A new approach for phase transitions in miscible multi-phase flow in porous media

The tightly coupled, strongly nonlinear nature of non-isothermal multi-phase flow in porous media poses a tough challenge for numerical simulation. This trait is even more pronounced, if miscibility is also considered. A primary reason why inclusion of miscibility tends to be problematic are the difficulties stemming from phase transitions: on the one hand, phase transitions need to be included since the presence or absence of fluid phases has a major impact on the flow behavior; on the other hand, convergence of the nonlinear solver may be severely affected if they are not handled robustly.In this work, we present a mathematically sound approach to include phase transitions in the nonlinear system of equations: first, the transition conditions are formulated as a set of local inequality constraints, which are then directly integrated into the nonlinear solver using a nonlinear complementarity function. Under this scheme, Newton-Raphson solvers exhibit considerably more robust convergence behaviour compared to some previous approaches, which is then illustrated by several numerical examples.     

Unified fractional differential approach for transient interporosity flow in naturally fractured media

A unified approach to modeling flows of slightly compressible fluids through naturally fractured media is presented. The unified fractional differential model is derived by combining the flow at micro scale for matrix blocks and macro scale for fractures, using the transient interporosity flow behavior at the interface between matrix blocks and fractures. The derived model is able to unify existing transient interporosity flow models formulated for different shapes of matrix blocks in any medium dimensions. The model is formulated in the form of a fractional order partial differential equation that involves Caputo derivative of order 1/2 with respect to time. Explicit solutions for the unified model are derived for different axisymmetrical spatial domains using Hankel or Hankel–Weber finite or infinite transforms. Comparisons between the predictions of the unified model and those obtained from existing transient interporosity flow models for matrix blocks in the form of slabs, spheres and cylinders are presented. It is shown that the unified fractional derivative model leads to solutions that are very close to those of transient interporosity flow models for fracture-dominant and transitional fracture-to-matrix dominant flow regimes. An analysis of the results of the unified model reveals that the pressure varies linearly with the logarithm of time for different flow regimes, with half slope for the transitional fracture-to-matrix dominant flow regime vs. the fracture and matrix dominant flow regimes. In addition, a new re-scaling that involves the characteristic length in the form of matrix block volume to surface area ratio is derived for the transient interporosity flow models for matrix blocks of different shapes. It is shown that the re-scaled transient interporosity flow models are governed by two dimensionless parameters Θ and Λ compared to only one dimensionless parameter Θ for the unified model. It is shown that the solutions of the transient interporosity flow models for different shapes of matrix blocks are almost identical for the re-scaled variables. Furthermore, the driving parameters for solution behavior are identified based on asymptotic approximations for different flow regimes. It is found that the matrix diffusion and the matrix area-to-volume ratio affect the solution behavior only for the transitional fracture-to-matrix dominant flow regime, that the capacitance ratio affects the solution behavior only for transitional and matrix dominant flow regimes and that the fracture diffusion is involved in all three flow regimes. Similar identification of the driving parameters is also presented in the re-scaled case.     

A parameter allocation approach for flow simulation using the WetSpa-Python model

Hydrologic models are simplified representations of natural hydrologic systems. Since these models rely on assumptions and simplifications to capture some aspects of hydrological processes, calibration of parameters is unavoidable. However, utilizing the philosophy of a recent modelling framework proposed by Bahremand (2016), we show how calibration of most model parameters can be avoided by allocating or presetting these parameters utilizing knowledge gained from sensitivity analyses, field observations and a priori specifications as a part of a parameter allocation procedure. This paper details the simulation of daily river flow of the Shemshak-Roudak watershed performed using the Python version of the WetSpa model. The WetSpa-Python model is a distributed model of hydrological processes applied at the watershed scale. The model was applied to the Shemshak-Roudak watershed of Iran with parameter allocation. Model calibration involved only two parameters. Straightforward methods were proposed for allocating model parameters, including three baseflow-related parameters and the determination of maximum active groundwater storage using a mass curve technique. Also, the Budyko curve was used to constrain a correction factor for potential evapotranspiration. The WetSpa-Python model was extended to include the influence of snowmelt. A failure to include snow in the hydrological processes of the WetSpa-Python model creates a significant discrepancy between the observed and simulated hydrographs during the spring. The results of daily simulations for 12 years (2002–2014) are in good agreement with observations of discharge (Kling-Gupta Efficiency = 0.84). These results demonstrate that it is feasible to simulate hydrographs with limited calibration given a knowledge of hydrological processes and an understanding of relationships between catchment characteristics and model parameters.     

