Transport in heterogeneous porous media: Prediction and uncertainty

This study presents a method for obtaining risk-qualified estimates of various statistics that characterize the migration of a nonreactive tracer in heterogeneous porous media. The steps required to get these estimates are a follows: (1) the solute body is assumed to be composed of a large number of imaginary solute particles; (2) a Lagrangian description of the migration of the solute particles in space is adopted; (3) the Lagrangian description is transformed into an Eulerian one by a quasi-linear method, whereby the translation of the particles in space is simulated through successive, spatially correlated displacements; (4) the plume's various statistics are obtained by averaging over the ensemble of simulated particles, and, lastly, (5) simultaneous simulation of the motion of two particles in space entails the spatial moments of the plume and their variances, and in addition, the concentration is obtained qualified by its variance. The model is compared with numerical simulations and is found to compare quite favorably even for log conductivity variances as large as 2.6. This study shows that (1) after a certain travel time, the concentration variance becomes largest next to the plume center and gets smaller with distance from the plume center; (2) the concentration coefficientmore » of variation grows with distance from the plume center and prediction of the low concentration on the periphery of the plume is subject to the largest uncertainty; (3) the concentration coefficient of variation grows with time while the concentration variance gets smaller with time; and (4) interpretation of field data depends on the interpolation method and in particular on the size of the averaging domain.« less

[1]  Geoffrey Ingram Taylor,et al.  Diffusion by Continuous Movements , 1922 .

[2]  R. Aris.  On the dispersion of a solute in a fluid flowing through a tube , 1956, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[3]  Franklin W. Schwartz,et al.  Mass transport: 1. A stochastic analysis of macroscopic dispersion , 1980 .

[4]  G. Dagan.  Stochastic modeling of groundwater flow by unconditional and conditional probabilities: 2. The solute transport , 1982 .

[5]  E. G. Vomvoris,et al.  A geostatistical approach to the inverse problem in groundwater modeling (steady state) and one‐dimensional simulations , 1983 .

[6]  C. Axness,et al.  Three‐dimensional stochastic analysis of macrodispersion in aquifers , 1983 .

[7]  G. Dagan.  Solute transport in heterogeneous porous formations , 1984, Journal of Fluid Mechanics.

[8]  Lynn W. Gelhar,et al.  Stochastic subsurface hydrology from theory to applications , 1986 .

[9]  David L. Freyberg,et al.  A natural gradient experiment on solute transport in a sand aquifer: 2. Spatial moments and the advection and dispersion of nonreactive tracers , 1986 .

[10]  E. Sudicky.  A natural gradient experiment on solute transport in a sand aquifer: Spatial variability of hydraulic conductivity and its role in the dispersion process , 1986 .

[11]  David L. Freyberg,et al.  Stochastic modeling of vertically averaged concentration uncertainty in a perfectly stratified aquifer , 1987 .

[12]  Gedeon Dagan,et al.  Theory of Solute Transport by Groundwater , 1987 .

[13]  Ronald G. Larson,et al.  Dispersion and Reservoir Heterogeneity , 1988 .

[14]  G. Dagan,et al.  Stochastic analysis of boundaries effects on head spatial variability in heterogeneous aquifers: 1. Constant head boundary , 1988 .

[15]  D. A. Barry,et al.  On the Dagan model of solute transport in groundwater: Application to the Borden site , 1988 .

[16]  Dennis McLaughlin,et al.  Stochastic analysis of nonstationary subsurface solute transport: 1. Unconditional moments , 1989 .

[17]  G. Dagan.  Flow and transport in porous formations , 1989 .

[18]  Yoram Rubin,et al.  Stochastic analysis of boundaries effects on head spatial variability in heterogeneous aquifers: 2. Impervious boundary , 1989 .

[19]  D. McLaughlin,et al.  Stochastic analysis of nonstationary subsurface solute transport: 2. Conditional moments , 1989 .

[20]  D. A. Barry,et al.  Three‐dimensional statistical moment analysis of the Stanford/Waterloo Borden tracer data , 1990 .

[21]  J. H. Cushman,et al.  Inverse methods for subsurface flow: A critical review of stochastic techniques , 1990 .

[22]  S. P. Neuman,et al.  A quasi‐linear theory of non‐Fickian and Fickian subsurface dispersion: 2. Application to anisotropic media and the Borden site , 1990 .

[23]  Y. Rubin.  Stochastic modeling of macrodispersion in heterogeneous porous media , 1990 .

[24]  Gedeon Dagan,et al.  Transport in heterogeneous porous formations: Spatial moments, ergodicity, and effective dispersion , 1990 .

[25]  G. Dagan.  Comment on “Stochastic analysis of nonstationary subsurface solute transport: 1. Unconditional moments” by W. Graham and D. McLaughlin , 1990 .

[26]  S. P. Neuman,et al.  A quasi-linear theory of non-Fickian and Fickian subsurface dispersion , 1990 .

[27]  Yoram Rubin,et al.  Prediction of tracer plume migration in disordered porous media by the method of conditional probabilities , 1991 .