The effects of immobile and mobile liquid saturations on the non-Darcy flow coefficient in propped fractures have been investigated. It was observed that an immobile liquid saturation of up to 20% PV can triple the non-Darcy flow coefficient and a small mobile liquid saturation will increase the non-Darcy flow coefficient by nearly an order of magnitude (over that of the dry case). The linear relationship between the logarithm of the non-Darcy flow coefficient and the logarithm of the proppant permeability for propped fractures, as proposed by Cooke, is shown to be invalid in the presence of an immobile or mobile liquid saturation. Constants are presented that can be used to obtain a more accurate approximation than has previously been available on the non-Darcy flow coefficient for single-phase flow in fractures propped with 10/20- and 20/40-mesh Ottawa sand. The experimental data obtained from this research are compared with those of others reported in the literature.


In the past several years, there has been considerable interest in the optimization of flow in high-capacity gas wells. As a result of this interest, much attention has been directed toward the phenomenon of non-Darcy flow in porous media, which is very important in high-capacity gas wells.

Viscous flow, where the pressure gradient is proportional to flow velocity, is described by Darcy's equation:

In 1901, Forchheimer proposed an equation that described the additional pressure drop observed in non-Darcy flow at high flow velocities:

For predominantly viscous flow at low flow rates, the first term (or Darcy term) is important, while the second (or non-Darcy) term is negligible. But at higher flow rates, the non-Darcy term becomes significant and may eventually dominate the Darcy term.

Non-Darcy flow effects are much more significant in gas wells than oil wells, chiefly because of the higher flow velocities as a result of the much lower viscosity of the gas. This is especially true in hydraulically fractured gas wells because the velocity in the highly conductive fracture can be very high, resulting in large pressure drops owing to non-Darcy flow. Failure to consider these pressure drops leads to error in the design of hydraulic fracturing treatments and optimum well spacings, which reduces the efficiency of completion methods for these reservoirs.

Work has been reported by both Cooke and Koh to analyze the non-Darcy flow effect in hydraulic fractures quantitatively. However, both investigated the non-Darcy flow effect for single-phase gas flow only, with no immobile or mobile liquid saturation present.

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