Global Sensitivity Study Research Articles

Analytical modeling and probabilistic evaluation of gas production from a hydraulically fractured shale reservoir using a quad-linear flow model

During hydraulic fracturing, secondary fractures are created around hydraulic fractures and serve as important channels connecting the shale matrix and the hydraulic fractures. We developed an analytical model to simulate shale gas production from a multi-stage fractured horizontal well. The analytical model is based on the trilinear flow model, but it is free from the assumption that the length of secondary fractures is equal to the half-distance between hydraulic fractures. This analytical model captures the fundamental characteristics of a hydraulically fractured shale reservoir by incorporating transient gas flow in the matrix, secondary fractures, and hydraulic fractures. Because this model describes four linear flow systems (unstimulated reservoir volume, matrix in the stimulated reservoir volume, secondary fracture, and hydraulic fracture), it is called the quad-linear flow model. Production data from two shale gas wells were used to validate the model. Moreover, using the variance-based method and quasi-Monte Carlo simulation, we developed a stochastic framework to perform a probabilistic assessment of shale gas production. We also conducted a global sensitivity study with nine uncertainty parameters to identify important parameters and their interactions that affect well productivity. The results indicate that the existence of dense secondary fractures (the distance between secondary fractures is small) results in higher initial production rate and ultimate recovery, but a sharper decline in production rate. Increasing the length of the secondary fractures can more effectively enhance gas production in the presence of dense secondary fractures. Moreover, the benefits of dense secondary fractures are mostly limited to a high porosity shale reservoir.

Modeling of solid oxide fuel cell (SOFC) electrodes from fabrication to operation: Microstructure optimization via artificial neural networks and multi-objective genetic algorithms

In this study, a modeling framework is proposed for the optimization of the solid oxide fuel cell (SOFC) electrode microstructures. This involves sequential simulations of the SOFCs from initial powder to final electrochemical performance with artificial intelligence-assisted multi-objective optimization. The effects of starting powder parameters such as particle size, particle size distribution (PSD) and pore former content on cathodic overpotential and degradation rate of SOFCs are studied. It is shown that fine particle size and/or low pore former content lead to low cathodic overpotential but high degradation rate in the investigated range of the parameters. Predictive models for the cathode overpotential and degradation rate are established by an artificial neural network using the simulation data. The Sobol global sensitivity study suggests that particle size and pore former content play important roles in determination of the cathode overpotential and degradation rate while the PSD effect is insignificant. A multi-objective genetic algorithm (MOGA) is used to minimize both the overpotential and degradation rate of the cathode. The Pareto front is obtained for the optimal design of cathode microstructures. Compared to the grid search method, the MOGA proves to be more robust and efficient for SOFC electrode microstructure optimization.

Stochastic and sensitivity analysis of shape error of inflatable antenna reflectors

Inflatable antennas are promising candidates to realize future satellite communications and space observations since they are lightweight, low-cost and small-packaged-volume. However, due to their high flexibility, inflatable reflectors are difficult to manufacture accurately, which may result in undesirable shape errors, and thus affect their performance negatively. In this paper, the stochastic characteristics of shape errors induced during manufacturing process are investigated using Latin hypercube sampling coupled with manufacture simulations. Four main random error sources are involved, including errors in membrane thickness, errors in elastic modulus of membrane, boundary deviations and pressure variations. Using regression and correlation analysis, a global sensitivity study is conducted to rank the importance of these error sources. This global sensitivity analysis is novel in that it can take into account the random variation and the interaction between error sources. Analyses are parametrically carried out with various focal-length-to-diameter ratios (F/D) and aperture sizes (D) of reflectors to investigate their effects on significance ranking of error sources. The research reveals that RMS (Root Mean Square) of shape error is a random quantity with an exponent probability distribution and features great dispersion; with the increase of F/D and D, both mean value and standard deviation of shape errors are increased; in the proposed range, the significance ranking of error sources is independent of F/D and D; boundary deviation imposes the greatest effect with a much higher weight than the others; pressure variation ranks the second; error in thickness and elastic modulus of membrane ranks the last with very close sensitivities to pressure variation. Finally, suggestions are given for the control of the shape accuracy of reflectors and allowable values of error sources are proposed from the perspective of reliability.

