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The coupled simulations of dynamic interactions between the well, hydraulicfractures and reservoir have significant importance in some areas of petroleumreservoir engineering. Several approaches to the problem of coupling betweenthe numerical models of these parts of the full system have been developed inthe industry in past years. One of the possible approaches allowing formulationof the problem as a fixed-point problem is studied in the present work.Accelerated Anderson's and Aitken's fixed-point algorithms are applied to thecoupling problem. Accelerated algorithms are compared with traditional Picarditerations on the representative set of test cases including ones remarkablyproblematic for coupling. Relative performance is measured, and the robustnessof the algorithms is tested. Accelerated algorithms enable a significant (up totwo orders of magnitude) performance boost in some cases and convergentsolutions in the cases where simple Picard iterations fail. Based on theanalysis, we provide recommendations for the choice of the particular algorithmand tunable relaxation parameter depending on anticipated complexity of theproblem.

Application of accelerated fixed-point algorithms to hydrodynamic well-fracture coupling