Generalized Sensitivity Analysis Research Articles

Artificial Intelligence-Centric Low-Enthalpy Geothermal Field Development Planning

Low-enthalpy geothermal energy can make a major contribution towards reducing CO2 emissions. However, the development of geothermal reservoirs is costly and time intensive. In particular, high capital expenditures, data acquisition costs, and long periods of time from identifying a geothermal resource to geothermal heat extraction make geothermal field developments challenging. Conventional geothermal field development planning follows a linear approach starting with numerical model calibrations of the existing subsurface data, simulations of forecasts for geothermal heat production, and cost estimations. Next, data acquisition actions are evaluated and performed, and then the models are changed by integrating the new data before being finally used for forecasting and economics. There are several challenges when using this approach and the duration of model rebuilding with the availability of new data is time consuming. Furthermore, the approach does not address sequential decision making under uncertainty as it focuses on individual data acquisition actions. An artificial intelligence (AI)-centric approach to field development planning substantially improves cycle times and the expected rewards from geothermal projects. The reason for this is that various methods such as machine learning in data conditioning and distance-based generalized sensitivity analysis assess the uncertainty and quantify its potential impact on the final value. The use of AI for sequential decision making under uncertainty results in an optimized data acquisition strategy, a recommendation of a specific development scenario, or advice against further investment. This approach is illustrated by applying AI-centric geothermal field development planning to an Austrian low-enthalpy geothermal case. The results show an increase in the expected value of over 27% and a reduction in data acquisition costs by more than 35% when compared with conventional field development planning strategies. Furthermore, the results are used in systematic trade-off assessments of various key performance indicators.

Development of sensitivity calculation capability of Legendre moments of scattering angular distributions in NECP-MCX

The capability of sensitivity coefficients calculation of keff and reaction rate ratios to Legendre moment of scattering angular distributions based on a fully continuous method has been developed in the Monte Caro code NECP-MCX. The sensitivity calculation was based on Iterated Fission Probability (IFP) and Contributon-Linked eigenvalue sensitivity/Uncertainty estimation via Track-length importance Characterization (CLUTCH) method for k-eigenvalue sensitivity analysis and Generalized Adjoint Responses in Monte Carlo (GEAR-MC) method for generalized sensitivity analysis. The Jezebel and Flattop problems are analyzed and the sensitivity results calculated by NECP-MCX are compared with those by Serpent and ERANOS to demonstrate the accuracy of NECPMCX. In addition, the CLUTCH-FC (CLUTCH coupled with forced collisions) method is implemented to reduce the variance of sensitivity coefficients of Legendre moment of scattering angular distributions with relatively small scattering cross sections. The numerical results indicate that 1) the sensitivity coefficients calculated by NECP-MCX agree well with those by Serpent and ERANOS, and 2) the CLUTCH-FC method is efficient in reducing the variance of sensitivity coefficients of Legendre moment of scattering angular distributions with relatively small scattering cross sections. The Figure of Merit (FOM) values of sensitivity coefficients calculated by the CLUTCH-FC method have increased by 1.9~306.0 times for Jezebel and Flattop problems compared to those calculated by the CLUTCH method.

Importance of different factors for modeling nitrate transport and retention in a tile-drained agricultural catchment with distance-based generalized sensitivity analysis

Modeling of nitrate transport and retention in agricultural land use areas provides useful information to support water quality assessment and management. The accuracy and precision of model simulations are highly dependent on model input factors for which the appropriate values are generally difficult to determine and from which various uncertainties are induced into the modeling procedure. In this study, we applied a Distance-based Generalized Sensitivity Analysis (DGSA) to a high-resolution (25 × 25 m) nitrate transport and retention model for a tile-drained agricultural catchment (4.4 km2) to investigate the extent to which model input factors affect the spatially distributed nitrate retention. The input factors included the nitrate leaching from the root zone, the partitioning of nitrate into tile drainage and groundwater flux, the groundwater flux out of the catchment, the hydrogeological properties, and the denitrification rates in groundwater. The DGSA results were examined in both spatially lumped and distributed perspective. We found that the partitioning of nitrate into tile drainage and groundwater flux was the most important factor for modeling nitrate retention while the hydrogeological properties were secondary but also important. Conversely, the nitrate leaching from the root zone and denitrification rates in groundwater were noninfluential. By increasing the resolution of the DGSA analysis from catchment to model pixel, we found that input factors noninfluential on catchment scale were influential on pixel scale in discrete areas, and, as a general take-home-message, input factors influential on nitrate retention in at least 25 % of the model pixels were sensitive on catchment scale as well. Improved understanding of sensitivity of modelling nitrate retention may help the modelers and water managers to decide which input factors to prioritize in the modelling and data collection to improve the accuracy and precision of the model responses.

