DEALING WITH SPATIAL HETEROGENEITY

We present a historical review of how the heterogeneity of rock formations has been treated in the past, from early times to the present, when studying groundwater flow and mostly permeability. The following major approaches will be summarized : (i) averaging, equivalent homogeneous media; (ii) electric analogue and numerical modelling; (iii) inverse modelling, inferring the heterogeneity from head measurements, need for additional constraints; (iv) concept of random variations of properties in space, geostatistical approach, estimation and simulation; (v) “Stochastic Shale” models, Boolean models, geostatistical facies models, calibration of facies models; (vi) the issue of upscaling; (vii) genetic approach.

We then ask: when does heterogeneity really matter? Two examples will be discussed: (i) a local DNAPL contamination case of a superficial aquifer, (ii) a large-scale water resources problem in northern Sahara. Intermediate case studies with various scales will also be considered.

We then proceed with a list of questions and suggestions concerning the need for further research in the field of heterogeneity : (i) transport problems versus flow problems; (ii) point or diffuse source terms; (iii) two-phase flow; (iv) triptych : problem to solve / methods to use and models to build / data to collect; (v) subsurface imaging and geophysics; (vi) new testing methods to display heterogeneity; (vi) creating a catalog of aquifer properties and description, (vii) the upscaling problem.

In conclusion, we believe that the future of “dealing with heterogeneity”, when necessary, is largely in the development and calibration of facies models. These will have to combine a genetic approach with a geostatistical (and Boolean) approach. The individual properties of each facies will have to be derived from specially designed tests to be interpreted directly with the facies models, and not with the standard “equivalent homogeneous medium” approach that we are using today as an intermediate “filter” between the tests and the models. Geophysics is likely to be a very important component of the data collection process. Averaging methods may still be needed, for large-scale and long-term problems. World-wide catalogs of aquifer properties and methods of description are urgently needed.