Abstract
In porous aquifers, groundwater flow and solute transport strongly depend on the sedimentary facies distribution at fine scale, which determines the heterogeneity of the conductivity field; in particular, connected permeable sediments could form preferential flow paths. Therefore, properly defined statistics, e.g. total and intrinsic facies connectivity, should be correlated with transport features. In order to improve the assessment of the relevance of this relationship, some tests are conducted on two ensembles of equiprobable realizations, obtained with two different geostatistical simulation methods—sequential indicator simulation and multiple point simulation (MPS)—from the same dataset, which refers to an aquifer analogue of sediments deposited in a fluvial point-bar/channel association. The ensembles show different features; simulations with MPS are more structured and characterised by preferential flow paths. This is confirmed by the analysis of transport connectivities and by the interpretation of data from numerical experiments of conservative solute transport with single and dual domain models. The use of two ensembles permits (1) previous results obtained for single realizations to be consolidated on a more firm statistical basis and (2) the application of principal component analysis to assess which quantities are statistically the most relevant for the relationship between connectivity indicators and flow and transport properties.
Résumé
Dans les aquifères poreux, l’écoulement d’eau souterraine et le transport de solutés dépend fortement de la distribution des faciès sédimentaires à l’échelle fine, ce qui détermine l’hétérogénéité du champ de conductivité hydraulique; en particulier, les sédiments perméables connectés peuvent donner lieu à des écoulements préférentiels. Ainsi, la connectivité totale et intrinsèque de faciès définie correctement de manière statistique devrait être corrélée avec les propriétés du transport. Afin d’améliorer l’évaluation de la signification de cette relation, des tests ont été menés sur deux ensembles de réalisations équiprobables, obtenues à partir de deux méthodes différentes de simulation numérique—simulation séquentielle à indicateurs et simulation en points multiples (SPM)—construites à l’aide du même jeu de données se rapportant à un analogue aquifère de sédiments déposés dans un environnement fluvial avec une association de barres et de chenaux ponctuels. Les ensembles montrent différentes caractéristiques ; les simulations avec SPM sont plus structurées et caractérisées par des écoulements préférentiels. Ceci est confirmé par l’analyse des connectivités lors du transport et par l’interprétation des données expérimentales numériques de transport conservatif issues de modèles en domaine simple et dual. L’utilisation des deux ensembles permet (1) de consolider des résultats obtenus au préalable pour des réalisations simples sur une base statistique plus solide et (2) l’application de l’analyse en composante principale pour évaluer quelles quantités sont les plus significatives du point de vue statistique pour la relation entre les indicateurs de connectivité et les propriétés d’écoulement et de transport.
Resumen
En acuíferos porosos, el flujo del agua subterránea y el transporte de soluto dependen fuertemente de la distribución de las facies sedimentarias a una escala fina, lo cual determina la heterogeneidad del campo de conductividad; en particular los sedimentos permeables conectados pueden forman trayectorias preferenciales de flujo. Por lo tanto, la estadística correctamente definida, por ejemplo la conectividad total e intrínseca de las facies, debe ser correlacionada con las características del transporte. Con el objeto de mejorar la evaluación de la relevancia de esta relación, se llevaron a cabo algunos ensayos en dos conjuntos de realizaciones equiprobables, obtenidas con dos métodos de simulación geoestadística diferente—simulación de indicador secuencial y simulación de múltiples puntos (MPS)—a partir de un mismo conjunto de datos, los cuales se refieren a una analogía de acuífero sedimentos depositados en una asociación albardón/canal fluvial. Los conjuntos muestran diferentes características; las simulaciones con MPS son más estructuradas y caracterizadas por trayectorias preferenciales de flujo. Esto está confirmado por el análisis de las conectividades del transporte y por la interpretación de datos de experimentos numéricos del transporte conservativo de soluto con modelos de dominios simples y dobles. El uso de los dos conjuntos permite (1) consolidar, sobre una base estadística más firme, los resultados previos obtenidos para realizaciones simples y (2) la aplicación del análisis de la componente principal para evaluar cuales cantidades son estadísticamente más relevantes para la relación entre los indicadores de conectividad y las propiedades de flujo y transporte.
