Projection-based embedded discrete fracture model using hybrid of two-point flux approximation and mimetic finite difference (TPFA-MFD) method

A method for generating flow simulation of fracture formation, for an anisotropic media with full permeability tensor, by a projection-based embedded discrete fracture model (pEDFM) using a hybrid of two-point flux approximation (TPFA) method and mimetic finite difference (MFD) method, i.e., (TPFA-MFD) method, the method comprising:

• discretizing of a generic fracture model of the anisotropic media, by a data processing system, for:
• identifying a plurality of grids comprising matrix grids and fracture grids based on a location of each grid in the generic fracture model;
• identifying three types of connections in a fracture network based on the location of each grid in the generic fracture model, wherein the three types of connections comprises:
• m-m connection corresponding to connection between two matrix grids;
• m-f connection corresponding to connection between a matrix grid and a fracture grid;
• and
• f-f connection corresponding to a connection between two fracture grids;
• and
• identifying effective m-m connections and/or effective m-f connections, wherein each effective m-m connection and/or each effective m-f connection comprises at least one low-conductivity fracture fl;
• constructing a treatment method for each low-conductivity fracture by the data processing system, for:
• identifying an inter-grid connection set Cont1 comprising a set of connections obtained from a generic pEDFM to treat the low-conductivity fractures with a non-projection transmissibility multiplier method is used that provides a flow area between adjacent grids, wherein the low-conductivity fractures are ignored;
• identifying an efficient set of connections Cont1eff based on the inter-grid connection set Cont1 as follows:
• Cont1eff=Cont1−Cont10 (6)
• wherein Cont10 is a set of connections with a flow area 0 in the inter-grid connection set Cont1;
• constructing a numerical flux calculation method for effective m-f and m-m connections, by the data processing system, for:
• determining flux continuity conditions of effective m-f and m-m connections using the hybrid TPFA-MFD method, wherein the hybrid TPFA-MFD method comprises:
• estimating a numerical flux on each effective m-f connection and/or effective m-m connection related to K-orthogonal grids using TPFA method;
• and
• estimating a numerical flux on each effective m-f connection and/or effective m-m connection related to non-K-orthogonal grids using MFD method;
• and
• performing a spatial discretization of a continuity equation of each matrix grid and each fracture grid in the effective m-m and m-f connections;
• and
• constructing global equations, by the data processing system, by combining the flux continuity conditions of the effective m-f and m-m connections and a time discretization scheme of implicit backward Euler scheme, and calculating distribution of pressure and water saturation by solving the global equations using a nonlinear solver based on Newton-Raphson method.