Assessment of the role of facies heterogeneity at the fine scale by numerical transport experiments and connectivity indicators

The heterogeneity of facies at the scale of individual lithological levels controls, at a macroscopic scale, water flow and contaminant transport in porous sediments. In particular the presence of organized features such as permeable connected levels, has a significant effect on travel times and dispersion. Here, the effects of facies heterogeneity on flow and transport are studied for three blocks, whose volume is of the order of a cubic meter, dug from alluvial sediments from the Ticino valley (Italy). Using the results of numerical tracer experiments on these domains, the longitudinal dispersion coefficient is computed with an Eulerian approach based on the fit of the breakthrough curves with the analytical solution of the convective-dispersive transport equation. Moreover, the dispersion tensor is computed with a Lagrangian approach from the second order moments of particle distributions. Three types of connectivity indicators are tested: (1) connectivity function; (2) flow, transport and statistical connectivity; (3) original (intrinsic, normal and total) indicators of facies connectivity. The connectivity function provides the most complete information. Some of the transport and statistical connectivity indicators are correlated with dispersivity. The simultaneous analysis of the three indicators of facies connectivity emphasizes the fundamental geometrical features that control transport.     

Comparison of three geostatistical methods for hydrofacies simulation: a test on alluvial sediments

The hydrodispersive properties of porous sediments are strongly influenced by the heterogeneity at fine scales, which can be modeled by geostatistical simulations. In order to improve the assessment of the properties of three different geostatistical simulation methods (Sequential indicator simulation, SISIM; Transition probability geostatistical simulation, T-PROGS; Multiple point simulation, MPS) a comparison test at different scales was performed for a well-exposed aquifer analogue. In the analysed volume (approximately 30,000?m³) four operative hydrofacies have been recognised: very fine sand and silt, sand, gravelly sand and open framework gravel. Several equiprobable realizations were computed with SISIM, MPS and T-PROGS for a test volume of approximately 400?m³ and for the entire volume, and the different outcomes were compared with visual inspection and connectivity analysis of the very or poorly permeable structures. The comparison of the different simulations shows that the geological model is best reproduced when the simulations are realised separately for each highest rank depositional element and subsequently merged. Moreover, the three methods yield different images of the volume; in particular MPS is efficient in mapping the geometries of the most represented hydrofacies, whereas SISIM and T-PROGS can account for the distribution of the less represented facies.     

Hierarchical simulation of aquifer heterogeneity: implications of different simulation settings on solute-transport modeling

The fine-scale heterogeneity of porous media affects the large-scale transport of solutes and contaminants in groundwater and it can be reproduced by means of several geostatistical simulation tools. However, including the available geological information in these tools is often cumbersome. A hierarchical simulation procedure based on a binary tree is proposed and tested on two real-world blocks of alluvial sediments, of a few cubic meters volume, that represent small-scale aquifer analogs. The procedure is implemented using the sequential indicator simulation, but it is so general that it can be adapted to various geostatistical simulation tools, improving their capability to incorporate geological information, i.e., the sedimentological and architectural characterization of heterogeneity. When compared with a standard sequential indicator approach on bi-dimensional simulations, in terms of proportions and connectivity indicators, the proposed procedure yields reliable results, closer to the reference observations. Different ensembles of three-dimensional simulations based on different hierarchical sequences are used to perform numerical experiments of conservative solute transport and to obtain ensembles of equivalent pore velocity and dispersion coefficient at the scale length of the blocks (meter). Their statistics are used to estimate the impact of the variability of the transport properties of the simulated blocks on contaminant transport modeled on bigger domains (hectometer). This is investigated with a one-dimensional transport modeling based on the Kolmogorov-Dmitriev theory of branching stochastic processes. Applying the proposed approach with diverse binary trees and different simulation settings provides a great flexibility, which is revealed by the differences in the breakthrough curves.     

Calibration of categorical simulations by evolutionary gradual deformation method

Methods to simulate facies (or categorical) fields are numerous. However, calibration of simulated facies fields to large-scale or dynamic data still remains an important challenge due to the discrete nature of the fields, the non-linearity of the response with respect to the facies fields, and the non-derivability of the objective function used in calibration. A new gradual deformation method (GDM) is presented and tested for the calibration of facies realizations obtained by patch-multipoint simulation (MPS). The proposed method borrows ideas from pluriGaussian simulation, evolutionary algorithms, and GDM. Various test cases are considered: proportion maps, section of seismic amplitudes, inlet to outlet travel time along the shortest path, and water-cut curves obtained with a flow simulator. Both conditional/unconditional MPS simulations and 2D/3D problems are considered. In all studied test cases, the new GDM approach has provided excellent calibration to the target variables. The method is general as it can be used in conjunction with any facies simulator.     