摘要
在孔隙含水层中地下水流和溶质运移强烈依赖于沉积物中颗粒精细分布的特征,它确定了传导场地的不均匀性,特别是相关联的可渗透沉积层形成优先的水流。因而,适当确定统计资料,例如:总的和固有的连通特质,需要关联其运移特征。以便评价其关系,这些实验产生了两个同等的认识,根据相同的资料以两种不同的地质统计方法—序次指标模拟和多重点模拟(MPS)—获得。其利用了沉积地层在水流的点状阻障/通道中含水层模拟评价。整体效果显示出不同的特征,MPS模拟更突出了优先水流的结构和特点。它根据分析传导连通性和稳定溶质在单/双域传导模型数值实验数据解译确认。应用在两个总体认识上:(1) 原结果在观测单域内的认识是以更牢靠的统计数据为基数,(2) 主成分分析的应用定量统计了在连通指标和流量及传导特性之间的相互关系。
Resumo
Em aquíferos porosos, o fluxo de água subterrânea e o transporte de solutos dependem fortemente da distribuição das fácies sedimentares à escala fina, que determina a heterogeneidade do campo de condutividades; em particular, os sedimentos permeáveis interconetados que podem formar caminhos de fluxo preferenciais. Por essa razão, é de esperar que certas estatísticas, definidas de forma adequada, tais como a conetividade total e intrínseca das fácies, se correlacionem com as caraterísticas de transporte. A fim de melhorar a avaliação da importância desta correlação, efetuaram-se alguns testes em dois conjuntos de realizações equiprováveis, obtidos com dois métodos geoestatísticos de simulação diferentes—simulação sequencial de indicadores e simulação por múltiplos pontos (MPS)—a partir do mesmo conjunto de dados, referente a um análogo de um aquífero de sedimentos depositados numa sequência fluvial de meandro/canal. Os dois conjuntos apresentam caraterísticas diferentes; as simulações com MPS são mais estruturadas e caraterizam-se por caminhos de fluxo preferenciais. Este facto é confirmado pela análise de conetividades de transporte e pela interpretação de dados de experiências numéricas de transporte de solutos conservativos com modelos de domínio único e duplo. O uso de dois conjuntos permite (1) que os resultados anteriores obtidos por realizações únicas possam ser consolidados numa base estatística mais firme e (2) a aplicação da análise de componentes principais para avaliar quais as quantidades estatisticamente mais relevantes para a relação entre os indicadores de conetividade e as propriedades de fluxo e transporte.
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References
Anderson MP, Woessner WW (1991) Applied groundwater modeling-simulation of flow and advective transport. Academic, San Diego, CA
Anderson MP, Aiken JS, Webb EK, Mickelson DM (1999) Sedimentology and hydrogeology of two braided stream deposits. Sediment Geol 129:187–199
Baratelli F, Giudici M, Vassena C (2010) Single and dual-domain models to evaluate the effects of preferential flow paths in alluvial sediments. Transp Porous Media. doi:10.1007/s11242-010-9695-4
Berkowitz B, Scher H (1998) Theory of anomalous chemical transport in random fracture network. Phys Rev E 57:5858–5869
Bersezio R, Pavia F, Baio M et al (2004) Aquifer architecture of the Quaternary alluvial succession of the Southern Lambro Basin (Lombardy, Italy). Il Quaternario 17:361–378
Bersezio R, Giudici M, Mele M (2007) Combining sedimentological and geophysical data for high resolution 3-D mapping of fluvial architectural elements in the Quaternary Po plain (Italy). Sediment Geol 202:230–248
Bibby R (1981) Mass transport of solutes in dual-porosity media. Water Resour Res 17:1075–1081
Cabello P, Cuevas JL, Ramos E (2007) 3D modelling of grain size distribution in Quaternary deltaic deposits (Llobregat Delta, NE Spain). Geol Acta 5:231–244
Caers J (2001) Geostatistical reservoir modelling using statistical pattern recognition. J Pet Sci Eng 29:177–188
Carle SF, Fogg GE (1996) Transition probability-based indicator geostatistics. Math Geol 28:453–477
Carle SF, Labolle EM, Weissmann GS, Van Brocklin D, Fogg GE (1998) Conditional simulation of hydrofacies architecture: a transition probability/Markov approach. In: Fraser GS, Davis JM (eds) Hydrogeologic models of sedimentary aquifers. Special Publication, Concepts in Hydrogeology and Environmental Geology, SEPM, Tulsa, OK, pp 147–170
Castiglioni GB, Pellegrini GB (2001) Note illustrative della Carta Geomorfologica della Pianura Padana. Suppl Geogr Fisic Dinam Quat 4:209
Coats KH, Smith BD (1964) Dead-end pore volume and dispersion in porous media. Soc Pet Eng J 3:245–255
Colombera L, Felletti F, Mountney NP, McCaffrey WD (2012) A database approach for constraining stochastic simulations of the sedimentary heterogeneity of fluvial reservoirs. AAPG Bull. doi:10.1306/04211211179
