Symmetric Cohesive Element Formulation for Fully Coupled 3D Hydraulic Fracture Modeling

A novel formulation for a symmetric cohesive element is presented here, for hydraulic fracture modeling problems that involve one fluid driven crack with a plane of symmetry coinciding with the fracture plane. The formulation enables analyses by modeling only half the domain for such problems. The modeling framework employed is the recently developed 3D finite element model in Abaqus which fully couples the rock deformation with the pore fluid Darcy flow. The symmetric cohesive element is an enhanced version of the previously developed 3D pore pressure cohesive element, uniquely capable of simulating Darcy flow in the undamaged state and a smooth transition to a tangential Poiseuille flow when damaged completely. Flow into the formation/fracture is modeled via specialized 1D pipe elements that can account for the wellbore fluid flow and frictional losses. Fluid leak-off into the formation is also modeled by means of a filter cake leak-off coefficient. The symmetric cohesive element is formulated by imposing appropriate constraint conditions on the displacement and pore pressure degrees of freedom, that enforce symmetric crack face behavior on either side of the fracture plane, i.e., the plane of symmetry. In addition, appropriate scaling factors are applied to various model parameters viz. the rock fracture energy, the pipe diameter, pipe friction factor and last but not the least, the viscosity of the fracturing fluid. The proposed approach with the aforementioned constraints and scaling factors is demonstrated to correctly simulate just half the domain of a symmetric hydraulic fracture, and yield results virtually identical to the full model, at half or less computational cost. Both lab and field scale examples are presented to demonstrate the effectiveness of the proposed approach.