Prediction of Terrestrial Heat Flow in Songliao Basin Based on Deep Neural Network

AbstractHeat flow is a geothermal parameter for indicating the heat source distribution and evaluating geothermal reservoirs. Only 1,230 heat flow points are distributed unevenly in China, mainly concentrated in high‐temperature geothermal and southeast regions. The Songliao Basin is a potential geothermal field in China. Still, only 20 measurement points are known, making evaluating the geothermal genetic mechanism difficult. Sparse data interpolation using deep learning methods is highly accurate and widely used in fields such as image processing. In this work, we propose a deep neural network for predicting heat flow in the Songliao Basin. More than 4,000 global heat flows and 23 geological and geophysical parameters are used as reference constraints for training. The uncertainty error of the prediction is estimated based on the correlation and distance‐based generalized sensitivity analysis. The results show that the maximum heat flow is 85 mW/m2, the average is 67.1 mW/m2, and the error with the measured data is 10.64%. The previous geophysical and geological interpretation results indicate that the heat flow is higher in the west and lower in the east, with high anomalies in the central region, which may be related to the uplift of the deep mantle and the depression of the shallow low‐velocity sedimentary layer. Some high‐temperature melt bodies are in the deep layers, forming the current potential geothermal field. The measured data validates that the DNN is an effective method for predicting regional‐scale heat flow, providing reliable heat source information for evaluating geothermal resources.

Sensitivity of Subsurface Permeability in Coastal Deltas to Their Morphodynamic and Geomorphic Characteristics

AbstractThe amount of fresh water moving through coastal deltas worldwide is controlled by the complex subsurface structures within a delta. Morphodynamic influences produced by the feeding river, waves, and tides, in addition to sea level transgressions and regressions, have resulted in deltaic aquifers that are highly heterogeneous. We use 171 unique two‐dimensional morphodynamic models to explore the range of subsurface permeability, hydraulic gradient, and groundwater flux within three end‐member delta types (fluvial, wave, and tidal). We quantify the connectiveness of the subsurface permeability and estimate the horizontal heterogeneity and anisotropy of the permeability. A distance‐based generalized sensitivity analysis is used to investigate the impact morphodynamic influences (fluvial, wave, and tidal), basin conditions (sediment concentration and bathymetric gradient), and geomorphic characteristics (number of channels, shape of the delta plain, and shoreline rugosity) have on the subsurface permeability, hydraulic gradient, and connectivity. We find that the median permeability in deltaic landforms is 4.0 × 10−12 m2 (relating to a hydraulic conductivity of 2.1 × 10−5 m/s), the average hydraulic gradient is 3.9 × 10−4, and the mean specific discharge is 1.3 × 10−8 m/s. High permeability bodies are highly connected and are associated with channelization. Subsurface permeability, hydraulic gradient, and the connectiveness of high permeability areas are sensitive to morphodynamic influences (fluvial, wave, and tidal) and the geomorphic characteristics (number of channels and shoreline rugosity) within a delta. Since morphodynamic influences and geomorphic characteristics are easily identified by looking at the surface of the delta, we suggest that the deltaic subsurface can be characterized by identifying features on the delta surface.