Davis JC (2002) Statistics and data analysis in geology. Wiley, New York
Dell’Arciprete D (2010) Connectivity, flow and transport models in a point bar-channel aquifer analogue. PhD Thesis, Università degli Studi di Milano, Italy
Dell’Arciprete D, Felletti F, Bersezio R (2010a) Simulation of fine-scale heterogeneity of meandering river aquifer analogues: comparing different approaches. In: Atkinson PM, Lloyd CD (eds) geoENV VII – geostatistics for environmental applications: quantitative geology and geostatistics, vol 16. Springer, Heidelberg, Germany, pp 127–137
Dell’Arciprete D, Bersezio R, Felletti F et al (2010b) Simulation of heterogeneity in a point-bar/channel aquifer analogue. Mem Descrit Carta Geol Italia XC:85–96
Dell’Arciprete D, Bersezio R, Felletti F et al (2012) Comparison of three geostatistical methods for hydrofacies simulation: a test on alluvial sediments. Hydrogeol J. doi:10.1007/s10040-011-0808-0
Deutsch CV, Journel AG (1992) Geostatistical software library and user’s guide. Oxford University Press, New York
Falivene O, Cabrera L, Muñoz JA, Arbués P, Fernández O, Sáez A (2007) Statistical grid-based facies reconstruction and modelling for sedimentary bodies alluvial-palustrine and turbiditic examples. Geol Acta 5:199–230
Feehley CE, Zheng C, Molz FJ (2000) A dual-domain mass transfer approach for modeling solute transport in heterogeneous aquifers: application to the Macrodispersion Experiment (MADE) site. Water Resour Res 36:2501–2515
Felletti F, Bersezio R, Giudici M (2006) Geostatistical simulation and numerical upscaling, to model groundwater flow in a sandy gravel, braided river, aquifer analogue. J Sediment Res 76:215–1229
Flach GP, Crisman SA, Molz FJ III (2004) Comparison of single-domain and dual-domain subsurface transport models. Ground Water 42:815–828
Fleckenstein JH, Niswonger RG, Fogg GE (2006) River-aquifer interactions, geologic heterogeneity, and low-flow management. Ground Water 44:837–852
Fogg GE, Noyes CD, Carle SF (1998) Geologically-based model of heterogeneous hydraulic conductivity in an alluvial setting. Hydrogeol J 6:131–143
Gerke HH, van Genuchten MT (1993) A dual-porosity model for simulating the preferential movement of water and solutes in structured porous media. Water Resour Res 29:305–319
Gerke HH, van Genuchten MT (1996) Macroscopic representation of structural geometry for simulating water and solute movement in dual-porosity media. Adv Water Resour 19:343–351
Giudici M, Vassena C (2007) About the symmetry of the upscaled equivalent transmissivity tensor. Math Geol. doi:10.1007/s11004-007-9101-0
Goovaerts P (1997) Geostatistics for natural resources evaluation. Oxford University Press, New York
Guan J, Molz FJ, Zhou Q et al (2008) Behavior of the mass transfer coefficient during the MADE-2 experiment: new insights. Water Resour Res. doi:10.1029/2007WR006120
Guin A, Ritzi RW Jr (2008) Studying the effect of correlation and finite-domain size on spatial continuity of permeable sediments. Geophys Res Lett. doi:10.1029/2007GL032717
Haggerty R, Gorelick SM (1995) Multiple-rate mass transfer for modeling diffusion and surface reactions in media with pore-scale heterogeneity. Water Resour Res 31:2383–2400
Harvey C, Gorelick SM (2000) Rate-limited mass transfer or macrodispersion: which dominates plume evolution at the Macrodispersion Experiment (MADE) site. Water Resour Res 36:637–650
Heinz J, Aigner T (2003) Hierarchical dynamic stratigraphy in various Quaternary gravel deposits, Rhine glacier area (SW Germany): implications for hydrostratigraphy. Int J Earth Sci (Geol Rundsch). doi:10.1007/s00531-003-0359-2
Journel AG, Gómez-Hernández JJ (1993) Stochastic imaging of the Wilmington Clastic Sequence. Society of Petroleum Engineers Formation Evaluation, March, SPE, Richardson, pp 33–40
Journel AG, Gundeso R, Gringarten E, Yao T (1998) Stochastic modelling of a fluvial reservoir: a comparative review of algorithms. J Petrol Sci Eng 21:95–121
Julian HE, Boggs JM, Zheng C, Feehley CE (2001) Numerical simulation of a natural gradient tracer experiment for the natural attenuation study: flow and physical transport. Ground Water 39:534–545
