MODEL COMPLEXITY AND SIMPLICITY: COMBINING THE STRENGTHS OF BOTH

We have the technology to simulate complex processes in complex media. While the outcomes of predictive simulation rarely match reality, a complex model domain can be made to look real. Hence rock types and hydraulic properties can be represented in the model at locations at which they were sampled. Moreover interpolation of both of these to the model’s mesh can be informed by expert knowledge. Because expert knowledge is stochastic in nature, it gains full expression when it is used as a stochastic field generator of rock dispositions and hydraulic properties, constrained by measurements at points at which either or both of these are known.

Unfortunately, while a complex model may provide good receptacles for expert knowledge, its ability to make use of information resident in measurements of system state through “history matching” may be limited. This can be viewed as calculation and maximization of the likelihood term of Bayes equation. The likelihood term can be just as important as the prior information term in quantifying and reducing the uncertainty of model predictions. However use of a complex model in the history-matching processes can place mathematical, numerical and computational obstacles between the information that is resident in measurements of system state, and the model itself. So while the uncertainty that exists prior to the use of that information can be quantified using a complex model, a simpler model must often be employed to reduce that uncertainty. But because a simpler model may provide poorer receptacles for expert knowledge than a complex model, its potential for reducing predictive uncertainty through the history-matching process may not be realized.

This tension between complexity and simplicity can be resolved by using a complex and simple model in partnership. Through repeated calibration of the simple model against outputs of the complex model generated using different stochastic realizations of the geological and hydraulic properties of reality, the “cost of simplicity” can be quantified. This cost expresses itself in bias, and a reduced ability of a simple model to compute predictive uncertainty. When the simple model is then calibrated against a real-world dataset, and used to make predictions, simplicity-induced bias can be corrected, and predictive uncertainty can be quantified.