Horner Plot

Test Your Knowledge

Quiz: Unlocking Reservoir Secrets with the Horner Plot

Instructions: Choose the best answer for each question.

1. The Horner plot is primarily used to analyze data from: a) Production logs b) Seismic surveys c) Pressure buildup tests d) Core samples

2. What does the extrapolated line on a Horner plot intersect at zero Horner time? a) Wellbore storage coefficient b) Skin factor c) Virgin reservoir pressure (P_i) d) Permeability

3. A high slope (m) on a Horner plot typically indicates: a) Low permeability and high wellbore storage b) High permeability and low wellbore storage c) High permeability and high wellbore storage d) Low permeability and low wellbore storage

4. Deviations from the straight-line trend on a Horner plot near the shut-in time could indicate: a) A perfectly homogeneous reservoir b) A lack of wellbore storage c) A skin effect d) A perfectly radial flow regime

5. The type curve matching method is used to: a) Determine the wellbore storage coefficient b) Account for non-ideal flow regimes c) Calculate the skin factor d) Estimate the virgin reservoir pressure (P_i)

Exercise: Applying the Horner Plot

Scenario:

A pressure buildup test was conducted on a well. The following data was recorded:

| Time (hours) | Pressure (psi) | |---|---| | 0 | 2000 | | 1 | 2200 | | 2 | 2300 | | 4 | 2400 | | 8 | 2500 |

Task:

1. Plot the data on a Horner plot using Horner time (t_H) as the x-axis and pressure (P) as the y-axis.
   • Horner time (t_H) = (t_s + t_p)/t_p, where t_s is the time since shut-in and t_p is the time since the initial injection began.
2. Extrapolate the straight line portion of the plot to zero Horner time.
3. Determine the virgin reservoir pressure (P_i) from the intersection point.
4. Comment on the slope of the extrapolated line and what it indicates about the reservoir.

Techniques

Chapter 1: Techniques

The Horner Plot: A Graphical Interpretation of Pressure Buildup Data

The Horner plot is a graphical technique used to analyze pressure buildup tests in oil and gas wells. It utilizes a specific time function called the Horner time to visualize the pressure data and extract crucial information about the reservoir.

Steps involved in creating a Horner plot:

1. Data Acquisition: Gather pressure data from a pressure buildup test, recording pressure readings at regular intervals after the well is shut-in.
2. Calculating Horner Time: The Horner time (t_H) is calculated for each data point using the formula: t_H = t + Δt, where t is the time elapsed since shut-in and Δt is the time elapsed since the start of the injection period.
3. Plotting the Data: Plot the pressure data (P) against the corresponding Horner time (t_H).
4. Extrapolation and Analysis: Extend the linear portion of the plot to intersect the pressure axis. The intersection point represents the virgin reservoir pressure (P_i). The slope of the extrapolated line provides information about the reservoir's permeability and wellbore storage.
5. Deviations and Interpretation: Deviations from the straight-line trend near the shut-in time indicate the presence of a skin effect, suggesting wellbore damage or stimulation.

Advantages of the Horner Plot:

• Simplicity and Visual Interpretation: The plot provides a straightforward visual representation of the pressure buildup data, allowing for easy identification of trends and anomalies.
• Extraction of Key Reservoir Properties: It helps determine the virgin reservoir pressure, permeability, skin factor, and wellbore storage coefficient.
• Optimization of Production Strategies: By understanding these parameters, engineers can optimize production rates and predict future well performance.

Limitations of the Horner Plot:

• Assumptions of Radial Flow: The technique assumes radial flow in the reservoir, which may not always be accurate.
• Possible Influence of Non-Ideal Flow Regimes: The plot can be affected by factors like linear or elliptical flow regimes, potentially leading to inaccurate interpretations.
• Impact of Wellbore Storage: Significant wellbore storage can obscure the true reservoir properties, requiring additional analysis or techniques.

Overall, the Horner plot is a valuable tool for initial analysis of pressure buildup tests, offering insights into the reservoir's characteristics and potential for production.

