Stochastic analysis of a field-scale unsaturated transport experiment

Modelling of field-scale transport of chemicals is of deep interest to public as well as private sectors, and it represents an area of active theoretical research in many environmentally-based disciplines. However, the experimental data needed to validate field-scale transport models are very limited due to the numerous logistic difficulties that one faces out.     

Numerical analysis of bacterial transport in saturated porous media

A mathematical model to describe bacterial transport in saturated porous media is presented. Reversible/irreversible attachment and growth/decay terms were incorporated into the transport model. Additionally, the changes of porosity and permeability due to bacterial deposition and/or growth were accounted for in the model. The predictive model was used to fit the column experimental data from the literature, and the fitting result showed a good match with the data. Based on the parameter values determined from the literature experimental data, numerical experiments were performed to examine bacterial sorption and/or growth during bacterial transport through saturated porous media. In addition, sensitivity analysis was performed to investigate the impact of key model parameters for bacterial transport on the permeability and porosity of porous media. The model results show that the permeability and porosity of porous media could be altered due to bacterial deposition and growth on the solid matrix. However, variation of permeability due to bacterial growth was trivial compared with natural permeability variation. Copyright © 2005 John Wiley & Sons, Ltd.     

Correlation between bacterial attachment rate coefficients and hydraulic conductivity and its effect on field-scale bacterial transport

It has been widely observed in field experiments that the apparent rate of bacterial attachment, particularly as parameterized by the collision efficiency in filtration-based models, decreases with transport distance (i.e., exhibits scale-dependency). This effect has previously been attributed to microbial heterogeneity; that is, variability in cell–surface properties within a single monoclonal population. We demonstrate that this effect could also be interpreted as a field-scale manifestation of local-scale correlation between physical heterogeneity (hydraulic conductivity variability) and reaction heterogeneity (attachment rate coefficient variability). A field-scale model of bacterial transport developed for the South Oyster field research site located near Oyster, Virginia, and observations from field experiments performed at that site, are used as the basis for this study. Three-dimensional Monte Carlo simulations of bacterial transport were performed under four alternative scenarios: (1) homogeneous hydraulic conductivity (K) and attachment rate coefficient (K_f); (2) heterogeneous K, homogeneous K_f; (3) heterogeneous K and K_f with local correlation based on empirical and theoretical relationships; and (4) heterogeneous K and K_f without local correlation. The results of the 3D simulations were analyzed using 1D model approximations following conventional methods of field data analysis. An apparent decrease with transport distance of effective collision efficiency was observed only in the case where the local properties were both heterogeneous and correlated. This effect was observed despite the fact that the local collision efficiency was specified as a constant in the 3D model, and can therefore be interpreted as a scale effect associated with the local correlated heterogeneity as manifested at the field scale.     

Geophysical monitoring of a field-scale biostimulation pilot project

The USGS conducted a geophysical investigation in support of a U.S. Naval Facilities Engineering Command, Southern Division field-scale biostimulation pilot project at Anoka County Riverfront Park (ACP), down-gradient of the Naval Industrial Reserve Ordnance Plant, Fridley, Minnesota. The goal of the pilot project is to evaluate subsurface injection of vegetable oil emulsion (VOE) to stimulate microbial degradation of chlorinated hydrocarbons. To monitor the emplacement and movement of the VOE and changes in water chemistry resulting from VOE dissolution and/or enhanced biological activity, the USGS acquired cross-hole radar zero-offset profiles, travel-time tomograms, and borehole geophysical logs during five site visits over 1.5 years. Analysis of pre- and postinjection data sets using petrophysical models developed to estimate VOE saturation and changes in total dissolved solids provides insights into the spatial and temporal distribution of VOE and ground water with altered chemistry. Radar slowness-difference tomograms and zero-offset slowness profiles indicate that the VOE remained close to the injection wells, whereas radar attenuation profiles and electromagnetic induction logs indicate that bulk electrical conductivity increased down-gradient of the injection zone, diagnostic of changing water chemistry. Geophysical logs indicate that some screened intervals were located above or below zones of elevated dissolved solids; hence, the geophysical data provide a broader context for interpretation of water samples and evaluation of the biostimulation effort. Our results include (1) demonstration of field and data analysis methods for geophysical monitoring of VOE biostimulation and (2) site-specific insights into the spatial and temporal distributions of VOE at the ACP.     

