A comprehensive fracture network conductivity model for tight unconventional reservoirs considering various proppant size, creep deformation, and proppant compaction and embedment

Graded proppant injection into complex fractures is frequently used to prop connected secondary fractures in tight unconventional reservoirs. A comprehensive conductivity model incorporating creep, decreasing proppant size distribution, proppant embedment and deformation, and unpropped fracture surface deformation is established to ascertain partially propped fracture network conductivity. The propped fracture width variation is described by creep deformation, proppant embedment, and proppant particle deformation. The corresponding fracture permeability is depicted by the Carman-Kozeny equation where the dynamic proppant pack porosity is calculated via proppant size and the number of proppant layers. For unpropped areas, the width is controlled by effective stress, and the permeability is a function of fracture aperture. The hydraulic–electric analogies concept is use to integrate the local conductivity of different areas and characterize the overall fracture network conductivity. The model is verified against long-term conductivity measurement data. Results show that the fracture width variation is mainly caused by rock creep and proppant embedment. Larger Kelvin shear modulus and Maxwell viscosity slow down the conductivity decline rate. The conductivity becomes stable after 4 days when the Kelvin shear modulus is increased to 5.4 × 108 Pa. The Maxwell shear modulus has the slightest influence on conductivity. Larger-size proppants offer higher overall conductivity and better maintain the conductivity. The fracture network conductivity is significantly larger than the conductivity of the main fracture fully supported by the graded proppants and that of the fracture branches. The three-dimensional (3D) conductivity diagram and two-dimensional (2D) conductivity maps are generated to better demonstrate time-dependent conductivity evolution.