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Introduction to Statistically Designed Experiments

Statistically designed experiments can save researchers time and money by reducing the number of necessary experimental trials, while resulting in more conclusive experimental results. Surprisingly, many researchers are still not aware of this efficient and effective experimental methodology. As reported in a 2013 article from Chemical & Engineering News, there has been a resurgence of this methodology in recent years (http://cen.acs.org/articles/91/i13/Design-Experiments-Makes-Comeback.html?h=2027056365). This presentation will provide a brief introduction to statistically designed experiments. The main advantages will be reviewed along with the some basic concepts such as factorial and fractional factorial designs. The recommended sequential approach to experiments will be introduced and finally a case study will be presented to demonstrate this methodology.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Statistical detection of differentially abundant ions in mass spectrometry-based imaging experiments with complex designs

Mass Spectrometry Imaging (MSI) characterizes changes in chemical composition between regions of biological samples such as tissues. This translates into a statistical goal of class comparison, i.e. determining analytes that change in abundance between conditions more systematically than as expected by random variation. To reach accurate and reproducible conclusions, statistical analysis must appropriately reflect the initial research question, the design of the MSI experiment, and all the associated sources of variation. This manuscript highlights the importance of following these general statistical principles. Using the example of two case studies with complex experimental designs, and with dierent strategies of data acquisition, we demonstrate the extent to which choices made at key points of this workflow impact the results, and provide suggestions for appropriate design and analysis of MSI experiments that aim at detecting dierentially abundant analytes.

NanoDESI, mass spectrometry, MSIQuickView↗

Statistical Design of Experiments Enables Rapid Exploration of Perfluorobutane Sulfonate Degradation

The phase-out of long-chain PFAS has led to the proliferation of highly recalcitrant short-chain analogs, and mineralization technologies for these short-chain PFAS are needed to mitigate their deleterious effects on environmental and human health. In this study, we utilize a statistical design of experiments, specifically, response surface methodology, to rapidly evaluate the electrochemical degradation of the short-chain PFAS, perfluorobutane sulfonate (PFBS). We evaluate the impacts of the three primary electrochemical parameters (concentration of PFBS, concentration of supporting electrolyte, and applied current) over multiple orders of magnitude on the three primary reaction outcomes of electrochemical PFBS degradation (incomplete PFBS decomposition, complete PFBS mineralization as fluorine, and anodic energy consumption). Our results correspond with literature and clearly identify the well-known tradeoff between energy consumption and complete mineralization. Intriguingly, partial PFBS decomposition and energy consumption demonstrate nonlinear dependencies in the current/supporting electrolyte concentration space and the current/PFBS concentration space, respectively. These findings highlight the utility of the response surface methodology model to efficiently interrogate a large parameter space, identifying both common results and less-obvious interactions between electrochemical parameters and their influences on reaction outcomes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Understanding and improving anode performance in an alkaline membrane electrolyzer using statistical design of experiments

The behavior of the oxygen-evolving positive electrode (i.e. anode) in the anion exchange membrane water electrolyzer (AEMEL) is complex and influenced by several factors. Very few studies have been performed to understand oxygen evolution reaction (OER) behavior by optimizing the individual factors that influence performance. Here, this study highlights the effects of catalyst loading, catalyst selection, porous transport layer (PTL) type and conductive additive content. The influence of each factor is elucidated through a design of experiments (DoE) approach with a full statistical analysis. Electrochemical data, alongside Pareto charts, parametric trends and their mutual interactions are discussed. This DoE approach is also helpful in making useful predictions and discovering new combinations to be tested. The end result was a high-performance AEMEL able to operate at a current density of 1.0 A/cm 2 at 1.80 V with IrOx OER and PtNi hydrogen evolution reaction (HER) catalysts using 0.3 M KOH fed to the anode. Even lower operating voltage was observed with PbRuOx catalyst at the anode, 1.64 V @ 1.0 A/cm 2 , though the cell decay rate was higher. Lastly, a IrOx/PtNi cell was stably operated continuously for 30 days (720 h) at 1.0 A/cm 2 . This study can serve as a guide for optimal electrode design with insights into component-performance compromises, which can aid in making design choices and performing techno-economic analyses.