Greenland Ice Sheet influence on Last Interglacial climate: global sensitivity studies performed with an atmosphere–ocean general circulation model

Abstract. During the Last Interglacial (LIG, ∼130–115 kiloyears (kyr) before present (BP)), the northern high latitudes were characterized by higher temperatures than those of the late Holocene and a lower Greenland Ice Sheet (GIS). However, the impact of a reduced GIS on the global climate has not yet been well constrained. In this study, we quantify the contribution of the GIS to LIG warmth by performing various sensitivity studies based on equilibrium simulations, employing the Community Earth System Models (COSMOS), with a focus on height and extent of the GIS. We present the first study on the effects of a reduction in the GIS on the surface temperature (TS) on a global scale and separate the contribution of astronomical forcing and changes in GIS to LIG warmth. The strong Northern Hemisphere summer warming of approximately 2 °C (with respect to pre-industrial) is mainly caused by increased summer insolation. Reducing the height by ∼ 1300 m and the extent of the GIS does not have a strong influence during summer, leading to an additional global warming of only +0.24 °C compared to the purely insolation-driven LIG. The effect of a reduction in the GIS is, however, strongest during local winter, with up to +5 °C regional warming and with an increase in global average temperature of +0.48 °C. In order to evaluate the performance of our LIG simulations, we additionally compare the simulated TS anomalies with marine and terrestrial proxy-based LIG temperature anomalies derived from three different proxy data compilations. Our model results are in good agreement with proxy records with respect to the warming pattern but underestimate the magnitude of temperature change when compared to reconstructions, suggesting a potential misinterpretation of the proxy records or deficits in our model. However, we are able to partly reduce the mismatch between model and data by additionally taking into account the potential seasonal bias of the proxy record and/or the uncertainties in the dating of the proxy records for the LIG thermal maximum. The seasonal bias and the uncertainty of the timing are estimated from new transient model simulations covering the whole LIG. The model–data comparison improves for proxies that represent annual mean temperatures when the GIS is reduced and when we take the local thermal maximum during the LIG (130–120 kyr BP) into account. For proxy data that represent summer temperatures, changes in the GIS are of minor importance for sea surface temperatures. However, the annual mean and summer temperature change over Greenland in the reduced GIS simulations seems to be overestimated as compared to the local ice core data, which could be related to the interpretation of the recorder system and/or the assumptions of GIS reduction. Thus, the question regarding the real size of the GIS during the LIG has yet to be answered.

Modeling and testing of snow penetration

Penetration by a cone into snow is commonly used to characterize snow properties. However, the effects of the diameter and half-angle of the cone on the mechanical properties of snow have not been systematically studied. In addition, no estimation of material parameters in a physically-based model has been made such that the results from penetration provide only an index of snow properties. In this paper, modeling and experimental methods are used to examine the effects of cone geometry on the maximum penetration force and associated hardness, with penetrometers ranging from 2.5 to 4mm in diameter, 15° to 45° in cone half-angle, and testing both fine-grained and coarse-grained snows. The material point method, in conjunction with the Drucker–Prager cap plasticity model, was used to obtain the theoretical penetration force-distance relationship. Global sensitivity studies were conducted that indicate that the cohesion accounts for 86% of the penetration force, followed distantly by friction angle which accounts for 27%. A general trend, for the simulation results was established: for a given half-angle, the penetration force increases with the increase of diameter which holds for most of the test data as well; for a given diameter, the penetration force decreases with the increase of half-angle, which holds for some of the test data. In addition, for a given half-angle, the hardness decreases with the increase of diameter; for a given diameter, the hardness decreases with the increase of half-angle. To take into consideration the uncertainty of test data, a simple interval-based metric was used to compare test data with simulation results; the comparison was satisfactory. The material parameters from the simulations can thus be considered as calibrated ones for the snow studied.

