Creep deformation of fracture surfaces analysis in a hydraulically fractured reservoir using the finite element method

In this study, we develop a Galerkin-type finite element (FE) solution to assess the creep deformation of fracture surfaces. These surfaces are treated as comparatively compliant rocks which are separated by a comparatively stiff proppant pack. Viscoelastic properties of fracture surfaces are assessed by the temperature and deformation dependent modulus. The key challenge is to appropriately develop the creep and the relaxation functions which are continuous spectrum material functions and are unique for each model. Time dependent mechanical properties are connected through an instantaneous elastic response and coupled by way of nonlinear and convolution integral relationships. Coupling is achieved by way of convolution integrals computed using the full-time history of the material functions. As a novel numerical procedure, we apply a more computationally efficient algorithm to use discrete-spectrum approximation to the creep and relaxation functions, thus, allowing for adjustment of the energy dissipativity of the model in a consistently low computation-time. The proposed approach is novel and is the only approach in the literature (to the best of authors’ knowledge) that considers the conductivity in an intended reservoir at the level of proppants. It will be demonstrated that the proposed model can be used for the assessment of fracture conductivity under short or long-term loading conditions when rock material properties can be determined.   Key words: Finite element method, reservoir engineering, numerical model, fractured reservoir.