A B-Spline Framework for Smooth Derivative Computation in Well Test Analysis Using Diagnostic Plots.

Area of Science:

• Hydrogeology
• Reservoir Engineering
• Data Analysis

Background:

• Well test analysis using derivative plots is standard in oil and gas but underutilized in hydrogeology.
• Computing derivatives from noisy field measurements using finite-difference schemes complicates analysis.

Purpose of the Study:

• To develop a robust B-spline framework for smooth derivative computation in well test analysis.
• To improve the interpretability of diagnostic plots for hydrogeologists.

Main Methods:

• Proposed a Constrained Quartic B-Splines with Free Knots framework.
• Implemented automatic equality derivative constraints, knot removal, and a Boolean shape parameter.
• Introduced a shape-preserving smoothing preprocess for extremely noisy signals.

Main Results:

• The B-spline framework produced smoother first and second derivative responses compared to the Bourdet algorithm.
• The Bourdet algorithm resulted in noisy and unreadable derivative responses, especially the second derivative.
• The proposed method effectively handles both simple and complex drawdown datasets.

Conclusions:

• The B-spline framework offers a significant improvement for reliable aquifer test evaluation using derivative-diagnostic plots.
• This approach addresses the limitations of traditional derivative computation methods in hydrogeology.
• The method provides smoother, more interpretable results crucial for accurate reservoir and well behavior analysis.