FIELD-SCALE EFFECTIVE MATRIX DIFFUSION COEFFICIENT FOR FRACTURED ROCK:RESULTS FROM LITERATURE SURVEY

Matrix diffusion is an important mechanism for solute transport in fractured rock. We recently conducted a literature survey on the effective matrix diffusion coefficient, D{sub m}{sup e}, a key parameter for describing matrix diffusion processes at the field scale. Forty field tracer tests at 15 fractured geologic sites were surveyed and selected for the study, based on data availability and quality. Field-scale D{sub m}{sup e} values were calculated, either directly using data reported in the literature or by reanalyzing the corresponding field tracer tests. Surveyed data indicate that the effective-matrix-diffusion-coefficient factor F{sub D} (defined as the ratio of D{sub m}{sup e} to the lab-scale matrix diffusion coefficient [D{sub m}] of the same tracer) is generally larger than one, indicating that the effective matrix diffusion coefficient in the field is comparatively larger than the matrix diffusion coefficient at the rock-core scale. This larger value can be attributed to the many mass-transfer processes at different scales in naturally heterogeneous, fractured rock systems. Furthermore, we observed a moderate trend toward systematic increase in the F{sub D} value with observation scale, indicating that the effective matrix diffusion coefficient is likely to be statistically scale dependent. The F{sub D} value ranges from 1 to 10,000 for observation scales from 5 to 2,000 m. At a given scale, the F{sub D} value varies by two orders of magnitude, reflecting the influence of differing degrees of fractured rock heterogeneity at different sites. In addition, the surveyed data indicate that field-scale longitudinal dispersivity generally increases with observation scale, which is consistent with previous studies. The scale-dependent field-scale matrix diffusion coefficient (and dispersivity) may have significant implications for assessing long-term, large-scale radionuclide and contaminant transport events in fractured rock, both for nuclear waste disposal and contaminant remediation

