Fracwave

Abstract

A breakthrough methodology has been developed that combines continuous wavelet transform (CWT) signal processing with deep learning to predict microseismic events during hydraulic fracturing operations. This innovative approach transforms treating pressure data into normalized CWT scalograms, creating unique signatures for different fracture propagation modes. The technique was validated using data from the Marcellus Shale Energy and Environment Laboratory (MSEEL) and demonstrates exceptional accuracy in predicting three-dimensional microseismic event clouds from treating pressure alone. The deep learning model achieves prediction errors below 0.025% for horizontal coordinates and below 0.2% for vertical coordinates, while generating results in near real-time (40 seconds for a 2-hour fracturing job).

Introduction

Understanding hydraulic fracture propagation events is crucial for optimizing completion designs, estimating fracture geometry, and maximizing production. Traditional methods like the Nolte-Smith technique and moving reference point (MRP) analysis, while useful, have limitations in real-time application and require complex workflows or prior knowledge of closure pressure.

Microseismic monitoring provides valuable insights into fracture propagation by detecting small-scale earthquakes resulting from rock ruptures during high-pressure fluid injection. However, microseismic monitoring is expensive and not always available. The ability to predict microseismic events from readily available treating pressure data would provide operators with critical fracture characterization capabilities at significantly reduced cost.

This study introduces a novel signal processing approach that treats hydraulic fracturing as an input-output system, where pumping rate and proppant concentration are inputs and treating pressure is the output. By analyzing the output signal using advanced CWT techniques, the method reveals fracture propagation dynamics without requiring simplifying assumptions common in traditional approaches.

Methodology

Normalized CWT Scalogram Technique

The foundation of this methodology lies in applying CWT to treating pressure data during hydraulic fracturing. CWT provides continuous scaling and shifting of wavelet functions, offering high resolution in both frequency and time domains. This makes it particularly suitable for analyzing non-stationary signals like treating pressure during fracturing operations.

Figure 1: The CWT mechanism involves comparing a selected wavelet (Complex Morlet Wavelet) to segments of the treating pressure signal, calculating correlation coefficients at different scales and time positions.

[Figure shows the wavelet transform mechanism: original signal → wavelet comparison at multiple scales → energy scalogram generation]

The process involves three key steps:

1. Signal Analysis: A Complex Morlet wavelet is systematically compared to the treating pressure signal across its entire duration
2. Scale Variation: The wavelet is stretched and compressed to capture both fine (high-frequency) and coarse (low-frequency) features
3. Energy Calculation: Wavelet coefficients are squared to create an energy scalogram showing dominant frequencies at each time interval

The energy scalogram undergoes normalization using minimum-maximum scaling to ensure consistency across different fracturing jobs:

(log₂ E)ₙₒᵣₘ = [(log₂ E) – (log₂ E)ₘᵢₙ] / [(log₂ E)ₘₐₓ – (log₂ E)ₘᵢₙ]

This normalization creates normalized CWT coefficients ranging from 0 to 1, enabling direct comparison between different wells and formations.

Fracture Event Classification

The normalized CWT scalogram reveals distinct signatures for different fracture propagation modes:

• Limited Width Propagation: Normalized coefficients 0.0-0.25 (blue regions)
• Length Growth: Normalized coefficients 0.4-0.6 (green regions)
• Height Growth/High Leak-off: Normalized coefficients 0.8-0.95 (red regions)

Figure 2: Example normalized CWT scalogram showing color-coded fracture propagation events over time. The scalogram acts as a “mathematical microscope” revealing subtle changes in treating pressure that correspond to different fracture behaviors.

[Figure shows heat map with time on x-axis, scale on y-axis, and color intensity representing normalized CWT coefficients, with distinct regions corresponding to different fracture events]

Deep Learning Architecture

The deep learning model employs a compact neural network designed specifically for regression tasks with tabular data. The architecture includes:

• Input Layer: 256 features from normalized CWT scalogram
• Hidden Layers: Sequential layers with batch normalization and ReLU activation
  • Linear(256→200) → ReLU → Linear(200→100) → ReLU
• Output Layer: Linear(100→3) for X, Y, Z coordinates of microseismic events

Figure 3: Deep learning framework architecture showing the flow from CWT scalogram input through hidden layers to microseismic event coordinate prediction.

[Figure shows neural network diagram with input layer (256 nodes), hidden layers, and output layer (3 nodes for X,Y,Z coordinates)]

The model was trained on 256,555 data points from 48 hydraulic fracture stages in the Marcellus Shale, with a 70/30 train/test split. Stratified K-fold cross-validation with 10 folds ensured robust performance evaluation across different microseismic event distributions.

