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.