Three-Dimensional Steady-state Groundwater Flow Modeling with Full Tensor Conductivities Using Finite Difference

A new three-dimensional steady-state groundwater-flow forward-simulator with full conductivity tensors using a nineteen-points block-centered finite-difference method is presented. Hydraulic conductivity tensors are defined at the block interfaces eliminating the need to average conductivity tensors at adjacent blocks to approximate their values at the interfaces. The capabilities of the code are demonstrated in three heterogeneous formulations, two of the examples are two-dimensional, and the third one is three-dimensional and uses a nonuniform discretization grid. A benchmark, in the context of conductivity upscaling, is carried out with the MODFLOW LVDA module, which uses hydraulic conductivity tensors at block centers and then approximates their values at the interfaces. The results show that the code developed outperforms the MODFLOW LVDA module when the block conductivity principal directions are not parallel to the Cartesian axis.Li ., L. (2009). Three-Dimensional Steady-state Groundwater Flow Modeling with Full Tensor Conductivities Using Finite Difference. http://hdl.handle.net/10251/14536Archivo delegad

Data assimilation of in situ soil moisture measurements in hydrological models: third annual doctoral progress report, work plan and achievements

Efficient water utilization and optimal water supply/distribution to increase food and fodder productivity are of utmost importance in confronting worldwide water scarcity, climate change, growing populations and increasing water demands. In this respect, irrigation efficiency, which is influenced by the type of irrigation and irrigation scheduling, is an essential issue for achieving higher productivity. To improve irrigation strategies in precision agriculture, soil water status can be more accurately described using a combination of advanced monitoring and modeling. Our study focuses on the combination of high resolution hydrological data with hydrological models that predict water flow and solute (pollutants and salts) transport and water redistribution in agricultural soils under irrigation. Field plots of a potato farmer in a sandy region in Belgium were instrumented to continuously monitor soil moisture and water potential before, during and after irrigation in dry summer periods. The aim is to optimize the irrigation process by assimilating online sensor field data into process based models. This research is part of Activity 305 ‘Precision agriculture and remote sensing’ of the VITO GWO and is also part of the strategic cooperation with UGent within the platform ‘Managing Natural Resources’. Over the past 2 years, we applied a combination of in-situ monitoring and numerical modeling -Hydrus 1D- to estimate water content fluctuations in a heterogeneous sandy grassland soil under irrigation with water table fluctuating between 80 and 155 cm. Over the last year, more sampling and analyses were carried out to further characterize the hydraulic properties over the entire field. Modeling results for the field demonstrated clearly the profound effect of the position of the GWL, and to a lesser extent, the effect of spatially variable soil hydraulic properties (Ks, n and α) on the estimated water content in the sandy two-layered soil under grass. Our results show that currently applied uniform water distribution using sprinkler irrigation seems not to be efficient since at locations with shallow groundwater, the amount of water applied will be excessive as compared to the plant requirements while in locations with a deeper GWL, requirements will not be met. To derive the optimal parameter set best describing the measured soil moisture content, 37 optimization scenarios were conducted with two to six parameters using various parameter combinations for the two soil layers. The best performing parameter optimization scenario was a 2-parameter scenario with Ks optimized for each layer. The results showed a better identifiability of the parameters (less correlations among parameters) with equal performance as compared to three, four or six parameter optimization. Model predictions using the calibrated model (with data from 2012) for an independent data set of soil moisture data in the validation period (2013) showed satisfactory performance of the model in view of irrigation management purposes. Comparing the degree of water stress for different optimization scenarios of groundwater depth, showed that grass was exposed to water stress in summer in 2013 but not for such a long period as compared to the 2012 growing season. The degree of water stress simulated with Hydrus 1D suggested to increase the irrigation amount in 2012 and 2013 and at least one or two times in the summer (June and July) and further distributing the amount of irrigation during the growing season, instead of using a huge amount of irrigation later in the season, as is common practice by the farmer. A second part of the study focused on finding a relation between measured soil hydraulic properties and apparent electrical conductivity ECa. Our measurements of hydraulic properties of the field clearly confirm that there is considerable spatial variability in the field and that this has an impact on the simulation of soil moisture content. Therefore this should be taken into account when upscaling soil hydraulic properties to the field scale in order to in understand and model flow, solute and energy fluxes in the field and develop strategies for efficient irrigation. Upscaling soil hydraulic properties to the field scale can be done by linking them to apparent electrical conductivity (ECa), which can be measured efficiently and inexpensively so a spatially dense dataset for describing within-field spatial soil variability can be generated. In this study relations between the spatial variation of soil hydraulic properties and apparent soil electrical conductivity ECa measured with EM38 and DUALEM-21S sensors at two depths of explorations (DOE) 0-50 and 0-100 cm were investigated. Two predictive modelling approaches, i.e. i) a simple regression and ii) applying Archie’s laws for saturated and unsaturated conditions in combination with MVG equations, were developed and it was compared how they were able to explain the observed values of hydraulic parameters. Results demonstrated the spatial variability and heterogeneity of ECa and soil hydraulic properties Ks, α and n. We derived a regression relationship between log Ks and ECa measured with DUALEM (r2≥0.70) and with EM38 (r2>0.46) sensors. The predicted results were tested vs measured data and confirmed that the performance of DUALEMp,100-Ks model is relatively better than that of the same sensor with lower DOE and of the EM38 sensor (RMSE = 1.31 cmh-1, R2 = 0.55). The relationships between MVG shape parameters and ECa datasets were generally poor (0.05<R2<0.26). In the second approach, we showed that the water retention curve can be translated to ECa-(h) and ECa-Se relations by combining the MVG equations and Archie’s law. Results also show that reformulating the MVG equations based on ECa-Se relationships can help to estimate unsaturated hydraulic conductivity at the field scale. In the third year, a second study site has been set up in a nearby field where potatoes are grown and has been instrumented with soil moisture sensors, tensiometers, groundwater level loggers and a weather station. Field hydraulic properties for the field will be derived using the equations developed for the first study site and the modeling approach developed for the first field will be tested here. Also quasi 3D-modelling of water flow at the field scale will be conducted. In this modeling set-up, the field will be modeled as a collection of 1D-columns representing the different field conditions (combination of soil properties, GWL, root zone depth). Combining this model with crop based models such as LINGRA-N or Aquacrop gives a direct simulation of the impact of irrigation strategies on crop yield at the field scale

