A Numerical Study On Hydraulic Fracturing For Low Permeability Reservoir

The reserves of unconventional resources such as shale or tight gas are huge. However, their natural deliverability is not sufficient to meet industrial need due to the low permeability. As hydraulic fractures can increase the drainage area effectively, hydraulic fracturing technique has become the main stimulation for low permeability reservoirs. To ensure the hydraulic fractures meet the stimulation requirement, it is necessary to study the hydraulic fracturing process and analyze the factors affecting the fracturing treatment.A hydraulic fracturing model based on the discrete fracture model and the generalized J integral is presented. The proposed model consists of seepage equations, solid equations, fluid-solid coupling and fracturing propagation criteria. To achieve high precision, the discrete fracture model is applied to calculate the fluid flux across the fracture surface in our work. Considering the effect of the in-situ stress, the solid field is decomposed into the initial part caused by the in-situ stress and the effective part caused by other external forces. Through this method, the system of equations for solid mechanics can be solved conveniently. In the proposed model, fracture will extend when the stress intensity factor (SIF) exceeds the fracture toughness. To avoid the hypothesis of infinite space and the numerical error resulting from the stress singularity, the generalized J integral is used to calculate the SIF. As we know, the grid system will change during hydraulic fracturing simulation. To improve the efficiency of simulation, the dynamic mesh technique is used. During simulation, the coarse grid system does not change while the dens grid system moves with the fracture tip.In order to verify the reliability of the proposed model, the radial fracture propagation is simulated. When the calculation domain is large enough, the numerical result is accordant with the analytic solution which is obtained under the hypothesis of infinite space. However, there exists difference between the two when the fracture and calculation domain are similar in size. We have studied the relationship between the SIF and the size of the calculation domain, both when the outer boundary conditions are set as zero stress and zero displacement. Numerical results indicate that the SIFs under the two different boundary conditions tend to the same value as the calculation domain increases. However, the difference between them will increase significantly when the size of the calculation domain decreases. The facts above show that the hypothesis of infinite space may result in significant error when the calculation domain is finite. At this time, it's important to deal with the boundary conditions correctly.The influence of the fracturing equipment parameters on the fracturing process is studied. Simulation results show that the inner radius of the pipe conveying fracturing fluid affects the working parameters of the fracturing equipment significantly. When the pipe radius is small, the pressure drop caused by friction along the pipe has a great proportion in the working pressure of the fracturing equipment and so does the power loss. Friction loss decreases with the increase of the pipe radius. However, when the radius exceeds some value, the decrease of the friction is very small. In addition, simulation results indicate that the fracture will extend forward until the working parameters of the hydraulic fracturing equipment reach the upper limit. By comparing the technical parameters of three different hydraulic fracturing equipments, we find that the parameters of these equipments limiting the fracture propagation are different when fracturing the same reservoir.Finally, we have studied the influence of the physical property parameters on the fracturing process. Simulation results indicate that physical property parameters of the seepage field including matrix permeability, fluid-solid coupling coefficient and fluid viscosity have significant influence on the working parameters of the hydraulic fracturing equipment. However, the influence of the physical property parameters of the seepage field on the changing process of the fracture geometry is very small. To extend the fracture to the same length, working pressure, output flow and output power of the hydraulic fracturing equipment will increase both when the matrix permeability is larger and when the fluid-solid coefficient and the fluid viscosity are smaller. In addition, the physical property parameters of the solid field such as elastic modulus and Poisson's ratio affect mainly the fracture geometry while they have little influence on the working parameters of the hydraulic fracturing equipment. When the hydraulic fracture propagates to the same length, the larger the elastic modulus or the Poisson's ratio is, the narrower the fracture will be.