A meshless streamline method for simulating flow in polymer flooding reservoirs

As a key technology for enhancing oil recovery, polymer flooding faces challenges such as complex reservoir geometry adaptation and significant numerical dissipation. While existing mesh-based simulation methods exhibit limitations in complex scenarios, emerging mesh-free approaches, though flexible, have yet to integrate streamline simulation techniques to address numerical dissipation issues in polymer flooding. To overcome these challenges, this study introduces the first meshless streamline simulation method for polymer flooding, achieving the application of the meshless streamline simulation (named EFVM-SL) in polymer flooding reservoirs. The method is based on the extended finite volume method (EFVM) framework, first solving the pressure field using EFVM, then combining Darcy’s law with a mesh-free generalized finite difference operator to calculate seepage velocity. Source-sink nodes are modified using an equivalent cylindrical radial velocity model, while a piecewise linear algorithm tracks streamlines and calculates time of flight (TOF). On streamlines, the upwind finite difference method solves the saturation and polymer concentration transport equations containing only convective terms, with node control volume average parameters obtained through TOF weighted averaging. A fixed-time update mechanism is introduced to dynamically adapt to total mobility variations caused by polymer injection, periodically updating the pressure field, seepage velocity, streamline distribution, and TOF. Numerical examples using homogeneous reservoirs (Cartesian point cloud and irregular point cloud) and irregular boundary reservoir models demonstrate that EFVM-SL significantly reduces numerical dissipation at polymer front compared to traditional EFVM methods. Leveraging the flexibility of point cloud discretization, it efficiently adapts to complex reservoir geometries, providing a precise and efficient simulation tool for polymer flooding development in complex reservoirs.