The ensemble Kalman filter (EnKF) is a widely used data assimilation method that has the capacity to sequentially update system parameters and states as new observations become available. One noticeable feature of the EnKF is that it not only can provide real-time updates of model parameters and state variables, but also can give the uncertainty associated with them in each assimilation step. The natural system is open and complex, rendering it prone to multiple interpretations and mathematical descriptions. In this paper, a multimodel data assimilation method is proposed by embedding the EnKF into the Bayesian model averaging framework to account for the uncertainty stemming from the model itself. An illustrative example, considering both hydrogeological and groundwater flow uncertainties, is employed to demonstrate the proposed multimodel data assimilation approach via the EnKF. Results show that statistical bias and uncertainty underestimation can occur when the data assimilation process relies on a single postulated model. The posterior model weight can adjust itself dynamically in time according to its consistency with observations. The performances of log conductivity estimation and head prediction are compared to the standard EnKF method based on the postulated single model and the proposed multimodel EnKF method. Comparisons show that the multimodel EnKF performs better in terms of statistical measures, such as log score and coverage, when sufficient observations have been assimilated in this case.

We explore the way in which uncertain descriptions of aquifer heterogeneity and groundwater flow impact one's ability to assess the worth of collecting additional data. We do so on the basis of Maximum Likelihood Bayesian Model Averaging (MLBMA) by accounting jointly for uncertainties in geostatistical and flow model structures and parameter (hydraulic conductivity) as well as system state (hydraulic head) estimates, given uncertain measurements of one or both variables. Previous description of our approach was limited to geostatistical models based solely on hydraulic conductivity data. Here we implement the approach on a synthetic example of steady state flow in a two‐dimensional random log hydraulic conductivity field with and without recharge by embedding an inverse stochastic moment solution of groundwater flow in MLBMA. A moment‐equations‐based geostatistical inversion method is utilized to circumvent the need for computationally expensive numerical Monte Carlo simulations. The approach is compatible with either deterministic or stochastic flow models and consistent with modern statistical methods of parameter estimation, admitting but not requiring prior information about the parameters. It allows but does not require approximating lead predictive statistical moments of system states by linearization while updating model posterior probabilities and parameter estimates on the basis of potential new data both before and after such data are actually collected.

Artificial intelligence methods for oil and gas reservoir development: Current progresses and perspectives