Knudby C, Carrera J (2005) On the relationship between indicators of geostatistical, flow and transport connectivity. Adv Water Resour. doi:10.1016/j.advwatres.2004.09.001
Kottegoda NT, Rosso R (1997) Statistics, probability and reliability for civil and environmental engineers. McGraw-Hill, New York
Kreft A, Zuber A (1978) On the physical meaning of the dispersion equation and its solutions for different initial and boundary conditions. Chem Eng Sci 33:1471–1480
LaBolle EM, Fogg GE, Eweis JB (2006) Diffusive fractionation of 3H and 3He in groundwater and its impact on groundwater age estimates. Water Resour Res. doi:10.1029/2005WR004756
Larsson MH, Jarvis NJ (1999) Evaluation of a dual-porosity model to predict field-scale solute transport in a macroporous soil. J Hydrol 215:153–171
Lee S-Y, Carle SV, Fogg GE (2007) Geologic heterogeneity and a comparison of two geostatistical models: sequential Gaussian and transition probability-based geostatistical simulation. Adv Water Resour 30:1914–1932
Lim KT, Aziz K (1995) Matrix-fracture transfer shape factors for dual-porosity simulators. J Pet Sci Eng 13:169–178
Liu G, Zheng C, Gorelick SM (2004) Limits of applicability of the advection-dispersion model in aquifers containing connected high-conductivity channels. Water Resour Res. doi:10.1029/2003WR002735
Liu Y, Harding A, Gilbert R, Journel A (2005) Multiple-point geostatistical simulation. In: Leuangthong O, Deutsch CV (eds) Geostatistics Banff 2004. Springer, New York
Llopis-Albert C, Capilla JE (2009) Gradual conditioning of non-Gaussian transmissivity fields to flow and mass transport data: 3. application to the Macrodispersion Experiment (MADE-2) site, on Columbus Air Force Base in Mississippi (USA). J Hydrol 371:75–84
Ma L, Selim HM (1995) Transport of a nonreactive solute in soils: a two-flow domain approach. Soil Sci 159(4):224–234
Miall AD (1996) The geology of fluvial deposits: sedimentary facies, basin analysis, and petroleum geology. Springer, Berlin
Ogata A, Banks RB (1961) A solution of the differential equation of longitudinal dispersion in porous media. US Geol Surv Prof Pap 411-A
Okabe H, Blunt MJ (2005) Pore space reconstruction using multiple-point statistics. J Pet Sci Eng 46:121–137
Poeter EP, Townsend P (1994) Assessment of critical flow path for improved remediation management. Ground Water 32:439–447
Pozdniakov SP, Bakshevskaya VA, Krohicheva IV, Danilov VV, Zubkov AA (2012) The influence of conceptual model of sedimentary formation hydraulic heterogeneity on contaminant transport simulation. Mosc Univ Geol Bull 67:43–51. doi:10.3103/S0145875212010097
Proce CJ, Ritzi RW, Dominic DF, Dai Z (2004) Modeling multiscale heterogeneity and aquifer interconnectivity. Ground Water 42:658–670
Ptak T, Teutsch G (1994) Forced and natural gradient tests in a highly heterogeneous porous aquifer-Instrumentation and measurements. J Hydrol 159:79–104
Ramanathan R, Guin A, Ritzi RW Jr et al (2010) Simulating the heterogeneity in braided channel belt deposits: 1. a geometric-based methodology and code. Water Resour Res. doi:10.1029/2009WR008111
Renard P, Allard D (2011) Connectivity metrics for subsurface flow and transport. Adv Water Resour. doi:10.1016/j.advwatres.2011.12.001
Ritzi RW (2000) Behaviour of indicator variogram and transition probabilities in relation to the variance in lengths of hydrofacies. Water Resour Res 36:3375–3381
Ritzi RW, Dai Z, Dominic DF, Rubin YN (2004) Spatial correlation of permeability in cross-stratified sediment with hierarchical architecture. Water Resour Res. doi:10.1029/2003WR002420
Ronayne MJ, Gorelick SM, Caers J (2008) Identifying discrete geologic structures that produce anomalous hydraulic response: an inverse modeling approach. Water Resour Res. doi:10.1029/2007WR006635
Ronayne MJ, Gorelick SM, Zheng C (2010) Geological modeling of submeter scale heterogeneity and its influence on tracer transport in a fluvial aquifer. Water Resour Res. doi:10.1029/2010WR009348
Schlüter S, Vogel HJ (2011) On the reconstruction of structural and functional properties in random heterogeneous media. Adv Water Resour 34:314–325