Sensitivity of Wave Fatigue Loads on Offshore Wind Turbines under Varying Site Conditions

Considerable variations in environmental site conditions can exist within large offshore wind farms leading to divergent fatigue loads on support structures. An efficient frequency-domain method to calculate wave-induced fatigue loads on offshore wind turbine monopile foundations was developed. A verification study with time-domain simulations for a 4MW offshore wind turbine showed result accuracies of more than 90% for equivalent bending moments at mudline and interface level. This accuracy and computation times in the order of seconds make the frequency-domain method ideal for preliminary design and support structure optimization. The model is applied in sensitivity analysis of fatigue loads using Monte-Carlo simulations. Local and global sensitivity studies and a probabilistic assessment give insight into the importance of site parameters like water depth, soil stiffness, wave height, and wave period on fatigue loads. Results show a significant influence of water depth and wave period. This provides a basis for design optimization, load interpolation and uncertainty analysis in large wind farms.

Error Analysis of a Mobile Terrestrial LiDAR System

The understanding of the effects of error on Mobile Terrestrial LiDAR (MTL) point clouds has not increased with their popularity. In this study, comprehensive error analyses based on error propagation theory and global sensitivity study were carried out to quantitatively describe the effects of various error sources in a MTL system on the point cloud. Two scenarios were envisioned; the first using the uncertainties for measurement and calibration variables that are normally expected for MTL systems as they exist today, and the second using an ideal situation where measurement and calibration values have been well adjusted. It was found that the highest proportion of error in the point cloud can be attributed to the boresight and lever arm parameters for MTL systems calibrated using non-rigours methods. In particular, under a loosely controlled error condition, the LiDAR to INS Z lever arm and the LiDAR to INS roll angle contributed more error in the output point cloud than any other parameter, including the INS position. Under tightly controlled error conditions, the INS position became the dominant source of error in the point cloud. In addition, conditional variance analysis has shown that the majority of the error in a point cloud can be attributed to the individual variables. Errors caused by the interactions between the diverse variables are minimal and can be regarded as insignificant.

Applying uncertainty quantification to multiphase flow computational fluid dynamics

Abstract Multiphase computational fluid dynamics plays a major role in design and optimization of fossil fuel based reactors. There is a growing interest in accounting for the influence of uncertainties associated with physical systems to increase the reliability of computational simulation based engineering analysis. The U.S. Department of Energy's National Energy Technology Laboratory (NETL) has recently undertaken an initiative to characterize uncertainties associated with computer simulation of reacting multiphase flows encountered in energy producing systems such as a coal gasifier. The current work presents the preliminary results in applying non-intrusive parametric uncertainty quantification and propagation techniques with NETL's open-source multiphase computational fluid dynamics software MFIX. For this purpose an open-source uncertainty quantification toolkit, PSUADE developed at the Lawrence Livermore National Laboratory (LLNL) has been interfaced with MFIX software. In this study, the sources of uncertainty associated with numerical approximation and model form have been neglected, and only the model input parametric uncertainty with forward propagation has been investigated by constructing a surrogate model based on data-fitted response surface for a multiphase flow demonstration problem. Monte Carlo simulation was employed for forward propagation of the aleatory type input uncertainties. Several insights gained based on the outcome of these simulations are presented such as how inadequate characterization of uncertainties can affect the reliability of the prediction results. Also a global sensitivity study using Sobol' indices was performed to better understand the contribution of input parameters to the variability observed in response variable.

Simulation of Helical Gear Heated by Induction Process Using 3D Model

This paper is devoted to develop a 3D model applied to helical gear heated by induction process. The global work is realised by multiphysicsimulation coupling electromagneticfields and heat transfer using Comsolsoftware. This model permits to establish the temperature distribution in function of simulation parameters. The results are very promising since they allow understanding the dissymmetry effect of heating that affect the real hardness profile. Finally, a global sensitivity study about nominal values of machine parameters is conducted to quantify the effect of power consumed by the part on the surface temperature.

