Characterizing permeability-porosity relationships of porous rocks using a stress sensitivity model in consideration of elastic-structural deformation and tortuosity sensitivity

Clarifying the relationship between stress sensitivities of permeability and porosity is of great significance in guiding underground resource mining.More and more studies focus on how to construct stress sensitivity models to describe the relationship and obtain a comprehensive stress sensitivity of porous rock.However,the limitations of elastic deformation calculation and incompleteness of considered tortuosity sensitivity lead to the fact that the existing stress sensitivity models are still unsatisfactory in terms of accuracy and generalization.Therefore,a more accurate and generic stress sensitivity model considering elastic-structural deformation of capillary cross-section and tortuosity sensitivity is proposed in this paper.The elastic deformation is derived from the fractal scaling model and Hooke's law.Considering the effects of elastic-structural deformation on tortuosity sensitivity,an empirical formula is proposed,and the conditions for its applicability are clarified.The predictive performance of the proposed model for the permeability-porosity relationships is validated in several sets of publicly available experimental data.These experimental data are from different rocks under different pressure cycles.The mean and standard deviation of relative errors of predicted stress sensitivity with respect to experimental data are 2.63%and 1.91%.Compared with other models,the proposed model has higher accuracy and better predictive generalization performance.It is also found that the porosity sensitivity exponent a,which can describe permeability-porosity relationships,is 2 when only elastic deformation is considered.a decreases from 2 when structural deformation is also considered.In addition,a may be greater than 3 due to the increase in tortuosity sensitivity when tortuosity sensitivity is considered even if the rock is not fractured.

Introducing the nth-Order Features Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (nth-FASAM-N): I. Mathematical Framework

This work presents the “nth-Order Feature Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (abbreviated as “nth-FASAM-N”), which will be shown to be the most efficient methodology for computing exact expressions of sensitivities, of any order, of model responses with respect to features of model parameters and, subsequently, with respect to the model’s uncertain parameters, boundaries, and internal interfaces. The unparalleled efficiency and accuracy of the nth-FASAM-N methodology stems from the maximal reduction of the number of adjoint computations (which are considered to be “large-scale” computations) for computing high-order sensitivities. When applying the nth-FASAM-N methodology to compute the second- and higher-order sensitivities, the number of large-scale computations is proportional to the number of “model features” as opposed to being proportional to the number of model parameters (which are considerably more than the number of features).When a model has no “feature” functions of parameters, but only comprises primary parameters, the nth-FASAM-N methodology becomes identical to the extant nth CASAM-N (“nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems”) methodology. Both the nth-FASAM-N and the nth-CASAM-N methodologies are formulated in linearly increasing higher-dimensional Hilbert spaces as opposed to exponentially increasing parameter-dimensional spaces thus overcoming the curse of dimensionality in sensitivity analysis of nonlinear systems. Both the nth-FASAM-N and the nth-CASAM-N are incomparably more efficient and more accurate than any other methods (statistical, finite differences, etc.) for computing exact expressions of response sensitivities of any order with respect to the model’s features and/or primary uncertain parameters, boundaries, and internal interfaces.

Parameter identification and global sensitivity analysis of Xin'anjiang model using meta-modeling approach

Parameter identification, model calibration, and uncertainty quantification are important steps in the model-building process, and are necessary for obtaining credible results and valuable information. Sensitivity analysis of hydrological model is a key step in model uncertainty quantification, which can identify the dominant parameters, reduce the model calibration uncertainty, and enhance the model optimization efficiency. There are, however, some shortcomings in classical approaches, including the long duration of time and high computation cost required to quantitatively assess the sensitivity of a multiple-parameter hydrological model. For this reason, a two-step statistical evaluation framework using global techniques is presented. It is based on （1） a screening method （Morris） for qualitative ranking of parameters, and （2） a variance-based method integrated with a meta-model for quantitative sensitivity analysis, i.e., the Sobol method integrated with the response surface model （RSMSobol）. First, the Morris screening method was used to qualitatively identify the parameters＇ sensitivity, and then ten parameters were selected to quantify the sensitivity indices. Subsequently, the RSMSobol method was used to quantify the sensitivity, i.e., the first-order and total sensitivity indices based on the response surface model （RSM） were calculated. The RSMSobol method can not only quantify the sensitivity, but also reduce the computational cost, with good accuracy compared to the classical approaches. This approach will be effective and reliable in the global sensitivity analysis of a complex large-scale distributed hydrological model.

