A damped iterative EnKF method to estimate relative permeability and capillary pressure for tight formations from displacement experiments

• A damped iterative EnKF algorithm has been developed.
• This technique has been applied for a coreflooding experiment in tight formation.
• Relative permeability and capillary pressure curves have been estimated simultaneously.
• The production history can be matched excellently.

A damped iterative EnKF algorithm together with its detailed workflow has been developed and applied to simultaneously estimate relative permeability and capillary pressure for the tight formations by history matching the conventional measurement data from waterflooding experiments. The water-wet core is collected from the Bakken formation, while its porosity and absolute permeability are measured to be 19.85% and 0.21 mD, respectively. More specifically, relative permeability and capillary pressure curves are firstly represented by using the B-spline model whose control knots are transformed into their corresponding pseudo-control knots to be tuned automatically, ensuring the monotonicity of either relative permeability or capillary pressure curves. Then, relative permeability and capillary pressure curves are finally determined by assimilating all of the measurement data from a real coreflooding experiment and history matching them as well. Compared with the initial cases, not only are the uncertainty ranges associated with both the updated relative permeability and capillary pressure curves reduced significantly by assimilating the measurement data, but also uncertainty ranges pertaining to the updated production history profiles have been decreased greatly. In addition, water relative permeability can be determined more accurately than oil relative permeability and capillary pressure owing to its preferential sensitivity to the measurement data.