A numerical implementation of the conceptual and earth models has been developed of the FORGE reservoir and surrounding area to estimate the spatial distribution of native state pressure, temperature, and stress conditions. The primary goal of this effort was threefold.
 Incorporate detailed 3D parameter distributions and complex boundary conditions identified from characterizing the site.
 Better understand the spatial distribution of stress and how it may influence reservoir stimulation.
 Establish a reference (or baseline) set of parameter and property distributions that can be used among the team (and modeling community at large) to ensure consistency and comparability of simulation results.
The data and results included here are from the reference models completed in November 2019, at the approximate end of Phase 2. A complete report on the Phase 2 Modeling and Simulation can be found here.
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Model Location and Dimensions
The Phase 3 numerical model domain sized to enclose a volume of the reservoir intersected by Wells 5632, 5832, 16A, 78B32, and 7832 and a significant subsurface volume below the FORGE site footprint. The model domain of 4.0 km x 4.0 km x 4.2 km is located approximately between depths of 4000 to 4200 meters below land surface. A nonuniform mesh spacing of average 40 m was used, with a total of 0.24 million tetrahedron elements. Finite element mesh of the model can be downloaded here. The image to the left shows the model geometries, the upper sedimentary layer (red), the lower granitoid layer mesh. This image also presents the global coordinate system where Zaxis is along vertical direction and Xaxis is along the minimum horizontal direction. 

The Phase 2 numerical model domain sized to enclose a volume of the reservoir intersected by Well 5832 and a significant subsurface volume below the FORGE site footprint. The model domain of 2.5 km x 2.5 km x 2.75 km is located approximately between depths of 400 to 3200 meters below land surface and aligned with the principle stress direction. A uniform mesh spacing of 50 m was used, with a total of 137,500 grid cells. Meshes were formulated in both UTM and a local coordinate systems, and can be downloaded here. The image to the left shows the boundaries of model domain (gray box), the Utah FORGE site outline projected into the subsurface (red), and the top of the granitoid surface colored by temperature. 

