共查询到20条相似文献，搜索用时 15 毫秒
1.
This study introduces the dispersive fluid flux of total fluid mass to the density-driven flow equation to improve thermohaline modeling of salt and heat transports in porous media. The dispersive fluid flux in the flow equation is derived to account for an additional fluid flux driven by the density gradient and mechanical dispersion. The coupled flow, salt transport and heat transport governing equations are numerically solved by a fully implicit finite difference method to investigate solution changes due to the dispersive fluid flux. The numerical solutions are verified by the Henry problem and the thermal Elder problem under a moderate density effect and by the brine Elder problem under a strong density effect. It is found that increment of the maximum ratio of the dispersive fluid flux to the advective fluid flux results in increasing dispersivity for the Henry problem and the brine Elder problem. The effects of the dispersive fluid flux on salt and heat transports under high density differences and high dispersivities are more noticeable than under low density differences and low dispersivities. Values of quantitative indicators such as the Nusselt number, mass flux, salt mass stored and maximum penetration depth in the brine Elder problem show noticeable changes by the dispersive fluid flux. In the thermohaline Elder problem, the dispersive fluid flux shows a considerable effect on the shape and the number of developed fingers and makes either an upwelling or a downwelling flow in the center of the domain. In conclusion, for the general case that involves strong density-driven flow and transport modeling in porous media, the dispersive fluid flux should be considered in the flow equation. 相似文献
2.
理论地震图方法在地震震源过程的研究中得到了广泛的应用。为了研究震源过程的细节,必须利用近场地震资料的高频信息,但是在应用Haskell矩阵法计算近场理论地震图时,格林函数的高频成分的数值不稳定性是计算宽频域理论地震图的一个基本困难。因此,目前仅有不超过10Hz的算例。本研究采用Haskell矩阵的一种新的分解组合形式,在数值计算时有效地避免了在计算过程中数值结果的溢出,实现了近场理论地震图的宽频域计算。同时,由于利用了矩阵运算中的解析关系,减少了运算的次数,从而提高了计算的速度。根据本算法建立的Fortran程序,在Univoc-1100计算机上进行了数值检验。结果表明,计算得到的格林函数至少在0-40Hz频率域范围内仍保持良好的数值稳定性。本文给出的这种Haskell矩阵分解组合形式的矩阵元素简单,且具有一定的对称性。对于这种分解所包含的物理意义,将有待进一步深入研究。 相似文献
3.
Guangqiu Jin Yongfei Hao Jie Wei Yihang Yang Xiaoxiao Shen Hongwu Tang Ling Li 《水文研究》2021,35(1):e13949
In this study, both laboratory experiments and numerical simulations were conducted to investigate the effect of density-driven flow on the transport of high-concentration pollutants in the hyporheic zone. The results show that the density gradient can change the flow of pore water and the strong density-driven flow can lead to an unstable flow, which increases the effect of preferential flow and thus causes the appearance of solute fingers in the hyporheic zone. Notably, these solute fingers become more obvious with the increase of depth. The appearance of solute fingers depends on the relative strength of the pumping exchange and density gradient, which are represented by the dimensionless number M* and N* respectively. Finger flows appear near the interface when M* is less than 0.5 N*. This study may contribute to better understanding the transport and destination of solutes and thus may provide some insights into the assessment on pollution incidents. 相似文献
4.
A new benchmark semi-analytical solution is proposed for the verification of density-driven flow codes. The problem deals with a synthetic square porous cavity subject to different salt concentrations at its vertical walls. A steady state semi-analytical solution is investigated using the Fourier–Galerkin method. Contrarily to the standard Henry problem, the cavity benchmark allows high truncation orders in the Fourier series and provides semi-analytical solutions for very small diffusion cases. The problem is also investigated numerically to validate the semi-analytical solution. The obtained results represent a set of new test case high quality data that can be effectively used for benchmarking density-driven flow codes. 相似文献
5.