Numerical mass balance for soil-moisture transport problems

The Galerkin finite element method coupled with the Crank-Nicolson time advance procedure is often used as a numerical analog for unsaturated soil-moisture transport problems. The Crank-Nicolson procedure leads to numerical mass balance problems which results in instability. A new temporal and spatial integration procedure is proposed that exactly satisfies mass balance for the approximating function used. This is accomplished by fitting polynomials continuously throughout the time and space domain and integrating the governing differential equations. To reduce computational effort, the resulting higher order polynomials are reduced to quadratic and linear piece-wise continuous polynomial approximation functions analogous to the finite element approach. Results indicate a substantial improvement in accuracy over the combined Galerkin and Crank-Nicolson methods when comparing to simplified problems where analytical solutions are available.     

Upscaling of field-scale soil moisture measurements using distributed land surface modeling

Accurate coarse-scale soil moisture information is required for robust validation of current- and next-generation soil moisture products derived from spaceborne radiometers. Due to large amounts of land surface and rainfall heterogeneity, such information is difficult to obtain from existing ground-based networks of soil moisture sensors. Using ground-based field data collected during the Soil Moisture Experiment in 2002 (SMEX02), the potential for using distributed modeling predictions of the land surface as an upscaling tool for field-scale soil moisture observations is examined. Results demonstrate that distributed models are capable of accurately capturing a significant level of field-scale soil moisture heterogeneity observed during SMEX02. A simple soil moisture upscaling strategy based on the merger of ground-based observations with modeling predictions is developed and shown to be more robust during SMEX02 than upscaling approaches that utilize either field-scale ground observations or model predictions in isolation.     

A comparison of two stochastic inverse methods in a field-scale application

Inverse modeling is a useful tool in ground water flow modeling studies. The most frequent difficulties encountered when using this technique are the lack of conditioning information (e.g., heads and transmissivities), the uncertainty in available data, and the nonuniqueness of the solution. These problems can be addressed and quantified through a stochastic Monte Carlo approach. The aim of this work was to compare the applicability of two stochastic inverse modeling approaches in a field-scale application. The multi-scaling (MS) approach uses a downscaling parameterization procedure that is not based on geostatistics. The pilot point (PP) approach uses geostatistical random fields as initial transmissivity values and an experimental variogram to condition the calibration. The studied area (375 km2) is part of a regional aquifer, northwest of Montreal in the St. Lawrence lowlands (southern Québec). It is located in limestone, dolomite, and sandstone formations, and is mostly a fractured porous medium. The MS approach generated small errors on heads, but the calibrated transmissivity fields did not reproduce the variogram of observed transmissivities. The PP approach generated larger errors on heads but better reproduced the spatial structure of observed transmissivities. The PP approach was also less sensitive to uncertainty in head measurements. If reliable heads are available but no transmissivities are measured, the MS approach provides useful results. If reliable transmissivities with a well inferred spatial structure are available, then the PP approach is a better alternative. This approach however must be used with caution if measured transmissivities are not reliable.     

土星磁层等离子体径向输运的数值模拟

本文建立了一个包含离心力效应的自洽稳态土星磁层模型,并且用等离子体细丝模型对土星磁层等离子体径向输运进行了数值模拟.模拟结果表明,Dione（土卫四）附近的等离子体可能因为发生离心交换不稳定性（Centrifugal Interchange Instability）而被输运到离土星更远的地方.这种输运现象的发生是由离心力主导的,等离子体的黏滞效应和能量转移对输运过程的影响非常小（几乎可以忽略不计）,但土星电离层电导率对输运过程有重要影响,电导率越低,径向输运过程越快,反之,高电导率在一定程度上会阻碍输运的进行.在土星电离层电导率σ=2 S时,Dione（距离土星6.3R_S, R_S为土星半径）附近的等离子体在5.52个小时中被输运到距离土星10R_S的地方.本文的模拟结果还表明,密度受到扰动的等离子体是不稳定的,如果洛仑兹力和等离子体热压强梯度不能与离心力平衡,径向输运就会发生.密度大的等离子体在向外输运过程中会绝热膨胀而温度降低,密度小的等离子体则在注入磁层过程中因为绝热压缩而温度升高.     

