Light oil is produced from an open hole horizontal well completed through hydraulic fracturing into a low permeability formation. Two penny-shaped, vertical hydraulic fractures are considered, and they intersect a network of activated natural fractures (modeled as a stack of “sugar cubes”, see Figure 1). The hydraulic fractures are propped, while the natural ones are not. The natural fractures also do not directly connected to the wellbore.

The considered reservoir section measures 500 ft in width, and 600 ft in both depth and height, as seen in Figure 2. The hydraulic fractures are built as discs 0.5-inch-thick at the center (where they intersect the well) and extend 225 feet in the other dimensions. The natural fracture “sugar cubes” have sides of 66.7 feet. The top and back-right boundaries are maintained at constant pressure ΔP, while the open hole well boundaries are at zero pressure (ΔP having thus the meaning of *drawdown pressure*). All other outer boundaries are taken as symmetry boundaries. The flow is isothermal at a temperature of 85°C, at which the fluid density and dynamic viscosity values are 0.694 g/cc and 0.256 cP, respectively.

The reservoir matrix has permeability and porosity values of 1 μD and 0.15, respectively. The corresponding values for the proppant pack (consisting of sand 350 μm in diameter) are 45.6 Darcy and 0.30. A Forchheimer beta factor is also calculated for the sand pack as 148 mm-1, via the Ergun relationship. The natural fractures are considered 0.2 mm thick, with 0.5 voidage fraction and a permeability of 50 Darcy.

Figures 3 and 4 show the pressure distribution (via surface color plots) and velocity streamlines for different perspectives of the model. As the produced liquid hydrocarbon converges towards the well bore, it does so preferentially through the hydraulic fractures; due to the radial nature of the flow, high fluid velocity are encountered in the hydraulic fracture in proximity of the wellbore.

The impact the natural fracture network (NFN) has on the production rate is exemplified in Figure 5, which compares total well flow rate values obtained with the NFN active versus inactive (red and green curves, respectively) for different values of the drawdown pressure ΔP. It is apparent that having the NFN open to flow dramatically increases the well production, despite it not being directly connected to the wellbore.

Figure 5 also shows the well production rate when the inertial effects in the proppant pack are neglected, with the NFN being active (blue curve). However for the particular low value (*Kres* = 1 μD) considered for the matrix permeability, the flow is within the Darcy regime and the blue and red curves overlap. The inertial effects start to have a sizable impact on the well production rate at much higher *Kres* values, of the order of ~ 0.1 mD: Figure 6 plots the Darcy and Forchheimer proppant pack flow solutions (blue and red curves, respectively) for *Kres* = 1 μD to 1 mD , with ΔP fixed at 5000 psi. In the current open hole well model, we can see that the inertial effects reduce the total well flow rate by 44% when *Kres* = 1 mD — and their impact is expected to be significantly larger for case-perforated wells, due to their restricted well inflow area.