08 HYDROGEN↗

Analysis of Solids Flow Rate through Nonmechanical L-Valve in an Industrial-Scale Circulating Fluidized Bed Using Group B Particles

A series of statistically designed experiments were conducted using two different Geldart Group B particles in a 0.3 m diameter circulating fluidized bed (CFB) cold model to evaluate the nonmechanical L-valve for controlling the solids flow rate. The objective of this study was to investigate the effects of standpipe aeration, L-valve aeration, solids inventory, and superficial gas velocity through the riser on the solids flow rate. A stochastic correlation was developed for calculating the solid flow rate as a function of these variables. It was found that the solid flow rate increased directly proportional to each of these variables. Dimensional analysis was used to generate an expression for the solids turnover ratio. The model developed in the present study is intended to simulate flow in the present CFB loop. In conclusion, it is not intended for scale-up and will probably not apply for alternative CFB loops with different geometries/pressure balance conditions.

42 ENGINEERING↗

Statistically-driven Experimental Design to Improve Reference-free Quantification of Small Molecules by Liquid Chromatography-Mass Spectrometry

Non-targeted analysis of small molecules and metabolites in unknown, complex samples using liquid chromatography-tandem mass spectrometry remains challenging. One of the main bottlenecks is the extensive unannotated regions of metabolomics mass spectrometry data, resulting in knowledge gaps. Small molecule annotation in mass spectrometry data has conventionally relied on reference standards and libraries for compound identification and confirmation, which can constrain compound identification to those molecules already known, thus limiting the ability to discover new knowledge and new markers. Retention time prediction can facilitate and expedite unknown compound identification in non-targeted analysis of complex metabolomics samples. Additionally, accurate retention time predictions can also inform sample mixture design for LC-MS/MS analyses. However, current machine learning-based methods for retention time prediction are typically developed for specific chromatographic platforms and are not generalizable across scales. And while technologies and methods to improve reference-free metabolite identification for more comprehensive annotation of unknowns has received much attention, development of the same for quantitation without reference standards has been much more limited, despite its importance in toxicological, environmental, food safety, forensics, and clinical applications. We believe that a reference-free quantitation strategy that exploits mass spectrometry data already collected for reference-free identification can provide much more insight on unknowns, and move the metabolomics field for more complete unknowns characterization. As such, we pursue two efforts to improve upon current state-of-the-art methods in non-targeted analysis: (1) machine learning-based retention time prediction and (2) statistical design of experiments framework for reference-free quantitation. In this work, we develop and demonstrate (1) a generalizable retention time prediction capability across chromatographic conditions and scales, and (2) a statistical design-based framework for response factor contribution elucidation and reference-free quantitation. Evaluation of our retention time prediction model, PrediToR, showed approximately 24% improvement over current models, and we observed approximately 10X improvement in concentration estimation accuracy from our statistical design-based response factor model over a primarily ionization efficiency-based model. We expect that future efforts to improve upon these new capabilities will further advance non-targeted analysis of small molecules towards truly reference-free metabolomics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Throughput Optimization of Molybdenum Carbide Nanoparticle Catalysts in a Continuous Flow Reactor Using Design of Experiments