Schwartz RC, Juo ASR, McInnes KJ (2000) Estimating parameters for a dual-porosity model to describe non-equilibrium, reactive transport in a fine-textured soil. J Hydrol 229:149–167
Seifert D, Jensen JL (1999) Using sequential indicator simulation as a tool in reservoir description: issues and uncertainties. Geology 31:527–550
Skopp J, Gardner WR, Tyler EJ (1981) Solute movement in structured soils: two-region model with small interaction. Soil Sci Soc Am J 45:837–842
Stauffer D, Aharony A (1994) Introduction to percolation theory. Taylor and Francis, London
Straubhaar J, Renard P, Mariethoz G, Froidevaux R, Besson O (2011) An improved parallel multiple-point algorithm. Math Geosci 43:305–328. doi:10.1007/s11004-011-9328-7
Strebelle S (2002) Conditional simulation of complex geological structures using multiple-point statistics. Math Geol 34:1–21
Strebelle S, Payrazyan K, Caers J (2003) Modeling of a deepwater turbidite reservoir conditional to seismic data using principal component analysis and multiple-point geostatistics. SPE J 8: 227–235
Sweet ML, Blewden CJ, Carter AM, Mills CA (1996) Modeling heterogeneity in a low-permeability gas reservoir using geostatistical techniques, Hyde Field, southern North Sea. AAPG Bull 80:1719–1735
Vassena C, Cattaneo L, Giudici M (2010) Assessment of the role of facies heterogeneity at the fine scale by numerical transport experiments and connectivity indicators. Hydrogeol J. doi:10.1007/s10040-009-0523-2
Warren JE, Root PJ (1963) The behavior of naturally fractured reservoirs. Soc Pet Eng J 3:45–255
Weissmann GS, Fogg GE (1999) Multi-scale alluvial fan heterogeneity modeled with transition probability geostatistics in a sequence stratigraphic framework. J Hydrol 226:48–65
Weissmann GS, Carle SF, Fogg GE (1999) Three-dimensional hydrofacies modeling based on soil surveys and transition probability geostatistics. Water Resour Res 35:1761–1770
Western A, Bloschl G, Grayson RB (2001) Toward capturing hydrologically significant connectivity in spatial patterns. Water Resour Res 37:83–97
Zappa G, Bersezio R, Felletti F, Giudici M (2006) Modeling heterogeneity of gravel-sand, braided stream, alluvial aquifers at the facies scale. J Hydrol. doi:10.1016/j.jhydrol.2005.10.016
Zhang Y, Benson DA (2008) Lagrangian simulation of multidimensional anomalous transport at the MADE site. Geophys Res Lett. doi:10.1029/2008GL033222
Zhang Y, Gable CW (2008) Two-scale modeling of solute transport in an experimental stratigraphy. J Hydrol. doi:10.1016/j.jhydrol.2007.10.017
Zhang Y, Benson DA, Baeumer B (2007a) Predicting the tails of breakthrough curves in regional-scale alluvial systems. Ground Water 45:473–484
Zhang Y, Benson DA, Meerschaert MM, LaBolle EM (2007b) Space-fractional advection-dispersion equations with variable parameters: diverse formulas, numerical solutions, and applications to the Macrodispersion Experiment site data. Water Resour Res. doi:10.1029/2006WR004912
Zheng C, Bianchi M, Gorelick SM (2011) Lessons learned from 25 years of research at the MADE site. Ground Water 49:649–662
Zimmerman RW, Chen G, Hadgu T, Bodvarsson GS (1993) A numerical dual-porosity model with semianalytical treatment of fracture/matrix flow. Water Resour Res 29:2127–2137
Zinn B, Harvey C (2003) When good statistical models of aquifer heterogeneity go bad: a comparison of flow, dispersion, and mass transfer in connected and multivariate Gaussian hydraulic conductivity fields. Water Resour Res 39, WR001146
Acknowledgements
This work was financially supported by the MIUR and the University of Milano through the research project of national interest “Integrated geophysical, geological, petrographical and modelling study of alluvial aquifer complexes characteristic of the Po plain subsurface: relationships between scale of hydrostratigraphic reconstruction and flow models” (PRIN 2007. PI: Mauro Giudici).
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Dell’Arciprete, D., Vassena, C., Baratelli, F. et al. Connectivity and single/dual domain transport models: tests on a point-bar/channel aquifer analogue. Hydrogeol J 22, 761–778 (2014). https://doi.org/10.1007/s10040-014-1105-5
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DOI: https://doi.org/10.1007/s10040-014-1105-5