Compositional three-phase relative permeability and capillary pressure models using Gibbs free energy

Sadeghi Neshat, Sajjad
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Both relative permeability and capillary pressure depend on composition as well as saturation, but classical models neglect this dependence. The objective of this research was to develop coupled three-phase relative permeability and capillary pressure models for implementation in a four-phase flow compositional equation-of-state simulator. The models applied to several complex but practical reservoir simulation problems. Models independent of phase label have many advantages in terms of both numerical stability and physical consistency. Identification of hydrocarbon and aqueous phases based on their molar Gibbs Free Energy (GFE) is a key feature of the new model. Instead of using labels (gas/oil/2nd liquid/aqueous) to define permeability parameters such as end points, residual saturation and exponents, the parameters are continuously interpolated between reference values using the Gibbs free energy of each phase at each time step. Consequently, the formulation used to implement other relevant physical parameters must be consistent with the new approach. A comprehensive but simple vii algorithm was developed for this purpose. The algorithm allows for very general threephase hysteresis in both relative permeability and capillary pressure. An important part of this thesis is analyzing the results of a recent series of experiments on the effect composition on relative permeability. These new data were used to calibrate the new GFE relative permeability model and apply it in a compositional reservoir simulator. The robustness of the new GFE model was shown through complex simulations such as solvent flooding, miscible/immiscible WAG processes, well stimulation processes using solvents to remove condensate and/or water blocks in both conventional and unconventional formations and other challenging applications involving both mass transfer between phases and phase changes. The interpolation of relative permeability parameters based on GFE instead of phase labels completely solves the discontinuity problem caused by phase flipping or misidentification. Therefore, simulations run significantly faster and are physically correct. The novelty of this research is in integrating and unifying relevant physical parameters including trapping number, hysteresis and capillary pressure into one rigorous algorithm with compositional consistency and in the development and application of a practical procedure for numerical compositional reservoir simulations.