From well-test data to input to stochastic continuum models: effect of the variable support scale of the hydraulic data

The question of how well the true underlying hydraulic conductivity statistics of heterogeneous media are captured by well tests is addressed. The hydraulic conductivity value and the corresponding support volume associated with a theoretical well are correlated, causing a bias in the statistics derived from well-test analyses. Statistics derived from numerically simulated well tests are compared with the known underlying conductivity statistics and the results indicate an under-prediction by simulations at higher hydraulic conductivities. The deviation starts at about mean conductivity and can be as large as an order of magnitude, with the conductivity in the vicinity of the well defining the upper boundary. In other words, the conductivity value interpreted from the well test cannot be larger than the value that the well test first encounters. Consequently, for data in this simulation exercise, the standard deviation, if only determined for the upper range of the conductivity values, would be underestimated by a factor of 1.6–2. While this specific range is likely to depend on the scale and degree of the underlying heterogeneity as well as the duration of the test, the results should be indicative of a more general behaviour and are likely to occur in other heterogeneous data as well.