Debates—Stochastic subsurface hydrology from theory to practice: why stochastic modeling has not yet permeated into practitioners?

This is the peer reviewed version of the following article: [Sanchez-Vila, X., and D. Fernàndez-Garcia (2016), Debates—Stochastic subsurface hydrology from theory to practice: Why stochastic modeling has not yet permeated into practitioners?, Water Resour. Res., 52, 9246–9258, doi:10.1002/2016WR019302], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/2016WR019302/abstract. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-ArchivingWe address modern topics of stochastic hydrogeology from their potential relevance to real modeling efforts at the field scale. While the topics of stochastic hydrogeology and numerical modeling have become routine in hydrogeological studies, nondeterministic models have not yet permeated into practitioners. We point out a number of limitations of stochastic modeling when applied to real applications and comment on the reasons why stochastic models fail to become an attractive alternative for practitioners. We specifically separate issues corresponding to flow, conservative transport, and reactive transport. The different topics addressed are emphasis on process modeling, need for upscaling parameters and governing equations, relevance of properly accounting for detailed geological architecture in hydrogeological modeling, and specific challenges of reactive transport. We end up by concluding that the main responsible for nondeterministic models having not yet permeated in industry can be fully attributed to researchers in stochastic hydrogeology.Peer ReviewedPostprint (author's final draft

Upscaling and Inverse Modeling of Groundwater Flow and Mass Transport in Heterogeneous Aquifers

Dividimos el trabajo en tres bloques: En el primer bloque, se han revisado las técnicas de escalado que utilizan una media simple, el método laplaciano simple, el laplaciano con piel y el escalado con mallado no uniforme y se han evaluado en un ejercicio tridimensional de escalado de la conductividad hidráulica. El campo usado como referencia es una realización condicional a escala fina de la conductividad hidráulica del experimento de macrodispersión realizado en la base de la fuerza aérea estadounidense de Columbus en Misuri (MADE en su acrónimo inglés). El objetivo de esta sección es doble, primero, comparar la efectividad de diferentes técnicas de escalado para producir modelos capaces de reproducir el comportamiento observado del movimiento del penacho de tritio, y segundo, demostrar y analizar las condiciones bajo las cuales el escalado puede proporcionar un modelo a una escala gruesa en el que el flujo y el transporte puedan predecirse con al ecuación de advección-dispersión en condiciones aparentemente no fickianas. En otros casos, se observa que la discrepancia en la predicción del transporte entre las dos escalas persiste, y la ecuación de advección-dispersión no es suficiente para explicar el transporte en la escala gruesa. Por esta razón, se ha desarrollado una metodología para el escalado del transporte en formaciones muy heterogéneas en tres dimensiones. El método propuesto se basa en un escalado de la conductividad hidráulica por el método laplaciano con piel y centrado en los interbloques, seguido de un escalado de los parámetros de transporte que requiere la inclusión de un proceso de transporte con transferencia de masa multitasa para compensar la pérdida de heterogeneidad inherente al cambio de escala. El método propuesto no sólo reproduce el flujo y el transporte en la escala gruesa, sino que reproduce también la incertidumbre asociada con las predicciones según puede observarse analizando la variabilidad del conjunto de curvas de llegada.Li ., L. (2011). Upscaling and Inverse Modeling of Groundwater Flow and Mass Transport in Heterogeneous Aquifers [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/12268Palanci

Stochastic analysis of three-dimensional hydraulic conductivity upscaling in a heterogeneous tropical soil

[EN] Hydraulic conductivity (K) heterogeneity is seldom considered in geotechnical practice for the impossibility of sampling the entire area of interest and for the difficulty of accounting for scale effects. Stochastic three-dimensional K upscaling can tackle these two problems, and a workflow is described with an application in a tropical soil. The application shows that K heterogeneity can be incorporated in the daily practice of the geotechnical modeler while discussing the aspects to consider when performing the upscaling so that the upscaled models reproduce the average fluxes at the fine scale.The authors thank the financial support by the Brazilian National Council for Scientific and Technological Development (CNPq) (Project 401441/2014-8). The doctoral fellowship award to the first author by the Coordination of Improvement of Higher Level Personnel (CAPES) is gratefully acknowledged. The first author thanks the International Mobility Grant awarded by CNPq (200597/2015-9) and Santander mobility. The authors also thank DHI-WASI for providing a FEFLOW Software license.Almeida De-Godoy, V.; Zuquette, L.; Gómez-Hernández, JJ. (2018). Stochastic analysis of three-dimensional hydraulic conductivity upscaling in a heterogeneous tropical soil. Computers and Geotechnics. 100:174-187. https://doi.org/10.1016/j.compgeo.2018.03.004S17418710