Global Sensitivity Analysis of Arrhythmic Risk Biomarkers in Cardiac Single Cell Models

Global sensitivity analysis is critical in understanding the role of ionic currents variability in modulating cellular electrophysiological properties of ventricular myocytes as well as in assessing the cardiac single cell arrhythmic risk biomarkers. This work involves a systematic investigation into the sensitivity of various preclinical cellular biomarkers of arrhythmic risk to changes in ionic current conductances and kinetics. We compare local and global sensitivity analysis approaches. The nonlinearity of the system is confirmed to play an important role when considering the effect of parameters on markers that involve information from different frequencies. In the case of such biomarkers as action potential duration (APD), maxima Cai and Nai concentrations, we find no significant changes in the overall order of the parameters' significance between local and global sensitivity studies. However, even for these single frequency markers we are able to give a more precise relative contribution of each parameter. Importantly, in the case of maximum S1-S2 slope marker, which integrates the information across a spectrum of frequencies of electrical stimuli, we find significant changes in the order of parameters as compared to the previously used methods for studying the sensitivity of cellular biomarkers. Moreover, the models consistently identify the L-type Calcium current (ICaL) as one of the dominant currents affecting the plateau of the action potential. Furthermore, in consistence with experimental data, the simulation results show that variation in conductances and kinetics of other channels does not affect the significance of ICaL's contribution. We demonstrate the critical role of global (vs local) sensitivity analysis in providing insights into the sensitivity of preclinical biomarkers, and hence mechanisms of repolarization and their rate dependence.

Vegetation-mediated impacts of trends in global radiation on land hydrology: a global sensitivity study

Incident solar radiation has changed in the last 50 years, as an initial dimming trend from 1960 to approximately 1990 was followed by an ongoing brightening period, with concomitant changes in the partitioning between direct and diffuse fractions. Such radiation changes are expected to affect the global water cycle. In this study, we use the Community Land Model (CLM) to perform global offline simulations for the period 1948–2004 and study the effects of solar forcing changes on trends in evapotranspiration and runoff. The modeled components of the hydrologic cycle respond strongly to the imposed radiation changes in several regions, especially in the tropics. Exceptions are regions with soil moisture-limited evapotranspiration regime, such as the U.S. Great Plains. In Europe and the Eastern US, the imposed 7 W m−2 solar dimming for 1960–1990 leads to an evapotranspiration reduction of 1.5 W m−2 or approximately 5% of the mean and an enhancement of runoff by equal percentage. In these regions, the imposed 6 W m−2 solar brightening leads to a 3 W m−2 increase of evapotranspiration in 1990–2004, and a runoff reduction of between 7 and 10% of the mean. Additional simulations investigating the impact of higher diffuse radiation fraction during 1960–1990 suggest mostly an increase of evapotranspiration in the tropics of 2.5 W m−2 (3% of mean) due to increased photosynthesis from shaded leaves, but with smaller opposite effects elsewhere because of lower ground evaporation. The runoff trend resulting from the imposed radiation/aerosols effect is of the same sign and approximate relative magnitude (but larger absolute magnitude) as those calculated, in various studies, for other potential drivers of runoff change such as climate, CO2, or land use. These results thus strengthen the claim that radiation effects on runoff are not to be neglected. Understanding the impacts of radiation on the water cycle will affect projections of river flow and freshwater availability for human consumption.

Modeling transport and fate of riverine dissolved organic carbon in the Arctic Ocean

The spatial distribution and fate of riverine dissolved organic carbon (DOC) in the Arctic may be significant for the regional carbon cycle but are difficult to fully characterize using the sparse observations alone. Numerical models of the circulation and biogeochemical cycles of the region can help to interpret and extrapolate the data and may ultimately be applied in global change sensitivity studies. Here we develop and explore a regional, three‐dimensional model of the Arctic Ocean in which, for the first time, we explicitly represent the sources of riverine DOC with seasonal discharge based on climatological field estimates. Through a suite of numerical experiments, we explore the distribution of DOC‐like tracers with realistic riverine sources and a simple linear decay to represent remineralization through microbial degradation. The model reproduces the slope of the DOC‐salinity relationship observed in the eastern and western Arctic basins when the DOC tracer lifetime is about 10 years, consistent with published inferences from field data. The new empirical parameterization of riverine DOC and the regional circulation and biogeochemical model provide new tools for application in both regional and global change studies.