A multiscale adjoint (MSADJ) method is developed to compute high-resolution sensitivity coefficients for subsurface flow in large-scale heterogeneous geologic formations. In this method, the original fine-scale problem is partitioned into a set of coupled subgrid problems, such that the global adjoint problem can be efficiently solved on a coarse grid. Then, the coarse-scale sensitivities are interpolated to the local fine grid by reconstructing the local variability of the model parameters with the aid of solving embedded adjoint subproblems. The approach employs the multiscale finite-volume (MSFV) formulation to accurately and efficiently solve the highly detailed flow problem. The MSFV method couples a global coarse-scale solution with local fine-scale reconstruction operators, hence yielding model responses that are quite accurate at both scales. The MSADJ method is equally efficient in computing the gradient of the objective function with respect to model parameters. Several examples demonstrate that the approach is accurate and computationally efficient. The accuracy of our multiscale method for inverse problems is twofold: the sensitivity coefficients computed by this approach are more accurate than the traditional finite-difference-based numerical method for computing derivatives, and the calibrated models after history matching honor the available dynamic data on the fine scale. In other words, the multiscale based adjoint scheme can be used to history match fine-scale models quite effectively. 相似文献
6.
K. Ponnambalam A. Vannelli T. E. Unny 《Stochastic Environmental Research and Risk Assessment (SERRA)》1989,3(1):17-29
Optimization of multi-reservoir systems operations is typically a very large scale optimization problem. The following are the three types of optimization problems solved using linear programming (LP): (i) deterministic optimization for multiple periods involving fine stage intervals, for example, from an hour to a week (ii) implicit stochastic optimization using multiple years of inflow data, and (iii) explicit stochastic optimization using probability distributions of inflow data. Until recently, the revised simplex method has been the most efficient solution method available for solving large scale LP problems. In this paper, we show that an implementation of the Karmarkar's interior-point LP algorithm with a newly developed stopping criterion solves optimization problems of large multi-reservoir operations more efficiently than the simplex method. For example, using a Micro VAX II minicomputer, a 40 year, monthly stage, two-reservoir system optimization problem is solved 7.8 times faster than the advanced simplex code in MINOS 5.0. The advantage of this method is expected to be greater as the size of the problem grows from two reservoirs to multiples of reservoirs. This paper presents the details of the implementation and testing and in addition, some other features of the Karmarkar's algorithm which makes it a valuable optimization tool are illuminated. 相似文献
7.
A test case has been developed for three-dimensional simulations of variable-density flow and solute transport in discretely-fractured porous media. The simulation domain is a low-permeability porous matrix cube containing a single non-planar fracture. The initial solute concentration is zero everywhere. A constant solute concentration is assigned to the top of the domain, which increases near-top fluid density and induces downward density-driven flow. The test case is therefore comparable to downwelling of a dense brine below a saline disposal basin or a waste repository. Numerous fingers and distinct convection cells develop early in the fracture but the fingers later coalesce and convection becomes less apparent. To help test other variable-density flow and transport models, results of the test case are presented both qualitatively (concentration contours and velocity fields) and quantitatively (penetration depth, mass flux, total mass stored, maximum fracture and matrix velocity). 相似文献
8.
Optimization of multi-reservoir systems operations is typically a very large scale optimization problem. The following are the three types of optimization problems solved using linear programming (LP): (i) deterministic optimization for multiple periods involving fine stage intervals, for example, from an hour to a week (ii) implicit stochastic optimization using multiple years of inflow data, and (iii) explicit stochastic optimization using probability distributions of inflow data. Until recently, the revised simplex method has been the most efficient solution method available for solving large scale LP problems. In this paper, we show that an implementation of the Karmarkar's interior-point LP algorithm with a newly developed stopping criterion solves optimization problems of large multi-reservoir operations more efficiently than the simplex method. For example, using a Micro VAX II minicomputer, a 40 year, monthly stage, two-reservoir system optimization problem is solved 7.8 times faster than the advanced simplex code in MINOS 5.0. The advantage of this method is expected to be greater as the size of the problem grows from two reservoirs to multiples of reservoirs. This paper presents the details of the implementation and testing and in addition, some other features of the Karmarkar's algorithm which makes it a valuable optimization tool are illuminated. 相似文献
9.
