Hydraulic fracturing, creating stimulated reservoir volumes, has been widely applied to obtain economic flow in shale gas/oil formations today. However, for a fractured shale vertical well, determining the volume of proppant placed into the pay zone still remains difficult. Previous methods are based mainly upon empirical approaches which, to a large extend, are uncertain and imperfect. This paper established a novel but simple mathematical model to calculate the volume of proppant, merely using optimized parameters of fracture network obtained from numerical simulation.

Since the permeability of fracture networks is several orders of magnitude larger than that of the reservoir and the geometry of them is considerably complex, the fracture networks are simplified as a high permeability zone (HPZ) according to the equivalent principle of seepage. HPZ units are selected to build this model based on the following assumptions: (1) the seepage flow in shale involves the matrix flow and fracture flow from HPZ units to wellbore under steady state, (2) a multilayer seepage model is utilized to describe the fluids flowing in HPZ unit and study the characteristic seepage behavior of dual porosity medium, (3) heterogeneity in fracture propagation direction is neglected, (4) the proppant is packed into the fracture uniformly.

The model reported here has been successfully applied to XC32 well in Sichuan Basin and its prediction is 408.8m3(40/70-mesh, ceramic proppant). In reality, 400.4m3 of proppant was used and fracturing monitoring showed that the HPZ parameters in the field (length 500~600m, width 130~200m) match well with previous optimized design (length 550m, width 100m). Besides, the resulting flow rate is 7.04×104m3/d in this case, which is a breakthrough for unconventional reservoirs in Sichuan Basin.

Because this model considered the vertical heterogeneity of the reservoir and simply utilized HPZ parameters, it is convenient and meaningful to direct the treatment design in the field.

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