Conditioning of Multiple-Point Statistics Facies Simulations to Tomographic Images

Geophysical tomography captures the spatial distribution of the underlying geophysical property at a relatively high resolution, but the tomographic images tend to be blurred representations of reality and generally fail to reproduce sharp interfaces. Such models may cause significant bias when taken as a basis for predictive flow and transport modeling and are unsuitable for uncertainty assessment. We present a methodology in which tomograms are used to condition multiple-point statistics (MPS) simulations. A large set of geologically reasonable facies realizations and their corresponding synthetically calculated cross-hole radar tomograms are used as a training image. The training image is scanned with a direct sampling algorithm for patterns in the conditioning tomogram, while accounting for the spatially varying resolution of the tomograms. In a post-processing step, only those conditional simulations that predicted the radar traveltimes within the expected data error levels are accepted. The methodology is demonstrated on a two-facies example featuring channels and an aquifer analog of alluvial sedimentary structures with five facies. For both cases, MPS simulations exhibit the sharp interfaces and the geological patterns found in the training image. Compared to unconditioned MPS simulations, the uncertainty in transport predictions is markedly decreased for simulations conditioned to tomograms. As an improvement to other approaches relying on classical smoothness-constrained geophysical tomography, the proposed method allows for: (1) reproduction of sharp interfaces, (2) incorporation of realistic geological constraints and (3) generation of multiple realizations that enables uncertainty assessment.     

非均质含水层中渗流与溶质运移研究进展简

Natural aquifer heterogeneity controls the groundwater flow and solute transport, and how to accurately quantify the flow and solute transport in heterogeneous aquifers has received wide attention by many scholars, and has become a hot research topic in earth science. Theoretically, a systematic review is given by the following aspect: flow and solute transport model, moment analysis, multi scale analysis. The resolved and remained issues for scale conversion in hydrogeology research are pointed out. Secondly, recent advances of heterogeneous field test, uncertainty and velocity connectivity are analyzed. Finally, the geophysical inversion of aquifer heterogeneity, stochastic theory and development of stochastic simulation software, scale conversion and uncertainty of velocity connectivity, and the relationship between heterogeneity and hydrogeological condition on the major four aspects of the future research direction is pointed out.     

Modelling a real-world buried valley system with vertical non-stationarity using multiple-point statistics

Stationarity has traditionally been a requirement of geostatistical simulations. A common way to deal with non-stationarity is to divide the system into stationary sub-regions and subsequently merge the realizations for each region. Recently, the so-called partition approach that has the flexibility to model non-stationary systems directly was developed for multiple-point statistics simulation (MPS). The objective of this study is to apply the MPS partition method with conventional borehole logs and high-resolution airborne electromagnetic (AEM) data, for simulation of a real-world non-stationary geological system characterized by a network of connected buried valleys that incise deeply into layered Miocene sediments (case study in Denmark). The results show that, based on fragmented information of the formation boundaries, the MPS partition method is able to simulate a non-stationary system including valley structures embedded in a layered Miocene sequence in a single run. Besides, statistical information retrieved from the AEM data improved the simulation of the geology significantly, especially for the deep-seated buried valley sediments where borehole information is sparse.     

Retention properties of flow paths in fractured rock

There is no straightforward way to extrapolate solute retention properties from typical site characterisation scales to typical scales in the performance assessment of the geological disposal of nuclear wastes. Solutes diffuse much deeper into the rock matrix under performance assessment flow conditions than under site characterisation flow conditions. The modelling approach applied in this study, associated with the Äspö Task Force, enables evaluation of the contribution of the individual immobile layers to the overall retention. This makes it possible to determine the influence of the immobile zone heterogeneity on solute retention under different flow conditions. It appears that there is a significant difference between the dominating immobile retention zones on site characterisation and performance assessment scales. Fractured rock is characterised by heterogeneity and in particular a large spread of hydraulic properties. This favours formation of the preferential flow paths by leading to a few dominating transport paths. Large hydraulic features are, on average, better hydraulic conductors than smaller ones. This causes spatial scale effects for the solute retention properties. In particular, the hydraulic properties at the early parts of flow paths are more favourable to retention than those at the later parts of the flow paths.     

