Simultaneous estimation of relative permeability and capillary pressure for tight formations using ensemble-based history matching method

An ensemble-based method has been developed and successfully applied to simultaneously estimate relative permeability and capillary pressure curves for tight formations by history matching the measurement data. The power-law and B-spline models are first used to represent the relative permeability and capillary pressure curves, respectively. Then, parameters of such two models are tuned automatically and finally determined once the measurement data is assimilated completely and history matched. The estimation of relative permeability and capillary pressure has been found to improve progressively and the corresponding uncertainties are mitigated gradually as more measurement data is assimilated. As assimilation of the measurement data is completed, an excellent agreement has been found between the updated and reference relative permeability and capillary pressure curves, though estimation accuracy suffers slightly when B-spline interpolation is used. Among all the to-be-estimated parameters, the endpoint of the capillary pressure curve shows its compromising accuracy, depending on its initial value.

► Simultaneously evaluate relative permeability and capillary pressure for tight formations. ► Relative permeability and capillary pressure curves are updated progressively. ► Standard deviations (or variances) of the parameters are reduced gradually. ► Shows good computational efficiency. ► Be well-suited for uncertainty analysis under consistent framework.