Chapter 2: Models

Beyond the Basics: Utilizing Different Flow Models for More Accurate Interpretation

While the basic Horner plot assumes radial flow, real-world reservoirs can exhibit different flow regimes like linear, elliptical, or even spherical flow. To account for these variations and improve the accuracy of analysis, advanced flow models are integrated into the Horner plot interpretation.

Commonly Used Flow Models:

1. Radial Flow Model: Assumes radial flow, suitable for wells in homogeneous reservoirs with no significant boundaries.
2. Linear Flow Model: Applies when flow is predominantly in a single direction, often seen in fractured reservoirs or near boundaries.
3. Elliptical Flow Model: Represents flow in a slightly elongated shape, occurring in heterogeneous reservoirs or near producing wells.
4. Spherical Flow Model: Applies in situations where flow is radially outward from a point source, commonly observed in gas reservoirs or near wellbores with significant storage.

Type Curve Matching:

To incorporate these flow models into the Horner plot, a technique called "Type Curve Matching" is employed. This involves comparing the pressure buildup data to pre-defined type curves that represent different flow regimes. By matching the data to the appropriate type curve, engineers can identify the dominant flow regime and refine the determination of reservoir properties.

Benefits of Incorporating Flow Models:

• More Accurate Reservoir Characterization: By considering the actual flow regime, the analysis provides a more accurate estimate of reservoir parameters like permeability and skin factor.
• Improved Production Forecasts: Accurate flow regime identification leads to better predictions of well productivity and potential for future production.
• Optimal Well Design and Placement: Understanding flow patterns allows for optimizing well placement and design to maximize recovery and minimize production costs.

Challenges with Flow Model Integration:

• Complexity and Data Requirements: Using advanced flow models often requires more complex calculations and a higher quality of data.
• Uncertainty in Model Selection: Choosing the appropriate flow model can be challenging, particularly in complex reservoirs with multiple flow regimes present.
• Limited Availability of Type Curves: Type curves for specific flow regimes or complex scenarios may not always be readily available.

Despite these challenges, integrating flow models into Horner plot analysis enhances the technique's accuracy and provides a more complete understanding of the reservoir's behavior.

Chapter 3: Software

Modern Tools for Analyzing Horner Plots: Software Solutions for Efficient and Accurate Interpretation

The advent of sophisticated software has revolutionized the analysis of Horner plots, automating complex calculations and providing advanced visualization capabilities. These software solutions empower engineers to efficiently extract valuable reservoir information and make informed decisions.

Key Features of Horner Plot Analysis Software:

• Data Import and Management: Streamlining the process of importing and managing pressure buildup data from various sources.
• Automatic Horner Time Calculation: Efficiently calculating Horner time for each data point, eliminating manual calculations.
• Type Curve Matching Tools: Facilitating the selection and matching of pressure data to appropriate type curves for different flow regimes.
• Graphical Visualization and Analysis: Providing interactive plots and tools for visual analysis, trend identification, and anomaly detection.
• Sensitivity Analysis and Uncertainty Quantification: Allowing for exploring the impact of different parameters on the results and quantifying uncertainties in the analysis.
• Report Generation and Documentation: Generating comprehensive reports with results, graphs, and detailed analysis for documentation and communication.

Examples of Popular Horner Plot Analysis Software:

• WellTest™: A comprehensive well test analysis software developed by Schlumberger, offering advanced features for Horner plot analysis.
• Reservoir Simulation Software: Many reservoir simulation software packages incorporate Horner plot analysis capabilities as part of their overall well test analysis workflow.
• Open-Source Tools: There are also open-source tools like Python libraries for well test analysis, providing flexibility and customization options.

Benefits of Utilizing Software:

• Increased Efficiency and Accuracy: Automating calculations and providing advanced visualization capabilities reduces human error and improves the accuracy of analysis.
• Time and Cost Savings: Software solutions streamline the analysis process, saving time and resources compared to manual methods.
• Enhanced Understanding and Decision-Making: The ability to visualize and explore data in various ways provides a deeper understanding of the reservoir and supports more informed decision-making.

