Chapter 3 Insights - Statistical Fundamentals

Chapter 3 of Monograph 5, titled "Principles and Fundamentals – Analysis and Statistics," focuses on statistical techniques and principles essential for constructing, analyzing, and applying Type Well Profiles (TWPs). It lays the groundwork for the more advanced discussions on uncertainty, data handling, and validation presented in later chapters. Below is a summary of its key topics:

Statistical Foundations for Uncertainty

Chapter 3 establishes a foundation for later discussions on uncertainty and error. It acknowledges that all TWPs carry inherent uncertainty, stemming from:

• Variability in analog well performance.
• Bias introduced during data handling or interpretation.
• Uncertainties in forecasting future well performance.

Distributions and Their Applications

The chapter begins by distinguishing between discrete and continuous distributions. Discrete distributions involve countable values (e.g., the number of runs in a series of baseball games), while continuous distributions involve measurable values like EUR (Estimated Ultimate Recovery) and initial production rates. TWPs often deal with continuous variables, which, when sampled adequately, fit into distributions like normal or lognormal. These distributions are characterized by central tendencies (mean, median, and mode) and variability measures (variance and standard deviation).

Central Tendency and Variability

Understanding central tendencies (mean, median, mode) is critical for TWP preparation:

• The mean is sensitive to extreme values and often represents the arithmetic average.
• The median is less affected by outliers and is frequently used in skewed distributions like lognormal.
• The mode represents the most frequent value.

The chapter emphasizes selecting the appropriate measure of central tendency based on the TWP's intended use. For instance, a median-based TWP might better represent central performance in lognormal distributions.

Statistical Analysis Tools

Key tools for graphical and numerical statistical analysis are introduced:

1. Histograms and Probit Plots: Visual representations of frequency distributions.
2. Confidence Intervals: Tools to estimate the reliability of predictions and data variability.
3. Exceedance Plots: Represent probabilities of exceeding specific production values, useful for assessing risk in well performance.

Standard Error and Aggregation

The critical concept of the standard error of the mean is emphasized, especially in the context of estimates of average EUR from small analog well sample sizes. Smaller sample sizes lead to higher uncertainty, affecting the reliability of the TWP. Aggregation, or combining multiple well profiles, reduces variability, and tools like trumpet plots are introduced to visualize this effect. These plots graphically represent how aggregation influences uncertainty. Importantly, the chapter demonstrates why the uncertainty associated with small analog well sets isn't eliminated by drilling larger portfolios.

Correlation in Data

Correlation between production metrics is a central theme in ensuring robust TWP analysis. The chapter notes the significance of identifying and handling correlations during analog well selection and production normalization. Mismanaging correlations can lead to biases, reducing the accuracy of TWPs.

Practical Implications

This chapter is not purely theoretical; it aligns statistical principles with practical TWP construction and application. By presenting robust statistical workflows, Monograph 5 ensures that users understand the reliability of TWPs for forecasting, benchmarking, and decision-making in resource evaluation.

Next week's topic - Understanding and Managing Bias in TWP's