The lithology at the site was divided into two broadly defined units, consisting of crystalline granitic basement rock (granitoid) and the overlying sedimentary basin fill. Vertices of points defining the contact surface can be downloaded here. The contact surface interpolated onto the numerical model mesh can be downloaded here. The image to the left shows the land surface (gray), the Utah FORGE site outline projected into the subsurface (red), and the top of the granitoid surface (green). 
Boundary and Initial Conditions
a) Boundary conditions for the fluid flow field equation:
 Prescribed zero pore pressure on the top surface;
 Prescribed pore pressure on the bottom surface;
 No flow boundary conditions for all side surfaces.
b) Boundary conditions for the thermal field equation:
 Prescribed temperature on the top surface;
 Prescribed and varied temperature input on the bottom surface. It can be downloaded here ;
 No heat flux boundary conditions for all side surfaces.
c) Boundary conditions for the stress field equation:
 Displacement along horizontal Xdirection at the two side surfaces perpendicular to Xaxis are constrained;
 Displacements along horizontal Ydirection at the side surface perpendicular to and cross over the negative Yaxis is constrained;
 Displacement along vertical Zdirection at the bottom surface is constrained;
 Atmosphere pressure is applied on the top surface for the normal traction;
 Prescribed both normal traction and shear traction along vertical (Zaxis) direction on the side surface perpendicular to and cross over the positive Yaxis;
 Body force due to gravity is applied.
By applying these boundary conditions and gravity (body force), the solution from native static model provides an initial conditions including pore pressure, temperature, and stress for further transient analysis where fluids are injected through wellbores.
Fracture Set Parameters
Fracture Intensity:
Description  P32 [1/m]  [%] 
South striking moderately dipping west  0.42  36.10% 
East striking steeply dipping south  0.35  30.10% 
SSW striking vertical  0.19  16.60% 
North striking steeply dipping east  0.2  17.20% 
1.15  100.00% 
Orientation:
Mean Trend  Mean Plunge  Mean Strike  Mean Dip  Fisher Concentration  Description 
88.5  46  178.5  44  15  South striking moderately dipping west 
1.5  13.5  91.5  76.5  30  East striking steeply dipping south 
131  5  221  85  30  SSW striking vertical 
260  17  350  73  10  North striking steeply dipping east 
Native State Modeling
Reservoir Properties
Initial reservoir properties used in the native state model were taken directly from characterization data when possible. In many cases, a range of possible values were available, and the mean or median was used, with the values being adjusted within the measured range during model calibration. In all cases, uniform reservoir properties are used within the alluvium. For the granitoid, heterogeneous property distributions are applied where appropriate and data are available. Tables below summarize the property values used. These are the “reference” values for the current state of FORGE.
Modeled Granitoid Parameters
Parameter  Units  Source/Comment  Link to data  
Compressibility  1/kPA  2.52E12  Upscaled DFN  
Kii (N25E)  m2  1.00E18  Core and reservoir testing, upscaled DFN  1160 
Kjj (N25E)  m2  1.00E18  Core and reservoir testing, upscaled DFN  1160 
Kkk (N25E)  m2  1.00E18  Core and reservoir testing, upscaled DFN  1160 
Porosity  —  1.00E03  Core and cuttings analysis, upscaled DFN  1052 
Rock grain density  kg/m3  2750  1052  
Specific heat capacity  J/kg K  790  
Grain thermal conductivity  W/m K  3.05  5832 thermal conductivity data  
Young’s Modulus  Pa  6.50E+10  Core analysis  1162 
Drained Poisson’s Ratio  —  0.3  Core analysis  1162 
Undrained Poisson’s Ratio  —  0.35  Assume B=0.8  
Biot coef  —  0.47  Literature  
Thermal expansion coef  —  6.00E06  
Mode 1 fracture toughness  MPa √m  2.48  1162 
Modeled Basin Fill Parameters
Parameter  Units  Value  Source/Comment  Link to data 
K  m2  1.70E14  Aquifer test  1140 
Porosity  —  0.12  Core cuttings analysis, native state calibration  1052 
Rock grain density  kg/m3  2500.0  Core cuttings analysis, native state calibration  1052 
Specific heat capacity  J/kg K  830.0  Literature  
Grain thermal conductivity  W/m K  2.0  Core cuttings analysis, native state calibration  5832_thermal conductivity data 
Young’s Modulus  Pa  3.0E10  Literature  
Drained Poisson’s Ratio  —  0.30  Literature  
Biot coef  —  0.60  Literature  
Thermal expansion coef  —  2.00E06  Literature 
Native State Model Results
The input script of the finite element model for running in MOOSE and FALCON can be downloaded here (\data_file\p3_ns_model_input_script.i). The images to the left from the top to the bottom present contoured results for the pore pressure for the fluid flow field, temperature for the thermal field, the vertical effective normal stress in the Zdirection, the horizontal effective normal stress in the Xdirection, the horizontal effective stress in the Ydirection, the shear stress in YZ plane along vertical direction, the mean stress (hydrostatic pressure), and von Mises stress for the solid field obtained from the native steady state model. All predicted field variables in the contours exhibit a linear distribution over the vertical direction where the minimum is on the top surface and the maximum is on the bottom surface. However, it also shows that all these pressure, temperature, and stresses exhibit appreciable variations along the horizontal direction. Furthermore, due to the applied shear traction besides the normal pressure traction boundary condition for the solid field, the stress shows a more significant variation across the interface between the sediment and granitoid. The shear stress level is roughly 10% of the vertical normal stress. Native Steady State modeling results can be downloaded here
The above native steady state model results are based on a series of calibrations that adjust some parameters to make the predicted field variables closely match the field measurements along wellbores. For example, the far field bottom temperature is slightly raised and the predicted distribution of temperature matches the temperature recorded from well logging. Importantly, it is evaluated from field fracture tests that the maximum principle stress is not exactly along the vertical direction but slightly rotates about either the maximum horizontal stress axis or the minimum horizontal stress axis. However, it is undetermined that this rotation is about which axis. By running various models with different boundary conditions, it is suggested that such a rotation is around the minimum horizontal stress axis.
The images above show the comparisons between the measured pore pressure, and temperature, field stresses and the model predicted pore pressure, and temperature, field stresses from the native static model for Wells 5632, 5832, 16A, 78B32, and 7832. General speaking, they match well except near the ground surface or on the bottom.
Modeling prior to 2022
Boundary and Initial Conditions
Boundary conditions for pressure, temperature, and stress were based on results obtained and compiled during Phase 2, which relied on both new data collection and information obtained from the literature. Due to the complex nature of the distributions of pressure, temperature, and stress, all boundary conditions in the native state model have varying degrees of spatial variability, which were implemented using Dirichlet conditions. Boundary conditions can be downloaded here. 