Results and Validation

Three-Case Validation Approach

The technique underwent rigorous validation through three distinct cases:

Case 1 – Simulated Fracture: Using a commercial planar 3D simulator with realistic geomechanical properties, the normalized CWT scalogram successfully identified three distinct fracture propagation stages, matching simulated fracture geometry evolution.

Case 2 – Field Data Comparison: Real field data from Well X1 was analyzed and compared with the previously validated MRP technique. The normalized CWT scalogram showed excellent correlation with MRP results while offering significantly faster analysis.

Case 3 – Microseismic Validation: Using MSEEL project data from wells MIP-3H and MIP-5H, the technique was directly calibrated against recorded microseismic events, providing physical validation of fracture event detection.

Performance Results

Figure 4: Comparison of predicted vs. actual microseismic events for Stage 20 in well MIP-5H, showing excellent agreement in both spatial distribution and temporal evolution.

[Figure shows 3D plot comparing actual microseismic events (blue dots) with predicted events (red dots), demonstrating spatial accuracy and event cloud similarity]

The deep learning model achieved remarkable accuracy:

• X and Y directions: <0.025% error for training data, <0.02% for testing data
• Z direction: <0.2% error for training data, with slightly higher but acceptable errors in testing
• Processing Speed: 20 seconds to generate CWT scalogram, 40 seconds to predict microseismic cloud
• Real-time Capability: Updates every 40 seconds during operations

Field Applications

The methodology was successfully applied to multiple fracture stages in the Marcellus Shale, demonstrating consistent performance across varying geological conditions. The technique accurately predicted:

• Fracture propagation direction and extent
• Temporal evolution of microseismic events
• Three-dimensional fracture geometry development
• Identification of height growth vs. length propagation periods

Industry Impact and Applications

Operational Benefits

This technology offers significant advantages for hydraulic fracturing operations:

Real-Time Monitoring: Unlike traditional microseismic monitoring, which requires expensive equipment and post-processing, this method provides near-instantaneous feedback using only treating pressure data.

Cost Reduction: Eliminates the need for dedicated microseismic monitoring equipment while providing similar insights into fracture propagation.

Enhanced Decision Making: Operators can make real-time adjustments to pumping parameters based on predicted fracture development, optimizing treatment effectiveness.

Completion Optimization: Understanding fracture propagation patterns enables better stage spacing, cluster positioning, and completion design.

Comparison with Existing Methods

Figure 5: Performance comparison between normalized CWT scalogram, MRP technique, and Nolte-Smith method showing superior event detection capability and simplified workflow.

[Figure shows side-by-side comparison of three methods analyzing the same treating pressure data, highlighting the clarity and detail provided by the CWT approach]

The normalized CWT technique offers several advantages over traditional methods:

• No closure pressure required (unlike Nolte-Smith)
• Simplified workflow (compared to MRP complexity)
• Real-time capability with continuous updates
• Higher resolution fracture event detection
• Quantitative predictions rather than qualitative interpretations

Technical Innovations

Signal Processing Advances

The application of CWT to fracture analysis represents a significant advancement in signal processing for petroleum engineering. The technique:

• Captures both transient and continuous fracture events
• Provides time-frequency resolution impossible with traditional Fourier methods
• Adapts to non-stationary nature of fracture propagation signals
• Maintains mathematical rigor while offering practical applicability

Machine Learning Integration

The deep learning component successfully bridges the gap between signal processing and physical phenomena:

• Transforms mathematical features into geological interpretations
• Learns complex relationships between pressure signatures and fracture geometry
• Generalizes across different formations and completion designs
• Provides probabilistic predictions with quantified uncertainty

Implementation Guidelines

Data Requirements

For successful implementation, operators need:

• High-resolution treating pressure data (1 Hz sampling recommended)
• Pumping rate and proppant concentration records
• Initial formation characterization for model calibration
• Historical microseismic data for initial training (if available)

Workflow Integration

Step 1: Real-Time Processing

• Continuous CWT analysis of treating pressure
• Automated scalogram generation and normalization
• Integration with existing data acquisition systems

Step 2: Event Prediction

• Deep learning model inference on CWT features
• Microseismic event coordinate prediction
• Fracture geometry estimation and visualization

Step 3: Decision Support

• Comparison with planned fracture geometry
• Identification of unexpected propagation behavior
• Recommendations for pumping parameter adjustments

Quality Control and Validation

Regular calibration against available microseismic data, pressure matching with fracture simulation models, and continuous refinement based on production outcomes ensure maintained accuracy and reliability.

