Tutorial 20: Theis Well Solution

What Superposition Reveals

The regional flow field is disrupted: Without pumping, water flows uniformly from the left river (h = 0 m) to the right river (h = −2 m). With pumping, the cone of depression bends flow lines toward the well. Some water that would have reached the right river is now captured by the well. The superimposed view shows this interaction — something net drawdown alone cannot reveal.

Capture zone implications: The distortion of regional flow defines the well's capture zone — the area that contributes water to the well. In this simple case, you can see how the well "steals" water from the regional flow. In Tutorial 3 (Particle Tracking) and Tutorial 18 (Probabilistic Capture Zones), you explored this concept in detail.

Why Go Transient?

Steady-state shows the end state: Given infinite time, the drawdown reaches a fixed shape — the cone of depression stabilizes when inflow from boundaries balances the pumping rate. But how long does it take to reach steady state? How does drawdown evolve in the first hours, days, and weeks?

Transient shows the process: The Theis solution is inherently transient — drawdown grows logarithmically with time. Early-time behavior is dominated by storage release (water squeezed from the aquifer matrix). Late-time behavior approaches steady state as boundary effects arrive. The transition between these regimes is exactly what pumping tests measure — and what the Theis solution predicts.

Monitoring wells see the evolution: A monitoring well near the pumping well records drawdown over time — the classic pumping test hydrograph. Matching this curve to the Theis solution yields T and S — the most common method of aquifer characterization in practice.

Key Concepts

Verification vs. validation: This tutorial demonstrates verification — does the numerical solver reproduce a known analytical answer? This is different from validation (Tutorial 8: Calibration), which asks whether the model reproduces field observations. Verification proves the code works correctly. Validation proves the model represents the real system. Both are necessary for a credible model.

The Theis checkbox is powerful: In traditional workflows, comparing numerical results to analytical solutions requires external scripts, spreadsheet calculations, or separate software. IGW-NET's built-in Theis feature eliminates this — one checkbox enables the analytical benchmark alongside the numerical solution. Verification becomes effortless.

From verification to practice: Once you've confirmed the numerical engine reproduces the Theis solution, you can confidently move to complex problems where no analytical solution exists — heterogeneous aquifers, irregular boundaries, multiple wells, contaminant transport. The verification gives you the foundation to trust the numerical results.

Superposition principle: The linearity of the confined-aquifer flow equation means drawdowns from multiple wells can be added together, and drawdown can be superimposed on any background flow field. This powerful principle breaks down for unconfined aquifers (nonlinear) and when wells interact with boundaries — but it remains a cornerstone of groundwater hydraulics and wellfield design.