Long-Term Hydraulic Fracture Conductivities Under Extreme Conditions
Authors: Cikes Marin 
Published: December 2007

Abstract
Proppants for hydraulic fracturing are subjected to very severe conditions of stress, temperature and chemical environment while they are expected to maintain their structural integrity for a period of many years. The performance of these proppants over time at simulated in-situ conditions has been a topic of laboratory investigation for several years, but in many cases the real conditions exceed the capabilities of the laboratory apparatus. In order to determine the proppant behavior under real reservoir conditions, production history and numerous pressure buildup tests of eight fractured wells have been analyzed. The reservoir conditions of these wells are so severe, that it was almost impossible to simulate them in laboratory. The formation temperature is 179-195 C (354-383 F), while the reservoir pressure varies between 44.5 and 50.0 MPa (6453-7250 psi). The producing fluid is large gravity (0.825 to 1.047 to air) sour gas (up to 22% CO2 and up to 0.02% H2S), while the producing water is practically deionized. The proppants are high strength zirconium oxide and sintered bauxite, while the amount of injected proppant varies between 100 and 628 tons (2.2E+05 to 1.38E+06 lbm). The net closure stress is in the range of 30 to 50 MPa (4350-7250 psi). The production time of these hydraulically fractured wells varies between five and ten years. Emphasis in this paper is given to the results of production history and pressure buildup tests analysis, as well as to the relationships of calculated fracture conductivity and reservoir conditions over time.

Introduction
Hydraulic fracturing treatments are required to ensure economic production rates from wells completed in low- to moderate-permeability formations for a long period of time. The relationship between the productivity improvement factor, obtained by hydraulic fracture stimulation and the dimensionless fracture conductivity, CfD, of the propped fracture, has been published first by Prats. A series of important contributions in the understanding of the behavior of hydraulically fractured wells was provided by Cinco et al. and Cinco and Samaniego. Since then, Cinco and his coworkers have produced a number of additional works. It follows from all that works that the productivity improvement factor is proportional to the dimensionless fracture conductivity, CfD, which is defined as:
(1)
As it can be seen, for given fracture length, xf, and reservoir permeability, k, the dimensionless fracture conductivity, CfD is proportional to proppant-pack permeability, kj, and fracture width, wf, or simple to fracture conductivity, kfwf. The fracture conductivity may be increased by enlarging the propped fracture width, which means by application of high proppant concentration, or by improving proppant-pack permeability. 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, formation temperature and chemical environment, non-Darcy flow effects in the fracture, damage from fracturing-fluid residue remaining after fracture cleanup, multiphase flow effects, well production history, etc.
Although the permeability of a lightly stressed proppant pack can be found theoretically as a function of the porosity of the pack, , and the mean diameter of the proppant grains, d50, that is:
(2)
the fracture conductivity dependence on effective closure stress, formation temperature, chemical environment, etc., can not be assessed theoretically.
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