Practical aspects of calibrating and selecting unit hydrograph-based models for continuous river flow simulation

Abstract

A continuous simulation rainfall-streamflow modelling approach that identifies unit hydrographs for total streamflow has been applied to an 11-year record from a national hydrometric monitoring network catchment in the UK. The model is of the parametrically parsimonious conceptual model (PPCM) type that can make efficient use of rainfall, streamflow and air temperature data readily available from established national and regional monitoring networks. A multiple split-sample model calibration and simulation analysis is presented that reveals some guiding principles for calibrating and applying PPCMs generally. The inadequacy of a one-dimensional objective function for calibrating best PPCMs is demonstrated. A two-dimensional objective function approach is superior but is shown to be unreliable in some cases, confirming the need for additional critical inspection of other model performance statistics, model parameters and time series plots as an integral part of the model calibration process. A strong tendency evident from the multiple split-sample analysis is that, for the catchment studied, models that fit relatively well in calibration mode perform relatively poorly in simulation mode.     

Approaches to the simulation of unconfined flow and perched groundwater flow in MODFLOW

Various approaches have been proposed to manage the nonlinearities associated with the unconfined flow equation and to simulate perched groundwater conditions using the MODFLOW family of codes. The approaches comprise a variety of numerical techniques to prevent dry cells from becoming inactive and to achieve a stable solution focused on formulations of the unconfined, partially-saturated, groundwater flow equation. Keeping dry cells active avoids a discontinuous head solution which in turn improves the effectiveness of parameter estimation software that relies on continuous derivatives. Most approaches implement an upstream weighting of intercell conductance and Newton-Raphson linearization to obtain robust convergence. In this study, several published approaches were implemented in a stepwise manner into MODFLOW for comparative analysis. First, a comparative analysis of the methods is presented using synthetic examples that create convergence issues or difficulty in handling perched conditions with the more common dry-cell simulation capabilities of MODFLOW. Next, a field-scale three-dimensional simulation is presented to examine the stability and performance of the discussed approaches in larger, practical, simulation settings.     

Comparison of optimization algorithms for parameter estimation of multi-phase flow models with application to geological carbon sequestration

Optimization of multi-phase transport models is important both for calibrating model parameters to observed data and for analyzing management options. We focus on examples of geological carbon sequestration (GCS) process-based multi-phase models. Realistic GCS models can be very computationally expensive not only due to the spatial distribution of the model but also because of the complex nonlinear multi-phase and multi-component transport equations to be solved. As a result we need to have optimization methods that get accurate answers with relatively few simulations. In this analysis we compare a variety of different types of optimization algorithms to understand the best type of algorithms to use for different types of problems. This includes an analysis of which characteristics of the problem are important in choice of algorithm. The goal of this paper is to evaluate which optimization algorithms are the most efficient in a given situation, taking into account shape of the optimization problem (e.g. uni- or multi-modal) and the number of simulations that can be done. The algorithms compared are the widely used derivative-based PEST optimization algorithm, the derivative-based iTOUGH2, the Kriging response surface algorithm EGO, the heuristics-based DDS (Dynamically Dimensioned Search), and the Radial Basis Function surrogate response surface based global optimization algorithms ‘GORBIT’ and ‘Stochastic RBF’. We calibrate a simple homogeneous model ‘3hom’ and two more realistic models ‘20layer’ and ‘6het’. The latter takes 2 h per simulation. Using rigorous statistical tests, we show that while the derivative-based algorithms of PEST are efficient on the simple 3hom model, it does poorly in comparison to surrogate optimization methods Stochastic RBF and GORBIT on the more realistic models. We then identify the shapes of the optimization surface of the three models using enumerative simulations and discover that 3hom is smooth and unimodal and the more realistic models are rough and multi-modal. When the number of simulations is limited, surrogate response surfaces algorithms perform best on multi-modal, bumpy objective functions, which we expect to have for most realistic multi-phase flow models such as those for GCS.     

