A pseudo 3D fracture propagation model with consideration of vertical flow resistance

Key words:  hydraulic fracturing  fracture propagation  pseudo 3D model  vertical flow resistance  crack opening displacement criterion

Abstract:

Pseudo 3D fracture propagation models can be used to simulate the process of hydraulic fracturing treatment, which have rapid convergence speed, satisfactory computing accuracy and flexible adaptation. However, these models neglected the effect vertical flow resistance, so they are unable to simulate fracture propagations in the formation lack of stress difference between the upper/lower layers, and the predicted fracture heights are larger than the real ones in most cases. In deriving a fracture width expression with vertical flow resistance and analyzing the accuracy of crack opening displacement (COD) criterion, it has realized that the correction with a small scale yielding is unnecessary for hydraulic fracturing. Therefore, an improved pseudo 3D fracture propagation model with vertical flow resistance was established considering a dual linear flow pattern and the loss of fracture fluid. The calculation results of a case study show that the new model is more accurate. In addition, the propagation of lower fracture height is very slow at the condition of a higher stress difference, which is good for fracturing in bottom water reservoirs. While at the condition of an extremely low stress difference, the fracture height is nearly equal to the fracture length, but there are still significant difference between upper and lower fracture heights due to the gravity effect.