Just Go With The Flow
March 1, 2008
Accurate prediction of how water and contaminants flow and interact in geological formations is critical for the effective and sustainable exploitation, management and remediation of ground water resources. Realistic quantification of these processes also is critical in the context of protection against accidental exposure to radioactive and toxic wastes stored in underground repositories.
Rock heterogeneity leads to the development of preferential flow paths and stagnant regions; and variability in flow paths and composition of the porous rock matrix allows different chemical reactions and rates of reaction to occur at sites in close proximity to one another. These irregular distributions of flow paths and chemical constituents occur over a wide scale – from the pore level to the kilometer scale – and exist in both saturated and unsaturated regimes. Because of this diversity, and because field measurements are sparse and often low-resolution or unreliable, quantification of water flow and contaminant migration must be predicated on computer simulations, based on mathematical models. These model predictions can be used to determine what additional measurements should be made, where they should be sited (i.e., where to drill), and to suggest rational water exploitation, contamination control and/or remediation schemes. With respect to ground water remediation, numerical models effectively have quantified methods involving pump-and-treat, air sparging, chemically reactive in-situ barriers, and bioremediation.
Years of intensive study have led to development of tools that provide reasonably good means to actually quantify and predict contaminant migration. And yet, our abilities to quantify even “simple” fluid flow in natural geological formations remain, in many cases, somewhat limited. While theories that treat homogeneous porous media are mathematically convenient, such homogeneity rarely, if ever, exists in the field. The heterogeneity of natural geological formations at a wide range of scales necessitates consideration of more sophisticated theories. Models of flow and chemical transport processes in these complex natural systems must account for the inherent heterogeneity and scaling properties of porous rocks, as well as the typically sparse and uncertain field data that can be obtained to characterize a geological formation.
With respect to fractured formations, which are ubiquitous in nature, the situation is further complicated. As a result of the variability in fracturing mechanisms, fracture sizes range from microfissures of the order of microns to major faults of the order of kilometers, while fracture network patterns range from relatively regular polygonal arrangements to apparently random distributions. The hydraulic and transport properties of these formations vary considerably, being dependent largely on the degree of fracture interconnection, aperture variations in the fractures, and chemical characteristics of the fractures and host rock.
Conceptual PicturesAs a first step to dealing with these different situations, appropriate conceptual pictures of fluid flow and chemical transport must be formulated. Problems of interest – all of which relate to sustainable management – focus on water supply, prevention or control of contamination, and/or remediation of contaminated water resources. The relevant processes can be classified broadly to include:
- Flow and transport in the vadose (partially saturated)
zone, from land surface to (and across) the water table.
- Flow and transport in the
saturated zone (generally below the water table), in porous rock materials.
- Flow and transport in the saturated zone (generally below the water table), in fractured rock.
In all three cases, flow and chemical transport can be either miscible (e.g., heavy metals, soluble organic chemicals, soluble pesticides/herbicides dissolved in water) or immiscible (two-phase, e.g., water infiltrating into the vadose zone, oil leaking into ground water). Moreover, the chemicals may be either passive or reactive, vis-à-vis the host rock material.
Types of MeasurementsConceptual understanding, model development, and laboratory and field testing of quantitative tools for prediction are, of course, predicated on the availability of measurements at the laboratory and field scales. Analyses usually are based on measurements from outcrops, core samples and various geophysical techniques, as well as on hydraulic and tracer testing within or between boreholes.
Data from geology – Geological data include measurements and mapping of heterogeneity patterns and soil/rock types. These measurements are taken at the field scale, and often are recorded in the form of probability distributions. Laboratory-scale measurements on core samples use a wide variety of methods, ranging from flow-cell experiments to scanning electron and optical microscopy, X-ray diffraction, X-ray emission spectroscopy and magnetic resonance imaging.
Data from geophysical techniques – A number of geophysical techniques can be used to obtain additional field-scale information on fracture and heterogeneity structures. The most commonly used techniques include various seismic and electrical methods, ground penetrating radar, and electrical methods. A variety of imaging and analysis techniques within boreholes also are available.
Data from borehole hydraulic and tracer testing – Field-scale data on aquifer properties often are obtained through hydraulic tests. Many of these techniques rely on packer testing, which can yield information on hydraulic conductivities and flow rates of either single fractures or bulk formation properties in the packed-off area. Tracer tests employ various patterns of tracer injection and pumping to characterize flow and transport properties of aquifers. Other techniques involve use of multilayer samplers containing diffusion cells to quantify fluid flow. Other data can be obtained by use of borehole flowmeters, by analysis of single borehole and crosshole tests, by analysis of water level and pressure response tests, and by use of air injection.
The very nature of formation heterogeneity in the subsurface precludes complete and detailed in-situ mapping and analysis, and thus, studies must rely largely on extrapolation and subjective considerations. As a consequence, mathematical convenience and wishful thinking often govern interpretation of the few data that are available. Few of the measurement techniques mentioned above actually measure heterogeneities directly. Rather, these detection and characterization methods usually measure a response to their presence. Thus, a fundamental problem in terms of aquifer characterization arises in the distinction between what is measured and what is determined. Often, statistical techniques from interpolation, extrapolation or synthesis of additional data are employed. As a result, the very interpretation of measurements often becomes model-dependent. A critical consequence of solving such an inverse problem is that nonuniqueness arises – different models lead to different characterizations, or different characterizations applied to the same model yield different results. Thus, it should be clear that limits on available hydrogeological information color any quantitative analysis – either implicitly or explicitly.
Directions for the FutureQuantitative numerical models have the ability to provide realistic predictions of flow and chemical transport behavior for a wide range of problems of interest. Model drawbacks are in part based on theoretical and/or computational limitations, and in part on a lack of high-resolution measurements. It is critical to recognize that often seemingly insignificant local or microscopic processes can play a dominant role in field-scale flow and transport behavior.
Given the wide variety of flow and transport processes, and the different perspectives that arise as a function of the actual problem of interest, selection of any given quantitative model must be based on problem-specific considerations. Clearly, there is no single generic model that is appropriate, and so, as a consequence, a range of probabilistic and statistical approaches must be introduced. Similarly, experiments at a variety of laboratory and field scales, under both fully and partially saturated conditions, are required in our efforts to understand and predict the broad spectrum of fluid flow and chemical transport behaviors.
Numerical models have proven effective in a wide range of applications related to field-scale ground water resource management. Many such models have been used to test laboratory-scale methods for contamination control and remediation methods, and to examine their potential application in the field. Moreover, notwithstanding model limitations, even simplified models can reveal interesting (and sometimes unexpected) features of flow and transport in aquifer systems; this information should be taken into account in any field application.
Developments in both modeling and laboratory and field-scale measurement capabilities are needed. From the practical, applications’ point of view, both types of developments – and the integration of experimental and numerical studies – should be considered integral components of any field-scale operation.