Adaptive Conditioning of Multiple-Point Statistical Facies Simulation to Flow Data with Probability Maps

Multiple-point statistics (MPS) provides a flexible grid-based approach for simulating complex geologic patterns that contain high-order statistical information represented by a conceptual prior geologic model known as a training image (TI). While MPS is quite powerful for describing complex geologic facies connectivity, conditioning the simulation results on flow measurements that have a nonlinear and complex relation with the facies distribution is quite challenging. Here, an adaptive flow-conditioning method is proposed that uses a flow-data feedback mechanism to simulate facies models from a prior TI. The adaptive conditioning is implemented as a stochastic optimization algorithm that involves an initial exploration stage to find the promising regions of the search space, followed by a more focused search of the identified regions in the second stage. To guide the search strategy, a facies probability map that summarizes the common features of the accepted models in previous iterations is constructed to provide conditioning information about facies occurrence in each grid block. The constructed facies probability map is then incorporated as soft data into the single normal equation simulation (snesim) algorithm to generate a new candidate solution for the next iteration. As the optimization iterations progress, the initial facies probability map is gradually updated using the most recently accepted iterate. This conditioning process can be interpreted as a stochastic optimization algorithm with memory where the new models are proposed based on the history of the successful past iterations. The application of this adaptive conditioning approach is extended to the case where multiple training images are proposed as alternative geologic scenarios. The advantages and limitations of the proposed adaptive conditioning scheme are discussed and numerical experiments from fluvial channel formations are used to compare its performance with non-adaptive conditioning techniques.     

Modeling Combined Geological and Grade Uncertainty: Application of Multiple-Point Simulation at the Apensu Gold Deposit, Ghana

Traditionally within the mining industry, single models for both grade and geology of orebodies are created upon which all mine development decisions are based. These models provide a single interpretation of the extent and continuity of the mineralization envelope based on solids and sections interpreted from relatively widely spaced drilling. The inherent variable behavior of grade and geology cannot be understood from a single estimated resource model. To account for uncertainty in the geology and mineralization envelope, Newmont Mining Corporation uses multiple-point statistics (MPS), an emerging spatial simulation framework, which can be employed to generate multiple, geologically realistic, realizations of data representing attributes of mineral deposits that display complex non-linear features. MPS uses a conceptual model of the geology, termed a training image, to infer these high-order spatial relationships. A detailed application of the MPS algorithm at the structurally controlled Apensu gold deposit, Ghana, demonstrates the practical intricacies of the MPS framework and documents efficiency and effectiveness. Multiple realizations of the Apensu deposit allow for an assessment of the geologic and volumetric uncertainty, which is further combined with grade simulations to generate a more complete picture of the true uncertainty of the deposit.     

Zeroing of the TL signal in sediment undergoing fluvioglacial transport. An example from Austerdalen, Western Norway

Theoretical considerations imply that the suitability of glacially-deposited sediments for thermoluminescence (TL) dating will be influenced by transport routes within the ice, and by facies of deposition. Measurments on sediments obtained from the Austerdalsbreen glacier in western Norway indicate that zeroing of sediment does not occur at the base of a valley glacier, but that englacial and supraglacial sediments showed evidence of bleaching but not total zeroing. Analysis of sediments from recent glacial and fluvioglacial landforms showed no evidence that they had been zeroed prior to deposition. Results indicate that the TL-age of glacial landforms will be a function of the derivation and travel paths of the sediments of which it is composed rather than of the form itself. It is concluded that as knowledge of the rates of bleaching associated with various facies of transport and deposition of glacial sediments improves, so the potential of the technique to act as a diagnostic sedimentological tool will increase, even when dating of glacial deposits by TL is impossible.     

多孔介质中非均匀流动特性的染色示踪试验研究

通过土壤染色剂进行的4组试验,对不同介质结构条件下的水流和溶质非均匀运动规律,非均匀流动变异信息分布特征关系以及全局性非均匀流动示踪方法进行了研究。结果表明,即使在相对比较均匀的介质条件下,流动也表现出明显的非均匀特性;对数正态分布能够较好的反映水流的运动分布模式,相比水流运动,溶质的运动和分布规律明显不同,表现出更多的不确定性和变异性。     