Future Developments

Technology Extensions

Research is ongoing to expand the methodology’s applicability:

• Multi-Formation Training: Developing models for different geological settings
• Enhanced Physics Integration: Incorporating geomechanical constraints
• Uncertainty Quantification: Probabilistic predictions with confidence intervals
• Multi-Well Analysis: Simultaneous monitoring of pad drilling operations

Digital Integration

Future developments will focus on:

• Integration with digital oilfield platforms
• Automated workflow optimization
• Machine learning model continuous improvement
• Integration with production forecasting models

Economic Impact

Cost-Benefit Analysis

The economic advantages of this technology are substantial:

• Microseismic Monitoring Savings: $100,000-500,000 per pad
• Completion Optimization: 10-20% improvement in production through better fracture design
• Reduced Treatment Failures: Early detection of screen-outs and poor propagation
• Operational Efficiency: Real-time adjustments reduce non-productive time

 

Conclusions

This research introduces a paradigm shift in hydraulic fracture monitoring and analysis. The combination of advanced signal processing through normalized CWT scalograms with deep learning creates a powerful tool for real-time fracture characterization. Key achievements include:

1. Breakthrough Accuracy: Prediction errors below 0.025% for horizontal microseismic event locations demonstrate unprecedented precision in fracture event prediction from treating pressure alone.
2. Real-Time Capability: Processing times of 40 seconds for complete fracture analysis enable true real-time monitoring and decision-making during hydraulic fracturing operations.
3. Comprehensive Validation: Three-case validation approach using simulated, field, and microseismic data provides robust confirmation of technique effectiveness across different scenarios.
4. Operational Simplicity: The method requires only treating pressure data, eliminating the complexity and cost of traditional microseismic monitoring while providing similar insights.
5. Universal Applicability: Successful application across multiple formations and fracture stages demonstrates the technique’s broad applicability in the petroleum industry.

The technology represents a significant advancement in completion engineering, offering operators the ability to optimize hydraulic fracturing operations in real-time while reducing costs and improving outcomes. As the industry continues to focus on efficiency and cost reduction, this methodology provides a practical solution that bridges advanced signal processing with operational decision-making.

The successful validation using publicly available MSEEL data demonstrates the technique’s reliability and sets the stage for widespread industry adoption. Future developments will focus on extending the methodology to additional formations and integrating with broader digital oilfield initiatives.

This work exemplifies how advanced mathematical techniques can be successfully applied to solve practical petroleum engineering challenges, providing both academic rigor and immediate industrial value.

You can read the details in the following paper Advanced Deep Learning for microseismic events prediction for hydraulic fracture treatment via Continuous Wavelet Transform

At ATCE 2025, we will evaluate the scalability of the model by validating its results against Rate Transient Analysis (RTA) for a Marcellus Shale well located 3–5 km away from the training dataset. (SPE-228059).

Hydraulic fracturing has long relied on microseismic monitoring, tracers, and fiber optics to infer fracture geometry and complexity. Yet every stage of every well already contains a widely overlooked signal: the pressure oscillations that occur at pump shutdown, known as water hammer (WH).

In our recent SPE Journal publication (SPE-225459), we introduced a novel technique that transforms this free but underestimated signal into a powerful diagnostic tool. By treating water hammer as a damped harmonic oscillator and analyzing its pressure response with the Continuous Wavelet Transform (CWT), we extract damping coefficients that correlate directly with fracture complexity in the reservoir.

he workflow applies the CWT using a complex Morlet wavelet to isolate the dominant frequency ridge of the WH signature, then calculates the damping coefficient from the logarithmic envelope decay. When applied across multiple fracture stages in Marcellus wells, the damping coefficient trends correlated strongly with natural fracture density interpreted from image logs. This provides operators with a cost-effective, pressure-only method to evaluate induced fracture complexity stage by stage.

Value for Unconventional Reservoirs

Unconventional reservoirs depend on maximizing stimulated reservoir volume (SRV) through the creation of complex fracture networks. Traditionally, operators rely on indirect diagnostics such as production logging, tracers, or costly microseismic surveys to estimate fracture effectiveness. The WH-CWT method directly leverages existing pressure data to provide real-time, low-cost insights into fracture complexity, even in the absence of other diagnostics.