Engineering Model for Detecting Sensitivity of the Coupling Capacitance Detector

The sensitivity engineering model of the coupling capacitance detector is built to provide the theoretic foundation for designing its circuits and electrodes scientifically. The sensitivity concept model of the capacitance proximity detector is discussed, and the detecting sensitivity of the coupling capacitance detector is analyzed theoretically. Then the sensitivity engineering model, which can reflect the main parameters relationship of the detecting circuit is set up based on the foregoing analyses. It is concluded that: ① the sensitivity is mainly correlative with some parameters including the voltage transmission factor of the demodulator, the oscillating voltage amplitude and the amplitude variation constant of the oscillator; ② the sensitivity is also influenced by the areas of electrodes and the distance between electrodes of the detector.

Snow and sea ice thermodynamics in the Arctic:Model validation and sensitivity study against SHEBA data

Evolution of the Arctic sea ice and its snow cover during the SHEBA year were simulated by applying a high-resolution thermodynamic snow/ice model （HIGHTSI）. Attention was paid to the impact of albedo on snow and sea ice mass balance, effect of snow on total ice mass balance, and the model vertical resolution. The SHEBA annual simulation was made applying the best possible external forcing data set created by the Sea Ice Model Intercomparison Project. The HIGHTSI control run reasonably reproduced the observed snow and ice thickness. A number of albedo schemes were incorporated into HIGHTSI to study the feedback processes between the albedo and snow and ice thickness. The snow thickness turned out to be an essential variable in the albedo parameterization. Albedo schemes dependent on the surface temperature were liable to excessive positive feedback effects generated by errors in the modelled surface temperature. The superimposed ice formation should be taken into account for the annual Arctic sea ice mass balance.

Parameter sensitivity study of the biogeochemical model in the China coastal seas

In order to develop a coupled basin scale model of ocean circulation and biogeochemical cycling,we present a biogeochemical model including 12 components to study the ecosystem in the China coastal seas（CCS）.The formulation of phytoplankton mortality and zooplankton growth are modified according to biological characteristics of CCS.The four sensitivity biological parameters,zooplankton assimilation efficiency rate（ZooAE_N）,zooplankton basal metabolism rate（ZooBM）,maximum specific growth rate of zooplankton（μ_（20）） and maximum chlorophyll to carbon ratio（Chl2C_m） are obtained in sensitivity experiments for the phytoplankton,and experiments about the parameter μ_（20＇）,half-saturation for phytoplankton NO_3 uptake（K_（NO_3）） and remineralization rate of small detritusN（SDeRRN） are conducted.The results demonstrate that the biogeochemical model is quite sensitive to the zooplankton grazing parameter when it ranges from 0.1 to 1.2 d^（-1）.The K_（NO_3） and SDeRRN also play an important role in determining the nitrogen cycle within certain ranges.The sensitive interval of KNO_3 is from 0.1 to 1.5（mmol/m^3）^（-1）,and interval of SEdRRN is from 0.01 and 0.1 d^（-1）.The observational data from September 1998 to July 2000 obtained at SEATS station are used to validate the performance of biological model after parameters optimization.The results show that the modified model has a good capacity to reveal the biological process features,and the sensitivity analysis can save computational resources greatly during the model simulation.

Sensitivity analysis of the De Nitrification and De Composition model for simulating regional carbon budget at the wetlandgrassland area on the Zoige Plateau,China