A linear systems approach to watershed transport simulation

Models that simulate loadings of pollutants from agricultural landscapes to surface waters often operate at time scales that are relatively coarse (e.g. daily) compared with how fast water moves in streams, suggesting a commensurate physical scale that is substantially larger than typical agricultural fields. In general, as pollutants enter water and move downstream, longitudinal dispersive effects and travel time de‐synchronization tend to cause flattening and broadening of concentration peaks—an effect with implications for potential impacts on ecological and human health, and for which adequate representation is thus important for risk assessment. In‐stream transport is often approximated in practice using numerical implementation of the one‐dimensional advection–dispersion equation (ADE), with streams discretized into linked homogeneous segments. However, when a daily time step is employed, limitations inherent in the finite difference methodology may constrain simulated dispersion in lotic waters to unrepresentative or unrealistic magnitudes. In this paper, a convolution‐based approach to surface water transport is suggested as an alternative to the ADE, for use in combination with daily input loading models. This approach offers the advantage of greater flexibility in representing longitudinal mixing by using impulse response functions (IRF) to represent inter‐segment transport. Networks of stream segments are represented using nested convolutions, implemented using forward and inverse discrete Fourier transform to simplify calculations. Enhanced representational flexibility arises from the freedom afforded the modeller in selecting each segment's IRF, which may be chosen to represent dispersive regimes ranging from pure advection (plug flow) to compete mixing, and beyond to the sort of long‐tailed mixing characterized by fractal inverse frequency power‐law scaling. The approach is explored in proof‐of‐concept exercises that make use of atrazine monitoring data sets collected over common time periods from upstream and downstream locations within the same watersheds. Published 2014. This article is a U.S. Government work and is in the public domain in the USA.     

A phased approach to enable hybrid simulation of complex structures

Hybrid simulation has been shown to be a cost-effective approach for assessing the seismic performance of structures. In hybrid simulation, critical parts of a structure are physically tested, while the remaining portions of the system are concurrently simulated computationally, typically using a finite element model. This combination is realized through a numerical time-integration scheme, which allows for investigation of full system-level responses of a structure in a cost-effective manner. However, conducting hybrid simulation of complex structures within large-scale testing facilities presents significant challenges. For example, the chosen modeling scheme may create numerical inaccuracies or even result in unstable simulations; the displacement and force capacity of the experimental system can be exceeded; and a hybrid test may be terminated due to poor communication between modules (e.g., loading controllers, data acquisition systems, simulation coordinator). These problems can cause the simulation to stop suddenly, and in some cases can even result in damage to the experimental specimens; the end result can be failure of the entire experiment. This study proposes a phased approach to hybrid simulation that can validate all of the hybrid simulation components and ensure the integrity large-scale hybrid simulation. In this approach, a series of hybrid simulations employing numerical components and small-scale experimental components are examined to establish this preparedness for the large-scale experiment. This validation program is incorporated into an existing, mature hybrid simulation framework, which is currently utilized in the Multi-Axial Full-Scale Sub-Structuring Testing and Simulation (MUST-SIM) facility of the George E. Brown Network for Earthquake Engineering Simulation (NEES) equipment site at the University of Illinois at Urbana-Champaign. A hybrid simulation of a four-span curved bridge is presented as an example, in which three piers are experimentally controlled in a total of 18 degrees of freedom (DOFs). This simulation illustrates the effectiveness of the phased approach presented in this paper.     

A phased approach to enable hybrid simulation of complex structures

Hybrid simulation has been shown to be a cost-effective approach for assessing the seismic performance of structures. In hybrid simulation,critical parts of a structure are physically tested,while the remaining portions of the system are concurrently simulated computationally,typically using a finite element model. This combination is realized through a numerical time-integration scheme,which allows for investigation of full system-level responses of a structure in a cost-effective manner. However,conducting hybrid simulation of complex structures within large-scale testing facilities presents significant challenges. For example,the chosen modeling scheme may create numerical inaccuracies or even result in unstable simulations; the displacement and force capacity of the experimental system can be exceeded; and a hybrid test may be terminated due to poor communication between modules(e.g.,loading controllers,data acquisition systems,simulation coordinator). These problems can cause the simulation to stop suddenly,and in some cases can even result in damage to the experimental specimens; the end result can be failure of the entire experiment. This study proposes a phased approach to hybrid simulation that can validate all of the hybrid simulation components and ensure the integrity largescale hybrid simulation. In this approach,a series of hybrid simulations employing numerical components and small-scale experimental components are examined to establish this preparedness for the large-scale experiment. This validation program is incorporated into an existing,mature hybrid simulation framework,which is currently utilized in the Multi-Axial Full-Scale Sub-Structuring Testing and Simulation(MUST-SIM) facility of the George E. Brown Network for Earthquake Engineering Simulation(NEES) equipment site at the University of Illinois at Urbana-Champaign. A hybrid simulation of a four-span curved bridge is presented as an example,in which three piers are experimentally controlled in a total of 18 degrees of freedom(DOFs). This simulation illustrates the effectiveness of the phased approach presented in this paper.     

