Application of Monte Carlo Simulation for Estimation of Vertical and Horizontal Biot's Constants Through Calibration of the Minimum Horizontal Stress in the Tight Gas Monteith Formation

Abstract

Abstract Tight formations are characterized by permeabilities equal to or less than 0.1 md. Due to these low permeability values, tight gas reservoirs have been economically produced through the implementation of multi-stage hydraulic fracturing. This operation requires a proper stimulation design, which depends on the knowledge of rock properties such as Biot's constants. Therefore, the purpose of this study is to determine vertical and horizontal Biot's constants through calibration of minimum horizontal stress (MHS) with the use of well logs and mini-frac data in the tight gas Monteith formation of the Western Canada Sedimentary Basin (W CSB). The procedure utilized in this work consists of the determination of actual MHS values from mini-frac tests. It is assumed that MHS is equal to fracture closure pressure (FCP). Two non-linear regression equations are used to estimate MHS. Statistical analysis is performed to test the appropriateness of the non-linear regression expressions for MHS modeling. Next, MHS values are calculated from well log data using an existing correlation and by the application of Monte Carlo simulation. Uniform, triangular and beta-PERT distributions are considered in this study. Then, MHS values obtained from the above two methods are matched for calibration purposes. Finally, both vertical and horizontal Biot's constants are determined from the match previously obtained. Statistical analysis of the two non-linear regression expressions for MHS modeling reveals that FCP ranges from 10.72 MPa to 17.78 MPa in the study area. From Monte Carlo simulations, it is found that horizontal Biot's constant values are most consistent among the different distributions considered in this study as compared with the case of the vertical Biot's constant. This large variation in vertical Biot's constants is a result of the uncertainty associated with the definition of the most suitable distribution for this variable. Horizontal Biot's constant values vary from 0.81 to 0.97 whereas vertical Biot's constant ranges from 0.66 to 0.95. It is concluded that beta-PERT distribution better represents Biot's constants, however, this finding has to be corroborated against experimental data. The methodology presented in this work is robust and represents a practical method to determine Biot's constants instead of following the assumptions considered by current commercial 3D hydraulic fracture simulators. This is the first time that non-linear regression techniques, statistical analysis, and Monte Carlo simulation are coupled all together with both well log and mini-frac data to estimate Biot's constants. This methodology can be easily applied in other tight formations.