Modelo de distribución de agua en suelo regado por goteo

[ES] Se desarrolla un modelo de simulación de la dinámica del agua en el suelo en riego localizado, denominado SIMDAS. Para el desarrollo del procedimiento numérico, se utiliza la teoría de flujo de agua en condiciones de no saturación, sin efecto histerético, resolviendo la ecuación de flujo axisimétrico sin y con extracción de agua por la planta a partir de un método en diferencias finitas, con la consideración de los distintos horizontes del suelo. Verificado el modelo en campo, los resultados que presenta son satisfactorios cuando no se contempla la presencia de cultivo, pero no lo son cuando interviene la extracción de agua por la planta. Por consiguiente, el grado de aceptabilidad es suficiente para fines de diseño agronómico de sistemas de riego localizado, pero no lo es para aquellos casos en que la extracción de agua por la planta interviene de manera destacada, como en el manejo y la programación de riegos.Ramírez De Cartagena Bisbe, F.; Sáinz Sánchez, MA. (1997). Modelo de distribución de agua en suelo regado por goteo. Ingeniería del Agua. 4(1):57-70. https://doi.org/10.4995/ia.1997.2716SWORD577041Armstrong C.F., Wilson T.V. (1983) Computer model for moisture distribution in stratified soils under a trickle source. Transactions of the American Society of Agricultural Engineers: 1704-1709.Belmans C., Wesswling J.G., Feddes R.A. (1983) Simulation model of the water balance of a cropped soil: SWATRE. Journal of Hidrology. 63 & 21: 271-286.Ben-Asher J., Charach CH., Zemel A. (1986) Infiltration and water extraction from trickle irrigation source: The effective hemisphere model. Soil Science Society of America Journal. 50: 882-887.Brandt A., BreslerE., Diner N., Ben-Asher J., Heller J., Goldberg. (1971) Infiltration from a trickle source: I. Mathematical models. Soil Science Society of America Proceedings, 35: 675-682.Bresler R E. (1975) Two-dimensional transport of solutes during nonsteady infiltration from a trickle source. Soil Science Society of America Proceedings, 39: 604-613.Feddes R.A., Kowalik P.J., Zaradny H. (1978) Simulation of field water use and crop yield. PUDOC, Wageningen. 189pp.Ghali S.G. (1986) Mathematical modelling of soil moisture dynamics in trickle irrigated fields. Thesis, University of Southampton (UK).Gupta S.C., Larson W.E. (1979) Estimating soil wáter retention characteristics from particle size distribution, organic matter percent, and bulk density. Water Resources Research, 15(6): 1633-1635.Hillel D. (1977) Computer simulation of soil-waters dynamics. A compendium of recent work. IDRC, Ottawa, Canada. 214 pp.Jackson R.D. (1972) On the calculation of hydraulic conductivity. Soil Science Society of America Proceedings. 36: 380-382.Keller J. (1978) Trickle irrigation. In Irrigation (Ch. 7). National Engineering Handbook USDA-SCS.Keller J., Karmelid. (1975) Trickle irrigation design. Rain Bird Corp. Glendora, California USA. 133 pp.Khatri K.C. (1984) Simulation of soil moisture migration from a point source. Thesis, McGill University, Quebec, Canada.Kunze R.J., Uehara G., Graham K. (1968) Factors important in the calculation of hydraulic conductivity. Soil Science Soc. Amer. Proc., 32: 760-765.Lafolie F., Guenelon R., Van Genuchten M.TH. (1989a.) Analysis of water flow under trickle irrigation: I. Theory and numerical solution. Soil Science Society of America Journal, 53: 1310-1318.Lafolie P., Guenelon R., Van Genuchten M.TH. (1989b.) Analysis of water flow under trickle irrigation: II. Experimental evaluation. Soil Science Society of America Journal. 53: 1318-1323.Marino M.A., Tracy J.C. (1988) Flow of water through root-soil environment. Journal of Irrigation and Drainage Engineering, 114 (4): 588-604.Marshall T.J. (1958) A relation between permeability and size distribution of pores. Journal of Soil Science, 9 (8): 1-8.Millington R.J., Quirk J.P. (1959) Permeability of porous media Nature, 183: 378-388.Molz F.J., Remson I. (1970) Extraction term models of soil moisture use by transpiring plants. Water Resources Research, 6 (5): 1346-1356.Philip J.R. (1971) General theorem on steady infiltration from surface sources, with application to point and line sources. Soil Science Society of America Proceedings, 35: 867-871.Pradad R. (1988) A linear root water uptake model Journal of Hidrology, 99: 297-306.Raats P.A.C. (1977) Laterally confined, steady flows of water from sources and to sinks in unsaturated soils. Soil Science Society of America Journal, 41:294-304.Ramírez De Cartagena F. (1994) Simulación numerica de la dinámica del agua en el suelo. Aplicacion al diseño de sistemas de riego LAF. Tesis Doctoral. ETSEA. Universidad de Lleida.Rawls W.J., Brakensiek D.L. (1982) Estimating soil water retention from soil properties. Journal of the Irrigation and Drainage Division, Proc. of the ASCE, 108, IR2: 166-171.Saxton K.E., Rawls W.J., Romberger J.S., Papendick R.I. (1986) Estimating generalized soil-water characteristics from texture. Soil Science Society of America Journal, 50: 1031-1036.Taghavi S.A., Mariño M.A., Rolston D.E. (1985) Infiltration from a trickle source in a heterogeneous soil medium. Journal of Hidrology, 78: 107-121.Van Der Ploeg R.R., Benecke P. (1974) Unsteady, unsaturated, n-dimensional moisture flow in soil: A computer simulation program. Soil Science Society of America Proceedings, 38: 881-885Vermeiren L., Jobling G.A. (1986) Riego localizado. Estudios FAO Riego y Drenaje, n°36. FAO. Roma. 203 pp.Warrick A.W., Lomen D.O., Amoozegarfard A. (1980) Linearized moisture flow with root extraction for three dimensional, steady conditions. Soil Science Society of America Journal, 44: 911-914

Scale dependence of the effective matrix diffusion coefficient: some analytical results

Matrix diffusion is an important process affecting solute transport in fractured rock, and the matrix diffusion coefficient is a key parameter for describing this process. Previous studies have indicated that the effective matrix-diffusion coefficient values, obtained from a number of field tracer tests, are enhanced in comparison with local values and may increase with test scale. In this communication, we develop analytical expressions for the effective matrix diffusion coefficient for two simple fracture-matrix systems, and demonstrate that heterogeneities in the rock matrix at different scales contribute to the scale dependence of the effective matrix diffusion coefficient

Quantitative Methods for Reservoir Characterization and Improved Recovery: Application to Heavy Oil Sands

