Numerical studies of solute transport in a fracture surrounded by rock matrix: Effect of lateral diffusion and chemical reactions on the overall dispersion

1994 ◽  
Vol 21 (8) ◽  
pp. 461-494 ◽  
Author(s):  
R.L. Buckley ◽  
S.K. Loyalka
Keyword(s):  
Solute Transport ◽  
Chemical Reactions ◽  
Matrix Effect ◽  
Lateral Diffusion ◽  
Rock Matrix ◽  
Numerical Studies

Convective-diffusive-reactive Taylor dispersion processes in particulate multiphase systems

1990 ◽  
Vol 429 (1877) ◽  
pp. 639-671 ◽  
Keyword(s):  
Solute Transport ◽  
Chemical Reactions ◽  
Coarse Grained ◽  
Solution Technique ◽  
Multiphase System ◽  
Homogeneous Material ◽  
Phase System ◽  
Multiphase Systems ◽  
Phenomenological Coefficients ◽  
Reaction Processes

Convective-diffusive transport of a chemically reactive solute is studied analytically for a general model of a multiphase system composed of ordered or disordered particles of arbitrary shapes and sizes. Use of spatially periodic boundary conditions permits analysis of particulate multiphase systems of effectively infinite size. Solute transport occurs in both the continuous and discontinuous bulk phases, as well as within and across the interfacial phase boundaries separating them. Additionally, the solute is allowed to undergo generally inhomogeneous first-order irreversible chemical reactions occurring in both the continuous and discontinuous volumetric phases, as well as within the interfacial surface phase. Our object is that of globally describing the solute transport and reaction processes at a macro- or Darcy-scale level, wherein the resulting, coarse-grained particulate system is viewed as a continuum possessing homogeneous material transport and reactive properties. At this level the asymptotic long-time solute macrotransport process is shown to be governed by three Darcy-scale phenomenological coefficients: the mean solute velocity vector ͞U *, dispersivity dyadic ͞D *, and apparent volumetric reactivity coefficient ͞K *. A variant of a Taylor-Aris method-of-moments scheme (Brenner & Adler 1982), modified to include solute disappearance via chemical reactions, is used to express these three macroscale phenomenological coefficients in terms of the given microscale phenomenological data and geometry. The general solution technique, illustrated here for a simple, ordered geometrical realization of a two-phase system, reveals the competitive influences of the respective volumetric/surface-excess transport and reaction processes, as well as the solute adsorptivity, upon the three macroscale transport coefficients.

Fluid and Solute Transport in a Network of Channels

1991 ◽  
Vol 257 ◽  
Author(s):  
Luis Moreno ◽  
Ivars Neretnieks
Keyword(s):  
Solute Transport ◽  
Fractured Rocks ◽  
Molecular Diffusion ◽  
Field Measurements ◽  
Channel Length ◽  
Special Technique ◽  
Distribution Data ◽  
Tracer Transport ◽  
Rock Matrix ◽  
Narrow Channels

ABSTRACTA model is proposed to describe flow and transport in fractured rocks. It is based on the concept of a network of channels. This approach is backed by observations in drifts and tunnels that flow in fractured rocks takes place in sparse narrow channels with widths typically less than 10 cm and a channel frequency of one channel per a few square meters to one channel per more than a hundred square meters. Observations in boreholes also indicate that there are large distances, tens to hundreds of meters, between the most conductive sections in boreholes.For visualization purposes our model is displayed on a rectangular grid. The individual channels are given stochastically selected conductances and volumes. Flowrate calculations have been performed in grids of sizes 20*20*20 channels in most cases but larger grids have also been used. For large standard.deviations in conductances, greater than 1.6 in the log normal distribution (base 10), channeling becomes pronounced with most of the water flowing in a few paths. The effluent patterns and flowrate distributions obtained in the simulations have been compared to three different field measurements in drifts and tunnels. Standard deviations of channels conductances were found to be between 1.6 and 2.4 or more in some cases. Channel lengths were found to vary between 1.2 m and 10.2 m in the different sites. In one site where detailed borehole measurements were available the channel length could be assessed independently and was found to be 1.2 m as compared to the 1.7 m obtained from the drift inflow measurements.A particle tracking technique was used to simulate solute transport in the network. Nonsorbing as well as sorbing tracer transport can be simulated and by a special technique also tracers which diffuse into the rock matrix can be simulated.Tracer measurements in one site, Stripa, were used to compare dispersivities. These were found to be large, having Peclet numbers less than 5 both in simulations and the field results. From the Stripa tracer data it was also found that the tracers were taken up into the rock matrix by molecular diffusion. The surface area needed for this uptake was estimated to be between 0.2-20 m2/m3 for different tracers. The wetted surface for the model estimated from flowrate distribution data indicate a wetted surface of 0.2- 0.4 m2/m3.

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