Investigating an extended multiphase flow model that includes specific interfacial area

Niessner and Hassnaizadeh (2008) proposed a set of governing equations to model multiphase flow in porous media based on first principles that includes fluid/fluid specific interfacial area as a state variable. Herein, we shed light on the lesser-discussed aspects of their proposed model, referred to as the extended model. Firstly, we show how the extended model facilitates real-time tracking of specific interfacial area. Secondly, we compare numerical solutions of the extended model to that of the traditional multiphase flow model with capillary dispersion and the analytical Buckley-Leverett solution. Thirdly, we provide a sensitivity analysis for the additional unknown parameters of the extended model -specific interfacial permeability and specific interfacial area generation. Lastly, a stability analysis is performed for the numerical solutions. As an auxiliary outcome, we provide an approach to solve the non-linear partial differential equations of the extended model by using torch.autograd as the automatic differentiation engine of PyTorch. Our results demonstrate that the extended model can provide saturation profiles similar to those generated by traditional models, but with the added benefit of real-time tracking of specific interfacial area. The generated specific interfacial area profiles were comparable to expected trends from previous numerical and experimental studies and highlighted the importance of the capillary pressure relationship and specific interfacial area generation term. The results also demonstrate an important balance between the permeability of the porous media and the interfacial permeability that must be maintained; otherwise, generated profiles become physically unrealistic. Overall, the extended model explains the evolution of specific interfacial area during multiphase flow at the cost of additional non-linearity and unknown parameters.