Application of Multiple Point Geostatistics to Non-stationary Images

Simulation of flow and solute transport through aquifers or oil reservoirs requires a precise representation of subsurface heterogeneity that can be achieved by stochastic simulation approaches. Traditional geostatistical methods based on variograms, such as truncated Gaussian simulation or sequential indicator simulation, may fail to generate the complex, curvilinear, continuous and interconnected facies distributions that are often encountered in real geological media, due to their reliance on two-point statistics. Multiple Point Geostatistics (MPG) overcomes this constraint by using more complex point configurations whose statistics are retrieved from training images. Obtaining representative statistics requires stationary training images, but geological understanding often suggests a priori facies variability patterns. This research aims at extending MPG to non-stationary facies distributions. The proposed method subdivides the training images into different areas. The statistics for each area are stored in separate frequency search trees. Several training images are used to ensure that the obtained statistics are representative. The facies probability distribution for each cell during simulation is calculated by weighting the probabilities from the frequency trees. The method is tested on two different object-based training image sets. Results show that non-stationary training images can be used to generate suitable non-stationary facies distributions.     

Modeling preferential water flow and solute transport in unsaturated soil using the active region model

Preferential flow and solute transport are common processes in the unsaturated soil, in which distributions of soil water content and solute concentrations are often characterized as fractal patterns. An active region model (ARM) was recently proposed to describe the preferential flow and transport patterns. In this study, ARM governing equations were derived to model the preferential soil water flow and solute transport processes. To evaluate the ARM equations, dye infiltration experiments were conducted, in which distributions of soil water content and Cl⁻ concentration were measured. Predicted results using the ARM and the mobile–immobile region model (MIM) were compared with the measured distributions of soil water content and Cl⁻ concentration. Although both the ARM and the MIM are two-region models, they are fundamentally different in terms of treatments of the flow region. The models were evaluated based on the modeling efficiency (ME). The MIM provided relatively poor prediction results of the preferential flow and transport with negative ME values or positive ME values less than 0.4. On the contrary, predicted distributions of soil water content and Cl⁻ concentration using the ARM agreed reasonably well with the experimental data, with ME values higher than 0.8. The results indicated that the ARM successfully captured the macroscopic behavior of preferential flow and solute transport in the unsaturated soil.     

Solute transport as affected by surface land characteristics in gravely calcareous arid soils

Gravely calcareous soils cover approximately most of arid lands (in percent); however, the solute transport behavior in these soils remains a current issue. This research aimed at estimating and correlating the solute transport parameters in gravely calcareous soils as being affected by different land uses through the knowledge of the soil morphological, physical, and chemical properties. Four different land use sites were selected: irrigated trees and bare, range, and alluvial sediment lands. Solute transport parameters of soil pore water velocity (V), dispersion coefficient (D), and retardation factor (R) were estimated using bromide breakthrough curve tests for surface soil columns. In addition, field Brilliant Blue FCF dye tracing experiment was conducted to determine the maximum dimensional movements. Soil morphological analysis was able to explain the heterogeneity in the solute transport parameters. Conductive solute transport mechanism with V of 17.99 m/day was favored in a high continuous pore system observed under tree lands. Presence of high gravel and CaCO₃ contents under range lands increased pore system tortuosity and thus increased D magnitude up to 1,339.88 cm²/day. Existence of thin surface crusts at both bare soils and alluvial sediments had considerably restricted V down to 1.46 m/day. Dye staining technique aided the explanation of the existing variations by providing visual evidence on the preferential flow paths and patterns governing the solute transport mechanism at each site.     

土壤中优势流的几个基本问题研究

优势流是指土壤在整个入流边界上接受补给,但只通过少部分土体的快速运移,优势流是一种普遍存在的现象,而不是一种特例,它受许多因素的控制,如土壤中的大空隙,土壤结构,土壤质地,土壤水分含量,土壤初始水分含量,水和溶质的施加速率及溶质的施加方法等,优势流的产生机理主要有两种,一种是由土壤介质的非均质所驱动的优势流;另一种是湿润锋的不稳定性所驱动的优势流,目前优势流的监测方法主要取土壤原状土,实验室内的土     

Assessing flow paths in a karst aquifer based on multiple dye tracing tests using stochastic simulation and the MODFLOW-CFP code