Data-based modelling approach for variable density flow and solute transport simulation in a coastal aquifer

Data-based models, namely artificial neural network (ANN), support vector machine (SVM), genetic programming (GP) and extreme learning machine (ELM), were developed to approximate three-dimensional, density-dependent flow and transport processes in a coastal aquifer. A simulation model, SEAWAT, was used to generate data required for the training and testing of the data-based models. Statistical analysis of the simulation results obtained by the four models show that the data-based models could simulate the complex salt water intrusion process successfully. The selected models were also compared based on their computational ability, and the results show that the ELM is the fastest technique, taking just 0.5 s to simulate the dataset; however, the SVM is the most accurate, with a Nash-Sutcliffe efficiency (NSE) ≥ 0.95 and correlation coefficient R ≥ 0.92 for all the wells. The root mean square error (RMSE) for the SVM is also significantly less, ranging from 12.28 to 77.61 mg/L.     

城市震害三维模拟系统的实现方法

本文以数字减灾、数字城市概念为背景,以地震辅助决策、虚拟应急救援演练、地震科普教育为目的,给出了城市震害三维模拟系统的总体思路和实施计划。主要利用现有的数字图像处理技术、遥感技术、三维建模技术、可视化技术、数据库技术和虚拟现实技术等技术,结合新的群体和单体震害预测方法及G IS技术提出了城市震害三维模拟的总体设想,分析了城市三维震害模拟系统所需要的关键技术手段,指明了城市三维震害模拟的技术思路,并且完成了在地震影响场作用下,通过城市建筑不同震害的颜色表示,在破坏纹理库和破坏构件模型库的支撑下,建立三维破坏建筑模型库,以相似准则为依据,进一步以单体为例调入三维建筑破坏模型,实现了城市建筑三维破坏状态展示,为数字三维城市破坏的模拟提供了一种较好的思路。     

A Neumann expansion approach to flow through heterogeneous formations

A stochastic approach is used for the study of flow through highly heterogeneous aquifers. The mathematical model is represented by a random partial differential equation in which the permeability and the porosity are considered to be random functions of position, defined by the average value, constant standard deviation and autocorrelation function characterized by the integral scale. The Laplace transform of the solution of the random partial differential equation is first written as a solution of a stochastic integral equation. This integral equation is solved using a Neumann series expansion. Conditions of convergence of this series are investigated and compared with the convergence of the perturbation series. For mean square convergence, the Neumann expansion method may converge for a larger range of variability in permeability and porosity than the classic perturbation method. Formal expressions for the average and for the correlation moments of the pressure are obtained. The influence of the variability of the permeability and porosity on pressure is analyzed for radial flow. The solutions presented for the pressure at the well, as function of the permeability coefficient of variation, may be of practical interest for evaluating the efficiency of well stimulation operations, such as hydraulic fracturing or acidizing methods, aimed at increasing the permeability around the well.     

A new approach to numerical simulation of source development of earthquake

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A simulation approach to quantify the parameters and limitations of the radiocarbon wiggle-match dating technique

Worldwide, radiocarbon (¹⁴C) wiggle-match dating is increasingly used to produce high-resolution, ‘near-absolute’, chronologies in a range of different contexts, yet the exact properties and limitations of the technique are not well understood. Here we present the results of extensive and systematic simulations that allow the precision limits of wiggle-match dating to be quantified for different time periods. We have also been able to quantify the effect of modeling decisions on possible precision in terms of how many measurements to make, how far apart to space them, and which calibration curve to employ. While recent trends towards large numbers of annually spaced measurements can improve precision, the effect is generally small, except when the dated sequence falls on a plateau in the calibration curve. Finally, we demonstrate that wiggle-matching against an unsmoothed record of atmospheric ¹⁴C can provide better precision than wiggle-matching against the smoothed IntCal20 or SHCal20 curves. We argue, however, that until intra-hemispheric variation in ¹⁴C is better understood, the hemispheric averages provided by IntCal20 and SHCal20 will be the more appropriate datasets for most wiggle-match applications.     

