Study Of Fluid-solid Coupled Algorithm On Hydraulic Fracturing Using Discontinuity Displacement Method

The unconventional oil and gas resource is a kind of clean energy which is abundant in reserves but the permeability of its reservoir is ultra-low.The technique of hydraulic fracturing bumps in reservoir high-pressure liquid to force complex ruptures of the formation,therefore it increases the matrix permeability and stimulates well productivity enormously.The methods of studying hydraulic fracturing mainly include in-site tests,laboratory experiments and numerical simulations.Based on displacement discontinuity method(DDM),this thesis proposes a weak coupled algorithm and devises a set of MATLAB and FORTRAN programs to simulate the crack extension and liquid leak-off during hydraulic fracturing process.The contents of this thesis are illustrated as follows.(1)In Chapter 2,the theory of J-integral and M-integral is applied to DDM framework and an effective algorithm is proposed to accurately evaluate the stress intensity factors(SIFs).Numerical examples indicate that the proposed approach can improve SIFs accuracy effectively compared with the pre-existing crack-tip element method and finer DDM elements also facilitate more precise results.(2)In Chapter 3,the solution of instantaneous point resource is derived from the saturated diffusion equation and this solution can add leak-off property to DDM elements.The liquid volume calculated form leak-off system will serve as boundary conditions to evaluate the displacement discontinuities(DDs),and in turn,the DDs outline the physical boundary of crack and can therefore be used to compute liquid volume.Iteration needs to be conducted to acquire the crack aperture,inner pressure within crack and pore pressure at field points.The proposed approach essentially falls within a weak coupling scheme and involves non-linear calculation due to the iteration process.No extra freedom is introduced in the algorithm but inner pressure emerges as an unknown variable,so the solver of the DDM program(TWODD)needs to be modified to acquire the DDs.This thesis doesn't reprogram the solver,instead,uses the dichotomy to search the inner pressure numerically.The dichotomy converges at a rapid rate and evaluates inner pressure accurately.Numerical examples indicate that the proposed algorithm can calculate crack aperture at any position of the crack at any time as well as evaluate the pore pressure at any filed points at any time.(3)In Chapter 4,the leak-off system and crack propagation are combined to form a complete weak coupling scheme.The maximum circumferential tension is selected as the rupture criterion and a set of MATLAB and FORTRAN programs are devised to simulate the crack extension driven by liquid.Under 2D circumstances,the numerical simulation of hydraulic fracturing involves in-situ stresses which are compressive at both directions and liquid pressure essentially serves as the motivation of crack propagation.This compares with the situation where an infinite plate with a central crack is subjected to uniaxial tension and the crack faces are free of traction.With the described situation,the so-called maximum circumferential stress criterion offers theoretical formula to predict the angle of crack extension.However,numerical result indicates that the formula is not valid in hydraulic fracturing since the boundary conditions of these two situations are different.Nevertheless,the idea that crack would propagate along the direction of maximum circumferential stress is still insightful,so this thesis abandons the theoretical formula to evaluate the maximum circumferential stress and searches for the maximum circumferential stress along the semicircle whose diameter is vertical to the crack tip element.This essentially proposes rupture criterion from a numerical perspective and can be used in any cases with complex crack configurations and far-filed stress boundary conditions.A numerical example,the I-II mixed hydraulic crack subjected to horizontal and vertical in-situ stresses,is conducted in Chapter 4,which is the most general situation of hydraulic fracturing in terms of elastic simulation in 2D cases.The numerical example proves that the programs this thesis develops can simulate the crack propagation,aperture change and pore pressure evolution during the entire hydraulic fracturing process subjected to any inner pressure and far-field stress conditions.