Fracture Conductivity in Hydraulic Fracture Stimulation
Authors: Davies D.R. , Kuiper T.O.H. 
Published: December 2007

Introduction
Hydraulic fracturing treatments are frequently required to ensure economic production rates from wells completed in low- to moderate-permeability formations. This type of stimulation treatment involves placing layers of proppant material in the created fracture (Fig. 1). Thus, the formation inflow area to the wellbore is greatly enhanced. The relationships between the productivity improvement factor, Fp, obtained by hydraulic fracture stimulation and the dimensionless fracture conductivity, CfD, of the propped fracture have been published by Prats. CfD is proportional to proppant-pack permeability, kf, and fracture width, bf:
.......................... (1)
The fracture conductivity may be increased by enlarging the propped fracture width, bf, by application of high proppant concentration. This has become popular during the last few years. Fig. 2 shows that a dimensionless fracture conductivity of 15 is a proper design value for (pseudo) steady-state flow conditions. This value is often not achieved in practice. Moreover, the fracture conductivity found from production-test interpretation on hydraulically fractured wells is often an order of magnitude smaller than expected. Tight reservoirs with high initial transient production rates require higher dimensionless fracture conductivities than indicated above because these transient rates can last for more than 1 year and significantly contribute to the economic success of the fracturing treatment. More sophisticated tools, such as type curves or reservoir simulators, are required to assess optimum fracture conductivity in these cases. Many factors influence the effective proppant-pack permeability, kf, e.g., proppant type, grain size, effective closure stress acting on the proppant pack and formation face, non-Darcy flow effects in the fracture (for gas wells), damage from fracturing-fluid residue remaining after fracture cleanup, and multiphase flow effects. These factors will be discussed individually.

Proppant-Pack Permeability (Low Closure Stress)
The permeability of a lightly stressed proppant pack is a function of the porosity of the pack, phi, and the mean diameter of the proppant grains, d50:
.............(2)
Notice the importance of the proppant-pack porosity. In addition, a wider grain-size distribution of a given d50 reduces the permeability -- hence the modern tendency to market narrow sieve fractions, with a bigger mean grain size within a given nominal mesh range. For gas wells, non-Darcy ("turbulence") flow effects in the propped fracture result in an extra pressure drop, :
.............................. (3)
where v is the fluid flow velocity and the non-Darcy flow factor, which is dependent on kf. Non-Darcy flow effects calculated from Guppy et al. for typical hydraulically fractured gas wells can reduce the effective fracture conductivity by more than a factor of 3.
Effective Closure Stress The fracture conductivity dependence on effective closure stress (minimum in-situ stress minus pore pressure) cannot be assessed theoretically; empirical relations based on extensive proppant conductivity measurements over a wide range of conditions are required. The majority of these measurements have been carried out on the most popular proppant size (20/40 mesh) with low liquid flow rates (negligible non-Darcy flow effects) at low temperature and short measurement times. Limited data are available for measurements with gas. The most recent measurements were conducted at reservoir temperature with long measurement times. Significantly lower proppant conductivities are measured for realistic reservoir conditions than reported for the early short-term conductivity tests (Fig. 3). Lack of reproducibility of absolute-permeability measurements between the various laboratories plagues this area of research because standard procedures for preparation - in particular pack porosity - have not been agreed on. The high closure stresses encountered in deeper wells require the use of artificial (intermediate- or high-strength) proppants to improve fracture conductivity. The recent long-term measurements discussed show a technical need for these stronger (and therefore more conductive) proppants at lower closure stresses (shallower depth). This is also true if coarser proppant sand grades are used in an attempt to increase fracture conductivity because crushing occurs at lower closure stress.
Multiphase Flow Effects Proppant-pack conductivity is normally measured with single-phase flow. Adding a second or third phase reduces the effective proppant-pack permeability to the original phase significantly. Fig. 4 shows a proppant-pack permeability decrease by more than a factor of 5 if water-saturated gas (two phases) flows through the pack. (Note that in Fig. 4 is called the normalized flow -- see Eq. 3.)
Fracturing-Fluid Damage The fracturing fluid is an essential part of a hydraulic fracturing treatment.
JPT
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