Numerical Simulation of the Beach Response Mechanism under Typhoon Lekima: A Case Study of the Southern Beach of Chudao

Typhoons play an important role in beach evolution. The storm surge and large waves caused by typhoons can cause significant changes in beach morphology in a short period of time. The mechanism of beach evolution and profile changes during typhoons is significantly different from that under non-typhoon dynamic conditions. The XBeach numerical model provides an effective tool for predicting the response of sandy coasts to typhoons. This study is based on field-collected long-term beach profile elevations and grain size data, which were used to establish a two-dimensional XBeach model for simulating the morphological evolution of Cudao Island Beach under Typhoon Lekima. The GSA (Generalized Sensitivity Analysis) method was used to determine the sensitivity order of several important parameters in this modeling. Four different moments of wave height variation were selected during the typhoon process to analyze and study beach evolution. The results show that Chudao South Beach is always in a state of erosion during the typhoon period. The wave water increase is apparent in the nearshore wave-breaking area. The beach shoulder in the northeastern part of the beach is short, and the profile, with a short length, responds quickly to the typhoon. The eroded sediment is mainly deposited in the lower part of the intertidal zone or even transported outside of the wave-breaking zone, and a small part is transported to the shore and deposited in the high-tide zone. The continuous sediment transport along the coast of Chudao Beach is an important factor that influenced the evolution of each profile during Typhoon Lekima.

Sensitivity analysis for causal effects with generalized linear models

Abstract Residual confounding is a common source of bias in observational studies. In this article, we build upon a series of sensitivity analyses methods for residual confounding developed by Brumback et al. and Chiba whose sensitivity parameters are constructed to quantify deviation from conditional exchangeability, given measured confounders. These sensitivity parameters are combined with the observed data to produce a “bias-corrected” estimate of the causal effect of interest. We provide important generalizations of these sensitivity analyses, by allowing for arbitrary exposures and a wide range of different causal effect measures, through the specification of the target causal effect as a parameter in a generalized linear model with the arbitrary link function. We show how our generalized sensitivity analysis can be easily implemented with standard software, and how its sensitivity parameters can be calibrated against measured confounders. We demonstrate our sensitivity analysis with an application to publicly available data from a cohort study of behavior patterns and coronary heart disease.

Sensitivity analysis of attenuation in convective rainfall at X-band frequency using the mountain reference technique

Abstract. The RadAlp experiment aims at improving quantitative precipitation estimation (QPE) in the Alps thanks to X-band polarimetric radars and in situ measurements deployed in the region of Grenoble, France. In this article, we revisit the physics of propagation and attenuation of microwaves in rain. We first derive four attenuation–reflectivity (AZ) algorithms constrained, or not, by path-integrated attenuations (PIAs) estimated from the decrease in the return of selected mountain targets when it rains compared to their dry weather levels (the so-called mountain reference technique – MRT). We also consider one simple polarimetric algorithm based on the profile of the total differential phase shift between the radar and the mountain targets. The central idea of the work is to implement these five algorithms all together in the framework of a generalized sensitivity analysis in order to establish useful parameterizations for attenuation correction. The parameter structure and the inherent mathematical ambiguity of the system of equations makes it necessary to organize the optimization procedure in a nested way. The core of the procedure consists of (i) exploring with classical sampling techniques the space of the parameters allowed to be variable from one target to the other and from one time step to the next, (ii) computing a cost function (CF) quantifying the proximity of the simulated profiles and (iii) selecting parameters sets for which a given CF threshold is exceeded. This core is activated for a series of values of parameters supposed to be fixed, e.g., the radar calibration error for a given event. The sensitivity analysis is performed for a set of three convective events using the 0∘ elevation plan position indicator (PPI) measurements of the Météo-France weather radar located on top of the Moucherotte mountain (altitude of 1901 m a.s.l. – above sea level). It allows the estimation of critical parameters for radar QPE using radar data alone. In addition to the radar calibration error, this includes the time series of radome attenuation and estimations of the coefficients of the power law models relating the specific attenuation and the reflectivity (A–Z relationship) on the one hand and the specific attenuation and the specific differential phase shift (A–Kdp relationship) on the other hand. It is noteworthy that the A–Z and A–Kdp relationships obtained are consistent with those derived from concomitant drop size distribution measurements at ground level, in particular with a slightly non-linear A–Kdp relationship (A=0.28 Kdp1.1). X-Band radome attenuations as high as 15 dB were estimated, leading to the recommendation of avoiding the use of radomes for remote sensing of precipitation at such a frequency.

