Some Background obout EnKF(Ensemble Kalman Filter)

The Kalman filter has historically been the most widely applied method for assimilating new measurements to continuously update the estimate of state variables. EnKF is a Monte Carlo approach, in which an ensemble of models is used. The correlations between model variables and theoretical data are computed directly form the ensemble. The conceptual framework of EnKF is suitable for real-time reservoir monitoring with data from permanent down-hole gauges. Many studies have shown that EnKF is plausible to be applied to the problem of history matching in petroleum industry.

• Applications
  1. Adjust property fields of reservoir such like porosity, permeability, saturation, pressure, faces distribution and so on
  2. Production optimization
• Advantage of EnKF
  1. Avoid calculating gradient
  2. Continually update model
  3. Quantify uncertainty
     
  4. Can be easily implemented with parallelism
• Challenge
  1. Reduce the number of ensemble members required for history matching and uncertainty quantification of large-scale reservoir
  2. Complex geology
  3. Strongly nonlinear and nonguassian problem
  My research interest lies in improved initial sampling and model error.

Cerrent Project

Current project is the application of Ensemble Kalman Filter in an offshore field case. Besides the original aquifers, there are also several injectors in the field. The total oil reserves are estimated to be 100 MMBOE. The reservoir simulator model is quite big; there are over 100,000 grids. grids in the reservoir simulation model. Traditional manual history matching of bottomhole pressure resulted in a geologically unrealistic permeability field. We try to use EnKF to solve this problem by continually updating the permeability and porosity fields to honor production data.

To implement EnKF we need an ensemble of initial models, so at first we used Sequential Gaussian Simulation and improved sampling to generate an ensemble of permeability and porosity fields, and then implemented EnKF using supercomputers at OSCER. The independence of ensemble members allows the benefit of parallism for EnKF implementation. The following plots show some results of the project, from which we can see that the production data are honored and uncertainty is also quantified.

Black line: ensemble models        Green line: mean of ensemble       purple points: observations

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