Finite element method has been employed to evaluate stress distribution within the sandstone formation as the result of a perforation job. The study is based on the followings: a radial reservoir with a perforated well located at the center of the reservoir, characteristics of both 3.5 and 10.5 gr. RDX charges, and the mechanical and thermal properties of the Berea sandstone. This research was performed in three distinct steps:
jet temperature effect,
jet pressure effect, and
combined jet temperature and pressure effects.
The results indicated that a 3.5 RDX charge with 2,500,000 psi initial pressure is capable of disturbing rock formation up to five inches longitudinally and two inches radially. The extent of this damage zone for a 10.5 gr. RDX charge having an initial pressure of 4,000,000 psi is eight inches longitudinally and four inches radially. The linear effect is within the first few inches of the perforation tunnel entrance. Within this region, rock grains are under an intensive sudden shock pressure wave of 2 to 4 million psi for fraction of a microsecond. As a result, rock physical structure will change to metamorphous with a lower bulk density than that of unshocked rock, causing a sudden decrease in formation porosity and hence formation permeability. This study however, shows that thermal stresses as the result of jet temperature (1,200 F), is insignificant.
Shaped-Charge. Formation damage caused by of a perforation job has long been known, studied, and documented. Nevertheless, the severity of this damage, where rock properties alter, is an ongoing research in the form of experimental and/or theoretical investigations.
A shaped charge is mechanically a simple device, yet complex in operation, consisting of a conical metallic liner, primer, explosive, and a container. Detonation of an explosive shaped charge, creates an intense pressure pulse jet with an initial pressure and velocity of up to 4,500,000 psi and 30,000 ft/s, respectively. This highly focused pressure wave strikes the rock formation and pushes aside rocks and pore fluids in its way to create a tunnel. As the shaped charge penetrates through the rocks, it propagates both as longitudinal and transverse waves. Longitudinal waves can be compressive or tensile in stress and can penetrate both in solid rocks or formation liquids. Liquids, however, do not have shear strength and therefore, do not transmit transverse waves. Shock wave reflection caused by shaped charge could therefore, have a positive or negative influence on perforation penetration. Reflected tensile waves tend to help penetration, while reflected compressive waves can either increase or decrease it.
As the jet proceeds and tunnel is formed, rock grains around the tunnel become compacted, altering the formation properties (i.e., porosity and permeability). This altered zone, also known as crushed zone, is believed to have a porosity of up to 70% less than that of unperforated formation. As shaped charge moves deeper into the formation, its energy decreases and has less effect on the formation properties the effect of this alteration, in some cases are shown to lead to an 80% reduction in well productivity. The extent of this damage, however, can be quantitatively evaluated using both the finite element analysis and the principle of quartz deformation known as shock metamorphism.
Phenomenon of Shock Metamorphism. A brief introductory on quartz crystal is given to better understand its behavior when subjected to a high pressure and/or temperature.
Quartz Crystal. Quartz is a crystalline form of silicon dioxide with a chemical formula of SiO2. Quartz is hard, brittle, and transparent with a density of 2.649 g/cm and a melting point of 1750 C (3.182 F). Quartz undergoes different phase changes if subjected to a high pressure and/or temperature. P. 25^