scholarly journals Global Sensitivity Analysis to Assess Salt Precipitation for CO2 Geological Storage in Deep Saline Aquifers

Geofluids ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-16 ◽  
Author(s):  
Yuan Wang ◽  
Jie Ren ◽  
Shaobin Hu ◽  
Di Feng

Salt precipitation is generated near the injection well when dry supercritical carbon dioxide (scCO2) is injected into saline aquifers, and it can seriously impair the CO2 injectivity of the well. We used solid saturation (Ss) to map CO2 injectivity. Ss was used as the response variable for the sensitivity analysis, and the input variables included the CO2 injection rate (QCO2), salinity of the aquifer (XNaCl), empirical parameter m, air entry pressure (P0), maximum capillary pressure (Pmax), and liquid residual saturation (Splr and Sclr). Global sensitivity analysis methods, namely, the Morris method and Sobol method, were used. A significant increase in Ss was observed near the injection well, and the results of the two methods were similar: XNaCl had the greatest effect on Ss; the effect of P0 and Pmax on Ss was negligible. On the other hand, with these two methods, QCO2 had various effects on Ss: QCO2 had a large effect on Ss in the Morris method, but it had little effect on Ss in the Sobol method. We also found that a low QCO2 had a profound effect on Ss but that a high QCO2 had almost no effect on the Ss value.

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 90
Author(s):  
Shufang Song ◽  
Lu Wang

Global sensitivity analysis (GSA) is a useful tool to evaluate the influence of input variables in the whole distribution range. Variance-based methods and moment-independent methods are widely studied and popular GSA techniques despite their several shortcomings. Since probability weighted moments (PWMs) include more information than classical moments and can be accurately estimated from small samples, a novel global sensitivity measure based on PWMs is proposed. Then, two methods are introduced to estimate the proposed measure, i.e., double-loop-repeated-set numerical estimation and double-loop-single-set numerical estimation. Several numerical and engineering examples are used to show its advantages.


2017 ◽  
Author(s):  
Christopher J. Skinner ◽  
Tom J. Coulthard ◽  
Wolfgang Schwanghart ◽  
Marco J. Van De Wiel ◽  
Greg Hancock

Abstract. Landscape Evolution Models have a long history of use as exploratory models, providing greater understanding of the role large scale processes have on the long-term development of the Earth’s surface. As computational power has advanced so has the development and sophistication of these models. This has seen them applied at increasingly smaller scale and shorter-term simulations at greater detail. However, this has not gone hand-in-hand with more rigorous verifications that are commonplace in the applications of other types of environmental models- for example Sensitivity Analyses. This can be attributed to a paucity of data and methods available in order to calibrate, validate and verify the models, and also to the extra complexity Landscape Evolution Models represent – without these it is not possible to produce a reliable Objective Function against which model performance can be judged. To overcome this deficiency, we present a set of Model Functions – each representing an aspect of model behaviour – and use these to assess the relative sensitivity of a Landscape Evolution Model (CAESAR-Lisflood) to a large set of parameters via a global Sensitivity Analysis using the Morris Method. This novel combination of behavioural Model Functions and the Morris Method provides insight into which parameters are the greatest source of uncertainty in the model, and which have the greatest influence over different model behaviours. The method was repeated over two different catchments, showing that across both catchments and across most model behaviours the choice of Sediment Transport formula was the dominate source of uncertainty in the CAESAR-Lisflood model, although there were some differences between the two catchments. Crucially, different parameters influenced the model behaviours in different ways, with Model Functions related to internal geomorphic changes responding in different ways to those related to sediment yields from the catchment outlet. This method of behavioural sensitivity analysis provides a useful method of assessing the performance of Landscape Evolution Models in the absence of data and methods for an Objective Function approach.


2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Lei Cheng ◽  
Zhenzhou Lu ◽  
Luyi Li

An extending Borgonovo’s global sensitivity analysis is proposed to measure the influence of fuzzy distribution parameters on fuzzy failure probability by averaging the shift between the membership functions (MFs) of unconditional and conditional failure probability. The presented global sensitivity indices can reasonably reflect the influence of fuzzy-valued distribution parameters on the character of the failure probability, whereas solving the MFs of unconditional and conditional failure probability is time-consuming due to the involved multiple-loop sampling and optimization operators. To overcome the large computational cost, a single-loop simulation (SLS) is introduced to estimate the global sensitivity indices. By establishing a sampling probability density, only a set of samples of input variables are essential to evaluate the MFs of unconditional and conditional failure probability in the presented SLS method. Significance of the global sensitivity indices can be verified and demonstrated through several numerical and engineering examples.


Author(s):  
Tian Longfei ◽  
Lu Zhenzhou ◽  
Hao Wenrui

The uncertainty of the in-plane mechanical properties of the laminate used in an aircraft wing structure is investigated. Global sensitivity analysis is used to identify the source of the uncertainties of the response performance. Due to the limitations of the existing global sensitivity analysis method for nonlinear models with correlated input variables, a new one using nonlinear regression is proposed. Furthermore, a contribution matrix is defined for engineering convenience. Two nonlinear numerical examples are employed in this article to demonstrate the ability of the proposed global sensitivity analysis method. After applying the proposed global sensitivity analysis method to the laminate model, the contribution matrices are obtained; from these matrices, researchers can identify the dominant variance contributions that contribute the most to the response variance. Factor analysis is then employed to analyze the global sensitivity analysis results and determine the most efficient methods to decrease the variances of the in-plane elastic constants. Monte Carlo simulation is used to demonstrate the efficiency of the methods in decreasing the variances.


