مجله ژئومکانیک نفت
سال پنجم شماره 1 (بهار 1401)

Nowadays, hydraulic fracturing is used in various fields such as stimulation of oil reservoirs, measurement of in-situ stresses, extraction of geothermal energy and extraction of conventional and unconventional hydrocarbon resources.Meanwhile in-situ stresses and porosity are the most important factors that affecting the propagation, opening and extension of the crack. In this research, the above parameters have been investigated using analytical and numerical methods. For numerical modeling in this research, the numerical method of displacement discontinuity, has been used, which is one of the methods with high ability in modeling discontinuity and failure. The program used is a quadratic element based on solid mechanics and fracture mechanics. In this research, by addition of the fluid flow module, the fluid mechanics is included in the analysis. In the fluid mechanics module, the effect of fluid flow on crack opening displacement is investigated. This part of the program is created by finite difference method in mode of forward time central space. Finally, after validation of the program, the effects of in situ stress and porosity on crack propagation were investigated. In order to generalize the results, the studied parameters have been presented in dimensionless forms. It is concluded that the best direction for creating a hydraulic fracture is in the direction of maximum principal stress. As the in-situ stress difference increases, less injection pressure is required to propagate the crack. In the crack with a 45 degrees angle relative to the maximum stress, a lower injection pressure is required to propagate the crack; then this crack after several step of growth deviates to the maximum stress direction. Increasing the porosity of the formation reduces the amount of Young's modulus and Poisson's ratio, which leads to increases the crack opening at higher porosity values.

Porosity is a very sensitive parameter for determining the velocity of waves, estimating geomechanical parameters and petrophysical properties of hydrocarbon reservoirs. Today, in oil industry this parameter is obtained by using the helium gas injection method on core samples. Determining porosity by methods such as core analysis requires a lot of time and money. Coring is difficult and costly. In addition, it is not possible to core in some wells (such as horizontal wells). Therefore, due to the lack of sufficient cores and lithological changes and heterogeneity of reservoir rock, the determination of this parameter by conventional methods is not very accurate. So far, many experimental relationships have been proposed to calculate porosity, but in most cases, the results in different regions are not desirable. In this study, in an oil well South-west Iran, porosity was measured using neutron, density and sonic logs and also a combination of these data. Then for 645 specimens of the same section, porosity was measured using helium gas injection test. Correlation analysis and mathematical manipulation resulted in an empirical equation for estimation of porosity based on a combination of three indicators: compressional wave velocity (Vp), density (), and the ratio of compressional to shear wave velocities (Vp/Vs). Artificial intelligence technics were used to optimize this empirical equation. As a result, porosity can be estimated at a lower cost and more accuracy for the whole length of drilling.