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A modified discrete element approach is introduced and used for modeling reservoir geomechanical response during fluid injection. The approach is based on the Discrete Element Method (DEM), where modifications are done to overcome some limitations of this method. The method is advantageous in modeling fracture developments in rocks. The approach is applied to two dimensional (2D) synthetic model based on the Gullfaks field in the North Sea as a case study. Two cases were modeled, one with low horizontal effective stress and the other with low vertical effective stress. Vertical fractures are developed in the first case, whereas horizontal fractures are developed in the second case. Finally these fractures are used with the help of a rock physical model to update the velocity model of the reservoir. The updating of the velocity model is important for interpretation of time-lapse seismics.