Ensemble Kalman Filter for estimation of rock properties in geothermal reservoirs

 

Obtaining better knowledge of properties inside groundwater reservoirs improves their evaluation for economic geothermal usage. Since in situ experimental data on rock properties as well as in situ observations on groundwater flow are naturally sparse, thermal and hydraulic properties are only known within a certain probability. Therefore, stochastic inverse methods like the Ensemble Kalman Filter (EnKF) are a sensible extension of purely deterministic numerical solutions of the hydrothermal equations (provided by the SHEMAT-Suite program at the GGE). The Ensemble Kalman Filter is a modern Monte Carlo version of the Kalman Filter adapted to minimizing computational cost. It is already a well-established, suitable tool for approaching geophysical questions, which often include a large number of variables. Still, there is some room for improvement, for instance concerning the potentially spurious assumption of Gaussian probability distributions for reservoir parameters like permeability. More technically, the locality of the observation needs to be included to counteract filter divergence.

Permeability is the crucial rock parameter for the description of hydrothermal fluid flow. A better knowledge of the permeability values at different locations inside a possible geothermal reservoir can give vital information about water and heat flow through the reservoir and may ultimately influence the decision to drill boreholes. Geological structures like fractures and intercalations complicate the modelling procedure, because observed reservoir parameters yield non-Gaussian and possibly multi-modal probability densities.

Linearity of the model and Gaussian probability densities of the random variables in question are important assumptions under which the traditional Kalman Filter delivers optimal estimates. The Ensemble Kalman Filter can deal with considerable deviations from the original assumptions. The research in this project will focus on modern methods derived from the EnKF (Normal Score EnKF, localized EnKF, covariance inflation…) and their applicability to the naturally occurring multi-modal densities in geothermal reservoirs. Ultimately, the goal of this project is to use the EnKF-methods on tracer experiments at the geothermal test site at Soultz-sous-Forêts.

Funding for this relatively young project (research started in October 2013) is provided by the Deutsche Forschungsgemeinschaft (DFG). Research is divided between the GGE at the Rheinisch-Westfälische Technische Hochschule Aachen (RWTH) and the Institute of Bio- and Geosciences (IBG) at the Forschungszentrum Jülich.

  Sketch of the qualitative effect of an EnKF-update due to data available at a certain time Urheberrecht: RWTH Aachen Figure 1: Sketch of the qualitative effect of an EnKF-update due to data available at a certain time.