A Prompt Sequential Method for Subsurface Flow Modeling Using the Modified Multi-scale Finite Volume and Streamline Methods

In this work, an innovative numerical algorithm accompanied by considerable accuracy is presented to reduce the computational cost of subsurface flow modeling. This method combines a modified multi-scale finite volume method (MMsFV) and streamline method based on the sequential approach. First, the modified multi-scale finite volume method, which includes a physical adaptation on the localization assumption, is employed to obtain a conservative velocity field with a similar cost to traditional upscaling methods. Then, the swift streamline method is utilized to solve the transport equation using the computed, conservative velocity field. The physical modification on the multi-scale framework imposes the nature of the actual flow moving from the multi-dimensional into 1-D local problems, which are constructed for calculating the boundary conditions in localization procedures. This physical modification is known as the modified variable boundary conditions (VBC) approach. The more accurate boundary conditions are generated for calculating basis and correction functions applied in multi-scale finite volume method. Here, the formulation and algorithm of the proposed and combined method, called the Modified Multi-scale Finite Volume Streamline (MMsFVSL) method, are presented for 2-D problems. Several test cases, including both incompressible single-phase and two-phase flow are investigated in which the obtained results show that the MMsFVSL method has a good accuracy with a high speed-up factor to reduce the total CPU time in the simulation process. Consequently, the MMsFVSL method offers a significantly efficient simulation algorithm capable of direct simulation for high resolution geological models.