Stress & Anisotropy Evolution Calculator

Estimate evolution of stress and 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), typically interpreted as the average stage-to-stage change in ISIP, together with elastic coupling. The app tracks changes in stress anisotropy and computes the corresponding change in stress orientation. Stage-by-stage plots and validity indicators help assess when stress interactions may begin to influence fracture behavior and completion performance. This is a screening and conceptual tool designed to isolate the first-order effects of stress anisotropy evolution on stress rotation. It is not a predictive geomechanical simulator.

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Input data:

Sv gradient (psi/ft): Vertical stress gradient used to compute Sv at depth and evaluate the stress regime.
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.
Shmin gradient (psi/ft): Minimum horizontal stress gradient. This is the primary stress affected by ΔP during each stage.
Reference depth (ft): Depth at which stresses are calculated from the input gradients.
Initial orientation of Shmax (deg): Initial azimuth (from North) of the maximum horizontal stress.
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).
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.
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.
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.
Number of stages to plot: Maximum number of stages displayed. The model may stop earlier if validity limits are reached.

StressEvolution

Assumptions:

ISIP-derived ΔP: ΔP represents the average stage-to-stage change in ISIP, interpreted as a proxy for the average change in Shmin. This assumption is most appropriate when lithology, pore pressure, completion design, and measurement conditions are approximately constant.
Constant or segmented ΔP per stage: ΔP is assumed constant over the modeled interval, or applied in separate segments when the ISIP trend changes, such as increasing, decreasing, or plateau behavior.
Positive vs. negative ΔP: Positive ΔP represents progressive stress buildup. Negative ΔP can be evaluated mathematically but may reflect processes outside the scope of the model (e.g., lithology, natural fractures, pore pressure, or operational effects).
Linear elastic response: Shmin changes with ΔP; SHmax responds through Poisson-based coupling.
Small-angle approximation: Rotation represents small deviations from alignment with the initial SHmax azimuth.
Constant vertical stress (Sv): Sv is held constant and is used only to evaluate stress-regime changes.
No spatial or time effects: Spatial stress shadows, pressure diffusion, depletion, leakoff, and time-dependent behavior are not explicitly modeled.
No explicit pore-pressure modeling: Pore pressure is assumed approximately constant within the modeled interval. Differences in pore pressure between wells or pressure communication effects may influence ISIP but are not modeled directly.
Rotation from horizontal stress anisotropy reduction: Rotation is driven only by changes in horizontal stress anisotropy, A=SHmax−Shmin. No explicit shear generation or non-coaxial stress perturbation is included.
Constant perturbation: The formulation assumes A⋅θ remains constant across stages, so rotation increases as anisotropy decreases and decreases as anisotropy increases.

Output:

Basic:

Final valid stage: Last stage where all model assumptions and validity limits are satisfied.
Shmax azimuth at final stage (deg): Direction of SHmax at the final valid stage after rotation.
Total Shmax rotation at final stage (deg): Cumulative change in SHmax direction from the initial orientation.
Shmax at final valid stage (psi): Maximum horizontal stress magnitude at the final valid stage.
Shmin at final valid stage (psi): Minimum horizontal stress magnitude at the final valid stage.
Initial stress anisotropy (%): Starting difference between SHmax and Shmin, expressed as a percentage.
Anisotropy at final valid stage (%): Remaining stress anisotropy at the final valid stage.

Advanced (optional)

Isotropy is reached at stage: Stage where SHmax equals Shmin (small or no stress anisotropy remains).
Small angle approximation violated at stage: Stage where rotation per step becomes too large for the model assumptions to remain valid.
Anisotropy decay fails at stage: Stage where a significant portion of the initial anisotropy has been consumed, reducing model reliability.
Reverse faulting (invalid regime) at stage: Stage where Shmin exceeds Sv, indicating a transition to reverse faulting and invalid model conditions.
Average angle rotation per stage (deg).
Shmax increase factor: Ratio describing how strongly SHmax increases relative to Shmin based on the selected Poisson's based coupling model.

Plots:

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.
SHmax Azimuth vs Stage: Tracks the rotation of the maximum horizontal stress direction as stages progress.
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.

Whether your completion design is likely to induce stress rotation.
How stage-to-stage interaction affects fracture orientation.
How sensitive the system is to small initial misalignments.
When stress evolution may impact fracture behavior.
Where results remain physically reliable.

Using this tool, you will learn:

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