Estimate SHmax rotation during multi-stage fracturing
This app calculates and visualizes how horizontal stresses evolve during multi-stage hydraulic fracturing and estimates the resulting rotation of SHmax. It updates Shmin and SHmax using user-defined pressure increments (ΔP) and elastic coupling, tracks the reduction in stress anisotropy, and computes the corresponding change in stress orientation. The app provides stage-by-stage plots and validity indicators to help assess when stress interactions may begin to influence fracture behavior and completion performance. This is a screening and conceptual tool designed to understand how anisotropy reduction can lead to stress rotation. It is not a predictive geomechanical simulator.
Input data:
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Sv gradient (psi/ft): Vertical stress gradient used to compute Sv at depth and evaluate the stress regime.
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SHmax gradient (psi/ft): Maximum horizontal stress gradient used to define the initial stress state. This changes during each stage according to Poisson's ratio and ΔP.
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Shmin gradient (psi/ft): Minimum horizontal stress gradient. This is the primary stress affected by ΔP during each stage.
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Reference depth (ft): Depth at which stresses are calculated from the input gradients.
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Initial orientation of Shmax (deg): Initial azimuth (from North) of the maximum horizontal stress.
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Initial Shmax misalignment: Small misalignment between regional stress and unavoidable local subsurface variability. Enables stress rotation as anisotropy decreases. The sign of the initial misalignment controls the direction of rotation. It should be chosen based on the expected direction of local perturbations (e.g., toward natural fractures or observed fracture trends).
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Instanteneous shut-in pressure (ISIP) increase ΔP per stage (psi): Average pressure increase applied at each stage. Controls the increase in Shmin and drives stress evolution. Should be approximately constant or applied in segments.
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Poisson's ratio: Controls how SHmax responds to changes in Shmin. Higher values imply stronger stress coupling. Zero means no coupling and Shmax remains constant.
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Model for ΔSHmax increase: Defines how SHmax increases with ΔP. Unconfined: weaker coupling → faster. anisotropy loss → more rotation. Confined: stronger coupling → slower anisotropy loss → less rotation.
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​Number of stages to plot: ​Maximum number of stages displayed. The model may stop earlier if validity limits are reached.
Assumptions:
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Constant ISIP ΔP per stage: Pressure increase is assumed constant (or applied in segments if variable).
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Linear elastic response: Shmin increases with ΔP; SHmax responds through Poisson-based coupling.
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Small-angle approximation: Rotation represents small deviations from alignment with initial SHmax azimuth.
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Constant vertical stress (Sv): Used only to evaluate stress regime changes.
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No spatial or time effects: Stress shadows, diffusion, or time-dependent behavior are not modeled.
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Rotation from horizontal stress anisotropy reduction: Rotation is due only to decrease in anisotropy (A). No explicit shear generation is included. The model isolates the role of anisotropy reduction in driving stress rotation. While other effects can influence local behavior, we assume that anisotropy remains the dominant first‑order control on the system’s rotational sensitivity.
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Constant perturbation: The formulation assumes A⋅θ remains constant across stages, so rotation increases as anisotropy A decreases.
Output:
Basic:
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Final valid stage: Last stage where all model assumptions and validity limits are satisfied.
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Shmax azimuth at final stage (deg): Direction of SHmax at the final valid stage after rotation.
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Total Shmax rotation at final stage (deg): Cumulative change in SHmax direction from the initial orientation.
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Shmax at final valid stage (psi): Maximum horizontal stress magnitude at the final valid stage.
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Shmin at final valid stage (psi): Minimum horizontal stress magnitude at the final valid stage.
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Initial stress anisotropy (%): Starting difference between SHmax and Shmin, expressed as a percentage.
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Anisotropy at final valid stage (%): Remaining stress anisotropy at the final valid stage.
Advanced (optional)
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​Isotropy is reached at stage: Stage where SHmax equals Shmin (small or no stress anisotropy remains).
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Small angle approximation violated at stage: Stage where rotation per step becomes too large for the model assumptions to remain valid.
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Anisotropy decay fails at stage: Stage where a significant portion of the initial anisotropy has been consumed, reducing model reliability.
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Reverse faulting (invalid regime) at stage: Stage where Shmin exceeds Sv, indicating a transition to reverse faulting and invalid model conditions.
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Average angle rotation per stage (deg).
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Shmax increase factor: Ratio describing how strongly SHmax increases relative to Shmin based on the selected Poisson's based coupling model.
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Plots:
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SHmax and Shmin vs Stage: Shows how horizontal stresses evolve with each stage. Shmin increases directly with ΔP, while SHmax increases more gradually depending on Poisson's ratio based coupling.
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SHmax Azimuth vs Stage: Tracks the rotation of the maximum horizontal stress direction as stages progress.
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Anisotropy and Angle Increment vs Stage: Displays the reduction in stress anisotropy alongside the increase in rotation per stage, highlighting how decreasing stress contrast leads to greater sensitivity to rotation.
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Whether your completion design is likely to induce stress rotation.
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How stage-to-stage interaction affects fracture orientation.
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How sensitive the system is to small initial misalignments.
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When stress evolution may impact fracture behavior.
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Where results remain physically reliable.
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Using this tool, you will learn:
​This app is not designed to work on mobile devices. If the app does not display properly, refresh the page.
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Tip: Click a cell to see a brief description.
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