Date of download: 10/9/2017 Copyright © ASME. All rights reserved. From: Modeling of Hydraulic Fracture Propagation in Shale Gas Reservoirs: A Three-Dimensional, Two-Phase Model J. Energy Resour. Technol. 2016;139(1):012903-012903-13. doi:10.1115/1.4033856 Figure Legend: Visual representation of height growth model

Date of download: 10/9/2017 Copyright © ASME. All rights reserved. From: Modeling of Hydraulic Fracture Propagation in Shale Gas Reservoirs: A Three-Dimensional, Two-Phase Model J. Energy Resour. Technol. 2016;139(1):012903-012903-13. doi:10.1115/1.4033856 Figure Legend: (a) Length (ft) versus time (min) and (b) width (in.) versus time (min). The grid sizes of 0.1, 1, 10, and 100 ft are studied.

Date of download: 10/9/2017 Copyright © ASME. All rights reserved. From: Modeling of Hydraulic Fracture Propagation in Shale Gas Reservoirs: A Three-Dimensional, Two-Phase Model J. Energy Resour. Technol. 2016;139(1):012903-012903-13. doi:10.1115/1.4033856 Figure Legend: Schematic of gridding system in both fracture and matrix domain

Date of download: 10/9/2017 Copyright © ASME. All rights reserved. From: Modeling of Hydraulic Fracture Propagation in Shale Gas Reservoirs: A Three-Dimensional, Two-Phase Model J. Energy Resour. Technol. 2016;139(1):012903-012903-13. doi:10.1115/1.4033856 Figure Legend: Schematic flowchart of the three-dimensional, two-phase numerical solution

Date of download: 10/9/2017 Copyright © ASME. All rights reserved. From: Modeling of Hydraulic Fracture Propagation in Shale Gas Reservoirs: A Three-Dimensional, Two-Phase Model J. Energy Resour. Technol. 2016;139(1):012903-012903-13. doi:10.1115/1.4033856 Figure Legend: Comparison results showing favorable comparison between PKN and model developed herein for fracture height evolution through time (a), and fracture width versus time (b)

Date of download: 10/9/2017 Copyright © ASME. All rights reserved. From: Modeling of Hydraulic Fracture Propagation in Shale Gas Reservoirs: A Three-Dimensional, Two-Phase Model J. Energy Resour. Technol. 2016;139(1):012903-012903-13. doi:10.1115/1.4033856 Figure Legend: Visual representation of three-layer height growth model input values

Date of download: 10/9/2017 Copyright © ASME. All rights reserved. From: Modeling of Hydraulic Fracture Propagation in Shale Gas Reservoirs: A Three-Dimensional, Two-Phase Model J. Energy Resour. Technol. 2016;139(1):012903-012903-13. doi:10.1115/1.4033856 Figure Legend: Height growth comparison result for seven-layer case. Solid lines indicate the result from the model developed herein while square symbols represent the results from the reference model.

Date of download: 10/9/2017 Copyright © ASME. All rights reserved. From: Modeling of Hydraulic Fracture Propagation in Shale Gas Reservoirs: A Three-Dimensional, Two-Phase Model J. Energy Resour. Technol. 2016;139(1):012903-012903-13. doi:10.1115/1.4033856 Figure Legend: Vertical stress profile for each layer

Date of download: 10/9/2017 Copyright © ASME. All rights reserved. From: Modeling of Hydraulic Fracture Propagation in Shale Gas Reservoirs: A Three-Dimensional, Two-Phase Model J. Energy Resour. Technol. 2016;139(1):012903-012903-13. doi:10.1115/1.4033856 Figure Legend: Height comparison between the model developed herein and DFN. (Left: height versus network length from the model developed herein and the black and grey to white color bar indicates the width of a fracture in ft; right: height versus width of the fracture at the perforation (primary fracture) from DFN. The contour map shows the width of a primary fracture as length increases.)

Date of download: 10/9/2017 Copyright © ASME. All rights reserved. From: Modeling of Hydraulic Fracture Propagation in Shale Gas Reservoirs: A Three-Dimensional, Two-Phase Model J. Energy Resour. Technol. 2016;139(1):012903-012903-13. doi:10.1115/1.4033856 Figure Legend: Final fracture network comparison (top view). Top network is from Jacot's result and the bottom is from the model developed herein. The horizontal well is located along the zero in x-axis and perforation is placed at (0,0).

Date of download: 10/9/2017 Copyright © ASME. All rights reserved. From: Modeling of Hydraulic Fracture Propagation in Shale Gas Reservoirs: A Three-Dimensional, Two-Phase Model J. Energy Resour. Technol. 2016;139(1):012903-012903-13. doi:10.1115/1.4033856 Figure Legend: Final fracture network characteristics (height, length, and aperture) from the model developed herein. This representation is for only half of a fracture network.

Date of download: 10/9/2017 Copyright © ASME. All rights reserved. From: Modeling of Hydraulic Fracture Propagation in Shale Gas Reservoirs: A Three-Dimensional, Two-Phase Model J. Energy Resour. Technol. 2016;139(1):012903-012903-13. doi:10.1115/1.4033856 Figure Legend: Fracture domain discretization along x-direction