Numerical modelling of the suspended sediment transport in Torres Strait

One-dimensional vertical and three-dimensional fine-resolution numerical models of sediment transport have been developed and applied to the Torres Strait region of northern Australia. The one-dimensional model, driven by measured waves and currents, was calibrated against measured suspended sediment concentrations using a sequential data assimilation algorithm. The algorithm produced a good match between model and data, but this was achieved only by allowing some temporal variability in parameter values, suggesting that there were underlying uncertainties in the model structure and forcing data. Implications of the assimilation results to the accuracy of the numerical modelling are discussed and the need for observational programmes having an extensive spatial and temporal coverage is highlighted. The three-dimensional sediment model, driven by modelled waves and currents, simulates sediment transport over the shelf during the monsoon and trade-wind seasons covering 1997–2000. The model predicts strong seasonal variability of the sediment transport on the shelf attributed to seasonally varying hydrodynamics, and illustrates significant inter-annual variability of the sediment fluxes driven by extreme events. The developed model provides a platform for testing scientific hypothesis. With additional calibration, including uncertainty analysis, it can also be used in a management context.     

Numerical simulations of transport of non-ergodic solute plumes in heterogeneous aquifers

Transport of non-ergodic solute plumes by steady-state groundwater flow with a uniform mean velocity, μ, were simulated with Monte Carlo approach in a two-dimensional heterogeneous and statistically isotropic aquifer whose transmissivity, T, is log-normally distributed with an exponential covariance. The ensemble averages of the second spatial moments of the plume about its center of mass, <S _{i i} (t)>, and the plume centroid covariance, R _{i i} (t) (i=1,2), were simulated for the variance of Y=log T, σ _Y ²=0.1, 0.5 and 1.0 and line sources normal or parallel to μ of three dimensionless lengths, 1, 5, and 10. For σ _Y ²=0.1, all simulated <S _{i i} (t)>−S _{i i} (0) and R _{i i} (t) agree well with the first-order theoretical values, where S _{i i} (0) are the initial values of S _{i i} (t). For σ _Y ²=0.5 and 1.0 and the line sources normal to μ, the simulated longitudinal moments, <S ₁₁(t)>−S ₁₁(0) and R ₁₁(t), agree well with the first-order theoretical results but the simulated transverse moments <S ₂₂(t)>−S ₂₂(0) and R ₂₂(t) are significantly larger than the first-order values. For the same two larger values of σ _Y ² but the line sources parallel to μ, the simulated <S ₁₁(t)>−S ₁₁(0) are larger than but the simulated R ₁₁ are smaller than the first-order values, and both simulated <S ₂₂(t)>−S ₂₂(0) and R ₂₂(t) stay larger than the first-order values. For a fixed value of σ _Y ², the summations of <S _{i i} (t)>−S _{i i} (0) and R _{i i} , i.e., X _{i i} (i=1,2), remain almost the same no matter what kind of source simulated. The simulated X ₁₁ are in good agreement with the first-order theory but the simulated X ₂₂ are significantly larger than the first-order values. The simulated X ₂₂, however, are in excellent agreement with a previous modeling result and both of them are very close to the values derived using Corrsin's conjecture. It is found that the transverse moments may be significantly underestimated if less accurate hydraulic head solutions are used and that the decreasing of <S ₂₂(t)>−S ₂₂(0) with time or a negative effective dispersivity, defined as , may happen in the case of a line source parallel to μ where σ _Y ² is small.     