Global sensitivity analysis of a 3D street canyon model—Part II: Application and physical insight using sensitivity analysis

In this work global sensitivity studies using Monte Carlo sampling and high dimensional model representations (HDMR) have been carried out on the k– ε closure computational fluid dynamic (CFD) model MISKAM, allowing detailed representation of the effects of changing input parameters on the model outputs. The scenario studied is that of a complex street canyon in the city of York, UK. The sensitivity of the turbulence and mean flow fields to the input parameters is detailed both at specific measurement points and in the associated canyon cross-section to aid comparison with field data. This analysis gives insight into how model parameters can influence the predicted outputs. It also shows the relative strength of each parameter in its influence. Four main input parameters are addressed. Three parameters are surface roughness lengths, determining the flow over a surface, and the fourth is the background wind direction. In order to determine the relative importance of each parameter, sensitivity indices are calculated for the canyon cross-section. The sensitivity of the flow structures in and above the canyon to each parameter is found to be very location dependant. In general, at a particular measurement point, it is the closest wall surface that is most influential on the model output. However, due to the complexity of the flow at different wind angles this is not always the case, for example when a re-circulating canyon flow pattern is present. The background wind direction is shown to be an important parameter as it determines the surface features encountered by the flow. The accuracy with which this is specified when modelling a full-scale situation is therefore an important consideration when considering model uncertainty. Overall, the uncertainty due to roughness lengths is small in comparison to the mean outputs, indicating that the model is well defined even with large ranges of input parameter uncertainty.

Uncertainties in the GSWP-2 precipitation forcing and their impacts on regional and global hydrological simulations

The Global Soil Wetness Project (GSWP) is an international initiative aimed at producing global data sets of soil wetness and energy and water fluxes by driving land surface models with state-of-the-art 1° by 1° atmospheric forcing and land surface parameters. It also provides a unique opportunity to develop and test land surface parameterizations at the global scale, using multi-year off-line simulations that are not affected by the systematic errors found in atmospheric models. Nevertheless, the accuracy and reliability of the 10−year GSWP-2 atmospheric forcing remain questionable. A first comparison using the high-resolution Rhone-AGGregation (Rhone-AGG) database reveals that the baseline GSWP-2 precipitation forcing is drastically overestimated over the Rhone river basin. Hydrological simulations driven with each dataset and using the ISBA land surface model and the MODCOU river routing model are also compared. The simulated river discharges are validated against a dense network of river gauges and are generally less realistic when using the GSWP-2 instead of the Rhone-AGG precipitation forcing. Secondly, the GSWP-2 precipitation forcing is compared with three alternative data sets (GPCP-2, CRU-2, CMAP) at the global scale. Moreover, the results of a global sensitivity study to the precipitation forcing conducted with six land surface models are shown. The TRIP river routing model is used to convert daily runoff from all models into river discharges, which are compared at 80 gauging stations distributed over the globe. In agreement with the regional evaluation, the results reveal that the baseline GSWP-2 precipitation forcing is generally overestimated over the mid and high latitudes, which implies systematic errors in the simulated discharges. This study reveals that the empirical wind corrections applied to the GSWP-2 precipitation forcing are exaggerated, whereas the GPCP satellite adjustments seem to be useful for simulating realistic annual mean river discharges over the East Siberian river basins.