Transition metal carbides (TMCs) have attracted significant attention because of their applications toward a wide range of catalytic transformations. However, the practicality of their synthesis is still limited because of the harsh conditions in which most TMCs are prepared. Recently, a solution-phase synthesis of phase-pure a-MoC1-x nanoparticles was presented. While this synthetic route yielded nanoparticles with exceptional catalytic performance, the reaction parameter space was not explored, and catalyst throughput was not optimized for scale-up. Continuous flow platforms coupled with statistical design of experiments (DoE) can provide a powerful method for understanding the reaction parameter space for optimizations. Here, we demonstrate the use of statistical DoE in tandem with response surface methodology for a parametric screening analysis to optimize the throughput of a MoC1-x nanoparticle synthesis utilizing a millifluidic flow reactor. A full factorial design was implemented to evaluate four input variables (reaction temperature, flow rate, solvent fraction of oleylamine, and precursor concentration) that carry statistically significant effects on three responses (throughput, residence time, and isolated yield). A Doehlert matrix was implemented to investigate each significant variable at a higher number of levels to optimize throughput. Our results give a nonintuitive set of experimental conditions that resulted in an optimized throughput of 2.2 g h-1. This translates to a 50-fold increase in throughput compared to the previously reported batch method. The catalytic performance of the MoC1-x nanoparticles produced under optimized throughput was demonstrated in the CO2 hydrogenation reaction. This DoE screening analysis and throughput optimization of MoC1-x synthesis open the door to an increased feasibility for scale-up.

design of experiments↗

Differences in Sb 2 Te 3 growth by pulsed laser and sputter deposition

High quality van der Waals chalcogenides are important for phase change data storage, thermoelectrics, and spintronics. Using a combination of statistical design of experiments and density functional theory, we clarify how out-of-equilibrium van der Waals epitaxial deposition methods can improve the crystal quality of Sb 2 Te 3 films. We compare films grown by radio frequency sputtering and pulsed laser deposition (PLD). The growth factors that influence the crystal quality for each method are different. For PLD grown films a thin amorphous Sb 2 Te 3 seed layer most significantly influences the crystal quality. In contrast, the crystalline quality of films grown by sputtering is rather sensitive to the deposition temperature and less affected by the presence of a seed layer. This difference is somewhat surprising as both methods are out-of-thermal-equilibrium plasma-based methods. Non-adiabatic quantum molecular dynamics simulations show that this difference originates from the density of excited atoms in the plasma. The PLD plasma is more intense and with higher energy than that used in sputtering, and this increases the electronic temperature of the deposited atoms, which concomitantly increases the adatom diffusion lengths in PLD. In contrast, the adatom diffusivity is dominated by the thermal temperature for sputter grown films. These results explain the wide range of Sb 2 Te 3 and superlattice crystal qualities observed in the literature. Finally, these results indicate that, contrary to popular belief, plasma-based deposition methods are suitable for growing high quality crystalline chalcogenides.

36 MATERIALS SCIENCE↗

Optimization of a Cyclone Using Multiphase Flow Computational Fluid Dynamics

The U.S. Department of Energy National Energy Technology Laboratory's (NETL) 50 kW th chemical looping reactor (CLR) has an underperforming cyclone, which was designed using empirical correlations. To improve the performance of this cyclone using computational fluid dynamics (CFD)-based modeling simulations, four critical design parameters including the vortex tube radius and length, barrel radius, and the inlet width and height were optimized. Here, NETL's open source multiphase flow with interphase exchange (MFiX) CFD code has been used to model a series of cyclones by systematically varying the geometric design parameters. To perform the optimization process, the surrogate modeling and sensitivity analysis followed by the optimization capability in nodeworks was used. The basic methodology for the process is to employ a statistical design of experiments (DOE) method to generate sampling simulations that fill the design space. Corresponding CFD models are then created, executed, and postprocessed. A response surface is created to characterize the relationship between input parameters and the quantities of interest (QoI). Finally, the CFD-surrogate is used by an optimization method to find the optimal design condition based on the objective and constraints prescribed. The resulting optimal cyclone has a larger diameter and longer vortex tube, a larger diameter barrel, and a taller and narrower solids inlet. The improved design has a predicted pressure drop 11 times lower than the original design while reducing the mass loss by a factor of 2.3.