Numerical simulations of transport of non-ergodic solute plumes in heterogeneous aquifers

Transport of non-ergodic solute plumes by steady-state groundwater flow with a uniform mean velocity, μ, were simulated with Monte Carlo approach in a two-dimensional heterogeneous and statistically isotropic aquifer whose transmissivity, T, is log-normally distributed with an exponential covariance. The ensemble averages of the second spatial moments of the plume about its center of mass, <S _{i i} (t)>, and the plume centroid covariance, R _{i i} (t) (i=1,2), were simulated for the variance of Y=log T, σ _Y ²=0.1, 0.5 and 1.0 and line sources normal or parallel to μ of three dimensionless lengths, 1, 5, and 10. For σ _Y ²=0.1, all simulated <S _{i i} (t)>−S _{i i} (0) and R _{i i} (t) agree well with the first-order theoretical values, where S _{i i} (0) are the initial values of S _{i i} (t). For σ _Y ²=0.5 and 1.0 and the line sources normal to μ, the simulated longitudinal moments, <S ₁₁(t)>−S ₁₁(0) and R ₁₁(t), agree well with the first-order theoretical results but the simulated transverse moments <S ₂₂(t)>−S ₂₂(0) and R ₂₂(t) are significantly larger than the first-order values. For the same two larger values of σ _Y ² but the line sources parallel to μ, the simulated <S ₁₁(t)>−S ₁₁(0) are larger than but the simulated R ₁₁ are smaller than the first-order values, and both simulated <S ₂₂(t)>−S ₂₂(0) and R ₂₂(t) stay larger than the first-order values. For a fixed value of σ _Y ², the summations of <S _{i i} (t)>−S _{i i} (0) and R _{i i} , i.e., X _{i i} (i=1,2), remain almost the same no matter what kind of source simulated. The simulated X ₁₁ are in good agreement with the first-order theory but the simulated X ₂₂ are significantly larger than the first-order values. The simulated X ₂₂, however, are in excellent agreement with a previous modeling result and both of them are very close to the values derived using Corrsin's conjecture. It is found that the transverse moments may be significantly underestimated if less accurate hydraulic head solutions are used and that the decreasing of <S ₂₂(t)>−S ₂₂(0) with time or a negative effective dispersivity, defined as , may happen in the case of a line source parallel to μ where σ _Y ² is small.     

Numerical simulations of non-ergodic solute transport in three-dimensional heterogeneous porous media

Numerical simulations of non-ergodic transport of a non-reactive solute plume by steady-state groundwater flow under a uniform mean velocity, , were conducted in a three-dimensional heterogeneous and statistically isotropic aquifer. The hydraulic conductivity, K(x), is modeled as a random field which is assumed to be log-normally distributed with an exponential covariance. Significant efforts are made to reduce the simulation uncertainties. Ensemble averages of the second spatial moments of the plume and the plume centroid variances were simulated with 1600 Monte Carlo (MC) runs for three variances of log K, _Y²=0.09, 0.23, and 0.46, and a square source normal to of three dimensionless lengths. It is showed that 1600 MC runs are needed to obtain stabilized results in mildly heterogeneous aquifers of _Y²0.5 and that large uncertainty may exist in the simulated results if less MC runs are used, especially for the transverse second spatial moments and the plume centroid variance in transverse directions. The simulated longitudinal second spatial moment and the plume centroid variance in longitudinal direction fit well to the first-order theoretical results while the simulated transverse moments are generally larger than the first-order values. The ergodic condition for the second spatial moments is far from reaching in all cases simulated and transport in transverse directions may reach ergodic condition much slower than that in longitudinal direction.     

