Automated Estimation of Aquifer Parameters from Arbitrary-Rate Pumping Tests in Python and MATLAB.

Area of Science:

• Hydrogeology
• Aquifer Testing
• Environmental Engineering

Background:

• Traditional aquifer test analysis often assumes constant pumping rates, limiting accuracy for variable pumping histories.
• Previous methods, like piecewise-linear reconstructions, offered improvements but had limitations in handling complex pumping scenarios.
• The classical Theis equation provides a foundational model but requires specific assumptions about pumping rates.

Purpose of the Study:

• To derive a convolutional form for pumping tests applicable to any pumping history.
• To develop a computationally efficient method for analyzing variable rate pumping tests, including nonlinear well losses.
• To provide tools for accurate aquifer parameter estimation using multiple observation wells and arbitrary pumping data.

Main Methods:

• Derivation of a convolutional solution using the time derivative of the well function's Green's function.
• Development of a deterministic model for calculating drawdown with arbitrary pumping histories and nonlinear well losses.
• Implementation of inversion codes in MATLAB and Python for parameter estimation and Bayesian analysis.

Main Results:

• The convolutional method significantly reduces computational demand, comparable to calculating the well function alone.
• The approach effectively incorporates nonlinear well losses and allows simultaneous inversion of data from multiple observation wells.
• Parameter dependencies and objective function construction critically influence interpreted aquifer parameters.

Conclusions:

• The derived convolutional method offers a robust and efficient framework for analyzing variable rate pumping tests.
• Accurate determination of aquifer parameters requires careful consideration of parameter dependencies and objective function formulation.
• Step-drawdown test optimization is often nonunique, highlighting the necessity of Bayesian inversion for comprehensive parameter estimation.