Initial pore pressure and temperature conditions used for the native state model were based on estimates in the earth model and assigned to the numerical model cells in a similar fashion used to assign the boundary conditions. Values for pore pressure were estimated based on the top boundary condition and interpolated downward as a function of depth. Temperate was directly interpolated from the earth model to the numerical model cells. Initial pore pressure and temperature conditions can be downloaded here. The image to the left shows the temperature applied to top of the model domain in degrees Celsius, in the local coordinate system implementation of the native state model. The location of Well 5832 is shown for reference. 

Initial stress conditions used for the native state model are based on calculations of the displacement of the rock matrix, and as such, are difficult to assign a priori. A value of zero displacement is assigned as an initial condition, letting the model iterate a few extra times to come to a converged solution. Initial stress conditions can be downloaded here. The image to the left shows the total pressure applied to top of the model domain in megapascals, in the local coordinate system implementation of the native state model. The location of Well 5832 is shown for reference. 

A representative population of natural fractures are included in the reference Discrete Fracture Network Model (DFN), which incorporates measured surface and well data to create planer fractures that communicate as a single hydrological and mechanical system. The reference DFN consists of a deterministic set of fractures intersecting Well 5832 where fracture locations and orientations are known, plus a stochastic set of fractures away from well control. The image to the left shows the orientations of the fractures in the reference DFN in an upper hemisphere stereonet (plotting fracture poles). The table below provides a summary of the three fracture sets identified. 
Fracture Set Parameters
EW Vertical  NS Inclined Dipping West  NE Steeply Dipping SE  
Set Intensity  P_{32 }[1/m]  0.78  1.41  0.31 
[%]  31  56  12  
Mean Set Orientation  Strike [deg]  96  185  215 
Dip [deg]  80 S  48 W  64 SE 
Modeled Granitoid Parameters
Parameter  Units  Min  Max  Source/Comment  Link to data 
Compressibility  1/kPA  2.52E12  8.51E08  Upscaled DFN  
Kii (N25E)  m2  1.75E21  1.20E16  Core and reservoir testing, upscaled DFN  1160 
Kjj (N25E)  m2  2.44E21  1.28E16  Core and reservoir testing, upscaled DFN  1160 
Kkk (N25E)  m2  2.93E21  1.10E16  Core and reservoir testing, upscaled DFN  1160 
Porosity  —  1.00E07  0.0118  Core and cuttings analysis, upscaled DFN  1052 
Rock grain density  kg/m3  2750.0  Core and cuttings analysis, native state calibration  1052  
Specific heat capacity  J/kg K  790.0  Literature  
Grain thermal conductivity  W/m K  3.05  Core and cuttings analysis, native state calibration  5832 thermal conductivity data  
Young’s Modulus  Pa  5.50E+10  6.20E+10  Core analysis  1162 
Drained Poisson’s Ratio  —  0.26  0.3  Core analysis  1162 
Undrained Poisson’s Ratio  —  0.35  0.4  Assume B=0.8  
Biot coef  —  0.5  0.7  Literature  
Thermal expansion coef  —  2.00E06  Literature  
Mode 1 fracture toughness  MPa √m  2.48  Core analysis  1162 
Native State Model Results
The modeled pressure, temperature, and stress along the trajectory of Well 5832 match the field measured data reasonably well. The pressure distribution is largely linear along the length of Well 5832 within the model domain and shows little to no differentiation between the overlying sedimentary basin fill and the granitoidhosted reservoir. The modeled temperature distribution also matches the field measured data and shows a break in slope at the sediment fillgranitoid contact. The image to the left shows subsampled results for the pore pressure, temperature, and stress obtained in the native state model (red X). Also shown are values from logging and testing Well 5832 (lines). Note that the pore pressure and temperature were logged over the entire length of Well 5832, while the stress is estimated from injection tests in the toe. 

The vertical stress was calibrated by adjusting the sediment density and porosity, as well as the density of the granitoid within the range of measured values until the modeled vertical stress match the field measurements at the toe of Well 5832. Native State modeling results can be downloaded here. The image to the left shows the estimated total vertical stress within the granitoid. 