A Comparative Study of Three-Dimensional Hydraulic Conductivity Upscaling at the MAcro-Dispersion Experiment (MADE) site, Columbus Air Force Base, Mississippi (USA)

Simple averaging, simple-Laplacian, Laplacian-with-skin, and non-uniform coarsening are the techniques investigated in this comparative study of three-dimensional hydraulic conductivity upscaling. The reference is a fine scale conditional realization of the hydraulic conductivities at the MAcro-Dispersion Experiment site on Columbus Air Force Base in Mississippi (USA). This realization was generated using a hole-effect variogram model and it was shown that flow and transport modeling in this realization (at this scale) can reproduce the observed non-Fickian spreading of the tritium plume. The purpose of this work is twofold, first to compare the effectiveness of different upscaling techniques in yielding upscaled models able to reproduce the observed transport behavior, and second to demonstrate and analyze the conditions under which flow upscaling can provide a coarse model in which the standard advection-dispersion equation can be used to model transport in seemingly non-Fickian scenarios. Specifically, the use of Laplacian-based upscaling technique coupled with a non-uniform coarsening scheme yields the best results both in terms of flow and transport reproduction, for this case study in which the coarse blocks are smaller than the correlation ranges of the fine scale conductivities. © 2011 Elsevier B.V.The authors gratefully acknowledge the financial support by ENRESA (Project 0079000029). The second author also acknowledges the financial support from China Scholarship Council. The two anonymous reviewers are gratefully acknowledged for their comments which helped improving the final version of the manuscript.Li ., L.; Zhou ., H.; Gómez-Hernández, JJ. (2011). A Comparative Study of Three-Dimensional Hydraulic Conductivity Upscaling at the MAcro-Dispersion Experiment (MADE) site, Columbus Air Force Base, Mississippi (USA). Journal of Hydrology. 404(3-4):278-293. https://doi.org/10.1016/j.jhydrol.2011.05.001S2782934043-

Modeling transient groundwater flow by coupling ensemble Kalman filtering and upscaling