Generalised soft multi-mode real options model (fuzzy-stochastic approach)

Researchers and practitioners are dealing intensively with the real option valuation. One of the generalised types is reversible the multi-mode American real options. These options are solved mainly by applying the stochastic discrete binomial models. Uncertainty is a typical feature of valuation, and two basic types of representation are distinguished: risk (stochastic) and imprecision (fuzzy). The fuzzy-stochastic models indicate the generalised real options modelling containing both aspects. The objective of the paper is to develop and apply the generalised fuzzy-stochastic multi-mode real options model. This model is based on fuzzy numbers, the discrete binomial model, and the decomposition principle. Input data, particularly underlying cash-flows, are given by fuzzy-random numbers; fuzzy numbers give terminal values, risk-free rate, switching cost. Furthermore, assumptions and computation procedures are also described. The proposed optimisation problem is used for the fuzzy multi-mode real option value calculation. Results are compared with sub-problems, crisp-stochastic multi-modes real options and partial fuzzy-stochastic multi-mode real options models. A stylised illustrative operational flexibility example of comparing the fuzzy-stochastic multi-mode real options models is presented and discussed. The model can serve to valuation, decision-making, generalised sensitivity analysis and control under a fuzzy-stochastic environment.

Local and Global Sensitivity Analysis of a Reactive Transport Model Simulating Floodplain Redox Cycling

AbstractReactive transport models (RTMs) are essential tools that simulate the coupling of advective, diffusive, and reactive processes in the subsurface, but their complexity makes them difficult to understand, develop and improve without accompanying statistical analyses. Although global sensitivity analysis (SA) can address these issues, the computational cost associated with most global SA techniques limits their use with RTMs. In this study, we apply distance‐based generalized sensitivity analysis (DGSA), a novel and computationally efficient method of global SA, to a floodplain‐scale RTM and compare DGSA results to those from local SA. Our test case focuses on the impact of 17 uncertain environmental parameters on spatially and temporally variable redox conditions within a floodplain aquifer. The input parameters considered include flow and diffusion rates, geochemical reaction rates, and the spatial distribution of sediment facies. Sensitivity was evaluated for three distinct components of the model response, encompassing both multidimensional and categorical output. Parameter rankings differ between local SA and DGSA, due to nonlinear effects of individual parameters and interaction effects between parameters. DGSA results show that fluid residence time, which is controlled by aquifer permeability, generally exerts a stronger control on redox conditions than do geochemical reaction rates. Sensitivity indices also demonstrate that sulfate reduction is key for establishing and maintaining reducing conditions throughout the aquifer. These results provide insights into the key drivers of heterogeneous redox processes within floodplain aquifers, as well as the main sources of uncertainty when modeling complex subsurface systems.

Multi-Objective Optimization of CO2 Sequestration in Heterogeneous Saline Aquifers under Geological Uncertainty

This paper presents a Pareto-based multi-objective optimization for operating CO2 sequestration with a multi-well system under geological uncertainty; the optimal well allocation, i.e., the optimal allocation of CO2 rates at injection wells, is obtained when there is minimum operation pressure as well as maximum sequestration efficiency. The distance-based generalized sensitivity analysis evaluates the influence of geological uncertainty on the amount of CO2 sequestration through four injection wells at 3D heterogeneous saline aquifers. The spatial properties significantly influencing the trapping volume, in descending order of influence, are mean sandstone porosity, mean sandstone permeability, shale volume ratio, and the Dykstra–Parsons coefficient of permeability. This confirms the importance of storable capacity and heterogeneity in quantitatively analyzing the trapping mechanisms. Multi-objective optimization involves the use of two aquifer models relevant to heterogeneity; one is highly heterogeneous and the other is less so. The optimal well allocations converge to non-dominated solutions and result in a large injection through one specific well, which generates the wide spread of a highly mobile CO2 plume. As the aquifer becomes heterogeneous with a large shale volume and a high Dykstra–Parsons coefficient, the trapping performances of the combined structural and residual sequestration plateau relatively early. The results discuss the effects of spatial heterogeneity on achieving CO2 geological storage, and they provide an operation strategy including multi-objective optimization.

