Groundwater Flow — Darcy's Law, Aquifer & Well Drawdown

Explore how groundwater moves through permeable rock using Darcy's Law. Visualise hydraulic head, equipotential lines, flow paths, and the cone of depression around pumping wells.

Aquifer type:
Cross-section view — click on aquifer to add/remove a pumping well
0.00
Darcy flux q (m/d)
10.0
Head difference Δh (m)
0.0
Drawdown s_w (m)
0.00
Seepage velocity (m/d)
Radius of influence (m)
Unconfined Aquifer: Water table is free to rise and fall. Darcy's Law: q = −K·(dh/dl). Water flows from high hydraulic head to low. Drawdown at well: h²−h_w² = (Q/πK)·ln(r/r_w) (Dupuit–Thiem equation).
About Groundwater Flow

Darcy's Law (1856): q = −K·(dh/dl) — specific discharge q (m/d) = hydraulic conductivity K × hydraulic gradient. Seepage velocity v = q/n (n = porosity).

Unconfined aquifer: Bounded above by the water table (atmospheric pressure). Most shallow aquifers are unconfined.

Confined aquifer: Saturated zone bounded above by an impermeable layer (aquitard). Hydraulic head can be above the top of the aquifer (artesian conditions).

Well hydraulics (Dupuit–Thiem): Steady-state drawdown in confined aquifer: h−h₀ = Q/(2πKb)·ln(r₀/r). In unconfined: h²−h₀² = Q/(πK)·ln(r₀/r).

Hydraulic conductivity K: gravel 10–1000 m/d; sand 1–100 m/d; silt 0.001–0.1 m/d; clay <0.0001 m/d.

About the Groundwater Flow Simulator

Groundwater flow is governed by Darcy's Law: Q = −KA(dh/dl), where Q is volumetric flow rate, K is hydraulic conductivity of the soil or rock, A is the cross-sectional area, and dh/dl is the hydraulic gradient — the rate of change of hydraulic head with distance. Water moves from high head to low head, analogously to how electric current flows from high to low potential. The governing partial differential equation is the groundwater flow equation (a form of the diffusion equation), solved numerically in this simulation on a 2D grid.

Aquifer properties determine how quickly groundwater responds to pumping or recharge. Confined aquifers, sandwiched between low-permeability aquitards, transmit pressure changes almost instantly but release little water per unit head decline (low storage). Unconfined (phreatic) aquifers have a free water table that rises and falls; they have high specific yield but slower pressure propagation. Pumping from a well creates a cone of depression in the head surface, inducing radial inward flow described by the Theis equation.

This simulator models 2D steady-state and transient groundwater flow, allowing you to place wells (sources/sinks), vary permeability zones, and watch hydraulic head contours and particle pathlines evolve. It illustrates principles used in water-supply engineering, contamination plume tracking, and geotechnical dewatering design.

Frequently Asked Questions

What is Darcy's Law?

Darcy's Law states Q = −KA(dh/dl): flow rate is proportional to hydraulic conductivity K and hydraulic gradient dh/dl. The negative sign means flow is in the direction of decreasing head. It was derived empirically by Henri Darcy in 1856 from sand-filter experiments and underpins all quantitative groundwater analysis.

What is hydraulic head?

Hydraulic head h = z + p/ρg combines elevation head and pressure head. It represents the total mechanical energy of water per unit weight in metres. Water flows from high head to low head regardless of the local slope. In a pressurised confined aquifer, head can exceed ground level — producing a flowing artesian well.

What is a cone of depression?

Pumping a well lowers hydraulic head near the well, creating a funnel-shaped depression in the head surface. Groundwater flows radially inward toward the well. The cone grows until recharge from surrounding areas balances the pumping rate. Overlapping cones from neighbouring wells reduce each other's yield — the principle behind wellfield spacing design.

What is the difference between an aquifer and an aquitard?

An aquifer is a permeable formation (sand, gravel, fractured rock) that stores and transmits groundwater. An aquitard is a low-permeability layer (clay, silt) that limits flow. Confined aquifers are sandwiched between aquitards and hold water under pressure; unconfined aquifers have a free upper water table in contact with unsaturated soil above.