The ensemble Kalman filter (EnKF) is coupled with upscaling to build an aquifer model at a coarser scale than the scale at which the conditioning data (conductivity and piezometric head) had been taken for the purpose of inverse modeling. Building an aquifer model at the support scale of observations is most often impractical since this would imply numerical models with many millions of cells. If, in addition, an uncertainty analysis is required involving some kind of Monte Carlo approach, the task becomes impossible. For this reason, a methodology has been developed that will use the conductivity data at the scale at which they were collected to build a model at a (much) coarser scale suitable for the inverse modeling of groundwater flow and mass transport. It proceeds as follows: (1) Generate an ensemble of realizations of conductivities conditioned to the conductivity data at the same scale at which conductivities were collected. (2) Upscale each realization onto a coarse discretization; on these coarse realizations, conductivities will become tensorial in nature with arbitrary orientations of their principal components. (3) Apply the EnKF to the ensemble of coarse conductivity upscaled realizations in order to condition the realizations to the measured piezometric head data. The proposed approach addresses the problem of how to deal with tensorial parameters, at a coarse scale, in ensemble Kalman filtering while maintaining the conditioning to the fine-scale hydraulic conductivity measurements. We demonstrate our approach in the framework of a synthetic worth-of-data exercise, in which the relevance of conditioning to conductivities, piezometric heads, or both is analyzed.The authors acknowledge Wolfgang Nowak and three anonymous reviewers for their comments on the previous versions of the manuscript, which helped substantially to improve it. The authors gratefully acknowledge the financial support by the Spanish Ministry of Science and Innovation through project CGL2011-23295. Extra travel grants awarded to the first and second authors by the Ministry of Education (Spain) are also acknowledged. The second author also acknowledges financial support from the China Scholarship Council.Li ., L.; Zhou ., H.; Franssen, H.; Gómez-Hernández, JJ. (2012). Modeling transient groundwater flow by coupling ensemble Kalman filtering and upscaling. Water Resources Research. 48(1):1-19. https://doi.org/10.1029/2010WR010214S119481Allaire , G. S. M. Kaber 2008 Numerical Linear Algebra, Texts Appl. Math. 55 Springer New YorkArulampalam, M. S., Maskell, S., Gordon, N., & Clapp, T. (2002). A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Transactions on Signal Processing, 50(2), 174-188. doi:10.1109/78.978374Behrens, R. A., MacLeod, M. K., Tran, T. T., & Alimi, A. C. (1998). Incorporating Seismic Attribute Maps in 3D Reservoir Models. SPE Reservoir Evaluation & Engineering, 1(02), 122-126. doi:10.2118/36499-paBurgers, G., Jan van Leeuwen, P., & Evensen, G. (1998). Analysis Scheme in the Ensemble Kalman Filter. Monthly Weather Review, 126(6), 1719-1724. doi:10.1175/1520-0493(1998)1262.0.co;2Capilla, J. E., & Llopis-Albert, C. (2009). Gradual conditioning of non-Gaussian transmissivity fields to flow and mass transport data: 1. Theory. Journal of Hydrology, 371(1-4), 66-74. doi:10.1016/j.jhydrol.2009.03.015Capilla, J. E., Rodrigo, J., & Gómez-Hernández, J. J. (1999). Mathematical Geology, 31(7), 907-927. doi:10.1023/a:1007580902175Carrera, J., Alcolea, A., Medina, A., Hidalgo, J., & Slooten, L. J. (2005). Inverse problem in hydrogeology. Hydrogeology Journal, 13(1), 206-222. doi:10.1007/s10040-004-0404-7Chen, Y., & Oliver, D. S. (2009). Cross-covariances and localization for EnKF in multiphase flow data assimilation. Computational Geosciences, 14(4), 579-601. doi:10.1007/s10596-009-9174-6Chen, Y., & Zhang, D. (2006). Data assimilation for transient flow in geologic formations via ensemble Kalman filter. Advances in Water Resources, 29(8), 1107-1122. doi:10.1016/j.advwatres.2005.09.007Durlofsky, L. J., Jones, R. C., & Milliken, W. J. (1997). A nonuniform coarsening approach for the scale-up of displacement processes in heterogeneous porous media. Advances in Water Resources, 20(5-6), 335-347. doi:10.1016/s0309-1708(96)00053-xEvensen, G. (2003). The Ensemble Kalman Filter: theoretical formulation and practical implementation. Ocean Dynamics, 53(4), 343-367. doi:10.1007/s10236-003-0036-9Fu, J., & Jaime Gómez-Hernández, J. (2009). Uncertainty assessment and data worth in groundwater flow and mass transport modeling using a blocking Markov chain Monte Carlo method. Journal of Hydrology, 364(3-4), 328-341. doi:10.1016/j.jhydrol.2008.11.014Fu, J., Tchelepi, H. A., & Caers, J. (2010). A multiscale adjoint method to compute sensitivity coefficients for flow in heterogeneous porous media. Advances in Water Resources, 33(6), 698-709. doi:10.1016/j.advwatres.2010.04.005Gaspari, G., & Cohn, S. E. (1999). Construction of correlation functions in two and three dimensions. Quarterly Journal of the Royal Meteorological Society, 125(554), 723-757. doi:10.1002/qj.49712555417Gómez-Hernández , J. J. 1991 A stochastic approach to the simulation of block conductivity values conditioned upon data measured at a smaller scale Stanford, Calif.Gómez-Hernández , J. J. A. G. Journel 1993 Joint sequential simulation of multi-Gaussian fields Geostatistics Troia '92 Amilcar Soares 1 85 94 Springer BerlinJaime Gómez-Hernández, J., & Mohan Srivastava, R. (1990). ISIM3D: An ANSI-C three-dimensional multiple indicator conditional simulation program. Computers & Geosciences, 16(4), 395-440. doi:10.1016/0098-3004(90)90010-qJaime Gómez-Hernánez, J., Sahuquillo, A., & Capilla, J. (1997). Stochastic simulation of transmissivity fields conditional to both transmissivity and piezometric data—I. Theory. Journal of Hydrology, 203(1-4), 162-174. doi:10.1016/s0022-1694(97)00098-xGuadagnini, A., & Neuman, S. P. (1999). Nonlocal and localized analyses of conditional mean steady state flow in bounded, randomly nonuniform domains: 1. Theory and computational approach. Water Resources Research, 35(10), 2999-3018. doi:10.1029/1999wr900160Hamill, T. M., Whitaker, J. S., & Snyder, C. (2001). Distance-Dependent Filtering of Background Error Covariance Estimates in an Ensemble Kalman Filter. Monthly Weather Review, 129(11), 2776-2790. doi:10.1175/1520-0493(2001)1292.0.co;2Hendricks Franssen , H. 2001 Inverse stochastic modelling of groundwater flow and mass transport Valencia, SpainHendricks Franssen, H. J., & Kinzelbach, W. (2008). Real-time groundwater flow modeling with the Ensemble Kalman Filter: Joint estimation of states and parameters and the filter inbreeding problem. Water Resources Research, 44(9). doi:10.1029/2007wr006505Franssen, H. J. H., & Kinzelbach, W. (2009). Ensemble Kalman filtering versus sequential self-calibration for inverse modelling of dynamic groundwater flow systems. Journal of Hydrology, 365(3-4), 261-274. doi:10.1016/j.jhydrol.2008.11.033Franssen, H.