Mechanistic foam flow model with variable flowing foam fraction and its implementation using automatic differentiation

•Mechanistic model of transient foam flow implemented using automatic differentiation.•Tracking in situ bubble density is a powerful method to understand gas mobility.•Simulation and experimental displacement results agree.•Trapped gas fraction depends on the pressure gradient, permeability, and bubble density. Foam injection is an effective method for modifying gas mobility in subsurface flow applications making it ideal for environmental remediation applications. Remediation of contaminated soils/aquifers of nonaqueous phase liquids using foamed surfactant solutions is a viable option but a predictive foam model is needed that is flexible to the addition of more accurate physical descriptions. Such a model is essential to ensure successful operations in soil remediation applications. The objective of this paper is to develop a full-physics, mechanistic transient foam flow model and integrate it into the multiphysics, modular AD-GPRS framework (Automatic Differentiation–General Purpose Research Simulator). We chose AD-GPRS because it allows rapid prototyping and addition of complex physics and modeling strategies. We develop the model ground-up from pore-scale observations and implement a new flowing foam fraction constitutive relation that depends on the local pressure gradient, local permeability, and flowing bubble density. Our model predicts the two flow regimes commonly observed in steady-state pressure gradient measurements: the low-quality regime and the high-quality regime. Additionally, the model is used to match transient experimental results of homogeneous and slightly heterogeneous cores with a wide range of permeability values. The implementation of this model within AD-GPRS allows testing of ideas and modeling strategies as well as inclusion of more complex physics or foam generation kinetics.