Karst systems show high spatial variability of hydraulic parameters over small distances and this makes their modeling a difficult task with several uncertainties. Interconnections of fractures have a major role on the transport of groundwater, but many of the stochastic methods in use do not have the capability to reproduce these complex structures. A methodology is presented for the quantification of tortuosity using the single normal equation simulation (SNESIM) algorithm and a groundwater flow model. A training image was produced based on the statistical parameters of fractures and then used in the simulation process. The SNESIM algorithm was used to generate 75 realizations of the four classes of fractures in a karst aquifer in Iran. The results from six dye tracing tests were used to assign hydraulic conductivity values to each class of fractures. In the next step, the MODFLOW-CFP and MODPATH codes were consecutively implemented to compute the groundwater flow paths. The 9,000 flow paths obtained from the MODPATH code were further analyzed to calculate the tortuosity factor. Finally, the hydraulic conductivity values calculated from the dye tracing experiments were refined using the actual flow paths of groundwater. The key outcomes of this research are: (1) a methodology for the quantification of tortuosity; (2) hydraulic conductivities, that are incorrectly estimated (biased low) with empirical equations that assume Darcian (laminar) flow with parallel rather than tortuous streamlines; and (3) an understanding of the scale-dependence and non-normal distributions of tortuosity.     

Conditional Latin Hypercube Simulation of (Log)Gaussian Random Fields

In earth and environmental sciences applications, uncertainty analysis regarding the outputs of models whose parameters are spatially varying (or spatially distributed) is often performed in a Monte Carlo framework. In this context, alternative realizations of the spatial distribution of model inputs, typically conditioned to reproduce attribute values at locations where measurements are obtained, are generated via geostatistical simulation using simple random (SR) sampling. The environmental model under consideration is then evaluated using each of these realizations as a plausible input, in order to construct a distribution of plausible model outputs for uncertainty analysis purposes. In hydrogeological investigations, for example, conditional simulations of saturated hydraulic conductivity are used as input to physically-based simulators of flow and transport to evaluate the associated uncertainty in the spatial distribution of solute concentration. Realistic uncertainty analysis via SR sampling, however, requires a large number of simulated attribute realizations for the model inputs in order to yield a representative distribution of model outputs; this often hinders the application of uncertainty analysis due to the computational expense of evaluating complex environmental models. Stratified sampling methods, including variants of Latin hypercube sampling, constitute more efficient sampling aternatives, often resulting in a more representative distribution of model outputs (e.g., solute concentration) with fewer model input realizations (e.g., hydraulic conductivity), thus reducing the computational cost of uncertainty analysis. The application of stratified and Latin hypercube sampling in a geostatistical simulation context, however, is not widespread, and, apart from a few exceptions, has been limited to the unconditional simulation case. This paper proposes methodological modifications for adopting existing methods for stratified sampling (including Latin hypercube sampling), employed to date in an unconditional geostatistical simulation context, for the purpose of efficient conditional simulation of Gaussian random fields. The proposed conditional simulation methods are compared to traditional geostatistical simulation, based on SR sampling, in the context of a hydrogeological flow and transport model via a synthetic case study. The results indicate that stratified sampling methods (including Latin hypercube sampling) are more efficient than SR, overall reproducing to a similar extent statistics of the conductivity (and subsequently concentration) fields, yet with smaller sampling variability. These findings suggest that the proposed efficient conditional sampling methods could contribute to the wider application of uncertainty analysis in spatially distributed environmental models using geostatistical simulation.     

Pathogen transport in groundwater systems: contrasts with traditional solute transport

Water quality affects many aspects of water availability, from precluding use to societal perceptions of fit-for-purpose. Pathogen source and transport processes are drivers of water quality because they have been responsible for numerous outbreaks resulting in large economic losses due to illness and, in some cases, loss of life. Outbreaks result from very small exposure (e.g., less than 20 viruses) from very strong sources (e.g., trillions of viruses shed by a single infected individual). Thus, unlike solute contaminants, an acute exposure to a very small amount of contaminated water can cause immediate adverse health effects. Similarly, pathogens are larger than solutes. Thus, interactions with surfaces and settling become important even as processes important for solutes such as diffusion become less important. These differences are articulated in “Colloid Filtration Theory”, a separate branch of pore-scale transport. Consequently, understanding pathogen processes requires changes in how groundwater systems are typically characterized, where the focus is on the leading edges of plumes and preferential flow paths, even if such features move only a very small fraction of the aquifer flow. Moreover, the relatively short survival times of pathogens in the subsurface require greater attention to very fast (<10 year) flow paths. By better understanding the differences between pathogen and solute transport mechanisms discussed here, a more encompassing view of water quality and source water protection is attained. With this more holistic view and theoretical understanding, better evaluations can be made regarding drinking water vulnerability and the relation between groundwater and human health.