-J. H., Gómez-Hernández, J., & Sahuquillo, A. (2003). Coupled inverse modelling of groundwater flow and mass transport and the worth of concentration data. Journal of Hydrology, 281(4), 281-295. doi:10.1016/s0022-1694(03)00191-4Hendricks Franssen, H. J., Alcolea, A., Riva, M., Bakr, M., van der Wiel, N., Stauffer, F., & Guadagnini, A. (2009). A comparison of seven methods for the inverse modelling of groundwater flow. Application to the characterisation of well catchments. Advances in Water Resources, 32(6), 851-872. doi:10.1016/j.advwatres.2009.02.011Houtekamer, P. L., & Mitchell, H. L. (1998). Data Assimilation Using an Ensemble Kalman Filter Technique. Monthly Weather Review, 126(3), 796-811. doi:10.1175/1520-0493(1998)1262.0.co;2Hu, L. Y. (2000). Mathematical Geology, 32(1), 87-108. doi:10.1023/a:1007506918588Indelman, P., & Abramovich, B. (1994). Nonlocal properties of nonuniform averaged flows in heterogeneous media. Water Resources Research, 30(12), 3385-3393. doi:10.1029/94wr01782Li, L., Zhou, H., & Jaime Gómez-Hernández, J. (2010). Steady-state saturated groundwater flow modeling with full tensor conductivities using finite differences. Computers & Geosciences, 36(10), 1211-1223. doi:10.1016/j.cageo.2010.04.002Li, L., Zhou, H., & Gómez-Hernández, J. J. (2011). A comparative study of three-dimensional hydraulic conductivity upscaling at the macro-dispersion experiment (MADE) site, Columbus Air Force Base, Mississippi (USA). Journal of Hydrology, 404(3-4), 278-293. doi:10.1016/j.jhydrol.2011.05.001Li, L., Zhou, H., & Gómez-Hernández, J. J. (2011). Transport upscaling using multi-rate mass transfer in three-dimensional highly heterogeneous porous media. Advances in Water Resources, 34(4), 478-489. doi:10.1016/j.advwatres.2011.01.001Li, L., Zhou, H., Hendricks Franssen, H. J., & Gómez-Hernández, J. J. (2011). Groundwater flow inverse modeling in non-MultiGaussian media: performance assessment of the normal-score Ensemble Kalman Filter. Hydrology and Earth System Sciences Discussions, 8(4), 6749-6788. doi:10.5194/hessd-8-6749-2011Mariethoz, G., Renard, P., & Straubhaar, J. (2010). The Direct Sampling method to perform multiple-point geostatistical simulations. Water Resources Research, 46(11). doi:10.1029/2008wr007621McLaughlin, D., & Townley, L. R. (1996). A Reassessment of the Groundwater Inverse Problem. Water Resources Research, 32(5), 1131-1161. doi:10.1029/96wr00160Naevdal, G., Johnsen, L. M., Aanonsen, S. I., & Vefring, E. H. (2005). Reservoir Monitoring and Continuous Model Updating Using Ensemble Kalman Filter. SPE Journal, 10(01), 66-74. doi:10.2118/84372-paOliver, D. S., & Chen, Y. (2010). Recent progress on reservoir history matching: a review. Computational Geosciences, 15(1), 185-221. doi:10.1007/s10596-010-9194-2Peters, L., Arts, R., Brouwer, G., Geel, C., Cullick, S., Lorentzen, R. J., … Reynolds, A. (2010). Results of the Brugge Benchmark Study for Flooding Optimization and History Matching. SPE Reservoir Evaluation & Engineering, 13(03), 391-405. doi:10.2118/119094-paRenard, P., & de Marsily, G. (1997). Calculating equivalent permeability: a review. Advances in Water Resources, 20(5-6), 253-278. doi:10.1016/s0309-1708(96)00050-4Rubin, Y., & Gómez-Hernández, J. J. (1990). A stochastic approach to the problem of upscaling of conductivity in disordered media: Theory and unconditional numerical simulations. Water Resources Research, 26(4), 691-701. doi:10.1029/wr026i004p00691Sánchez-Vila, X., Girardi, J. P., & Carrera, J. (1995). A Synthesis of Approaches to Upscaling of Hydraulic Conductivities. Water Resources Research, 31(4), 867-882. doi:10.1029/94wr02754Sanchez-Vila, X., Guadagnini, A., & Carrera, J. (2006). Representative hydraulic conductivities in saturated groundwater flow. Reviews of Geophysics, 44(3). doi:10.1029/2005rg000169Strebelle, S. (2002). Mathematical Geology, 34(1), 1-21. doi:10.1023/a:1014009426274Sun, A. Y., Morris, A. P., & Mohanty, S. (2009). Sequential updating of multimodal hydrogeologic parameter fields using localization and clustering techniques. Water Resources Research, 45(7). doi:10.1029/2008wr007443Tran, T. (1996). The ‘missing scale’ and direct simulation of block effective properties. Journal of Hydrology, 183(1-2), 37-56. doi:10.1016/s0022-1694(96)80033-3Tran , T. X. Wen R. Behrens 1999 Efficient conditioning of 3D fine-scale reservoir model to multiphase production data using streamline-based coarse-scale inversion and geostatistical downscalingTureyen, O. I., & Caers, J. (2005). A parallel, multiscale approach to reservoir modeling. Computational Geosciences, 9(2-3), 75-98. doi:10.1007/s10596-005-9004-4Wen, X.-H., & Gómez-Hernández, J. J. (1996). Upscaling hydraulic conductivities in heterogeneous media: An overview. Journal of Hydrology, 183(1-2), ix-xxxii. doi:10.1016/s0022-1694(96)80030-8Wen, X.-H., Deutsch, C. V., & Cullick, A. S. (2002). Construction of geostatistical aquifer models integrating dynamic flow and tracer data using inverse technique. Journal of Hydrology, 255(1-4), 151-168. doi:10.1016/s0022-1694(01)00512-1Wen, X. H., Durlofsky, L. J., & Edwards, M. G. (2003). Mathematical Geology, 35(5), 521-547. doi:10.1023/a:1026230617943Whitaker, J. S., & Hamill, T. M. (2002). Ensemble Data Assimilation without Perturbed Observations. Monthly Weather Review, 130(7), 1913-1924. doi:10.1175/1520-0493(2002)1302.0.co;2White , C. D. R. N. Horne 1987 Computing absolute transmissibility in the presence of fine-scale heterogeneityYeh, W. W.-G. (1986). Review of Parameter Identification Procedures in Groundwater Hydrology: The Inverse Problem. Water Resources Research, 22(2), 95-108. doi:10.1029/wr022i002p00095Zhang, D., Lu, Z., & Chen, Y. (2007). Dynamic Reservoir Data Assimilation With an Efficient, Dimension-Reduced Kalman Filter. SPE Journal, 12(01), 108-117. doi:10.2118/95277-paZhou, H., Li, L., & Jaime Gómez-Hernández, J. (2010). Three-dimensional hydraulic conductivity upscaling in groundwater modeling. Computers & Geosciences, 36(10), 1224-1235. doi:10.1016/j.cageo.2010.03.008Zhou, H., Gómez-Hernández, J. J., Hendricks Franssen, H.-J., & Li, L. (2011). An approach to handling non-Gaussianity of parameters and state variables in ensemble Kalman filtering. Advances in Water Resources, 34(7), 844-864. doi:10.1016/j.advwatres.2011.04.014Zimmerman, D. A., de Marsily, G., Gotway, C. A., Marietta, M. G., Axness, C. L., Beauheim, R. L., … Rubin, Y. (1998). A comparison of seven geostatistically based inverse approaches to estimate transmissivities for modeling advective transport by groundwater flow. Water Resources Research, 34(6), 1373-1413. doi:10.1029/98wr0000

