In this model, the increments of normal force F i n, the tangential force F i s and the moment M can be calculated from the relative motion of bonded particles, and are given by: where kn and ks are the normal and shear stiffness.
(3) Breakdown pressure with the low viscosity fluid was lower than with high viscosity fluid.
The saturation factor in each domain is defined as: where Vr is the volume of domain as shown in Figure.
The pore pressure reduces the effective stress of the rock near the borehole, which facilitates the generation of cracks.In the work of Wang.In Figure 11, the pore-pressure field in models shows that the pore pressure increase caused by reservoir skeleton deformation is more pronounced as the injection rate increases, which can also be an effect of the local stress concentration around the injection borehole.Therefore, the value of e 0 and e inf are determined according to Equation (12 after Al-Busaidi 34, based on the permeability k of real rock, or by simulating the permeability test corresponding to the characteristics of an actual specimen: where V is the volume.Firstly, the failure takes place at the weakest bond surrounding the injection borehole, and cracks propagate along a direction with borehole pressure drop.The calculation of the new fluid pressure is given as: where Pf1 and Pf2 are fluid pressure related to Domain 1 and Domain 2, respectively, before the bond failure.The patrician 3 manual pdf breakdown pressure values obtained from modeling and the theoretical values calculated according to Equation (16) under different in situ stress ratios are shown in Figure.The fluid pressure in the borehole and the available space can drive crack growth; at the same time, the pore-pressure changes due to cracks development and the deformation of the reservoir.As the normal force at a contact increases, the aperture related to force can be given as: where n is the effective normal stress at the contact (in MPa).Additionally, Figure 11 shows two main fractures that developed when the injection rate was.0 105 m3/s, while four main fractures grew under the injection rate.0 104 m3/s.28 applied this approach to model fault slip and they were able to use udec to estimate the energy release associated with induced seismicity.Advanced search 23, views 2, crossRef citations, altmetric, original Articles, fragmentation and heave modelling using a coupled discrete element gas flow code.
52 also investigated how the viscosity of the fracturing fluid affects fracture propagation using three different viscosities (viscous oil, water, and supercritical CO2 and the results show that hydraulic fracturing with low viscosity fluids form a more complex fracture network in rocks.
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Figure 9 and Figure 10 both show that the distribution of fractures is corresponding with the pore pressure field.46 the influence of the initial stress parameters and the tensile strength of a coal seam on the breakdown pressure under certain injection conditions are analyzed, and a regression equation (Equation (10) in Wang.In the present model, the hydraulic aperture of the flow channel between two particles changes as a function of normal forces.As the geomaterial is opaque, it is impossible to directly observe the subsurface hydraulic-fracture geometries.In this section the effect of the viscosity of the fracturing fluid on crack initiation and propagation are discussed, which were simulated under conditions with an injection rate.0 105 m3/s, and a confining pressure of 20 MPa in the x-direction and 15 MPa.The reservoirs are connected by pipes ( Figure 2 a, red lines which are perpendicular to corresponding particle contacts.Therefore, for taking into account the saturation conditions, a saturation factor is introduced in the fluid flow algorithm in this study.In past research work, the efficiency of the bonded particle method for hydraulic fracturing simulation has been overlooked.Itascas universal distinct element code (udec) and three-dimensional distinct element code (3DEC) are two representative explicit DEM methods for modeling and assessing complex fracture growth driven by fluids.In order to validate the reliability of hydraulic fracturing simulation by the bonded particle method, also the influence of the in-situ stress ratio on breakdown pressure is studied under the assumption that the initial pore-pressure is 0 (P0 0 the dynamic viscosity of the injection.