A stochastic approach to nonlinear unconfined flow subject to multiple random fields

In this study, the KLME approach, a moment-equation approach based on the Karhunen–Loeve decomposition developed by Zhang and Lu (Comput Phys 194(2):773–794, 2004), is applied to unconfined flow with multiple random inputs. The log-transformed hydraulic conductivity F, the recharge R, the Dirichlet boundary condition H, and the Neumann boundary condition Q are assumed to be Gaussian random fields with known means and covariance functions. The F, R, H and Q are first decomposed into finite series in terms of Gaussian standard random variables by the Karhunen–Loeve expansion. The hydraulic head h is then represented by a perturbation expansion, and each term in the perturbation expansion is written as the products of unknown coefficients and Gaussian standard random variables obtained from the Karhunen–Loeve expansions. A series of deterministic partial differential equations are derived from the stochastic partial differential equations. The resulting equations for uncorrelated and perfectly correlated cases are developed. The equations can be solved sequentially from low to high order by the finite element method. We examine the accuracy of the KLME approach for the groundwater flow subject to uncorrelated or perfectly correlated random inputs and study the capability of the KLME method for predicting the head variance in the presence of various spatially variable parameters. It is shown that the proposed numerical model gives accurate results at a much smaller computational cost than the Monte Carlo simulation.     

Numerical simulation of an unsaturated flow equation

A numerical model for an unsaturated flow problem by using the finite element method is established in order to simulate liquid moisture flow In an unsaturated zone with homogeneous soil and deep subsurface water, and with different initial and boundary conditions. For infiltration or evaporation problems, a traditional method usually yields oscillatory non-physics profiles. However, nonoscillatory solutions are obtained and non-physics solutions for these problems are evaded by using the mass-lumped finite element method. Moreover, the kind of boundary condition is handled very well. Project supported by the National Key Project of Fundamental Research ”Climate Dynamics and Climate Prediction Theory“ and China Postdoctoral Science Foundation.     

A linearized approach to flow resistance uncertainty in a 2-D finite volume model of flood flow

A linearized approach to quantifying predictive uncertainty in a 2-D model of shallow water flow in response to uncertainty in friction parameterization is presented. The resulting uncertain finite volume (UFV) method is tested against Monte Carlo simulations for uncertain models over channel only, floodplain only and channel and floodplain meshes. The results show that the UFV model performs well in predicting mean and standard deviations of water depths, for problems with two independent Manning's n values, with standard deviations of up to 0.02 m^1/3 s⁻¹ with a mean value of 0.03 m^1/3 s⁻¹. For depth averaged velocities, mean values are well represented, but standard deviations are poorly predicted by UFV. UFV also performs well when modelling flow over an uneven fractal topography and for a distributed (11 degrees of freedom) parameterization. A computation time advantage of >50 when compared to the Monte Carlo method is observed.     

Practical finite analytic methods for simulation of advection-dominated solute transport

Abstract

The practical finite-analytic (PFA) method was applied to the solution of the one-dimensional advection–dispersion equation (ADE) for solute transport in porous media under advection-dominated (high Peclet number, Pe) conditions. Several PFA spatial-temporal computational molecules were developed for Cauchy and pulse loading boundary conditions. The PFA solutions were compared with solutions from the upwind method and quadratic upwind differencing (QUICK) scheme. For all boundary conditions the trapezoidal explicit PFA (EPFA) computational molecule gave the most accurate results at very high Pe number as long as the Courant number (Cr) was close to one. Stability analysis shows that the PFA molecules are always stable for high Pe number.     

Approximation approach to the SRM based on root decomposition in the simulation of spatially varying ground motions

The spectral representation method(SRM) is widely used to simulate spatially varying ground motions.This study focuses on the approximation approach to the SRM based on root decomposition,which can improve the efficiency of the simulation.The accuracy of the approximation approach may be affected by three factors: matrix for decomposition,distribution of frequency interpolation nodes and elements for interpolation.The influence of these factors on the accuracy of this approach is examined and the following conclusions are drawn.The SRM based on the root decomposition of the lagged coherency matrix exhibits greater accuracy than the SRM based on the root decomposition of the cross spectral matrix.The equal energy distribution of frequency interpolation nodes proposed in this study is more effective than the counter pith with an equal spacing.Elements for interpolation do not have much of an effect on the accuracy,so interpolation of the elements of the decomposed matrix is recommended because it is less complicated from a computational efficiency perspective.