Although mathematical models(e.g., De Nitrification and De Composition(DNDC) provide a powerful tool to study regional carbon budget, it is still difficult to obtain accurate simulation results because there exists large uncertainties in modeling regional carbon budget. Through the investigation on the sensitivity of model output parameters to the input parameters, sensitivity analysis(SA) has been proved to be able to identify the key sources of uncertainties and be helpful to reduce the model uncertainties. However, some input parameters with discrete values(e.g., land use type and soil type) and the regional effect of the sensitive parameters were rarely examined in SA. In this paper, taking the Zoige Plateau as a case area, we combined the one-factor-ata-time(OAT) with Extended Fourier Amplitude Sensitivity Test(EFAST) to conduct a SA of DNDC for simulating the regional carbon budget, including Gross Primary Productivity(GPP), Net Primary Productivity(NPP), Net Ecosystem Productivity(NEP), autotrophic respiration(Ra), soil microbial heterotrophic respiration(Rh) and ecosystem respiration(Re). The result showed that the combination of OAT and EFAST could test the contribution of the input parameters with discrete values to the output parameters. In DNDC model, land use type and soil type had a significant impact on the regional carbon budget of the Zoige Plateau, and daily temperature was also confirmed to be one of the most important parameters for carbon budget. For the other input parameters, with the change of land use type or soil type at regional scale, the sensitive parameters of carbon budget would vary accordingly. The SA results would provide scientific evidence to optimize DNDC model and they suggested that we should pay attention to the spatial/temporal effect of SA and try to use the appropriate data in simulation of the regional carbon budget.

Parameters Sensitivity Analysis and Correction for Concrete Damage Plastic Model

In order to understand the effect of hardening ductility parameters and softening ductility parameters of the concrete damage plastic model in LS-DYNA,a sensitivity and reliability analysis of these parameters through a convenient cube unit test was conducted. The results showed that the peak strength strain was independent of the hardening ductility parameter DH,but affected by AH,BH,and CH. The softening ductility was mainly related to the softening ductility parameter AS,but not affected by the damage ductility exponent BS. In case that the model with default parameters failed to match the AS-controlled damage softening phase,an optimized model with an AS correction was developed. The corrected model with the AS value of 2 matched well with the code model,and exhibited good feasibility in predicting the stress-strain curve of different grades of concrete. Moreover,the practicability of the corrected model was further validated by the conventional triaxial test. The simulated curve exhibited favorable consistence with the trial curve. Therefore,the model with parameter correction could provide a prospective reference for predicting the mechanical properties of concrete.

Impact of the Time Scale of Model Sensitivity Response on Coupled Model Parameter Estimation

That a model has sensitivity responses to parameter uncertainties is a key concept in implementing model parameter es- timation using filtering theory and methodology. Depending on the nature of associated physics and characteristic variability of the fluid in a coupled system, the response time scales of a model to parameters can be different, from hourly to decadal. Unlike state estimation, where the update frequency is usually linked with observational frequency, the update frequency for parameter estimation must be associated with the time scale of the model sensitivity response to the parameter being esti- mated. Here, with a simple coupled model, the impact of model sensitivity response time scales on coupled model parameter estimation is studied. The model includes characteristic synoptic to decadal scales by coupling a long-term varying deep ocean with a slow-varying upper ocean forced by a chaotic atmosphere. Results show that, using the update frequency deter- mined by the model sensitivity response time scale, both the reliability and quality of parameter estimation can be improved significantly, and thus the estimated parameters make the model more consistent with the observation. These simple model results provide a guideline for when real observations are used to optimize the parameters in a coupled general circulation model for improving climate analysis and prediction initialization.

Sensitivity of Statistical Models for Extremes Rainfall Adjustment Regarding Data Size: Case of Ivory Coast

The objective of this study is to analyze the sensitivity of the statistical models regarding the size of samples. The study carried out in Ivory Coast is based on annual maximum daily rainfall data collected from 26 stations. The methodological approach is based on the statistical modeling of maximum daily rainfall. Adjustments were made on several sample sizes and several return periods (2, 5, 10, 20, 50 and 100 years). The main results have shown that the 30 years series (1931-1960;1961-1990;1991-2020) are better adjusted by the Gumbel (26.92% - 53.85%) and Inverse Gamma (26.92% - 46.15%). Concerning the 60-years series (1931-1990;1961-2020), they are better adjusted by the Inverse Gamma (30.77%), Gamma (15.38% - 46.15%) and Gumbel (15.38% - 42.31%). The full chronicle 1931-2020 (90 years) presents a notable supremacy of 50% of Gumbel model over the Gamma (34.62%) and Gamma Inverse (15.38%) model. It is noted that the Gumbel is the most dominant model overall and more particularly in wet periods. The data for periods with normal and dry trends were better fitted by Gamma and Inverse Gamma.

Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N): II. Paradigm Application to a Bernoulli Model Comprising Uncertain Parameters

This work presents the application of the recently developed “Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N)” to a simplified Bernoulli model. The 5th-CASAM-N builds upon and incorporates all of the lower-order (i.e., the first-, second-, third-, and fourth-order) adjoint sensitivities analysis methodologies. The Bernoulli model comprises a nonlinear model response, uncertain model parameters, uncertain model domain boundaries and uncertain model boundary conditions, admitting closed-form explicit expressions for the response sensitivities of all orders. Illustrating the specific mechanisms and advantages of applying the 5th-CASAM-N for the computation of the response sensitivities with respect to the uncertain parameters and boundaries reveals that the 5th-CASAM-N provides a fundamental step towards overcoming the curse of dimensionality in sensitivity and uncertainty analysis.

NEW ANTIMICROBIAL SENSITIVITY TESTS OF BIOFILM OF STREPTOCOCCUS MUTANS IN ARTIFICIAL MOUTH MODEL

Objective To develop a new antimicrobial sensitivity test model for oral products in vitro.Methods A biofilm artificial mouth model for antimicrobial sensitivity tests was established by modifying the LKB chromatography chamber. Using sodium fluoride and Tea polyphenol as antimicrobial agent and Streptococcus mu-tans as target, sensitivity tests were studied. Results The modeling biofilm assay resulted in a MIC of 1. 28mg/ ml for fluoride against S. mutans, which was 32 times the MIC for broth maco-dilution method. The differential resistance of bacteria bioflim to antimicrobial agent relative to planktonic cells was also demonstrated. Conclusion The biofilm artificial mouth model may be useful in oral products test.

Sensitivities of Numerical Model Forecasts of Extreme Cyclone Events

A global forecast model is used to examine various sensitivities of numerical predictions of three extreme winter storms that occurred near the eastern continental margin of North America: the Ohio Valley blizzard of January 1978, the New England blizzard of February 1978, and the Mid-Atlantic cyclone of February 1979. While medium-resolution simulations capture much of the intensification, the forecasts of the precise timing and intensity levels suffer from various degrees of error. The coastal cyclones show a 5-10 hPa dependence on the western North Atlantic sea surface temperature, which is varied within a range (± 2.5℃) compatible with interannual fluctuations. The associated vertical velocities and precipitation rates show proportionately stronger dependences on the ocean temperature perturbations. The Ohio Valley blizzard, which intensified along a track 700-800 km from the coast, shows little sensitivity to ocean temperature. The effect of a shift of - 10?latitude in the position of the snow boundary is negligible in each case. The forecasts depend strongly on the model resolution, and the coarse-resolution forecasts are consistently inferior to the medium-resolution forecasts. Studies of the corresponding sensitivities of extreme cyclonic events over eastern Asia are encouraged in order to identify characteristics that are common to numerical forecasts for the two regions.

Analysis of Frequency Characteristics and Sensitivity of Compliant Mechanisms

Based on a modified pseudo-rigid-body model,the frequency characteristics and sensitivity of the large-deformation compliant mechanism are studied.Firstly,the pseudo-rigid-body model under the static and kinetic conditions is modified to enable the modified pseudo-rigid-body model to be more suitable for the dynamic analysis of the compliant mechanism.Subsequently,based on the modified pseudo-rigid-body model,the dynamic equations of the ordinary compliant four-bar mechanism are established using the analytical mechanics.Finally,in combination with the finite element analysis software ANSYS,the frequency characteristics and sensitivity of the compliant mechanism are analyzed by taking the compliant parallel-guiding mechanism and the compliant bistable mechanism as examples.From the simulation results,the dynamic characteristics of compliant mechanism are relatively sensitive to the structure size,section parameter,and characteristic parameter of material on mechanisms.The results could provide great theoretical significance and application values for the structural optimization of compliant mechanisms,the improvement of their dynamic properties and the expansion of their application range.

