The practical problem arises in enhancing oil recovery and is relevant to hydraulic fracturing process and subsequent frontal displacement of fluids from subterranean environment. Entrapment of residual fluid by the displacing one lowers down the displacement quality leaving most of residual viscous fluid in porous matrix.

The present paper provides the data on hydraulic fracture simulation accounting for accumulation of damages in elastoviscoplastic medium, as well as the effect of inhomogenity of porous media properties on fracture propagation. After hydraulic fracture formation terminated the cleanup procedure begins. Fracturing fluid is evacuated from the well and fracture being displaced by the oil and gas flow under the influence of pressure differential. The quality of fracture cleanup determines in the long run the effectiveness of oil recovery measures. Fracturing fluid being left entrapped in the fracture decreases its effective oil collecting area. Thus stability and quality of displacement of fracturing fluid is of key importance to provide free way for the oil and gas flow.

However, in frontal displacement of a more viscous fluid by a less viscous one from porous medium by applying pressure differential the Rayleigh-Taylor or Saffman-Taylor instability of the interface could bring to formation and growth of "fingers" of gas penetrating the bulk fluid. The growth of fingers and their further coalescence could not be described by the linear analysis. Growth of fingers causes irregularity of the mixing zone.

The present study investigates analytically, numerically and experimentally the instability of the displacement of viscous fluid by a less viscous one from porous medium and evaluates characteristic size of entrapment zones. Both miscible and immiscible displacement was investigated. Extensive direct numerical simulations allowed to investigate the sensitivity of the displacement process to variation of values of the main governing parameters.

Taking into account non-linear effects in fluids displacement allowed to explain new experimental results on the pear-shape of fingers and periodical separation of their tip elements from the main body of displacing fluid. The effects of porous medium inhomogenity on the instability of fluids displacement were investigated both numerically and experimentally. It was demonstrated that definite inhomogenity could essentially stabilize displacement.

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