42 ENGINEERING↗

Comparing Designed Training Sets to Optimize Multivariate Regression Models for Pr, Nd, and Nitric Acid Using Spectrophotometry

Chemometric regression models were developed for the quantification of praseodymium (Pr, 0–1000 µg/mL), neodymium (Nd, 0–1000 µg/mL), and nitric acid (HNO 3 , 0.1–5 M) using spectrophotometry. Designed calibration sets were composed of 20 samples each: 10 model points and 10 lack-of-fit (LOF) points. The D-optimal designs effectively minimized the number of samples required to build models, and each design resulted in similar prediction performance, suggesting that statistical design of experiments can provide a reliable framework for selecting training set samples in three-variable systems. Partial least squares regression (PLSR) models were validated against a one-factor-at-a-time validation set composed of 125 samples (three variables, five levels). The top PLS-1 models resulted in average percent root mean square error of prediction error values of 3.5%, 1.7%, and 1.2% for Pr(III), Nd(III), and HNO 3 , respectively. Power set augmentations of the model and LOF samples were investigated to optimize the number of training set samples. PLSR models built using just required model points (10) had similar predictive capabilities as models including the LOF points (20) but with fewer samples. The number of validation samples was also varied systematically to learn how many samples are needed to validate regression models. This work addresses long-standing questions in the field of chemometrics to help make this approach amenable to the near-real-time quantification of hazardous species in remote settings.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Chemics-Reactors: A Preliminary Python Program for Implementing Network Models of Multiphase Reactors

We discuss the design and implementation of a preliminary software package written in Python 3 that is intended to represent complex multiphase reactors as networks of ideal continuous stirred tank reactors. This software also implements statistical design of experiments, uncertainty quantification, and global sensitivity analysis. These advanced features can provide important qualitative and quantitative insights into the effect of operating conditions and model parameters on predicted reactor performance. We demonstrate the utility of the program by modeling the vapor phase catalytic upgrading of bio-oil in a bubbling fluidized bed reactor.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Optimization of Spirulina for biomanufacturing and the delivery of protein therapeutics

Lumen Bioscience has developed a novel cyanobacterial platform that enormously decreases the cost of pharmaceuticals used to prevent and treat illnesses. Arthrospira platensis (spirulina), is a photosynthetic microorganism that has been consumed as a dietary supplement for centuries in part because of its high protein content. Commercial cultivation operations have matured over the last 50 years to allow large-scale cultivation in outdoor ponds. Lumen recently discovered methods that transform this commercially important cyanobacterium into a genetically tractable platform for bioengineering. The high protein accumulation in spirulina makes it an ideal chassis for heterologous protein expression, and centuries of safe human consumption suggest its utility as an administration vehicle for biologic drugs. Lumen can express a broad range of recombinant proteins in spirulina and has developed manufacturing processes and strains to mucosally deliver bioactive proteins to treat and/or prevent disease. For example, Lumen has produced an oral cocktail of dried whole-cell spirulina biomass, containing 3 toxin-neutralizing antibodies and 1 endolysin, that is efficacious in a preclinical in vivo models of C. difficile infection. Lumen has also demonstrated that intranasal administration of a spirulina-manufactured neutralizing antibody can prevent disease by a respiratory pathogen, SARS-CoV-2, in a hamster model. Lumen’s current pipeline includes therapeutics to treat or prevent C. difficile infection, COVID-19, inflammatory bowel disease, cardiometabolic disease, and traveler’s diarrhea. Lumen deploys strategies to maximize the expression of these therapeutics for optimal dose sizing, a key limiting factor with past food crop-based expression systems. Spirulina can express exogenous proteins at unusually high levels (>15% of dry weight) but reaching this maximum value requires optimization of multiple interacting factors. We describe our current statistics design of experiments approach that optimizes these factors with minimal replicates. This maximizes exogenous protein expression allowing Lumen to generate spirulina-based therapeutics for a rapidly expanding range of medical uses.