An analytical model for pyrolysis of a single biomass particle

Decreasing in emissions of greenhouse gases to confront the global warming needs to replace fossil fuels as the main doer of the world climate changes by renewable and clean fuels produced from biomass like wood waste which is neutral on the amount of CO2. An analytical and engineering model for pyrolysis process of a single biomass particle has been presented. Using a two-stage semi global kinetic model which includes both primary and secondary reactions, the effects of parameters like shape and size of particle as well as porosity on the particle temperature profile and product yields have been investigated. Comparison of the obtained results with experimental data shows that our results are in a reasonable agreement with previous researchers' works. Finally, a sensitivity analysis is done to determine the importance of each parameter on pyrolysis of a single biomass particle which is affected by many constant parameters.

Second-Order Adjoint Sensitivity Analysis Methodology for Computing Exactly Response Sensitivities to Uncertain Parameters and Boundaries of Linear Systems: Mathematical Framework

This work presents the “Second-Order Comprehensive Adjoint Sensitivity Analysis Methodology (2nd-CASAM)” for the efficient and exact computation of 1st- and 2nd-order response sensitivities to uncertain parameters and domain boundaries of linear systems. The model’s response (i.e., model result of interest) is a generic nonlinear function of the model’s forward and adjoint state functions, and also depends on the imprecisely known boundaries and model parameters. In the practically important particular case when the response is a scalar-valued functional of the forward and adjoint state functions characterizing a model comprising N parameters, the 2nd-CASAM requires a single large-scale computation using the First-Level Adjoint Sensitivity System (1st-LASS) for obtaining all of the first-order response sensitivities, and at most N large-scale computations using the Second-Level Adjoint Sensitivity System (2nd-LASS) for obtaining exactly all of the second-order response sensitivities. In contradistinction, forward other methods would require (N2/2 + 3 N/2) large-scale computations for obtaining all of the first- and second-order sensitivities. This work also shows that constructing and solving the 2nd-LASS requires very little additional effort beyond the construction of the 1st-LASS needed for computing the first-order sensitivities. Solving the equations underlying the 1st-LASS and 2nd-LASS requires the same computational solvers as needed for solving (i.e., “inverting”) either the forward or the adjoint linear operators underlying the initial model. Therefore, the same computer software and “solvers” used for solving the original system of equations can also be used for solving the 1st-LASS and the 2nd-LASS. Since neither the 1st-LASS nor the 2nd-LASS involves any differentials of the operators underlying the original system, the 1st-LASS is designated as a “first-level” (as opposed to a “first-order”) adjoint sensitivity system, while the 2nd-LASS is designated as a “second-level” (rather than a “second-order”) adjoint sensitivity system. Mixed second-order response sensitivities involving boundary parameters may arise from all source terms of the 2nd-LASS that involve the imprecisely known boundary parameters. Notably, the 2nd-LASS encompasses an automatic, inherent, and independent “solution verification” mechanism of the correctness and accuracy of the 2nd-level adjoint functions needed for the efficient and exact computation of the second-order sensitivities.

Observations and Modeling of Incoming Longwave Radiation to Snow Beneath Forest Canopies in the West Tianshan Mountains, China

Forest canopy reduces shortwave radiation and increases the incoming longwave radiation to snowpacks beneath forest canopies. Furthermore, the effect of forest canopy may be changed by complex topography. In this paper, we measured and simulated the incoming longwave radiation to snow beneath forest at different canopy openness in the west Tianshan Mountains, China(43°16'N, 84°24'E) during spring 2013. A sensitivity study was conducted to explore the way that terrain influenced the incoming longwave radiation to snow beneath forest canopies. In the simulation model, measurement datasets, including air temperature, incoming shortwave radiation above canopy, and longwave radiation enhanced by adjacent terrain, were applied to calculate the incoming longwave radiation to snow beneath forest canopy. The simulation results were consistent with the measurements on hourly scale and daily scale. The effect of longwave radiation enhanced by terrain was important than that of shortwave radiation above forest canopy with different openness except the 20% canopy openness. The longwave radiation enhanced due to adjacent terrain increases with the slope increase and temperature rise. When air temperature(or slope) is relatively low, thelongwave radiation enhanced by adjacent terrain is not sensitive to slope(or air temperature), but the sensitivity increases with the decrease of snow cover area on sunny slope. The effect of longwave radiation is especially sensitive when the snow cover on sunny slope melts completely. The effect of incoming shortwave radiation reflected by adjacent terrain on incoming longwave radiation to snow beneath forest canopies is more slight than that of the enhanced longwave radiation.