A temperature-dependent mechanical model to assess the stability of degrading permafrost rock slopes

Abstract. Over the last 2 decades, permafrost degradation has been observed to be a major driver of enhanced rock slope instability and associated hazards in high mountains. While the thermal regime of permafrost degradation in high mountains has been addressed in several modelling approaches, no mechanical models that thoroughly explain rock slope destabilisation controls in degrading permafrost have been developed. Meanwhile, recent laboratory studies have shown that degrading permafrost affects both, rock and ice mechanical strength parameters as well as the strength of rock–ice interfaces. This study presents a first general approach for a temperature-dependent numerical stability model that simulates the mechanical response of a warming and thawing permafrost rock slope. The proposed procedure is exemplified using a rockslide at the permafrost-affected Zugspitze summit crest. Laboratory tests on frozen and unfrozen rock joint and intact rock properties provide material parameters for discontinuum models developed with the Universal Distinct Element Code (UDEC). Geophysical and geotechnical field surveys reveal information on permafrost distribution and the fracture network. This model can demonstrate how warming decreases rock slope stability to a critical level and why thawing initiates failure. A generalised sensitivity analysis of the model with a simplified geometry and warming trajectory below 0 ∘C shows that progressive warming close to the melting point initiates instability above a critical slope angle of 50–62∘, depending on the orientation of the fracture network. The increase in displacements intensifies for warming steps closer to 0 ∘C. The simplified and generalised model can be applied to permafrost rock slopes (i) which warm above −4 ∘C, (ii) with ice-filled joints, (iii) with fractured limestone or probably most of the rock types relevant for permafrost rock slope failure, and (iv) with a wide range of slope angles (30–70∘) and orientations of the fracture network (consisting of three joint sets). Here, we present a benchmark model capable of assessing the future destabilisation of degrading permafrost rock slopes.

Parameter identification for multiperiodic functions

In this paper, we first present the idea of multiperiodic extension for a given function. These functions called the multiperiodic or the extended period functions have more than one period or a vector period instead of a scalar number. We present a method to estimate the parameters of these multiperiodic functions using the data collected from their given functions. The results on the parameter estimation, sensitivity functions and generalized sensitivity analysis of the multiperiodic extensions of the functions show that this method is useful for estimating the parameters of a larger model describing a more complex system on the basis of the parameter estimation of the smaller model describing a simpler or a smaller system.

A generalized sensitivity analysis method based on variance and covariance decomposition of summatory functions for multi-input multi-output systems

Sensitivity analysis is a useful means to quantify the impact of a set of input variables on an output response. However, many traditional sensitivity analysis methods are applicable only to multi-input single-output (MISO) systems and are powerless for multi-input multi-output (MIMO) systems. This paper presents a global sensitivity analysis method based on variance and covariance decomposition (VCD-GSA) of summatory functions for MIMO systems. For a MIMO system with n input variables and m output responses, a set of summatory functions can be constructed by the addition and subtraction of any two output response functions. Each output response function is represented using this set of summatory functions. The variances and covariances of all the output responses are obtained by the integral calculation of the high-dimensional model representations(HDMRs) of these summatory functions. We define the total fluctuation by the sum of the variances and covariances on multiple responses, and the partial fluctuations by the sum of partial variances of a series of summatory functions. Subsequently, we define the s-order sensitivity index of the MIMO system by the ratio of the partial fluctuation on s-order function terms in HDMRs and total fluctuation. The variable sensitivity index is the sum of all of the s-order sensitivity indices, including the contribution of the input variable. The proposed VCD-GSA method is suitable for a uniform or Gaussian distribution. It is also suitable for some complex problems involving variables with correlation. Several numerical examples and engineering applications demonstrate the advantage and practicality of the proposed VCD-GSA method.

A New, Catchment-Scale Integrated Water Quality Model of Phosphorus, Dissolved Oxygen, Biochemical Oxygen Demand and Phytoplankton: INCA-Phosphorus Ecology (PEco)