Heinnickel, Mark↗

How data science methods can improve the quality and efficiency of ICF and HEDP research

Data Science methods (many that are Bayesian based) are widely used in the physical sciences to estimate model parameters from experimental data, synthesize heterogeneous data, calibrate models, design experiments, and determine statistical significance of data. These methods provide a wealth of advantages over traditional analysis techniques because: 1) uncertainties are rigorously defined and propagated naturally through complex systems including covariance, 2) prior information is captured within the analysis framework (including rad-MHD and rad-hydro simulations), 3) competing models can be selected and/or ruled out using quantitative criteria, and 4) complex, heterogeneous data can be incorporated simultaneously. While these methods have been widely adopted as the gold standard in fields such as particle physics, astronomy, and biology, they have been slow to catch on in Inertial Confinement Fusion (ICF) and High Energy Density Physics (HEDP) research. Recently, several teams at LLNL, SNL, LANL, and the LLE have been exploring the use of these tools in their research and have found success. Here we propose that a concerted effort to consolidate these independent research efforts by developing and deploying common tools for use across the complex can revolutionize the way we approach data analysis, assimilation of theory and experiment, and decision making. The Bayesian formalism provides a means to accomplish this, but we are lacking certain infrastructure to make it happen on a large scale. Furthermore, once adopted, these techniques can be used to develop standards by which discoveries can be judged, similar to the so-called 5σ rule in high energy particle physics. Such standards may be used in the future to address the issue of unknown reproducibility in ICF and HED experiments caused by low shot rate and high cost per experiment. Our goals as a group are to advance the state of the art in HED measurement science by enabling: 1) better inferences from data with well-defined uncertainties, 2) better use of the data we have and continue to collect, 3) intelligent synthesis of data, 4) evaluation of the statistical significance of our data, and 5) informed decision making regarding the design of new experiments and instruments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Statistical Multiobjective Optimization of Thiospinel CoNi 2 S 4 Nanocrystal Synthesis via Design of Experiments

Thiospinels, such as CoNi 2 S 4 , are showing promise for numerous applications, including as catalysts for the hydrogen evolution reaction, hydrodesulfurization, and oxygen evolution and reduction reactions; however, CoNi 2 S 4 has not been synthesized as small, colloidal nanocrystals with high surface-area-to-volume ratios. Traditional optimization methods to control nanocrystal attributes such as size typically rely upon one variable at a time (OVAT) methods that are not only time and labor intensive but also lack the ability to identify higher-order interactions between experimental variables that affect target outcomes. Herein, we demonstrate that a statistical design of experiments (DoE) approach can optimize the synthesis of CoNi 2 S 4 nanocrystals, allowing for control over the responses of nanocrystal size, size distribution, and isolated yield. After implementing a 2 5–2 fractional factorial design, the statistical screening of five different experimental variables identified temperature, Co:Ni precursor ratio, Co:thiol ratio, and their higher-order interactions as the most critical factors in influencing the aforementioned responses. Second-order design with a Doehlert matrix yielded polynomial functions used to predict the reaction parameters needed to individually optimize all three responses. A multiobjective optimization, allowing for the simultaneous optimization of size, size distribution, and isolated yield, predicted the synthetic conditions needed to achieve a minimum nanocrystal size of 6.1 nm, a minimum polydispersity (σ/$\bar{d}$) of 10%, and a maximum isolated yield of 99%, with a desirability of 96%. The resulting model was experimentally verified by performing reactions under the specified conditions. Furthermore, our work illustrates the advantage of multivariate experimental design as a powerful tool for accelerating control and optimization in nanocrystal syntheses.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Using the Carbon Capture Simulation Initiative (CCSI) Tool to Design the Experiments in the Parametric Campaign of a Novel Compact Absorber for Carbon Capture