Direct atmospheric greenhouse gas emissions can be greatly reduced by CO2 sequestration in deep saline aquifers. One of the most secure and important mechanisms of CO2 trapping over large time scales is solubility trapping. In addition, the CO2 dissolution rate is greatly enhanced if density-driven convective mixing occurs. We present a systematic analysis of the prerequisites for density-driven instability and convective mixing over the broad temperature, pressure, salinity and permeability conditions that are found in geological CO2 storage. The onset of instability (Rayleigh–Darcy number, Ra), the onset time of instability and the steady convective flux are comprehensively calculated using a newly developed analysis tool that accounts for the thermodynamic and salinity dependence on solutally and thermally induced density change, viscosity, molecular and thermal diffusivity. Additionally, the relative influences of field characteristics are analysed through local and global sensitivity analyses. The results help to elucidate the trends of the Ra, onset time of instability and steady convective flux under field conditions. The impacts of storage depth and basin type (geothermal gradient) are also explored and the conditions that favour or hinder enhanced solubility trapping are identified. Contrary to previous studies, we conclude that the geothermal gradient has a non-negligible effect on density-driven instability and convective mixing when considering both direct and indirect thermal effects because cold basin conditions, for instance, render higher Ra compared to warm basin conditions. We also show that the largest Ra is obtained for conditions that correspond to relatively shallow depths, measuring approximately 800 m, indicating that CO2 storage at such depths favours the onset of density-driven instability and reduces onset times. However, shallow depths do not necessarily provide conditions that generate the largest steady convective fluxes; the salinity determines the storage depth at which the largest steady convective fluxes occur. Furthermore, we present a straight-forward and efficient procedure to estimate site-specific solutal Ra that accounts for thermodynamic and salinity dependence. 相似文献
10.
We compare two geophysical survey measurements of the same type made at different times in order to characterize the change in the geological medium during the elapsed time. The aim of this study is to develop a strategy using a full non-linear inversion algorithm as the interpretation tool. In this way, not only the location and the form of the changes are recovered, but also the changes in the material parameters of the geological medium can be estimated. In order to solve this fully non-linear problem, the so-called ‘multiplicative regularized contrast source inversion’ (MR-CSI) method is employed. The unique property of this iterative method is that it does not solve the forward problem at each iterative step. This makes it possible to use the non-linear inversion algorithm for large-scale computation problems. The numerical results show that by taking into account the non-linear nature of the problem, interpretation of the time-lapse data can be significantly improved, compared with that obtained using linear inversion. 相似文献
11.
Widely used numerical models of solute transport processes in subsurface aquifers are limited to nonlocally refined rectangular, or logically rectangular, structured grids. This presents an unsuitable option to efficient numerical simulations maintaining an acceptable level of accuracy. Optimal selection of locally refined cells for efficient solute transport models is challenging to the current generation of numerical models. We present a novel and relatively simple to implement algorithm addressing these shortcomings. This method operates in four steps involving travel times simulations, a grid coarsening stage followed by a selective local grid refinement based on a cell-wise indicator, and a final postprocessing step. The refinement index is the sum of weighted logarithmic distributions of scaled forward and backward travel times. We calculate representative flow and transport properties at the two scales of the composite grid with a flow-based upscaling technique. We present two test problems to demonstrate the performances of this new gridding algorithm. We obtain the most important speedups for composite grids generated with the highest indicator thresholds. When hydrodynamic dispersion effects increase, we obtain less important speedups. An important outcome of this work is that grid design depends on nature and strength of the underlying flow and solute transport processes. Therefore, we suggest developing solute transport workflows integrating this grid generation algorithm as an integral component to build comprehensive and efficient groundwater models. 相似文献
12.
Comparing the performances of four stochastic optimisation methods using analytic objective functions, 1D elastic full‐waveform inversion,and residual static computation 
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下载免费PDF全文 Angelo Sajeva Mattia Aleardi Bruno Galuzzi Eusebio Stucchi Emmanuel Spadavecchia Alfredo Mazzotti 《Geophysical Prospecting》2017,65(Z1):322-346
We compare the performances of four stochastic optimisation methods using four analytic objective functions and two highly non‐linear geophysical optimisation problems: one‐dimensional elastic full‐waveform inversion and residual static computation. The four methods we consider, namely, adaptive simulated annealing, genetic algorithm, neighbourhood algorithm, and particle swarm optimisation, are frequently employed for solving geophysical inverse problems. Because geophysical optimisations typically involve many unknown model parameters, we are particularly interested in comparing the performances of these stochastic methods as the number of unknown parameters increases. The four analytic functions we choose simulate common types of objective functions encountered in solving geophysical optimisations: a convex function, two multi‐minima functions that differ in the distribution of minima, and a nearly flat function. Similar to the analytic tests, the two seismic optimisation problems we analyse are characterised by very different objective functions. The first problem is a one‐dimensional elastic full‐waveform inversion, which is strongly ill‐conditioned and exhibits a nearly flat objective function, with a valley of minima extended along the density direction. The second problem is the residual static computation, which is characterised by a multi‐minima objective function produced by the so‐called cycle‐skipping phenomenon. According to the tests on the analytic functions and on the seismic data, genetic algorithm generally displays the best scaling with the number of parameters. It encounters problems only in the case of irregular distribution of minima, that is, when the global minimum is at the border of the search space and a number of important local minima are distant from the global minimum. The adaptive simulated annealing method is often the best‐performing method for low‐dimensional model spaces, but its performance worsens as the number of unknowns increases. The particle swarm optimisation is effective in finding the global minimum in the case of low‐dimensional model spaces with few local minima or in the case of a narrow flat valley. Finally, the neighbourhood algorithm method is competitive with the other methods only for low‐dimensional model spaces; its performance sensibly worsens in the case of multi‐minima objective functions. 相似文献
13.