Numerical methods for reactive transport on rectangular and streamline-oriented grids

Coupling advection-dominated transport to reactive processes leads to additional requirements and limitations for numerical simulation beyond those for non-reactive transport. Particularly, both monotonicity avoiding the occurence of negative concentrations, and high-order accuracy suppressing artificial diffusion, are necessary to study accurately the reactive interactions of compounds transported in groundwater. These requirements are met by non-linear Eulerian methods. Two cell-centered Finite Volume schemes are presented for the simulation of advection-dominated reactive transport. The first scheme is based on rectangular grids, whereas the second scheme requires streamline-oriented grids the generation of which is explained in an accompanying paper. Although excellent results for conservative transport are obtained by the scheme for rectangular grids, some artificial transverse mixing occurs in the case of multi-component transport. This may lead to erroneous reaction rates if the compounds interact. The transport scheme for streamline-oriented grids, on the other hand, avoids artificial transverse mixing. A quantitative comparison is given by two test cases. A conservative tracer simulation for a five-spot configuration in a heterogeneous aquifer shows a high coincidence of the breakthrough curves obtained for the two methods, whereas a test case of two reacting compounds shows significant differences. In this test case, a rate of convergence with respect to the overall reaction rates lower than first-order is calculated for the rectangular grid.     

爆破地震动效应的数值模拟分析

爆破设计中,场地条件复杂时经验公式的应用受到一定限制。本文采用波动有限元分析方法,研究复杂场地条件下工程爆破时场地的地震动效应,研究爆破地震动特征及衰减规律。根据某重点工程场地岩土参数的原位测试和试验结果,用自行研制的软件包进行场地爆破地震动效应的数值模拟分析,为工程爆破设计及施工前建筑物、仪器设备的加固提供了依据。施工试爆实测结果与本文数值模拟分析给出的结果一致,说明本文方法是可行的,对其它工程也有借鉴作用。     

Salt transport on islands in the Okavango Delta: Numerical investigations

This study uses a numerical model to investigate the groundwater flow and salt transport mechanisms below islands in the Okavango Delta. Continuous evapotranspiration on the islands results in accumulation of solutes and the formation of a saline boundary layer, which may eventually become unstable. A novel Lagrangian method is employed in this study and compared to other numerical methods. The numerical results support the geophysical observations of density fingering on Thata Island. However, the process is slow and it takes some hundreds of years until density fingering is triggered. The results are sensitive to changes of the hydraulic gradient and the evapotranspiration rate. Small changes may lead to different plume developments. Results further demonstrate that density effects may be entirely overridden by lateral flow on islands embedded in a sufficiently high regional hydraulic gradient.     

Numerical analysis of one-dimensional nonlinear acoustic wave

Numerical investigations on one-dimensional nonlinear acoustic wave with third and fourth order nonlinearities are presented using high-order finite-difference (HFD) operators with a simple flux-limiter (SFL) algorithm. As shown by our numerical tests, the HFDSFL method is able to produce more stable, accurate and conservative solutions to the nonlinear acoustic waves than those computed by finite-difference combined with the flux-corrected-transport algorithm. Unlike the linear acoustic waves, the nonlinear acoustic waves have variable phase velocity and waveform both in time-space (t-x) domain and frequency-wavenumber (f-k) domain; of our special interest is the behaviour during the propagation of nonlinear acoustic waves: the waveforms are strongly linked to the type of medium nonlinearities, generation of harmonics, frequency and wavenumber peak shifts. In seismic sense, these characteristics of nonlinear wave will introduce new issues during such seismic processing as Normal Moveout and f-k filter. Moreover, as shown by our numerical experiment for a four-layer model, the nonlinearities of media will introduce extra velocity errors in seismic velocity inversion.     

地-井瞬变电磁响应特征数值模拟分析

井中瞬变电磁法(Bore-hole transient electromagnetic method-BHTEM)是指接收线圈在钻井中观测瞬变场响应用以勘查深部矿产资源的勘探方法,其中以地-井(地面激发井中接收)组合方式研究最多、应用最广.本文应用时域有限差分法(FDTD),建立包含薄板导体的均匀半空间二维数学模型,采用线源为激发源,选用Mur吸收边界条件,对矩形回线源在半空间中产生的瞬变电磁场进行数值模拟,计算了低阻板状导体在均质半空间和有低阻覆盖层影响情况下的地-井瞬变电磁异常响应,并对响应的特征及规律进行研究分析,为研究地-井TEM提供参考.