Impact of Random Function Choice on Groundwater Mass Transport Modelling

Abstract

Stochastic analysis of 2-D groundwater flow requires adopting a random function (RF) model for transmissivity. The parameters of this random function are decided upon after analysing measured data and other relevant information. Decisions on whether the RF is multiGaussian or not, stationary or not, multimodal or not, must be taken. We analyse the impact that some of these decisions may have in modelling groundwater flow in the Culebra dolomite formation at the WIPP site. The data set, consisting of 36 measurements, displays an apparent spatial trend and an apparent bimodality. Four RF models are selected, all of them MultiGaussian; in two of the models, the normally distributed random variable is log-transmissivity, in the other two, the random variable is the normal-score transform of transmissivity; in two of the models, the RF is stationary, in the other two the RF is non-stationary in the mean, explicitly accounting for the apparent spatial trend. For all four RF models, 200 conditional realizations of transmissivity are generated, and groundwater travel times from the centre of the domain to the southern boundary are computed. In addition, transport was modelled with and without intra-cell dispersion. Regarding RF model choice, the results show little difference between the use of stationary and non-stationary RF models, the main reason being the control that the conditioning data exert on all realizations. On average, the arrival positions at a given control plane are very close; only the variance of arrival positions differs, being smaller for the non-stationary RF than for the stationary one. When normal scores are used, the bimodality observed in the sample data is imposed in all realizations. If not, the sample data are supposed to belong to a normal population with same mean and variance, departure of the sample data histogram from the normal distribution is considered sampling fluctuation. We conclude that data conditioning implicitly accounts for the apparent trend, however, whether to extend the conditioning so as to reproduce exactly the same sample data histogram is a decision that must be carefully evaluated. Regarding intra-cell dispersion, the resulting breakthrough curves are very different depending on whether it is accounted for or not. For this data set, this is the single most influential decision.