Constructing correlated random fields in the laboratory for observations of fluid and mass transport

We demonstrate that correlated, random permeability fields with user-specified values of desired statistical properties can be constructed in the laboratory. Two columns were each packed wet with 101 5-cm layers of ordered, sieved sand whose permeabilities were individually measured prior to packing. The ordering of 13 size classes of sand in each column was determined by sampling a numerically generated random field, sorting the numerical data into bins having bounds defined by the geometric means of adjacent site-class permeabilities, and assigning the bin size-class permeability value to the spatial locations associated with the numerical data collected in each bin. The insitu permeabilities of the layers of the packed columns were obtained using a 102-port, constant-head permeameter setup. The calculated means (-13.6 for both columns), variances (0.26 and 0.98), and negative-exponential-variogram correlation scales (17 cm for both columns) of the in-situ natural-log-permeability fields agreed well with the target statistics that had been used to generate the numerical random field. The variance of observed hydraulic head as a function of distance along each column was calculated for several volumetric flow rates. The scaling of the head variance data to the statistics of the permeability field agreed well with stochastic theoretical predictions for one-dimensional bounded domains. Although head observations in saturated flow are reported here, the experimental vessels could be used to observe unsaturated flow as well as mass transport processes, and furthermore can be extended to more realistic two- and three-dimensional permeability fields. The methodology offers value in allowing an investigator to (1) carefully control selected physical variables (e.g., flow direction, temperature, chemical reactions) while observing a phenomenon of interest in a heterogeneous permeability setting statistically similar to that which has been shown to be characteristic of a number of field sites, and (2) control and quantify the statistics of the permeability field needed as inputs for predictive stochastic models.