This is particularly valuable in resource plays where thousands of stages may be completed annually and marginal wells cannot justify the expense of advanced diagnostics. By linking damping behavior to fracture tortuosity and natural fracture interaction, operators can rapidly identify which stages achieved high complexity and which underperformed, supporting design optimization, well-to-well benchmarking, and economic decision-making.

Model Assumptions and Limitations

The model assumes that water hammer can be represented as a partially damped harmonic oscillator with an added exponential decay term to capture fluid leakoff effects. Under this assumption, damping is governed primarily by fracture tortuosity, interaction with natural fractures, and leakoff into the formation. The approach further assumes:

• Immediate pump shutdown is necessary to avoid overlapping signals from stepped closures.

• Consistent fracturing design across stages allows damping coefficient variations to be attributed mainly to differences in induced complexity rather than treatment changes.

• The complex Morlet wavelet adequately captures oscillatory behavior and phase shifts in the WH signal.

While the method has shown strong correlation with fracture density logs and robust performance in Marcellus wells, operators should note that gradual pump shutdowns, noise, or highly heterogeneous reservoirs can complicate interpretation. Even in such cases, overdamped signatures often provide useful qualitative indications of poor fracture-wellbore communication.

Key findings include:

• Damping coefficients serve as reliable indicators of fracture complexity and natural fracture intensity.

• WH responses can be classified from high-amplitude oscillations to overdamped signals, reflecting changes in fracture tortuosity and communication.

• Nonlinear optimization methods, especially basinhopping, successfully matched modeled WH responses with field data, achieving R² values above 0.86 in most cases.

This new approach leverages data already collected during every hydraulic fracturing stage, requiring no additional field instrumentation. The information is freely available and can be analyzed for each job. The only operational step is a hard pump shutdown for approximately five minutes—no special gauges, sensors, or extra procedures are needed. By reframing water hammer as more than background noise, this method unlocks valuable insights for fracture diagnostics, completion design optimization, and stage-by-stage performance evaluation.

For full methodology, mathematical formulation, case studies, and correlation with fracture density logs, see the peer-reviewed article in the SPE Journal:  SPE-225459 or watch our the following webinar : Decoding Induced Fracture Complexity: Water Hammer Damping Analysis with Continuous Wavelet Transform

The Fracwave Research Group at the University of Houston has developed a new stimulation technology that is now field-ready for deployment. Known as Nanoparticle-Enhanced Plasma Pulse Stimulation (PPPS), this electrified method combines microsecond plasma discharges with engineered nanoparticle fluids to create complex fractures deep in the formation—without massive water volumes, chemicals, or proppant.

Why PPPS, Why Now

For decades, acidizing and hydraulic fracturing have been the mainstay of stimulation. Yet both face mounting limits. Acidizing works primarily in carbonates and carries corrosion and scaling risks. Hydraulic fracturing requires millions of gallons of water and extensive logistics, while concerns over induced seismicity and environmental footprint continue to grow.

The industry needs a stimulation method that is formation-agnostic, operationally efficient, and ESG-aligned. PPPS was designed precisely to fill this gap.

How It Works

Surface capacitor banks release controlled electrical pulses down coiled tubing to a rugged plasma tool. Once discharged, the tool ignites a nanoparticle-laden fluid. Thermite-like reactions amplify the discharge into shock pulses greater than 100,000 psi, generating fractures that extend well beyond the near-wellbore. The fluids are engineered for conductivity and cleanup, leaving no proppant behind.

What Makes It Different

PPPS is compact, precise, and versatile. A treatment requires only coiled tubing, a power unit, and the plasma tool—a fraction of the equipment footprint of a frac spread. The system is effective in tight oil and gas reservoirs, depleted producers, water injectors, and even high-temperature geothermal formations where conventional fluids fail. By eliminating water and proppant demand, PPPS offers a significant cost and logistics advantage, while also aligning with corporate sustainability commitments.

Ready for Field Pilots

Following extensive design and validation, PPPS is now prepared for multi-well pilot trials. Candidate applications include horizontal producers where enhanced connectivity is needed, vertical wells where near-wellbore damage limits performance, and injectors where increased index is sought at lower pressures.

Performance will be measured by fold-of-increase in productivity or injectivity, fracture confirmation through imaging or logging, and diagnostic improvements in pressure transient and rate transient analysis. The safety case is strong, with short-duration pulses, precise zonal placement, and reduced surface intensity.

