Numerical Simulation Of PKN Hydraulic Fracture Based On FrackOptima

Hydraulic fracturing plays a critical role in various practical industrial applications,particularly in economic development of unconventional reservoir to improve production of oil and gas.Thus,some two-dimensional theoretic hydraulic-fracturing models,such as the KGD model,the penny-shaped model,and the PKN model,have been developed to quantify the fracturing and the effects of parameters on it.We shall focus on the PKN model in this thesis.The derivation of the governing equation of the PKN model has not been found in literatures available.Therefore,we have derived the governing equation of the PKN model in details from the basic theories of linear elastic fracture mechanics and fluid mechanics.Then,we have presented the derivation of the two classical semi-analytical solutions to the model in the storage-dominated stage and the leak-off-dominated stage respectively and our improvement of it with the finite-difference method.In addition,we have also presented the derivation of the dimensionless asymptotic semi-analytical solutions to the model under the two stages,validating our improvement of the classical solutions.At last,we have studied the PKN-type hydraulic fracturing with a fully-three-dimensional simulator Frack Optima,and have compared the numerical results with the semi-analytical results.The comparisons demonstrate satisfying matches between the numerical results and the semi-analytical results with the maximum error lower than 10%,when only five elements are placed along the fracture height.The study validates the accuracy and efficiency of the simulator,providing theoretic basis to further implement the simulator for optimization of practical fracturing treatment.