A new look at traditional deterministic flow models and their calibration in the context of randomly heterogeneous media

We examine the tradition of modelling subsurface flow deterministically from a stochastic viewpoint. In particular, we show that traditional deterministic flow equations do apply to randomly heterogeneous media, albeit in an approximate manner, provided they are interpreted in a non-traditional manner. Our paper explains why parameter estimates obtained by traditional inverse methods tend to vary as one modifies the database. It also makes clear that the traditional Monte Carlo method of assessing uncertainty in the output of a calibrated deterministic model generally overestimates the predictive capabilities of the model. The only valid way to assess predictive uncertainty is by means of a stochastic model.