Process-based models are commonly used to design management strategies to reduce excessive algal growth and subsequent hypoxia. However, management targets typically focus on phosphorus control, under the assumption that successful nutrient reduction will solve hypoxia issues. Algal responses to nutrient drivers are not linear and depend on additional biotic and abiotic controls. In order to generate a comprehensive assessment of the effectiveness of nutrient control strategies, independent nutrient, dissolved oxygen (DO), temperature and algal models must be coupled, which can increase overall uncertainty. Here, we extend an existing process-based phosphorus model (INtegrated CAtchment model of Phosphorus dynamics) to include biological oxygen demand (BOD), dissolved oxygen (DO) and algal growth and decay (INCA-PEco). We applied the resultant model in two eutrophied mesoscale catchments with continental and maritime climates. We assessed effects of regional differences in climate and land use on parameter importance during calibration using a generalised sensitivity analysis. We successfully reproduced in-stream total phosphorus (TP), suspended sediment, DO, BOD and chlorophyll-a (chl-a) concentrations across a range of temporal scales, land uses and climate regimes. While INCA-PEco is highly parameterized, model uncertainty can be significantly reduced by focusing calibration and monitoring efforts on just 18 of those parameters. Specifically, calibration time could be optimized by focusing on hydrological parameters (base flow, Manning’s n and river depth). In locations with significant inputs of diffuse nutrients, e.g., in agricultural catchments, detailed data on crop growth and nutrient uptake rates are also important. The remaining parameters provide flexibility to the user, broaden model applicability, and maximize its functionality under a changing climate.

Assessing an efficient hybrid of Monte Carlo technique (GSA-GLUE) in Uncertainty and Sensitivity Analysis of vanGenuchten Soil Moisture Characteristics Curve

Studying model uncertainty and identifying the parameter uncertainty in the modeling of water flow through the soil is useful to improve water and soil management. This research aimed to assess the uncertainty of the parameters of soil water retention curve (SWRC) models using an efficient hybrid of the Monte Carlo technique e.g. generalized likelihood uncertainty estimation (GLUE). GLUE estimates the parameters of vanGenuchten, vanGenuchten-Mualem, and vanGenuchten-Burdine models for four soil classes. Also, to evaluate the relative importance of the model parameters, generalized sensitivity analysis (GSA) was performed. The results of the uncertainty analysis showed that among the studied models, the vanGenuchten-Mualem model with the indices of S = 0.05, T = 0.4, d-factor = 0.25 and, PCI = 100 was considered as the most accurate model with the least uncertainty. Also, the results of GSA were demonstrated that alpha and n parameters were sensitive parameters in the models. Consequently, identifying the uncertainty of the SWRC model structure and its parameters, relevant models with higher accuracy can be used in the study of soil water processes, and better water resource allocation.

Numerical Analysis of Time‐Dependent Conduit Magma Flow in Dome‐Forming Eruptions With Application to Mount St. Helens 2004–2008

AbstractConduit models of volcanic eruptions simulate magma evolution through phase transitions and material changes during ascent. We present a time‐dependent one‐dimensional model of a chamber‐conduit system to examine the temporal evolution of dome‐forming eruptions. As magma ascends, volatiles exsolve and may escape vertically through the column or laterally through the conduit walls. Magma solidifies which increases viscosity, leading to a natural transition from viscous flow at depth to frictional sliding along the conduit walls near the surface, resulting in the extrusion of a semisolid plug. The model evaluates time‐ and depth‐dependent pressure, velocity, porosity, and relative amounts of exsolved water to carbon dioxide. Transient effects arise when magma outflux from the chamber appreciably decreases pressure over the magma ascent timescale. For low magma permeability, transient effects increase porosity and velocity relative to steady‐state solutions. For high magma permeability, efficient vertical and lateral gas escape depresses porosity and velocity at later times. We use the model to predict three time series data sets from the 2004–2008 eruption of Mount St. Helens: extruded volume, ground deformation, and carbon dioxide emissions. We quantify sensitivity of model predictions to input parameters using the distance‐based generalized sensitivity analysis. Chamber volatile content, volume, and excess pressure influence the amplitude of observables, while conduit radius, frictional rate dependence and magma permeability influence temporal evolution. High magma permeability can cause marked departures from exponentially decaying flux and may explain the unique temporal evolution of deformation observed at the only nearby continuous GPS station in operation at the eruption onset.

