https://doi.org/10.1140/epje/s10189-023-00296-5
Regular Article - Flowing Matter
Inference of relative permeability curves in reservoir rocks with ensemble Kalman method
1
Kevin T. Crofton Department of Aerospace and Ocean Engineering, Virginia Tech, 24060, Blacksburg, VA, USA
2
Thomas Lord Department of Mechanical Engineering and Materials Science, Duke University, 27708, Durham, NC, USA
3
National Security Institute, Virginia Tech, 24060, Blacksburg, VA, USA
4
Department of Civil, Environmental and Ocean Engineering, Stevens Institute of Technology, 07030, Hoboken, NJ, USA
5
Stuttgart Center for Simulation Science, University of Stuttgart, 70569, Stuttgart, Baden-Württemberg, Germany
Received:
1
February
2023
Accepted:
1
May
2023
Published online:
12
June
2023
Multiphase flows through reservoir rocks are a universal and complex phenomenon. Relative permeability is one of the primary determinants in reservoir performance calculations. Accurate estimation of the relative permeability is crucial for reservoir management and future production. In this paper, we propose inferring relative permeability curves from sparse saturation data with an ensemble Kalman method. We represent these curves through a series of positive increments of relative permeability at specified saturation values, which guarantees monotonicity within, and boundedness between 0 and 1. The proposed method is validated by the inference performances in two synthetic benchmarks designed by SPE and a field-scale model developed by Equinor that includes certain real field features. The results indicate that the relative permeability curves can be accurately estimated within the saturation intervals having available observations and appropriately extrapolated to the remaining saturations by virtue of the embedded constraints. The predicted well responses are comparable to the ground truths, even though they are not included as the observation. The study demonstrates the feasibility of using ensemble Kalman method to infer relative permeability curves from saturation data, which can aid in the predictions of multiphase flow and reservoir production.
T.I.: Quantitative AI in Complex Fluids and Complex Flows: Challenges and Benchmarks. Guest editors: Luca Biferale, Michele Buzzicotti, Massimo Cencini.
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