Improved prediction of interwell reservoir heterogeneity was needed to increase productivity and to reduce recovery cost for California's heavy oil sands, which contain approximately 2.3 billion barrels of remaining reserves in the Temblor Formation and in other formations of the San Joaquin Valley. This investigation involved application of advanced analytical property-distribution methods conditioned to continuous outcrop control for improved reservoir characterization and simulation

A two-class population balance equation yielding bimodal flocculation of marine or estuarine sediments

Bimodal flocculation of marine and estuarine sediments describes the aggregation and breakage process in which dense microflocs and floppy macroflocs change their relative mass fraction and develop a bimodal floc size distribution. To simulate bimodal flocculation of such sediments, a Two Class Population Balance Equation (TCPBE), which includes both size-fixed microflocs and size varying macroflocs, was developed. The new TCPBE was tested by a model-data fitting analysis with experimental data from 1-D column tests, in comparison with the simple Single-Class PBE (SCPBE) and the elaborate Multi-Class PBE (MCPBE). Results showed that the TCPBE was the simplest model that is capable of simulating the major aspects of the bimodal flocculation of marine and estuarine sediments. Therefore, the TCPBE can be implemented in a large-scale multi-dimensional flocculation model with least computational cost and used as a prototypic model for researchers to investigate complicated cohesive sediment transport in marine and estuarine environments. Incorporating additional biological and physicochemical aspects into the TCPBE flocculation process is straight forward also

An interpretation of potential scale dependence of the effective matrix diffusion coefficient

Matrix diffusion is an important process for solute transport in fractured rock, and the matrix diffusion coefficient is a key parameter for describing this process. Previous studies indicated that the effective matrix diffusion coefficient values, obtained from a large number of field tracer tests, are enhanced in comparison with local values and may increase with test scale. In this study, we have performed numerical experiments to investigate potential mechanisms behind possible scale-dependent behavior. The focus of the experiments is on solute transport in flow paths having geometries consistent with percolation theories and characterized by local flow loops formed mainly by small-scale fractures. The water velocity distribution through a flow path was determined using discrete fracture network flow simulations, and solute transport was calculated using a previously derived impulse-response function and a particle-tracking scheme. Values for effective (or up-scaled) transport parameters were obtained by matching breakthrough curves from numerical experiments with an analytical solution for solute transport along a single fracture. Results indicate that a combination of local flow loops and the associated matrix diffusion process, together with scaling properties in flow path geometry, seems to be the dominant mechanism causing the observed scale dependence of the effective matrix diffusion coefficient (at a range of scales)

FIELD-SCALE EFFECTIVE MATRIX DIFFUSION COEFFICIENT FOR FRACTURED ROCK:RESULTS FROM LITERATURE SURVEY

Matrix diffusion is an important mechanism for solute transport in fractured rock. We recently conducted a literature survey on the effective matrix diffusion coefficient, D{sub m}{sup e}, a key parameter for describing matrix diffusion processes at the field scale. Forty field tracer tests at 15 fractured geologic sites were surveyed and selected for the study, based on data availability and quality. Field-scale D{sub m}{sup e} values were calculated, either directly using data reported in the literature or by reanalyzing the corresponding field tracer tests. Surveyed data indicate that the effective-matrix-diffusion-coefficient factor F{sub D} (defined as the ratio of D{sub m}{sup e} to the lab-scale matrix diffusion coefficient [D{sub m}] of the same tracer) is generally larger than one, indicating that the effective matrix diffusion coefficient in the field is comparatively larger than the matrix diffusion coefficient at the rock-core scale. This larger value can be attributed to the many mass-transfer processes at different scales in naturally heterogeneous, fractured rock systems. Furthermore, we observed a moderate trend toward systematic increase in the F{sub D} value with observation scale, indicating that the effective matrix diffusion coefficient is likely to be statistically scale dependent. The F{sub D} value ranges from 1 to 10,000 for observation scales from 5 to 2,000 m. At a given scale, the F{sub D} value varies by two orders of magnitude, reflecting the influence of differing degrees of fractured rock heterogeneity at different sites. In addition, the surveyed data indicate that field-scale longitudinal dispersivity generally increases with observation scale, which is consistent with previous studies. The scale-dependent field-scale matrix diffusion coefficient (and dispersivity) may have significant implications for assessing long-term, large-scale radionuclide and contaminant transport events in fractured rock, both for nuclear waste disposal and contaminant remediation