Electron tomography of nanoparticle clusters: Implications for atmospheric lifetimes and radiative forcing of soot

Nanoparticles are ubiquitous in nature. Their large surface areas and consequent chemical reactivity typically result in their aggregation into clusters. Their chemical and physical properties depend on cluster shapes, which are commonly complex and unknown. This is the first application of electron tomography with a transmission electron microscope to quantitatively determine the three‐dimensional (3D) shapes, volumes, and surface areas of nanoparticle clusters. We use soot (black carbon, BC) nanoparticles as an example because it is a major contributor to environmental degradation and global climate change. To the extent that our samples are representative, we find that quantitative measurements of soot surface areas and volumes derived from electron tomograms differ from geometrically derived values by, respectively, almost one and two orders of magnitude. Global sensitivity studies suggest that the global burden and direct radiative forcing of fractal BC are only about 60% of the value if it is assumed that BC has a spherical shape.

Influence of the Interannual Variability of Vegetation on the Surface Energy Balance—A Global Sensitivity Study

Abstract The degree to which the interannual variability of vegetation phenology affects hydrological fluxes over land is investigated through a series of simulations with the Mosaic land surface model, run both offline and coupled to the NASA Seasonal-to-Interannual Prediction Project (NSIPP) atmospheric general circulation model (GCM). Over a 9-yr period, from 1982 to 1990, interannual variations of global biophysical land surface parameters (i.e., vegetation density and greenness fraction) are derived from Normalized Difference Vegetation Index (NDVI) data collected by the Advanced Very High Resolution Radiometers (AVHRRs). First the sensitivity of evapotranspiration to interannual variations in vegetation properties is evaluated through offline simulations that ignore feedbacks between the land surface and the atmospheric models, and interannual precipitation variations. Evapotranspiration is shown to be highly sensitive to variations in vegetation over wet continental surfaces that are not densely ve...

Global sensitivity studies of the direct radiative forcing due to anthropogenic sulfate and black carbon aerosols

The direct radiative forcing (DRF) of sulfate and black carbon (BC) aerosols is investigated using a new multispectral radiation code within the R30 Geophysical Fluid Dynamics Laboratory general circulation model (GCM). Two independent sulfate climatologies from chemical transport models are applied to the GCM; each climatology has a different atmospheric burden, vertical profile, and seasonal cycle. The DRF is calculated to be approximately −0.6 and −0.8 W m−2 for the different sulfate climatologies. Additional sensitivity studies show that the vertical profile of the sulfate aerosol is important in determining the DRF; sulfate residing near the surface gives the strongest DRF due to the effects of relative humidity. Calculations of the DRF due to BC reveal that the DRF remains uncertain to approximately a factor of 3 due to uncertainties in the total atmospheric burden, the vertical profile of the BC, and the assumed size distribution. Because of the uncertainties in the total global mass of BC, the normalized DRF (the DRF per unit column mass of aerosol in watts per milligram (W mg−1)) due to BC is estimated; the range is +1.1 to + 1.9 W mg−1 due to uncertainties in the vertical profile. These values correspond to a DRF of approximately +0.4 W m−2 with a factor of 3 uncertainty when the uncertainty in the total global mass of BC is included. In contrast to sulfate aerosol, the contribution to the global DRF from cloudy regions is very significant, being estimated as approximately 60%. The vertical profile of the BC is, once again, important in determining the DRF, but the sensitivity is reversed from that of sulfate; BC near the surface gives the weakest DRF due to the shielding effects of overlying clouds. Although the uncertainty in the estimates of the DRF due to BC remains high, these results indicate that the DRF due to absorption by BC aerosol may contribute a significant positive radiative forcing and may consequently be important in determining climatic changes in the Earth‐atmosphere system.

Monitoring systems and determination of actual fatigue usage

Abstract At GKN, fatigue monitoring of important components has been conducted since 1979. The monitoring methods depend on the mechanisms of damage; quasi-static loads are regarded as well as dynamic loads. The components were selected for monitoring on the basis of a system analysis. The data resulting from monitoring are used to optimise operation mode steadily. Experience shows that the use of monitoring data as input for fatigue assessment is the most realistic and cost-effective way. This fatigue assessment uses global and local sensitivity studies to evaluate the load-stress relation for each component. These relations can be programmed to produce stress vs. time curves. These are processed according to ASME rules to give a realistic fatigue usage.