Gas absorption towers with structured packing and solvent have been used for Carbon Dioxide (CO 2 ) Capture for about many decades. To overcome process limitations and practical disadvantages for CO 2 capture from the stationary emitter (e.g. NG and coal power plant), many new designs have been proposed and explored at the various scales in the last decade with aim of either low energy penalty or low capital cost. To reduce the size of the absorption tower and hence the total cost of CO 2 capture, the University of Kentucky Center for Applied Energy Research Center (UK CAER) has designed and built a novel CO 2 capture absorption tower or Compact Absorber, integrated into an existing large-bench scale CO 2 capture unit. The Compact Absorber has three sections. The top of the column is a fogging section where the solvent is sprayed through a nozzle producing droplets flowing downward in a co-current fashion with the flue gas. The center of the column is a frothing section where the solvent and flue gas flow through regenerative frothing screens designed by Industrial Climate Solutions, Inc. The bottom of the column is a typical structured packing section were the flue gas and solvent flow in a counter-current fashion. The parametric campaign will be conducted in order to optimize the operating parameters for CO 2 capture including liquid/gas ratio, lean loading, and temperature, liquid residence time. A simulated flue gas with 14% CO 2 will be used along with a UK CAER developed proprietary solvent. The 100-hour parametric campaign is designed using a statistical approach of the Sequential Design of Experiments (sDOE). sDOE is one of the CCSI tools that provides an adaptive statistical approach for designing future experiments based on the results of previous experiments. Application of a typical DOE provides the user with the minimum number of experiments required to get the same data, but sDOE allows the user to make an informed choice of experiments based on the results of previous experiments. The complete absorption column has been constructed and has been partially commissioned. Initial data has been collected by operating using the fogging section and the frothing section. The fogging section produces solvent droplets of about 100 μm sauter mean diameter and as small as 25 μm using a hydraulic nozzle by BETE. The frothing section produces bubbles of about 5mm with high mixing of solvent promoting the higher mass transfer from gas to liquid. The absorber reaches the capture efficiency of about 50% with only two sections in operation. Based on the current results, it can be deduced that increasing the solvent feed temperature and including the packed section for absorption the capture efficiency will increase further. Initial data will be collected using all three sections of the absorber and will be used for sDOE. Non-Uniform Space Filling model of sDOE will be used to prioritize the input conditions resulting into maximum capture efficiency. sDOE is performed using the platform called Framework Optimization, Quantification of Uncertainty, and Surrogates (FOQUS). The method and results demonstrating the progress of the parametric campaign from the initial set of experiments to the final stage of obtaining optimized parameters using sDOE tool will be presented in detail.

20 FOSSIL-FUELED POWER PLANTS↗

Prediction of spout diameter in gas-solid spouted beds using factorial design of experiments approach with the aid of advanced optical fibre probe

In this study, the effects of five operating and design variables (solid density, static bed height, particle diameter, superficial gas velocity, and inlet diameter) on the average spout diameter of a 0.152 m inside diameter gas-solid spouted bed have been assessed experimentally using advanced gas-solid optical fibre probe technique. Statistical analysis of the experimental data including the factorial design of the experiments using MINITAB17 statistical software has been performed to determine the extent of the effects of these variables on the spout diameter as a case study. It was found that all five operating and design variables, except the solid density together with the 2-ways interactions between particles size and inlet diameter, in addition to gas velocity and inlet diameter, have a significant effect on the average spout diameter. Regression analysis was performed to correlate these variables with the average spout diameter for the gas-solid spouted beds. The obtained preliminary regression correlation was able to closely predict the average spout diameter of this work with the mean relative deviation value of 0.7 %.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Design and analysis of confirmation experiments

The statistical literature and practitioners have long advocated the use of confirmation experiments as the final stage of a sequence of designed experiments to verify that the optimal operating conditions identified as part of a response surface methodology strategy are attainable and able to achieve the value of the response desired. Yet, until recently there has been a gap between this recommendation and details about how to perform an analysis to quantitatively assess whether the confirmation runs are adequate. Likewise, there has been little in the way of specific recommendations for the number and nature of the confirmation runs that should be performed. In this article, we propose analysis methods to assess agreement between the mean response from previous experiments and the confirmation experiment, and suggest a strategy for the design of confirmation experiments that more fully explores the region around the optimum.

97 MATHEMATICS AND COMPUTING↗