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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Figure 1. ( 0 ) graph 4. Isotropic case, fractal model

The model given above in Section 3 assumes that the fracture network is distributed radially over the formation. This model could be improved in many ways. For example , one my try to take into account the dependence of the conductivity of a fractured reservoir on pressure. In practice, however, there is no need for this, since the performed model has a more significant problem. An essential assumption of the previous model was that the network of microfractures is distributed uniformly over the angle, and the critical pressure contour itself always retains a radial shape. In p ractice, however, when the flu id in jected at the high-pressure into the formation, several dominant branches from the we llbore will grow. The very system of microfractures will have a random, fracta l structure. It is intuit ively c lear that such stochasticity is somehow connected with the distribution of heterogeneous properties of the formation. The model g iven in Section 3, however, sheds light on the nature of this stochasticity. In fact, in the problem, the propagation of the pressure front separating two media with different mobilities is considered. This problem is mathematica lly analogous to the problem o f d isplacement of one fluid by another flu id in the porous media . Th is problem has a stable solution if the mobility of the displaced fluid is greater than that of the displacing fluid. In stable case, the propagation of the front must develop from the less mobile zone to the more mobile one.

Figure 2. Saffman-Taylor instability during the flooding qualitevly represents the fracture form

In the case of fracture propagation, however, the reverse situation is observed. The fracturing front will a lways extend from the more mob ile fractured zone to the less moving zone of the unstimu lated format ion, due to condition 0 ⁄ < ⁄ . In this situation, instability analogous to the Saffman-Taylor instability must be realized in problems of this type. On any local inhomogeneity of the medium, a finger could form, which begins to grow with acceleration, preventing the propagation of the front in the other parts of the front.