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ANISOTROPIC FLOW IN HETEROGENETIC GRANULAR MEDIA:
ANALYSIS OF COMPLEX FLOW SYSTEMS

An On-Line Version of a Column First Published in the:
National Environmental Journal Sept./Oct. 1994 Vol. 4 No. 5 Pages 24-25

by: David B. Vance

Heterogeneity in granular aquifers has profound effect on the fate and transport of impacting contaminants as well as subsequent remediation efforts. Anisotropic advective flow, dispersion, diffusional transport, contaminant adsorption and other physical/chemical processes taking place in these systems is complex. Total understanding of those processes at any given site is impossible in a practical sense, and attempting to gather comprehensive data in support of that understanding is prohibitively expensive. This column touches on anisotropic advective groundwater flow in these systems. A physical description of granular heterogeneity and its effect, will be followed by a brief review of recent developments in modeling technology.

Heterogeneity and subsequent anisotropic groundwater flow conditions should be considered normal at the majority of contaminated sites. Near surface granular aquifers that are impacted by the release of contaminants are usually poorly indurated and can be classified according to depositional regime as follows:

  • Fluvial which includes rivers, streams and alluvial fans;
  • glacial such as tills;
  • lacustrine lake deposits; and
  • eolian sand dune systems.

 In these depositional systems (particularly fluvial and glacial) it is common to have granular deposits of high permeability contrast juxtaposed to each other and therein lies the source of great complexity.

Granular media advective flow regimes can be classified into three broad types:

  • uniform, medium to coarse granular soils capable of supporting significant intergranular advective flow;
  • low permeability silts, clays and tills in which any advective flow actually occurs in permeable channels such as fractures or joints; and
  • complex interbedded soils with zones of high permeability contrast resulting in anisotropic advective flow.

 Sediment source and energy of transport are the primary controllers of the characteristics of deposited materials. A rain storm, rising tide, or flood carry an initial high energy load of coarser material (that may be mixed with finer grained silts and clays). As a given deposition event begins to subside the largest grains settle first, followed by granular materials of decreasingly smaller sizes. The last stage may involve quiescent waters from which the finest clay and silt particles will settle over a significant period of time. The result of a given episode is a layer stratified by size within the overall soil mass. At the smallest scale heterogeneity is expressed by variations in pore size and shape; on the bench scale by variance in particle size; on the scale of a road cut as layering; and on larger scales as changes in size of the layers, pinch outs and facies changes. In layered sediments of this type horizontal flow is dominated by the most permeable units in the sequence and vertical flow by the least permeable. Mega scale heterogeneity can also be created by processes such as braided stream deposits or glacial till systems, where lenticular pods of sand may be deposited in a matrix of lower permeability silts and clays.

Material that is two or three orders of magnitude higher in permeability than the bulk soil matrix will totally govern the groundwater flow system, one inch of sand can dominate the flow through tens of feet of silt or clay. The practical problem this presents is the determination of the spatial configuration of the physically small but hydraulically dominant units in the soil matrix. One of the potentially most damaging situations are conditions in which the permeable channels or layers are preferentially exposed to the surface. These zones are susceptible to contaminant impact followed by surface recharge which can act as a hydraulic driver of contaminants within a matrix that overall does not support high rates of advective groundwater flow, even in the more permeable (but unexposed) portions of the coarser soil units.

The testing and analysis of these anisotropic heterogenetic flow systems is potentially extremely complex. As a matter of practicality a significant number of assumptions must be made in the analysis of these aquifers. As readily available computing power has increased over the past decades the number and degree of required assumptions have declined in the more sophisticated applications. Irrespective, two prime assumptions are that at some scale the heterogenetic soil can be treated as a homogenous block and secondly, that the spatial configuration of the heterogeneity has been defined. Increasing computational power typically allows for a finer mesh of blocks, but it has not addressed the issue of spatial configuration.

A significant new tool that is beginning to be put to use is the employment of fractal concepts to study the hydrology of heterogenetic soils. This approach points to a serious flaw in the value of using finer blocks in the modeling matrix. If the geometry of the heterogeneity is fractal in the soil matrix (which evidence increasingly indicates it often is) the assumption that the matrix can be represented by averaging is false. A fractal matrix will not become homogenous with averaging irrespective of block size.

With further use of the concepts of fractal analysis it is possible to model general features and hydraulic behavior and interpolate hydraulic dynamics from sparse data, an ability of potentially great value in these complex groundwater flow systems. With this approach water level, flow and soil data can be used from an operating groundwater recovery system to fine tune understanding of the site. Through an iterative process the fractal model is used to resolve hydrogeological attractors in the flow system. Known hydraulic properties are used to model drawdown in the forward iteration and observed drawdown and flow rates are used to model hydraulic properties in the inverse iteration. This process has the potential to be a powerful tool in definition of heterogenetic anisotropic groundwater systems.

At this juncture computer capacity allows for primitive two dimensional modeling in this manner. With improvements it will soon be possible to robustly model three dimensional systems. This technology will spatially identify which portions of the soil matrix have the greatest impact on the groundwater flow regime. It can also subtly determine areas where data gaps of high impact exist and which require additional testing wells.

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Copyright 2002 David B. Vance

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