Author(s):  
Wei Chen ◽  
Ruichen Jin ◽  
Agus Sudjianto

The importance of sensitivity analysis in engineering design cannot be over-emphasized. In design under uncertainty, sensitivity analysis is performed with respect to the probabilistic characteristics. Global sensitivity analysis (GSA), in particular, is used to study the impact of variations in input variables on the variation of a model output. One of the most challenging issues for GSA is the intensive computational demand for assessing the impact of probabilistic variations. Existing variance-based GSA methods are developed for general functional relationships but require a large number of samples. In this work, we develop an efficient and accurate approach to GSA that employs analytic formulations derived from metamodels of engineering simulation models. We examine the types of GSA needed for design under uncertainty and derive generalized analytical formulations of GSA based on a variety of metamodels commonly used in engineering applications. The benefits of our proposed techniques are demonstrated and verified through both illustrative mathematical examples and the robust design for improving vehicle handling performance.


Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2425
Author(s):  
Zdeněk Kala

This article presents new sensitivity measures in reliability-oriented global sensitivity analysis. The obtained results show that the contrast and the newly proposed sensitivity measures (entropy and two others) effectively describe the influence of input random variables on the probability of failure Pf. The contrast sensitivity measure builds on Sobol, using the variance of the binary outcome as either a success (0) or a failure (1). In Bernoulli distribution, variance Pf(1 − Pf) and discrete entropy—Pfln(Pf) − (1 − Pf)ln(1 − Pf) are similar to dome functions. By replacing the variance with discrete entropy, a new alternative sensitivity measure is obtained, and then two additional new alternative measures are derived. It is shown that the desired property of all the measures is a dome shape; the rise is not important. Although the decomposition of sensitivity indices with alternative measures is not proven, the case studies suggest a rationale structure of all the indices in the sensitivity analysis of small Pf. The sensitivity ranking of input variables based on the total indices is approximately the same, but the proportions of the first-order and the higher-order indices are very different. Discrete entropy gives significantly higher proportions of first-order sensitivity indices than the other sensitivity measures, presenting entropy as an interesting new sensitivity measure of engineering reliability.


Author(s):  
Qiming Liu ◽  
Nichen Tong ◽  
Xu Han

Commonly, variance-based global sensitivity analysis methods are popular and applicable to quantify the impact of a set of input variables on output response. However, for many engineering practical problems, the output response is not single but multiple, which makes some traditional sensitivity analysis methods difficult or unsuitable. Therefore, a novel global sensitivity analysis method is presented to evaluate the importance of multi-input variables to multi-output responses. First, assume that a multi-input multi-output system (MIMOS) includes [Formula: see text] variables and [Formula: see text] responses. A set of summatory functions [Formula: see text] and [Formula: see text] are constructed by the addition and subtraction of any two response functions. Naturally, each response function is represented using a set of summatory function. Subsequently, the summatory functions [Formula: see text] and [Formula: see text] are further decomposed based on the high dimensional model representation (HDMR), respectively. Due to the orthogonality of all the decomposed function sub-terms, the variance and covariance of each response function can be represented using the partial variances of all the decomposed function sub-terms on the corresponding summatory functions, respectively. The total fluctuation of MIMOS is calculated by the sum of the variances and covariances on all the response functions. Further, the fluctuation is represented as the sum of the total partial variances for all the [Formula: see text]-order function sub-terms, and the total partial variance is the sum of [Formula: see text] partial variances for the corresponding [Formula: see text]-order function sub-terms. Then, the function sensitivity index (FSI) [Formula: see text] for s-order function sub-terms is defined by the ratio of the total partial variance and total fluctuation, which includes first-order, second-order, and high-order FSI. The variable sensitivity index [Formula: see text] of variable [Formula: see text] is calculated by the sum of all the FSIs including the contribution of variable [Formula: see text]. Finally, numerical example and engineering application are employed to demonstrate the accuracy and practicality of the presented global sensitivity analysis method for MIMOS.


2021 ◽  
Vol 0 (0) ◽  
Author(s):  
William Becker ◽  
Paolo Paruolo ◽  
Andrea Saltelli

Abstract Global sensitivity analysis is primarily used to investigate the effects of uncertainties in the input variables of physical models on the model output. This work investigates the use of global sensitivity analysis tools in the context of variable selection in regression models. Specifically, a global sensitivity measure is applied to a criterion of model fit, hence defining a ranking of regressors by importance; a testing sequence based on the ‘Pantula-principle’ is then applied to the corresponding nested submodels, obtaining a novel model-selection method. The approach is demonstrated on a growth regression case study, and on a number of simulation experiments, and it is found competitive with existing approaches to variable selection.


Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2489
Author(s):  
Zhiwei Bai ◽  
Hongkui Wei ◽  
Yingying Xiao ◽  
Shufang Song ◽  
Sergei Kucherenko

For multidimensional dependent cases with incomplete probability information of random variables, global sensitivity analysis (GSA) theory is not yet mature. The joint probability density function (PDF) of multidimensional variables is usually unknown, meaning that the samples of multivariate variables cannot be easily obtained. Vine copula can decompose the joint PDF of multidimensional variables into the continuous product of marginal PDF and several bivariate copula functions. Based on Vine copula, multidimensional dependent problems can be transformed into two-dimensional dependent problems. A novel Vine copula-based approach for analyzing variance-based sensitivity measures is proposed, which can estimate the main and total sensitivity indices of dependent input variables. Five considered test cases and engineering examples show that the proposed methods are accurate and applicable.


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