Upscaling of water flow and mass transport in a tropical soil: numerical, laboratory and field studies

Los modelos numéricos son herramientas fundamentales para realizar predicciones de muchos problemas enfrentados por ingenieros geotécnicos y geoambientales. Sin embargo, para que estos modelos puedan realizar predicciones confiables, los parámetros de entrada del modelo deben ser estimados considerando el efecto escala. En este contexto, esta tesis se concentra en las reglas del cambio de escala de los parámetros de flujo y transporte de masa en un suelo tropical a través de estudios numéricos, de laboratorio y de campo. Esta está organizada en cuatro partes. Primero, la heterogeneidad, correlación y correlación cruzada entre los parámetros de transporte de solutos (dispersividad, ¿, y coeficiente de partición, Kd) y las propiedades del suelo fueron estudiadas en detalle. En esta parte fue verificado que la conductividad hidráulica (K) y los parámetros de transporte de solutos son altamente heterogéneos, mientras que las propiedades del suelo no lo son. La correlación espacial de ¿ y K con variables estadísticamente significativas fue estudiada. Este resultado probablemente podrá mejorar la estimación en casos de estudios de pequeña escala debido a que solo fue observada correlaciones de hasta 2,5 m. Este estudio fue un primer intento de evaluar la variación espacial en el coeficiente de correlación de los parámetros de transporte de un soluto reactivo y de un no reactivo, indicando las variables más relevantes y aquella que debería ser incluida en estudios futuros. En la segunda parte, el efecto escala en K, dispersividad y coeficiente de partición de potasio y clorito fue estudiado experimentalmente a través de experimentos de laboratorio y de campo. El objetivo de esta parte fue contribuir a la discusión sobre el efecto escala en K, ¿ y Kd, y entender como estos parámetros se comportan con el cambio de escala de medición. La dispersividad tiende a aumentar con la altura de la muestra de manera exponencial. El coeficiente de partición tiende a aumentar con la altura, el diámetro y el volumen de la muestra. Estas diferencias encontradas en los parámetros de acuerdo con la escala de medición deben ser considerados cuando estos valores sean usados posteriormente como datos de entrada de modelos numéricos; de otra manera, las respuestas pueden ser malinterpretadas. Tercero, análisis estocásticos tridimensionales de cambio de escala de la conductividad hidráulica fueron realizados usando los métodos de promedios simples y de Laplace con piel para una variedad de tamaños de bloques usando mediciones reales de K. En esta parte son demostrados los errores que pueden ser introducidos al usar métodos determinísticos de cambio de escala usando promedios simples de las mediciones de K sin llevar en consideración la correlación espacial. La aplicación muestra que la heterogeneidad de K puede ser incorporada en la práctica diaria del modelador geotécnico. Los aspectos que considerar durante un proceso de cambio de escala también son discutidos. Finalmente, la dependencia del exponente de la norma-p como función del tamaño del bloque fue analizada. En la última parte, una aplicación de cambio de escala estocástico del coeficiente de dispersión hidrodinámica D y del factor de retardo R fue realizada usando datos reales con el objetivo de reducir la falta de casos de investigación experimental de cambio de escala de parámetros de transporte de solutos reactivos. El cambio de escala de D fue realizado usando el método de macrodispersión. El método de promedio simple de norma-p fue usado para realizar el cambio de escala de R. Una buena propagación de incertidumbres fue alcanzada. Métodos simples de cambio de escala pueden ser introducidos en la práctica del modelaje usando programas comerciales de transporte y conseguir reproducir el transporte en escala gruesa, pero puede requerir correcciones con el objetivo de reducir el efecto de suavizado de la heterogeneidad causado por elNumerical models are becoming fundamental tools to predict a range of complex problems faced by geotechnical and geo-environmental engineers. However, to render the model reliable for future predictions, the model input parameters must be determined with consideration of the scale effects. In this context, this thesis focuses on upscaling of water flow and mass transport in a tropical soil by means of numerical, laboratory and field studies. This thesis is organized in four parts. First, the heterogeneity, correlation and cross-correlation between solute transport parameters (dispersivity, ¿, and partition coefficient, Kd) and soil properties were studied in detail. In this part, it was verified that the hydraulic conductivity (K) and solute transport parameters are highly heterogeneous, while soil properties not. Spatial correlation of ¿, K, and statistically significant variables were studied, and it would probably improve the estimation only in a small-scale study, since the spatial correlation were only observed up to 2.5 m. This study was a first attempt to evaluate the spatial variation in the correlation coefficient of transport parameters of a reactive and a nonreactive solute, indicating the more relevant variables and the one that should be included in future studies. In the second part, scale effect on K, dispersivity and partition coefficient of potassium and chloride is studied experimentally by means of laboratory and field experiments. The purpose of was to contribute to the discussion about scale effects on K, ¿ and Kd and understanding how these parameters behave with the change in the scale of measurement. Results shows that K increases with scale, regardless of the method of measurement. Dispersivity trends to increases