Collaboration Opportunity

Fracwave is now inviting operators, service companies, and technology partners to join in bringing PPPS into the field. Operators can nominate wells and provide performance data, while service companies can support tool manufacturing and integration. In return, collaborators gain early access to a disruptive technology with the potential to reduce costs, lower environmental footprint, and improve well performance across reservoir types.

A Call to Action

The transition to cleaner, more adaptable stimulation is already underway. With PPPS now field-ready, the next step is collaboration. Fracwave is preparing a kickoff workshop to align specifications, finalize candidate wells, and begin deployment planning.

PPPS offers efficiency, sustainability, and performance in one package. The question is no longer whether the technology works—it is which companies will move first to prove it in the field.

How Companies Can Collaborate

With PPPS now field-ready, the next step is industry collaboration. The Fracwave Research Group invites operators, service companies, and technology partners to join in advancing this technology through structured multi-well pilots.

Operators can contribute candidate wells across diverse applications—tight oil and gas horizontals, depleted producers, injectors, and high-temperature geothermal wells. In return, they gain first-mover access to field data demonstrating how electrified stimulation can lower costs, reduce water use, and improve recovery.

Service companies can support with tool manufacturing, coiled tubing integration, and pulsed-power delivery. This creates the opportunity to establish a new service line built around compact, electrified stimulation instead of conventional large-scale frac fleets.

Technology partners and investors can collaborate on scaling the surface capacitor systems, refining nanoparticle fluid supply chains, and accelerating deployment across basins. Their involvement ensures the system can move quickly from pilot to commercial scale.

Together, these collaborations form the backbone of PPPS deployment. By sharing wells, expertise, and operational data, partners not only help validate the technology but also position themselves at the forefront of a cleaner, more efficient future for well stimulation.

Contact us to discuss more.

We are excited to announce that our team, Fracwave from the University of Houston, together with collaborators from VERTEX group at the Colorado School of Mines, will present three breakthrough studies at the upcoming SPE Annual Technical Conference and Exhibition (ATCE 2025) in The Woodlands, Texas. Collectively, these contributions showcase how wavelet analysis, deep learning, and real-time drilling intelligence are transforming fracture diagnostics for both unconventional reservoirs and next-generation geothermal systems.

Unlocking SRV with Wavelets and Deep Learning

Tuesday, October 21 (15:15 – 15:45, Station 5 – ePosters)

Calibration of Stimulated Reservoir Volume (SRV) Estimation Using Continuous Wavelet Transform (CWT) and Advanced Deep Learning With Rate Transient Analysis (RTA): A Case Study From The Marcellus Shale (SPE-228059).

We demonstrate how the humble treating pressure signal can be elevated into a powerful diagnostic tool. By marrying wavelet transforms with deep learning, we deliver SRV predictions that align with RTA – without relying on costly microseismic surveys. This scalable, pressure-only workflow pushes shale reservoir diagnostics into the digital age.

Expanding the Frontier with Real-Time Fracture Detection

Monday, October 20 (14:50 – 15:15, Room 342BE)

Real-time Automated Fracture Detection in Geothermal Wells Using Low-cost Drilling Data (SPE-227991).

Presented by VERTEX research group from Colorado School of Mines in collaboration with the University of Houston, this study introduces a novel approach that combines CWT with machine learning to extract fracture signatures directly from low-cost drilling data such as ROP, MSE, and torque. Achieving over 95% predictive accuracy, the workflow enables real-time fracture detection that reduces drilling risks, lowers costs, and accelerates geothermal well construction.

Bringing New Clarity to Utah FORGE Geothermal Stimulation

Wednesday, October 22 (08:55 – 09:20, Room 342BE)

Advanced Fracture Diagnostics in Utah FORGE Enhanced Geothermal Systems (EGS): Integrating Continuous Wavelet Transform (CWT), Microseismic, and Fiber-Optic Data for Enhanced Stimulation Insights (SPE-228063).

Here, we integrate pressure-derived wavelet diagnostics with fiber-optic strain sensing and microseismic catalogs into a holistic framework. This approach provides unprecedented clarity on fracture propagation in high-temperature granite and offers a real-time decision-making lens for one of the world’s most advanced geothermal laboratories.

Why It Matters

Across shale gas and geothermal frontiers, our mission remains the same: turning complex signals into actionable insights. From boosting SRV prediction in the Marcellus to unraveling fracture dynamics in Utah FORGE and enabling real-time drilling intelligence, we are laying the data-driven foundation for smarter, cleaner, and more efficient subsurface energy systems.

We look forward to sharing these advances – and the vision driving them – at ATCE 2025.