Risk Assessment and Simulation of Injectivity Decline Under Uncertainty

SummaryWaterflooding can lead to substantial incremental oil production. Implementation of water-injection projects requires the project to fit into the risk (defined here as negative outcomes relative to defined project objectives) and uncertainty (defined here as the inability to estimate a value precisely) a company is willing to take.One of the key risks for water injection into a shallow reservoir is injection-induced fractures extending into the caprock. If this risk is seen as “intolerable” in an as-low-as-reasonably-practicable (ALARP) analysis, a decision might be made not to proceed with the project. In this study, we evaluated caprock integrity by conducting simulations of long-term water injection that include the effects of formation damage caused by internal/external plugging, geomechanical stress changes, and fracture propagation in the sandstone and bounding shale.The risk of fracture growth into the caprock was assessed by conducting Latin hypercube sampling considering a set of modeling parameters each associated with an uncertainty range. This allowed us to identify the range of operating parameters in which the risk of fracture-height growth was acceptable. Our simulations also allowed us to identify important factors that affect caprock integrity. To cover the uncertainty in geomechanical reservoir evaluation, the operating envelope is identified such that the risk to the caprock integrity is reduced. This requires introducing a limit for the bottomhole pressure (BHP), including a safety margin.The limit of the BHP is then used as a constraint in the uncertainty analysis of water injectivity. The uncertainty analysis should cover the various development options, the parameterization of the model, sampling from the distribution of parameters- and distance-based generalized sensitivity analysis (dGSA) as well as probabilistic representation of the results. The results indicate that the time to reach the BHP limit varies substantially, dependent on the chosen development scenario. Injection of water (1000 m3/d), with total suspended-solids content ranging from 0.1 to 0.5 ppm by volume (ppmv) and particle size from 1 to 5 µm, into long horizontal wells (2000 m) results in injection times of more than 10,000 days even for the P10 percentile. However, injection of poor-quality water (injection rate 600 m3/d, well length 600 m), with total suspended-solids content ranging from 0.5 to 5 ppmv and particle size from 10 to 30 µm, leads to the BHP limit of 10 (P10) to 740 (P90) days.The dGSA can be used to determine which parameter has a stronger impact on the BHP and, hence, on the project, and should be measured if warranted by a value-of-information analysis. In the case reported here, dGSA showed that the filter-cake permeability has a big impact on the results and, hence, will be determined by laboratory measurements.The final development option to be chosen depends on a traditional net-present-value analysis.

Generalized sensitivity analysis of responses to nuclear data in 2-D/1-D transport code KYADJ

Nuclear data are important input parameters in reactor physics design. The uncertainty of the reactor calculation mainly originates from nuclear data variance. The approaches to evaluate the uncertainty are divided into the statistics sampling method and the “Sandwich” rule. The “Sandwich” rule is suitable for problems with plenty of input parameters and the key step of this method is sensitivity analysis. Sensitivity analysis includes the Forward Sensitivity Analysis Procedure (FSAP) and the Adjoint Sensitivity Analysis Procedure (ASAP). FSAP is simple to apply, but the increase of input parameters will cause a large number of repeated calculations. At present, ASAP based on the Classical Perturbation Theory (CPT) and the Generalized Perturbation Theory (GPT) is applied to various neutronics codes. GPT requires the solution of the generalized adjoint equations for responses. It is difficult for many neutronics codes to solve the generalized adjoint equation. In this paper, sensitivity analysis is developed in the two dimensions (2-D) and one dimension (1-D) coupled transport code KYADJ. KYADJ adopts the Forward Sensitivity Analysis Procedure based on the Reduced-Order Modeling (FSAP-ROM) to carry out the generalized sensitivity analysis. FSAP-ROM is tested by the PB-2 BWR pin cell benchmark and the SF96 lattice model. The error is verified by results from the Reactor Monte-Carlo (RMC) code and the direct forward perturbation calculations.

Generalized sensitivity analysis of nonlinear programs using a sequence of quadratic programs

ABSTRACTLocal sensitivity information is obtained for KKT points of parametric NLPs that may exhibit active set changes under parametric perturbations; under appropriate regularity conditions, computationally relevant generalized derivatives of primal and dual variable solutions of parametric NLPs are calculated. Ralph and Dempe obtained directional derivatives of solutions of parametric NLPs exhibiting active set changes from the unique solution of an auxiliary quadratic program. This article uses lexicographic directional derivatives, a newly developed tool in nonsmooth analysis, to generalize the classical NLP sensitivity analysis theory of Ralph and Dempe. By viewing said auxiliary quadratic program as a parametric NLP, the results of Ralph and Dempe are applied to furnish a sequence of coupled QPs, whose unique solutions yield generalized derivative information for the NLP. A practically implementable algorithm is provided. The theory developed here is motivated by widespread applications of nonlinear programming sensitivity analysis, such as in dynamic control and optimization problems.