exponentially with the sample height. Partition coefficient, tend to increase with sample length, diameter and volume. These differences in the parameters according to the scale of measurement must be considered when these observations are later used as input to numerical models, otherwise the responses can be misrepresented. Third, stochastic analysis of three-dimensional hydraulic conductivity upscaling was performed using a simple average and the Laplacian-with-skin methods for a variety of block sizes using real K measurements. In this part it was demonstrated the errors that can be introduced by using a deterministic upscaling using simple averages of the measured K without accounting for the spatial correlation. The application shows that K heterogeneity can be incorporated in the daily practice of the geotechnical modeler. The aspects to consider when performing the upscaling were also discussed. Finally, the dependence of the exponent of the p-norm as a function of the block size was analyzed. In the last part, an application of stochastic upscaling of hydrodynamic dispersion coefficient (D) and retardation factor (R) was performed using real data aiming to reduce the lack in experimental upscaling of reactive solute transport research. Upscaling of D was done using macrodispersion method. Simple average method based on p-norm was used to perform R upscaling. A good propagation of the uncertainties was achieved. Simple upscaling methods can be incorporated to the modeling practice using commercial transport codes and properly reproduce de transport at coarse scale but may require corrections to reduce smoothing of the heterogeneity caused by the upscaling procedure.Els models numèrics s'estan constituint en eines fonamentals per a realitzar prediccions d'una àmplia gamma de problemes enfrontats per enginyers geotècnics i geoambientales. No obstant açò, perquè aquests models puguen realitzar prediccions fiables, els paràmetres d'entrada del model han de considerar l'efecte escala. En aquest context, aquesta tesi es concentra en les regles del canvi d'escala dels paràmetres de flux i transport de massa en un sòl tropical a través d'estudis numèrics, de laboratori i de camp. Aquesta tesi està organitzada en quatre parts. Primer, l'heterogeneïtat, correlació i correlació creuada entre els paràmetres de transport de soluts (dispersivitat, ¿, i coeficient de partició, Kd) i les propietats del sòl van ser estudiades detalladament. En aquesta part va ser verificat que la conductivitat hidràulica (K) i els paràmetres de transport de soluts són altament heterogenis, mentre que les propietats del sòl no ho són. La correlació espacial de ¿ i K amb variables estadísticament significatives va ser estudiada. Aquest resultat probablement podrà millorar l'estimació en casos d'estudis de xicoteta escala a causa que solament va ser observada correlacions de fins a 2,5 m. Aquest estudi va ser un primer intent d'avaluar la variació espacial en el coeficient de correlació dels paràmetres de transport d'un solut reactiu i d'un no reactiu, indicant les variables més rellevants i aquelles que haurien de ser inclosas en estudis futurs. En la segona part, l'efecte escala en K, dispersivitat i coeficient de partició de potassi i clorito va ser estudiat experimentalment a través d'experiments de laboratori i de camp. L'objectiu d'aquesta part va ser contribuir a la discussió sobre l'efecte escala en K, ¿ i Kd, i entendre com aquests paràmetres es comporten amb el canvi d'escala de mesurament. La dispersivitat tendeix a augmentar amb l'altura de la mostra, és a dir, amb la longitud del transport, de manera exponencial. El coeficient de partició tendeix a augmentar amb l'altura, el diàmetre i el volum de la mostra. Aquestes diferències en els paràmetres d'acord amb l'escala de mesurament han de ser considerats quan aquests valors siguen usats posteriorment com a dades d'entrada de models numèrics; d'una altra manera, les respostes poden ser malament interpretades. Tercer, anàlisis estocàstiques tridimensionals de canvi d'escala de la conductivitat hidràulica van ser realitzats usant els mètodes de mitjanes simples i de Laplace amb pell per a una varietat de grandàries de blocs usant mesuraments reals de K. En aquesta part són demostrats els errors que poden ser introduïts en usar mètodes determinístics de canvi d'escala usant mitjanes simples dels mesuraments de K sense tindre en consideració la correlació espacial. L'aplicació mostra que l'heterogeneïtat de K pot ser incorporada en la pràctica diària del modelador geotècnic. Els aspectes a considerar durant un procés de canvi d'escala també són discutits. Finalment, la dependència de l'exponent de la norma-p com a funció de la grandària del bloc va ser analitzada. En l'última part, una aplicació de canvi d'escala estocàstic del coeficient de dispersió hidrodinámica D i del factor de retard R va ser realitzada usant dades reals amb l'objectiu de reduir la falta de casos de recerca experimental de canvi d'escala de paràmetres de transport de soluts reactius. El canvi d'escala de D va ser realitzat usant el mètode de macrodispersió. El mètode de mitjana simple de norma-p va ser usat per a realitzar el canvi d'escala de R. Una bona propagació d'incerteses va ser aconseguida. Mètodes simples de canvi d'escala poden ser introduïts en la pràctica de la modelació usant programes comercials de transport i aconseguir reproduir el transport en escala gruixuda, però pot requerir correccions amb l'objectiu de reduir l'efecte de suavitzat de l'heterogeneïtat causat pel procés de canvi d'escala.Almeida De Godoy, V. (2018). Upscaling of water flow and mass transport in a tropical soil: numerical, laboratory and field studies [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/102405TESI

