Foam has been used for decades in petroleum industry for enhanced oil recovery (EOR) due to its mobility adjustment ability. A variety of mechanistic models have been proposed to study foam flow in porous media from multiple scales. In these models, such as population balance models, some important parameters (e.g., foam generation/coalescence rate, flowing foam fraction) are treated empirically since they cannot be obtained from conventional lab experiments. To improve the accuracy and reliability of foam description in these foam-assisted processes, pore network model interwoven with invasion percolation with memory (IPM) method has become a powerful tool in studying foam flow characteristics in porous media, which can predict relative permeability and flowing gas fraction with fully consideration of pore-scale mechanisms of foam generation, destruction, and propagation. However, the assumption of exactly sufficient incremental pressure difference used in conventional IPM-based pore-scale foam modeling is rigorous, not only making it difficult to conduct relevant experimental validations, but also creating potential algorithmic conflicts when simulates displacements in weak foam regime or displacements incorporated with foam coalescence mechanisms. In this study, a novel mixed-sorting rule, which proceeds the displacement by describing the transition between immobile foam bank and mobilized foam flow quantitively, is incorporated into IPM-based foam propagation model. In this way, the immobile foam bank is identified based on effective lamellae generation rate, whereas the mobilized foam flow is distinguished by frontal displacing velocity, respectively. Results estimated with proposed method successfully capture key properties that define pore-scale foam behavior at excessive pressure constraints from formation of immobile foam bank, foam mobilizing pressure thresholds, and fractal dimension of displacement pattern, etc.
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