamics (CFD) simulation solves several coupled transport equations including continuity, momentum, species, and energy. Chemical reactions further couple these equations through heats of reaction and rates of formation of products and rates of destruction of reactants. A fractional-step method separates changes attributed to chemical reactions from transport phenomena like convection and diffusion. When the governing equations are split into the transport and reacting components, efficient and independent methodologies can be exploited to solve the different systems. Specifically, discretization of field variable transport equations results in large, sparse matrices which are loosely coupled. These systems are solved in succession using iterative techniques that take advantage of the matrix structure. In contrast, chemical reactions tightly couple field variables locally within the domain (e.g., within a single computational cell) resulting in low dimensional but dense, nonlinear systems that are better solved using direct integration techniques.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Deep learning interfacial momentum closures in coarse-mesh CFD two-phase flow simulation using validation data

Multiphase flow phenomena have been widely observed in the industrial applications while it remains a challenging yet unsolved problems. Three-dimensional computational fluid dynamics (CFD) approaches resolve the flow fields on a finer special and temporal scales which can complement the dedicated experimental study. However, closures have to be introduced to reflect the underlying physics in multiphase flow. Among them, the interfacial forces, including drag, lift, turbulent dispersion and wall lubrication forces, play in important role on the bubble’s distribution and migration in liquid-vapor two-phase flow. Development of those closures traditionally rely on the experimental data and analytical derivation with simplified assumptions which usually cannot deliver a universal solution across wide range of flow conditions. In this paper, a data-driven approach, named as Feature Similarity Measurement (FSM), is developed and applied to improve the simulation capability of two-phase flow with coarse-mesh CFD approach. Interfacial momentum transfer in adiabatic bubbly flow serves as the focus of the present study. Both a mature and a simplified set of interfacial closures are taken as the low fidelity data. Experimental data and fine mesh CFD simulations results are adopted as high-fidelity data. Qualitative and quantitative analysis are performed in this paper which reveals that FSM can substantially improve the prediction of coarse mesh CFD model regardless of the choice of interfacial closures and it provides scalability and consistency across discontinuous flow regimes. Furthermore, it demonstrates that data-driven method can aid the multiphase flow modeling by exploring the connections between local physical features and simulation errors.

97 MATHEMATICS AND COMPUTING↗

Impact of Variable Gas Mixtures on Bubble Size Distribution and Mass Transfer in Gas Fermentation Reactors

Gas fermentation has emerged as a promising new technology for the generation of fuels and chemicals from mixtures of greenhouse and energy rich gas streams (CO2/CH4/H2/CO) via microbial bioreaction. Example pathways include biomethanation (CO2/H2 to CH4), biogas upgrading, CO fermentation and wet-waste conversion. Effective Gas-liquid mass-transfer is an important physical phenomenon that determines the design and scale-up of these systems. There is currently a knowledge-gap regarding bubble-size distributions when using a mixture of gases with vastly different properties, which can have a significant impact on overall mass-transfer. For example, hydrogen bubbles are more buoyant compared to other relatively heavier gases (CO2/CH4/CO), resulting in a large distribution of residence times and bubble sizes. This work therefore develops a deeper understanding of bubble dynamics and interphase mass transfer in such heterogenous gas mixtures through well-resolved computational models. We use a detailed multiphase computational-fluid-dynamics (CFD) model to study the impact of gas-mixtures on overall mass-transfer in bubble column and air-lift reactors. The CFD tool previously developed by the authors (1) for simulating aerobic fermentation reactors at scale is used in this study. The Reynolds-averaged mass, momentum, energy, and species transport equations are solved for interpenetrating gas and liquid phase in this model. We use a population balance-based bubble-size-distribution model that is validated against small-scale experiments in our solver. Results pertaining to multiple simulations of gas-fermentation reactors are presented where gas mixtures with varying compositions of CO2/CH4/CO/H2 are imposed at the sparger boundaries. The spatio-temporal variations in bubble-size distribution and mass transfer coefficient is analyzed for varying superficial velocities and gas-compositions for varying sizes of bubble-column and airlift reactors.

BIOMASS FUELS,MATHEMATICS AND COMPUTING↗

High-fidelity pool boiling simulations on multiple nucleation sites using interface capturing method

Boiling has proved to be one of the most efficient means for heat transfer and is a very important phenomenon during severe accident scenarios in light water reactors. High-fidelity pool boiling simulations can provide a numerical database for improving mechanistic boiling models by allowing for specific evaluation of interactions among bubbles. Previously published pool boiling simulations investigated two nucleation sites in which bubble growth at one site suppressed nucleation at the other site. Based on previous study results, more complicated interface-capturing simulations on pool boiling were conducted using PHASTA code with locally refined unstructured mesh. First, different boundary conditions (BCs) were assessed to support robustness and reproducibility of the boiling model. Then, a scale study was conducted at a larger domain with nine nucleation sites where either nine or four nucleation sites are activated. Involving more nucleation sites increased the complexity of bubble interactions from surrounding sites. Finally, bubble departure behavior influenced by wall heat flux was investigated. In this work, when heat flux was increased, the order of bubble departure changed, but diagonal bubbles always departed after one another. The departure time interval between the first and second bubble reduced as heat flux increased. The corresponding frequency was almost linearly proportional to the heat flux. In addition, bubble departure behavior was found to be greatly influenced by the nucleation site pattern. Multiple nucleation sites resulted in superimposed inhibitive effects from surrounding sites to each bubble, which extensively delayed the departure. This new observation was not discussed in previously published works. The work presented here provides new insight on the fundamental understanding of boiling phenomena, contributes to the development of a 3D multiphase computational fluid dynamics (M-CFD) model, and provides a more comprehensive database for data-driven pool boiling studies.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Interface Capturing Simulations on Pool Boiling Performance With Multiple Nucleation Sites

