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Long wave evolution on free falling viscous films is described using a new evolution equation. The scaling proposed here brings in the viscous and pressure correction terms that are missing in the existing long-wave equations. Small amplitude expansion of the equation gives a dissipative form of the Kuromoto-Sivashinsky equation. Improved accuracy of the new equation over existing equations is demonstrated by comparison of neutral curves with Orr-Sommerfeld equations and experimental data.

Channel fracturing combines geomechanical modeling, intermittent proppant pumping and degradable fibers and fluids to attain heterogeneous placement of proppant within a hydraulic fracture. The aim of this well stimulation technique is to promote the formation of stable voids or streaks within the proppant pack which serve as highly conductive channels for transport of oil and gas throughout the hydraulic fracture.More than 10,000 channel fracturing treatments have been performed in over 1,000 wells during the last three years in shale-, carbonate-, and sandstone-rich reservoirs worldwide. The collective dataset on job execution and well performance shows the following trends: (a) low occurrence of near wellbore screen-outs (>99.9% of all treatments achieving 100% proppant placement); (b) reduction in the amount of proppant required to complete treatments (in average, 43% less proppant than conventional techniques aiming at placing a homogeneous proppant pack as implemented in offset wells); (c) average initial and long-term well productivity and flowing pressures consistently meeting or exceeding those of wells completed with conventional fracturing techniques. This paper summarizes findings from a comprehensive technical study focused on ascertaining the enabling mechanisms for these trends. Results from laboratory experiments (large-scale slot flow, conductivity, proppant settling), yard tests (well site delivery characteristics, proppant slug integrity), and well performance evaluations (surface treatment data, well production data and reservoir simulations supported by history matching) are analyzed collectively to reach the following assessments: (a) heterogeneous proppant placement is achieved; (b) the low incidence of screen-outs is the result of the combination of reduced usage of proppant and intermittent pumping of proppant-free, fiber-laden slugs ("sweeps") which mitigate accumulation of proppant in the near-wellbore area; (c) well productivity trends are driven by the concomitant occurrence of enhanced fracture conductivity -enabled by the presence of heterogeneities within the proppant pack-and the development of larger fractured area within the reservoir effectively contributing to production. The development of larger effective contact area is enabled by the use of fibers, which enhance proppant transport within the fracture and mitigate proppant settling.

An equation is derived for describing wave evolution on the surface of a vertically falling viscous film. The traditional long-wavelength scaling is replaced by a new scaling to reduce the (We) must be used instead of the Reynolds number (Re) to distinguish between viscous and inertia dominated regimes for vertically falling films. This equation includes viscous dissipation and pressure correction terms that are missing in the existing single evolution equations at the same order. Comparison of the neutral stability curves and growth rates predicted by different models to that of the Orr-Sommerfeld (OS) equation shows that our equation matches with the OS results better than the existing single evolution equations. However, our equation is not free from finite time blowup. Selective regularization leads to a two mode model in flow rate and film thickness. The regularized equation is free from finite time blowup and predicts two families of solitary waves. Numerical simulations of the derived equation and its regularized version in the traveling wave coordinate show the transition of wave structure from regular (periodic) to chaotic profiles. Model predictions on maximum wave amplitude on the low celerity branch show good agreement with experimental data.