This work concludes the investigations into the stability of haline flows in saturated porous media. In the first part [33] a stability criterion for density-driven flow in a saturated homogeneous medium was derived excluding dispersion. In the second part [34], the effects of dispersion were included. The latter criterion made reasonable predictions of the stability regimes (indicated by the number of fingers present) as a function of density and dispersivity variations. We found out that destabilising variables caused an increase in the number of fingers and vice versa. The investigation is extended here for the effects of the medium heterogeneity. The cell problem derived via homogenization theory [20] is solved and its solution used to evaluate the elements of the macrodispersion tensor as functions of time for flow aligned parallel to gravity. The longitudinal coefficient exhibits asymptotic behaviour for favourable and moderately unfavourable density contrasts while it grows indefinitely for higher density contrasts. The range of densities stabilised by medium heterogeneities can thus be estimated from the behaviour of the coefficient. The d3f software program is used for the numerical simulations. The code uses the cell-centred finite volume and the implicit Euler techniques for the spatial and temporal discretisations respectively. 相似文献
14.
本文将面向目标的自适应算法应用于三维大地电磁数值模拟.使用基于非结构网格的矢量有限单元法对起伏地表大地电磁正演模拟问题进行求解.使用利用垂向电流密度在物性界面上的连续性对后验误差进行估算的算法指导网格优化.由于全局自适应算法针对观测点优化网格的能力较差,本文通过求解正演问题的对偶问题计算后验误差的加权系数,并对相关加权系数进行改进,从而实现了面向目标的自适应算法.与传统基于结构化网格的电磁正演算法相比,采用非结构网格能够更好地拟合起伏地表和地下不规则异常体.由于使用了面向目标的自适应算法,本文能够使用更少的网格达到较高的计算精度.通过对比本文模拟结果与半空间响应和全局自适应算法计算结果,并通过对比使用改进前和改进后加权系数得到的网格剖分结果验证了本文算法的有效性. 相似文献
15.
一种激发极化法2.5维正演的自适应有限元方法（英文） 总被引：2，自引：2，他引：0
传统的基于结构化网格有限元法采用的单元比较规则如矩形等,且网格剖分和加密要靠手动实现,所以传统的基于结构化网格有限元法不能准确和灵活地模拟复杂介质。本文采用易于模拟复杂介质模型的非结构化三角形网格进行剖分,且利用对偶加权后验误差估计指导网格自动细化过程,然后在电位模拟的基础上计算雅可比偏导矩阵,并依据Seigel（1959）理论实现激发极化法2.5维自适应有限元正演模拟算法。通过对垂直接触面模型进行正演分析,接收点附近网格得到了明显加密,电位数值解平均相对误差收敛到0.4%,视极化率平均相对误差收敛到1.2%,表明经自适应网格细化后,该算法数值解最终能收敛到精确解附近。最后对两个较复杂模型进行了正演计算与分析,进一步验证了该算法的准确性和灵活性。 相似文献
16.
