Constraining a compositional flow model with flow‐chemical data using an ensemble‐based Kalman filter

Abstract

Isothermal compositional flow models require coupling transient compressible flows and advective transport systems of various chemical species in subsurface porous media. Building such numerical models is quite challenging and may be subject to many sources of uncertainties because of possible incomplete representation of some geological parameters that characterize the system's processes. Advanced data assimilation methods, such as the ensemble Kalman filter (EnKF), can be used to calibrate these models by incorporating available data. In this work, we consider the problem of estimating reservoir permeability using information about phase pressure as well as the chemical properties of fluid components. We carry out state-parameter estimation experiments using joint and dual updating schemes in the context of the EnKF with a two-dimensional single-phase compositional flow model (CFM). Quantitative and statistical analyses are performed to evaluate and compare the performance of the assimilation schemes.Our results indicate that including chemical composition data significantly enhances the accuracy of the permeability estimates. In addition, composition data provide more information to estimate system states and parameters than do standard pressure data. The dual state-parameter estimation scheme provides about 10% more accurate permeability estimates on average than the joint scheme when implemented with the same ensemble members, at the cost of twice more forward model integrations. At similar computational cost, the dual approach becomes only beneficial after using large enough ensembles.

A Bayesian consistent dual ensemble Kalman filter for state-parameter estimation in subsurface hydrology

“…Such a separation of the update steps is expected to provide more consistent estimates of the parameters. The dual update framework was indeed shown to provide better performances than the joint EnKF, at the cost of increased computational burden (see for instance, Moradkhani et al, 2005b;Samuel et al, 2014;Gharamti et al, 2014a).…”

“…One classical approach that has been proposed to tackle this issue is the so-called dual filter, which separately updates the state and parameters using two interactive EnKFs, one acting on the state and the other on the parameters (Moradkhani et al, 2005b). The dual EnKF has been applied to streamflow forecasting problems using rainfall-runoff models (e.g., Lü et al, 2013;Samuel et al, 2014), subsurface contaminant (e.g., Tian et al, 2008;Lü et al, 2011;Gharamti et al, 2014b), and compositional flow models (e.g., Phale and Oliver, 2011;Gharamti et al, 2014a), to cite but a few. Gharamti et al (2014a) concluded that the dual scheme provides more accurate state and parameter estimations than the joint scheme when implemented with large enough ensembles.…”

“…The dual EnKF has been applied to streamflow forecasting problems using rainfall-runoff models (e.g., Lü et al, 2013;Samuel et al, 2014), subsurface contaminant (e.g., Tian et al, 2008;Lü et al, 2011;Gharamti et al, 2014b), and compositional flow models (e.g., Phale and Oliver, 2011;Gharamti et al, 2014a), to cite but a few. Gharamti et al (2014a) concluded that the dual scheme provides more accurate state and parameter estimations than the joint scheme when implemented with large enough ensembles. In terms of complexity, however, the dual scheme requires integrating the filter ensemble twice with the numerical model at every assimilation cycle, and is therefore computationally more demanding.…”

On the efficiency of the hybrid and the exact second-order sampling formulations of the EnKF: a reality-inspired 3-D test case for estimating biodegradation rates of chlorinated hydrocarbons at the port of Rotterdam

“…Data assimilation (DA) methods follow a Bayesian formulation by combining prior information of a dynamical system with available measurements to obtain an analysis of the system state and parameters (Hoteit et al, 2012;Gharamti et al, 2014a). Sequential DA techniques, such as the ensemble Kalman filter (EnKF), assimilate the data as they become available.…”

“…The complexity of the forecast step grows with the ensemble size. If one supposes that C M is the cost for integrating the model to the next observation time, the computational requirement of the forecast step is NN e C M , where N is the final simulation time (Gharamti et al, 2014a). The superscripts a, f and i denote the analysis, forecast and ensemble number, respectively.…”