International Journal for Numerical Methods in Engineering · 2006 · 66 citations · 29 references
EngineeringComputational EngineeringPetroleum EngineeringComputational MechanicsFluid DynamicsReservoir SimulationFracture MechanicsFracture PropagationFractured Reservoir FlowFractured Reservoir SimulationIterative SolversNumerical Methods For Differential EquationsFracture SimulationFractured Media FlowFractured Media ModelingFractured Porous MediaLinearizationMatrix-fracture TransferNumerical Modeling Of Rock FractureWater Injection
Abstract In this work, we compare the fully implicit (FI) and implicit pressure‐explicit saturation (IMPES) formulations for the simulation of water injection in fractured media. The system of partial differential equations is discretized within the discrete‐fracture framework using a control‐volume method. A unique feature of the methodology is that there is no need for the computation of matrix–fracture transfer terms. The non‐linear system of equations resulting from the FI formulation is solved with state‐of‐the‐art Newton and tensor methods. Direct and Krylov iterative methods are employed to solve the system resulting from the Newton linearization. The performance of the FI and IMPES formulations is compared with numerical testing. Results show that the contrast between matrix and fracture properties affects the performance of both IMPES and FI formulations and that the tensor method outperforms all the Newton solvers for the near‐singular Jacobian matrix. Copyright © 2006 John Wiley & Sons, Ltd.
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