Application of upscaling methods for fluid flow and mass transport in multi-scale heterogeneous media : A critical review

Physical and biogeochemical heterogeneity dramatically impacts fluid flow and reactive solute transport behaviors in geological formations across scales. From micro pores to regional reservoirs, upscaling has been proven to be a valid approach to estimate large-scale parameters by using data measured at small scales. Upscaling has considerable practical importance in oil and gas production, energy storage, carbon geologic sequestration, contamination remediation, and nuclear waste disposal. This review covers, in a comprehensive manner, the upscaling approaches available in the literature and their applications on various processes, such as advection, dispersion, matrix diffusion, sorption, and chemical reactions. We enclose newly developed approaches and distinguish two main categories of upscaling methodologies, deterministic and stochastic. Volume averaging, one of the deterministic methods, has the advantage of upscaling different kinds of parameters and wide applications by requiring only a few assumptions with improved formulations. Stochastic analytical methods have been extensively developed but have limited impacts in practice due to their requirement for global statistical assumptions. With rapid improvements in computing power, numerical solutions have become more popular for upscaling. In order to tackle complex fluid flow and transport problems, the working principles and limitations of these methods are emphasized. Still, a large gap exists between the approach algorithms and real-world applications. To bridge the gap, an integrated upscaling framework is needed to incorporate in the current upscaling algorithms, uncertainty quantification techniques, data sciences, and artificial intelligence to acquire laboratory and field-scale measurements and validate the upscaled models and parameters with multi-scale observations in future geo-energy research.© 2021 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)This work was jointly supported by the National Key Research and Development Program of China (No. 2018YFC1800900 ), National Natural Science Foundation of China (No: 41972249 , 41772253 , 51774136 ), the Program for Jilin University (JLU) Science and Technology Innovative Research Team (No. 2019TD-35 ), Graduate Innovation Fund of Jilin University (No: 101832020CX240 ), Natural Science Foundation of Hebei Province of China ( D2017508099 ), and the Program of Education Department of Hebei Province ( QN219320 ). Additional funding was provided by the Engineering Research Center of Geothermal Resources Development Technology and Equipment , Ministry of Education, China.fi=vertaisarvioitu|en=peerReviewed

Representative hydraulic conductivities in saturated groundwater flow

Heterogeneity is the single most salient feature of hydrogeology. An enormous amount of work has been devoted during the last 30 years to addressing this issue. Our objective is to synthesize and to offer a critical appraisal of results related to the problem of finding representative hydraulic conductivities. By representative hydraulic conductivity we mean a parameter controlling the average behavior of groundwater flow within an aquifer at a given scale. Three related concepts are defined: effective hydraulic conductivity, which relates the ensemble averages of flux and head gradient; equivalent conductivity, which relates the spatial averages of flux and head gradient within a given volume of an aquifer; and interpreted conductivity, which is the one derived from interpretation of field data. Most theoretical results are related to effective conductivity, and their application to real world scenarios relies on ergodic assumptions. Fortunately, a number of results are available suggesting that conventional hydraulic test interpretations yield (interpreted) hydraulic conductivity values that can be closely linked to equivalent and/or effective hydraulic conductivities. Complex spatial distributions of geologic hydrofacies and flow conditions have a strong impact upon the existence and the actual values of representative parameters. Therefore it is not surprising that a large body of literature provides particular solutions for simplified boundary conditions and geological settings, which are, nevertheless, useful for many practical applications. Still, frequent observations of scale effects imply that efforts should be directed at characterizing well‐connected stochastic random fields and at evaluating the corresponding representative hydraulic conductivitie