How is groundwater flow modelling used in practice?

Numerical groundwater models (MODFLOW is the industry standard) are used to design water-supply wellfields, predict contamination plume migration for remediation, assess dewatering requirements for construction excavations, and evaluate the long-term sustainability of aquifer extraction under climate change scenarios.

About Groundwater Flow

Groundwater flow describes the movement of water through the pore spaces and fractures of subsurface rock and sediment, governed by Darcy's law: q = minus K times (dh/dl), where q is the volumetric flow rate per unit area (Darcy flux), K is hydraulic conductivity (a property of both the medium and fluid), and dh/dl is the hydraulic gradient (change in hydraulic head per unit distance). Published by Henri Darcy in 1856 from experiments on sand filters in Dijon, France, this linear law describes laminar groundwater flow in porous media with remarkable generality.

An aquifer is a saturated permeable geological unit that can store and transmit water in economically useful quantities. Confined aquifers are bounded above by an impermeable layer (aquitard) and may be under artesian pressure (water rises above the aquifer top when tapped, and historically flowed at the surface in artesian wells). Unconfined (water table) aquifers have a free surface that rises and falls with recharge and pumping. The governing equation for transient groundwater flow combines Darcy's law with mass conservation: divergence of (K times gradient h) = Ss times partial h / partial t, where Ss is specific storage. Steady-state flow satisfies Laplace's equation.

This simulator solves the 2D groundwater flow equation on a heterogeneous domain using finite difference or finite element methods, visualizing hydraulic head contours and flow velocity vectors. You can add pumping wells and observe cone-of-depression drawdown, change permeability distributions to simulate heterogeneous aquifers, and observe how flow responds to boundary conditions — demonstrating concepts essential for water resource management, contaminant transport prediction, and geotechnical engineering.

Frequently Asked Questions

What is hydraulic head and why is it the key variable in groundwater flow?

Hydraulic head h = z + P divided by (rho times g) is the total mechanical energy per unit weight of groundwater, where z is elevation and P/(rho times g) is pressure head (velocity head is negligible for slow groundwater flow). Groundwater flows from regions of high hydraulic head to low hydraulic head — the hydraulic gradient drives flow, not pressure alone or elevation alone. Mapping hydraulic head from water level measurements in wells reveals flow directions, recharge zones, and discharge areas — the foundation of groundwater resource assessment.

What is hydraulic conductivity and what controls it?

Hydraulic conductivity K (m/s or m/d) quantifies how easily water flows through a porous medium — it combines the intrinsic permeability of the medium (pore size, connectivity, shape) with fluid properties (density and viscosity). Gravels are highly permeable (K ~ 10^-2 to 10^-1 m/s); sands ~10^-5 to 10^-3 m/s; silts ~10^-7 to 10^-5 m/s; clays ~10^-11 to 10^-8 m/s — a range of 10 orders of magnitude. Field determination of K uses pumping tests (measuring head drawdown versus time and distance) or slug tests (adding or removing water from a well and measuring recovery).

What is a cone of depression and how does pumping affect groundwater levels?

When water is pumped from a well, the water table or piezometric surface drops in the vicinity of the well, creating a cone-shaped depression of declining hydraulic head centered on the well. The cone grows outward over time until the pumping rate is balanced by inflow from the surrounding aquifer. The Theis equation describes transient drawdown: s(r,t) = (Q / 4 pi T) times W(u), where s is drawdown, Q is pumping rate, T is transmissivity, and W(u) is the well function with u = r squared times S divided by (4 T t). Cones of depression from adjacent wells can interfere, reducing yield — a critical consideration in wellfield design.

How does groundwater contamination transport work?

Contaminants dissolved in groundwater are transported by advection (carried at the average groundwater velocity v = q/n, where n is porosity) and dispersion (spreading due to pore-scale velocity variations and molecular diffusion). Dense non-aqueous phase liquids (DNAPLs like chlorinated solvents) sink to the aquifer base and act as long-term contaminant sources decades after spill remediation; light NAPLs (gasoline) float at the water table. Predicting contaminant plume migration and designing pump-and-treat or in-situ remediation requires calibrated 3D groundwater flow and transport models.