High-fidelity pool boiling simulations can provide a numerical database for improving mechanistic boiling models by allowing for specific evaluation of interactions among bubbles. Previously published pool boiling simulations investigated two nucleation sites in which bubble growth at one site suppressed nucleation at the other site. Based on previous study results, more complicated interface-capturing simulations on pool boiling were conducted using PHASTA code with locally refined unstructured mesh.First, different boundary conditions (BCs) were assessed to support robustness and reproducibility of the boiling model. Then, a scale study was conducted at a larger domain with nine nucleation sites, four of which were activated. Involving more nucleation sites increased the complexity of bubble interactions from surrounding sites. Finally, bubble departure behavior influenced by wall heat flux was investigated. When heat flux was increased, the order of bubble departure changed, but diagonal bubbles always departed after one another. The departure time interval between the first and second bubble reduced as heat flux increased. The corresponding frequency was almost linearly proportional to the heat flux. In addition, bubble departure behavior was found to be greatly influenced by the nucleation site pattern. Multiple nucleation sites resulted in superimposed inhibitive effects from surrounding sites to each bubble, which extensively delayed the departure.The work presented here provides new insight on the fundamental understanding of boiling phenomena, contributes to the development of a 3D multiphase computational fluid dynamics (M-CFD) model, and provides a more comprehensive database for data-driven pool boiling studies.

Fan, Joy↗

Multiphase Reacting Flow Simulations and Optimization of Commercial-Scale Aerobic Bioreactors

Aerobic bioreactors are widely used in the synthesis of value-added products in pharmaceutical and biotechnology industries, wherein microbial bioreactions aid in the conversion of sugars to macromolecules. These reactors are also being actively investigated as a cost-effective pathway for the production of low-value commodities such as biofuels and animal feed. Reactor scale-up is one of the important challenges when designing these systems. Gas and liquid phase transport, mass-transfer, and mixing physics at large length scales can significantly affect microbial conversion rates, particularly when the microbial reaction requires a narrow set of conditions. These phenomena are difficult to study in small-scale bench-top reactors that are typically well-mixed. Predictive computational fluid dynamics (CFD) based simulations can therefore aid in the design and optimization of these reactors. This work presents multiphase Euler-Euler CFD simulations of commercial-scale (~ 500 m3) aerobic bioreactors. Our mathematical model treats the gas and liquid as interpenetrating phases. This approach reduces the computational complexity of tracking individual gas bubbles that are several orders of magnitude smaller than reactor dimensions. We solve the Reynolds averaged Navier-Stokes (RANS) multiphase equations that account for phase and chemical species transport, interphase mass and momentum transfer and uses a phenomenological model for oxygen uptake by microbes. We use a customized solver derived from open-source CFD toolbox, OpenFOAM, to perform these simulations, which has been validated against small-scale reactors in our previous work. This work examines the performance of three different reactor designs, viz. bubble column reactor, airlift reactor with an internal draft tube, and a stirred-tank reactor with Rushton impellers. Reactor oxygen mass-transfer coefficient, gas hold-up, and oxygen distribution are critically analyzed among reactors, and sensitivity studies pertaining to gas flow rates and reactor geometry will be presented.

09 BIOMASS FUELS↗

CARD: CFD for Advanced Reactor Design

Software Tools and Expertise To Address Multiphase Flow Challenges in<p>Research, Design, and Optimization</p><p>This is the annual CARD project update to be presented at the 2024 FECM/NETL Spring R&amp;D Project Review Meeting.</p>

Dietiker, Jeff↗

Critical analysis of velocimetry methods for particulate flows from synthetic data

Particle tracking methods that extract high-fidelity particle velocity data from high speed video of particle laden flows is a common experimental technique applied to chemical processes. These measurements are used to better understand the motion of particles and fluids in complex systems and create data against which computational models are validated. However, the methods, codes, and experimental setups all have limitations. It is imperative that practitioners verify the methods and their implementation as well as understand the limitations of experimental setups. This work focuses on quantifying the visible depth of field in a high particle concentration fluidized bed. Following a precedent set by the particle imaging velocimetry community, a particle velocity field is manufactured using a computational fluid dynamics and discrete element method simulation. Photo realistic high-speed videos are rendered based on the simulated data using the three-dimensional creation software Blender. Particle velocities are extracted from the synthetic high-speed videos using three variants of Particle Tracking Velocimetry and Optical Flow Velocimetry methodologies. Here, the tracked results are then compared to the known solution, quantifying the error associated with the assumed visible depth. The results indicate that at depth of one particle diameter, all three particle tracking codes give accurate measurements, largely within 5%. However, the error increases when the full bed video measurements are compared to the known solution at one particle diameter, i.e., mimicking a validation study. Finally, for some statistics the constant depth assumption only increases the error slightly, for others significantly.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