PSI - Issue 6

Paderin Grigory et al. / Procedia Structural Integrity 6 (2017) 276–282 Paderin G.V./ Structural Integrity Procedia 00 (2017) 000 – 000

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Thus, the solution obtained above does not itself have much physical mean ing. Certa in informat ion on the nature of the fracture propagation in the case of isotropic horizontal rock stresses could perform experiments on the Saffman-Taylor instability for the axially symmetric flooding problem (Maloy 1985) . The only difference in the nature of the Saffman-Taylo r instability between flooding and growth of the micro fracture system is that in one case the inhomogeneity of permeability plays a role, and in the second, the heterogeneity of the strength characteristics of the medium is important. In our simp lified model, this is . Since the degree of fractal characteristic is primarily geomet ric value, the stronger influence on this value should be made by the geometric parameters, like the variogram radius. But heterogeneity of permeability and heterogeneity of strength properties should correlate, and the radii of their variograms should be approximately equal. 5. Anisotropic case In the case when the stress state horizontally is characterized by two different perpendicular stresses, 1 < 2 , the crack should grow mostly in the direction 2 . This fact could be seen if we introduce two dimensionless coefficients: 1 = 1 + − 0 ; 2 = 2 + − 0 (19) These coefficients characterize the propagation velocity of a crack perpendicular to the pressure 1 and 2 , respectively. Because 2 > 1 , the parameter responsible for the crack propagation velocity ( 2 ) < ( 1 ) , i.e . spread perpendicularly to the maximum stress of the network of cracks is more difficult. The parameters 2 − 1 and ( 2 − 1 ) 1 ⁄ are logica l then to be called the parameters of anisotropy. It is clear that in the isotropic case both parameters are 0. In high an isotropy case, first “finger” should be perpendicular to the minimum stress. In this case it indeed may absorb the whole fluid flow, and the magistral regime will start. In this paper, a continuum mathematica l model of double porosity was proposed. In its simplified version, it allows a qualitative analysis of fracture propagation modes in the formation, depending on the reservoir conditions and the injection regime. The advantage of this model was that it did not suppose the nature of the fracture network propagation predetermined, whereas most modern models assume propagation mainly along one plane. Consideration of the simplest axia lly symmet ric isotropic problem, makes it possible to obtain an analyt ical solution. Solution showed that the character of the distribution of fracturing in the formation is closely re lated to the Saffman-Taylor instability, usually obtained at the interface between two fluid displacing each o ther. The evaluated dimensionless parameters of the problem performed a qualitative conclusion about the speed of fracture network propagation depending on the injection parameters, strength properties of the formation material, rock stresses and the reservoir pressure. Thus, it was shown that the propagation velocity of a crack increases with increasing inject ion rate and decreases with increasing strength of the rock to fracture, as well as with increasing rock stresses. Areas of values of dimensionless parameters responsible for d ifferent reg imes of fracture propagation, mag istral, mainly in one direction, and fractal in all possible directions were also qualitatively determined. The analysis showed that the parameters for the distribution of the bran ched crack system as a whole are influenced by such parameters as the injection regime, the viscosity of the fluid, and the conditions of the reservoir stress state. Also for the fractal regime, the degree of reservoir heterogeneity is important, since it is precisely on its characteristic inhomogeneities the fracturing front will disintegrate. Th is heterogeneity c ould be logically modeled using geostatistical methods, using in numerica l simulat ion such parameters as the variogram rad ius and the relative standard deviation of strength characteristics. Finally, it should be noted that the absolute value of the strength properties of the material does not play a determining role in the fracture growth regime . Hav ing determined any characteristic of the materia l, such as brittleness, it is impossible to state for sure wh ich systemof cracks would form. Taking into account the fact that the 6. Conclusion