How is groundwater flow important for climate change adaptation?

Groundwater provides ~50% of global drinking water and ~40% of irrigation water. Climate change threatens these resources through: reduced recharge in drying regions as precipitation decreases and evapotranspiration increases; saltwater intrusion in coastal aquifers as sea level rises; land subsidence from aquifer overdraft (Jakarta, Mexico City, and California's San Joaquin Valley subsiding 0.3-0.9 m/year from groundwater extraction); and changing groundwater-surface water interactions as stream baseflows decline with falling water tables. Groundwater flow models are essential planning tools for managing these interconnected threats to water security.

About this simulation

This simulation visualises groundwater movement through porous rock under Darcy's law, q = −K·(dh/dl), where K is hydraulic conductivity and dh/dl the hydraulic gradient. Three settings — unconfined, confined and regional flow — show the water table or piezometric surface responding to recharge and pumping. Switching on a well draws head down into a cone of depression sized by the Dupuit–Thiem equation, whilst seepage velocity is Darcy flux divided by porosity.

🔬 What it shows

A cross-section with the water table for unconfined conditions, a dashed piezometric surface under an aquitard when confined, or two layers with regional flow arrows. Equipotential lines and moving particles trace flow direction; clicking the canvas adds a well whose cone of depression bends the head surface and particle paths towards it.

🎮 How to use

Choose Unconfined, Confined or Regional Flow from the tabs, then click the canvas to place or remove a pumping well. Adjust Hydraulic Conductivity K (0.1–100 m/d), Hydraulic Gradient i (0.001–0.1), Pumping Rate Q (0–3000 m³/d), Porosity n (0.05–0.50), Aquifer Thickness b (5–60 m) and Recharge (0–800 mm/yr) to watch the Darcy flux, head difference, drawdown, seepage velocity and radius of influence readouts respond live.

💡 Did you know?

Hydraulic conductivity spans roughly ten orders of magnitude between materials: clean gravel can conduct water at up to 1000 m/d, whilst intact clay conducts less than 0.0001 m/d — deciding whether ground makes a productive aquifer or a barrier to contaminants.

Frequently asked questions

What is Darcy's law and how does the simulation use it?

Darcy's law, published by Henri Darcy in 1856, states flow through a porous medium equals −K·(dh/dl): hydraulic conductivity K multiplied by the hydraulic gradient, with the minus sign showing flow runs from high head to low head. The simulator uses this relation directly for the Darcy flux readout and to drive the seepage velocity and particle motion for whichever aquifer type is selected.

What's the difference between the confined and unconfined settings?

Unconfined, the aquifer has a free water table that rises and falls, drawn as a solid blue line. Confined, an impermeable aquitard sits above it, so pressure is carried instead by a dashed piezometric surface that can rise above ground level under artesian conditions. The regional flow tab shows two stacked layers exchanging water between shallow and deep flow paths.

How is the drawdown around the well calculated?

Once a well is placed, the simulation applies the steady-state Dupuit–Thiem solution: drawdown grows with pumping rate Q and shrinks with hydraulic conductivity K and aquifer thickness b, following a logarithmic profile in distance from the well out to a fixed radius of influence. This produces the visible cone of depression and the drawdown figure s_w shown in the stats row.

What effect does the recharge slider have?

Recharge represents rainfall reaching the water table, entered in millimetres per year. In the unconfined and regional settings it lifts the water table into a gentle mound between the domain edges, competing with the hydraulic gradient and any pumping well to shape the overall head surface, much as recharge competes with abstraction in a real aquifer.

What do the seepage velocity and radius of influence readouts mean?

Seepage velocity is the Darcy flux divided by porosity n, the true average speed of water moving through the connected pore spaces rather than the bulk flow rate. The radius of influence is the distance from the well at which drawdown becomes negligible; in this simulator it is fixed at 200 m, so conductivity, thickness and pumping rate change how deep the cone reaches within that boundary.