Software tools have become indispensable for analyzing Horner plots, providing a powerful and efficient means to extract critical reservoir information and optimize production strategies.

Chapter 4: Best Practices

Maximizing the Effectiveness of Horner Plot Analysis: Key Best Practices for Accurate and Reliable Results

While the Horner plot is a powerful tool, its effectiveness depends heavily on the quality of data and the implementation of best practices during the analysis. Following these guidelines ensures accurate and reliable results:

1. Data Quality and Acquisition:

• Accurate and Consistent Data: Ensure accurate pressure readings obtained with calibrated instruments and consistent time intervals.
• Sufficient Data Points: Gather enough data points to capture the complete pressure buildup response, including early-time behavior and late-time stabilization.
• Proper Well Shut-in: Ensure a complete and undisturbed well shut-in to minimize flow interference and obtain a representative pressure buildup.

2. Pre-Analysis Procedures:

• Initial Data Screening: Review the pressure data for any inconsistencies, outliers, or gaps that require correction.
• Wellbore Storage Correction: Apply appropriate corrections for wellbore storage effects to minimize its influence on the analysis.
• Skin Factor Estimation: Consider techniques for estimating the skin factor before applying the Horner plot analysis.

3. Horner Plot Interpretation:

• Visual Analysis and Trend Identification: Carefully examine the plot for linear trends, deviations, and any other anomalies that require further investigation.
• Type Curve Matching: Use appropriate type curves for different flow regimes to ensure accurate interpretation and parameter determination.
• Sensitivity Analysis: Perform sensitivity analysis to assess the impact of different parameters on the results and quantify uncertainties.

4. Interpretation and Reporting:

• Clear and Concise Communication: Present the analysis results clearly and concisely, including interpretations, limitations, and uncertainties.
• Documentation and Archival: Maintain proper documentation of the analysis process, data used, and results for future reference and reproducibility.

By adhering to these best practices, engineers can maximize the effectiveness of Horner plot analysis and obtain reliable insights into reservoir behavior.

Chapter 5: Case Studies

Real-World Applications of Horner Plots: Illustrative Examples of Reservoir Characterization and Production Optimization

The Horner plot has been widely applied in various scenarios, providing valuable insights for reservoir characterization and production optimization. Here are some illustrative case studies demonstrating its practical applications:

Case Study 1: Identifying Reservoir Boundaries

• Scenario: A pressure buildup test was conducted in a new oil well. The Horner plot showed a deviation from the linear trend at later times, indicating a potential boundary effect.
• Analysis: Type curve matching identified the deviation as characteristic of linear flow, suggesting the presence of a nearby impermeable boundary.
• Outcome: The identified boundary was incorporated into reservoir modeling, leading to a more accurate estimation of reservoir size and potentially impacting well placement and development strategies.

Case Study 2: Evaluating Well Stimulation Effectiveness

• Scenario: A gas well was stimulated using acid fracturing to improve production. A Horner plot analysis was performed before and after the stimulation.
• Analysis: The post-stimulation Horner plot showed a significant increase in the slope of the extrapolated line, indicating a substantial improvement in permeability.
• Outcome: The analysis confirmed the success of the stimulation treatment and provided valuable data for assessing the effectiveness of future stimulation projects.

Case Study 3: Optimizing Production Rates

• Scenario: A well in a tight gas reservoir exhibited rapid pressure decline, suggesting a need to optimize production rates. A Horner plot analysis was used to assess the reservoir properties.
• Analysis: The plot revealed low permeability and high wellbore storage, indicating a high potential for production optimization.
• Outcome: Based on the analysis, a production strategy was developed that involved gradually increasing the production rate to optimize well performance and maximize gas recovery.

These case studies demonstrate the versatility of Horner plots in various aspects of reservoir engineering, providing crucial insights for decision-making and optimizing production strategies.

Conclusion

The Horner plot, with its simplicity and versatility, remains an indispensable tool for analyzing pressure buildup tests. By integrating advanced flow models, utilizing software tools, and following best practices, engineers can maximize its effectiveness, leading to more accurate reservoir characterization, production optimization, and informed decision-making for maximizing oil and gas recovery.