《Advances in water resources》1998,21(1):27-46
This work examines variable density flow and corresponding solute transport in groundwater systems. Fluid dynamics of salty solutions with significant density variations are of increasing interest in many problems of subsurface hydrology. The mathematical model comprises a set of non-linear, coupled, partial differential equations to be solved for pressure/hydraulic head and mass fraction/concentration of the solute component. The governing equations and underlying assumptions are developed and discussed. The equation of solute mass conservation is formulated in terms of mass fraction and mass concentration. Different levels of the approximation of density variations in the mass balance equations are used for convection problems (e.g. the Boussinesq approximation and its extension, fully density approximation). The impact of these simplifications is studied by use of numerical modelling.Numerical models for nonlinear problems, such as density-driven convection, must be carefully verified in a particular series of tests. Standard benchmarks for proving variable density flow models are the Henry, Elder, and salt dome (HYDROCOIN level 1 case 5) problems. We studied these benchmarks using two finite element simulators - ROCKFLOW, which was developed at the Institute of Fluid Mechanics and Computer Applications in Civil Engineering and FEFLOW, which was developed at the Institute for Water Resources Planning and Systems Research Ltd. Although both simulators are based on the Galerkin finite element method, they differ in many approximation details such as temporal discretization (Crank-Nicolson vs predictor-corrector schemes), spatial discretization (triangular and quadrilateral elements), finite element basis functions (linear, bilinear, biquadratic), iteration schemes (Newton, Picard) and solvers (direct, iterative). The numerical analysis illustrates discretization effects and defects arising from the different levels of the density of approximation. We contribute new results for the salt dome problem, for which inconsistent findings exist in literature. Applications of the verified numerical models to more complex problems, such as thermohaline and three-dimensional convection systems, will be presented in the second part of this paper. 相似文献
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18.
Density-dependent flow and transport solutions for coastal saltwater intrusion investigations, analyses of fluid injection into deep brines, and studies of convective fingering and instabilities of denser fluids moving through less dense fluids typically formulate the groundwater flow equation in terms of pressure or equivalent freshwater head. A formulation of the flow equation in terms of hydraulic head is presented here as an alternative. The hydraulic-head formulation can facilitate adaptation of existing constant-density groundwater flow codes to include density-driven flow by avoiding the need to convert between freshwater head and hydraulic head within the code and by incorporating density-dependent terms as a compartmentalized “correction” to constant-density calculations already performed by the code. The hydraulic-head formulation also accommodates complexities such as unconfined groundwater flow and Newton-Raphson solution schemes more readily than the freshwater-head formulation. Simulation results are presented for four example problems solved using an implementation of the hydraulic-head formulation in MODFLOW. 相似文献
19.
《Advances in water resources》2004,27(4):323-334
A forward particle tracking Eulerian Lagrangian localized adjoint method (ELLAM) is applied to the multicomponent reactive transport problem using a split operator approach. Two split operator algorithms are compared, the Strang algorithm and the sequential non-iterative algorithm (SNIA). The reaction equations are integrated using a coupled predictor corrector algorithm with adaptive time stepping. Reaction time steps are adjusted at the inflow boundary to reflect the actual time of transport inside the solution domain.Results show that split operator ELLAM formulations are competitive with direct or fully coupled ELLAM solutions for reactive transport problems. The SNIA algorithm is more accurate than the Strang splitting algorithm when large time steps are used. The reaction algorithm employed dominates computational effort in runs with large time step sizes. To illustrate the use of the method in practical problems, the model is fitted to aerobic aniline degradation data from laboratory scale column experiments. Model inversion is achieved using non-linear regression with a shuffled complex evolution optimization algorithm and parameter uncertainty is assessed using a Bayesian uncertainty analysis procedure. 相似文献
20.
This study presents two-dimensional direct numerical simulations for sediment-laden current with higher density propagating forward through a lighter ambient water.The incompressible NavierStokes equations including the buoyancy force for the density difference between the light and heavy fluids are solved by a finite difference scheme based on a structured mesh.The concentration transport equations are used to explore such rich transport phenomena as gravity and turbidity currents.Within the framework of an Upwinding Combined Compact finite Difference(UCCD)scheme,rigorous determination of weighting coefficients underlies the modified equation analysis and the minimization of the numerical modified wavenumber.This sixth-order UCCD scheme is implemented in a four-point grid stencil to approximate advection and diffusion terms in the concentration transport equations and the first-order derivative terms in the Navier-Stokes equations,which can greatly enhance convective stability and increase dispersive accuracy at the same time.The initial discontinuous concentration field is smoothed by solving a newly proposed Heaviside function to prevent numerical instabilities and unreasonable concentration values.A two-step projection method is then applied to obtain the velocity field.The numerical algorithm shows a satisfying ability to capture the generation,development,and dissipation of the Kelvin-Helmholz instabilities and turbulent billows at the interface between the current and the ambient fluid.The simulation results also are compared with the data in published literatures and good agreements are found to prove that the present numerical model can well reproduce the propagation,particle deposition,and mixing processes of lock-exchange gravity and turbidity currents. 相似文献