Proof of the Monotonicity of Grid Size and Its Application in Grid-Size Selection for Mesoscale Models

Terrain characteristics can be accurately represented in spectrum space. Terrain spectra can quantitatively reflect the effect of topographic dynamic forcing on the atmosphere. In wavelength space, topographic spectral energy decreases with decreasing wavelength, in spite of several departures. This relationship is approximated by an exponential function. A power law relationship between the terrain height spectra and wavelength is fitted by the least-squares method, and the fitting slope is associated with grid-size selection for mesoscale models. The monotonicity of grid size is investigated, and it is strictly proved that grid size increases with increasing fitting exponent, indicating that the universal grid size is determined by the minimum fitting exponent. An example of landslide-prone areas in western Sichuan is given, and the universal grid spacing of 4.1 km is shown to be a requirement to resolve 90% of terrain height variance for mesoscale models, without resorting to the parameterization of subgrid-scale terrain variance. Comparison among results of different simulations shows that the simulations estimate the observed precipitation well when using a resolution of 4.1 km or finer. Although the main flow patterns are similar, finer grids produce more complex patterns that show divergence zones, convergence zones and vortices. Horizontal grid size significantly affects the vertical structure of the convective boundary layer. Stronger vertical wind components are simulated for finer grid resolutions. In particular, noticeable sinking airflows over mountains are captured for those model configurations.

The Coordinated Influence of Indian Ocean Sea Surface Temperature and Arctic Sea Ice on Anomalous Northeast China Cold Vortex Activities with Different Paths during Late Summer

The Northeast China cold vortex(NCCV)during late summer(from July to August)is identified and classified into three types in terms of its movement path using machine learning.The relationships of the three types of NCCV intensity with atmospheric circulations in late summer,the sea surface temperature(SST),and Arctic sea ice concentration(SIC)in the preceding months,are analyzed.The sensitivity tests by the Community Atmosphere Model version 5.3(CAM5.3)are used to verify the statistical results.The results show that the coordination pattern of East Asia-Pacific(EAP)and Lake Baikal high pressure forced by SST anomalies in the North Indian Ocean dipole mode(NIOD)during the preceding April and SIC anomalies in the Nansen Basin during the preceding June results in an intensity anomaly for the first type of NCCV.While the pattern of high pressure over the Urals and Okhotsk Sea and low pressure over Lake Baikal during late summer-which is forced by SST anomalies in the South Indian Ocean dipole mode(SIOD)in the preceding June and SIC anomalies in the Barents Sea in the preceding April-causes the intensity anomaly of the second type.The third type is atypical and is not analyzed in detail.Sensitivity tests,jointly forced by the SST and SIC in the preceding period,can well reproduce the observations.In contrast,the results forced separately by the SST and SIC are poor,indicating that the NCCV during late summer is likely influenced by the coordinated effects of both SST and SIC in the preceding months.

在斜向非定常流动中由层流向湍流转变对模型尺度螺旋桨性能和压力脉动的影响

In this paper,after the successful applications to open water propeller performance estimations,the influence of transition sensitive and modified mass transfer models tuned to account for the laminar flow in the prediction of the cavitation inception of marine propulsors is investigated from the point of view of the unsteady functioning and induced pressure pulses.The VP1304(also known as PPTC)test case,for which dedicated data were collected during several workshops,is considered first.After preliminary analyses using RANS,also Detached Eddy Simulations(DES)are included to better account for the vortex dynamics and its influence on pressure pulses.Similarly to what observed in uniform inflow,results show a better agreement with the available measurements of propeller performances and confirm the reliability of the proposed approaches for unsteady,non-cavitating,model scale propeller predictions.The overall cavitation pattern is improved too by the application of the transition sensitive correction to the mass transfer model,but the complex dynamics of bubble cavitation observed in experiments prevents quantitatively better predictions in terms of thrust/torque breakdown and induced pressure pulses levels regardless the use of RANS or DES methods.