## 2 Geology and Geophysical Model of Forty Niner Ridge Field in Brushy Canyon Formation  
The target field in this study is the Forty Niner Ridge field in the Permian Basin in New Mexico, U.S. The Brushy Canyon formation consists of fine-grained sandstone layers of 150 m which represent a significant reservoir interval. However, the low permeability and petrophysical heterogeneity of the formation rock limits primary recovery to as little as 10-15% of the original oil in place (OOIP), suggesting that horizontal wells should be drilled and hydraulically fractured [22]. In the target field, four horizontal wells were drilled in four different directions from 2006 to 2014. To perform this study, the G&G (Geology and Geophysics) reservoir model was first constructed based on well logging data from 17 wells, completion reports, and production reports. First, logging data interpretation was performed by using Schlumberger's Petrel and Techlog simulators to construct the reservoir and to calculate petrophysical properties. As shown in Figure 1, the formation layering was conducted by interpreting the gamma ray patterns from measured physical log data. After determining the existence of bad holes from the caliper log and bit size using Techlog, shale volume, effective porosity, and total water saturation were calculated by synthesizing bad hole, gamma ray, neutron and bulk density, and resistivity logs. Then, based on the petrophysical properties, geomechanical properties of the reservoir were calculated by applying the following correlation equations. From the core analysis results of the same Brushy Canyon formation 6 km west from the target area, a regression analysis was performed to determine the porosity/ permeability relationship as Equation (1) [22]. \[k=10^{(0.315038\varnothing+3.69966)} \tag{1}\]  
where \(\varnothing\) is porosity. From the field technical progress document, the pore pressure gradient was reported as 9.856 MPa/km [22]. Due to the absence of the field measurement data for the rock strength and elastic properties, correlations based on the similar rock mineralogy were adopted to calculate geomechanical properties such as the uniaxial compressive strength (UCS) and the Young's modulus [23]. UCS correlation (2) derived from multivari  
Figure 1: The layer formation process of the reservoir by connecting the similar trends in the gamma ray logs obtained from 17 wells. able regression equation by [PERSON] et al. (2018) and static Young's modulus (MPa), Estatic, (3) from [PERSON]'s empirical correlation ([PERSON] et al., 2009) were applied ([PERSON] et al., 2009; [PERSON] et al., 2018). \[UCS=147.536-395.292\varnothing-15.292\rho+7.724S_{w} \tag{2}\]  
\[E_{static}=(UCS-2.280)\times 1677.992 \tag{3}\]  
where \(\rho\) is density (g/cm\({}^{3}\)) and \(S_{w}\) is water saturation. The \(\sigma_{\rm Hmax}/\sigma_{\rm hmin}\) acting on our reservoir model was reflected in the model based on the research results published by [PERSON] and [PERSON] (2018) ([PERSON] and [PERSON], 2018). They provided regional faulting regime value (\(A_{\varnothing}\)) proposed by [PERSON] (1997) to represent the relative magnitudes of the three principal stresses (\(\sigma_{\rm v}\), \(\sigma_{\rm Hmax}\), and \(\sigma_{\rm hmin}\)) ([PERSON] and [PERSON], 2018). The value ranges from 0 (the most extensional possible condition of radial normal faulting) to 3 (the most compressive possible condition of radial reverse faulting). The value is defined mathematically by Equations (4) and (5)  
\[A_{\varnothing}=(n+0.5)+(-1)^{n}\;(\varnothing-0.5) \tag{4}\]  
and  
\[\varnothing=\frac{\sigma_{2}-\sigma_{3}}{\sigma_{1}-\sigma_{3}} \tag{5}\]  
where, \(\sigma_{1}\), \(\sigma_{2}\), and \(\sigma_{3}\) are the magnitudes of the maximum, intermediate, and minimum principal stresses, respectively, and n is 0 for normal faulting, 1 for strike-slip faulting, and 2 for reverse faulting.