This tutorial describes the 2D Steady Flow in Homogeneous Aquifers — Particle Tracking applet.
The model uses the superposition principle to compute the 2D steady-state velocity potential resulting from
any combination of injection wells, extraction wells, and a uniform regional flow in a homogeneous,
confined aquifer. Once the head field is computed, particles are tracked along streamlines forward or backward
in time to visualize flow paths and compute travel times. Wells and particles are placed interactively
by clicking on the plot canvas.
1 Interface Overview
The applet window is organized into five zones stacked vertically:
① Plot Canvas — main 2D domain; wells and particles are placed here; head contours and flow paths are drawn here
②
Demo Bar — dropdown to load preset scenarios plus links to tutorials
③
Controls Row — flow-direction compass · aquifer properties · coordinate readout · well/particle buttons · options buttons
④
Q Totals Bar — real-time display of total injection and extraction pumping rates
⑤
Credits — authorship information
Typical workflow: choose a demo (or set parameters from scratch) → place wells on the canvas → click Compute → insert particles → observe flow paths.
2 Demo Selector
The Demo dropdown at the top loads pre-configured well and particle layouts for common scenarios:
Demo
Single Injection Well with regional flow and boundary particles ▼
User Interface Tutorial
Solution Tutorial
| Demo | Description |
|---|---|
| Basic Model | Empty domain — build your own well configuration from scratch |
| Single Injection Well… | One injection well with regional background flow; boundary particles show flow paths entering the domain |
| Single Extraction Well… | One extraction well with regional flow; boundary particles illustrate the capture zone |
| Doublet (no regional flow) | One injection + one extraction well with no background gradient |
| Doublet with regional flow | Doublet system with an applied regional hydraulic gradient |
| Doublet + regional + boundary | Full doublet scenario with boundary-released particles to trace divide and capture |
Warning: Selecting a new demo resets all wells, particles, and aquifer properties. Save any custom setup before switching demos.
3 Plot Canvas
Reading the Display
The canvas shows a plan view (top-down) of the 2D aquifer domain. After clicking Compute:
- Head contours appear as evenly spaced lines connecting points of equal hydraulic head.
- Wells are shown as colored symbols (circles, squares, triangles, or crosses). Injection wells push flow outward; extraction wells pull flow inward.
- Particle pathlines are drawn as colored curves with arrows indicating flow direction. Forward-tracked particles move in the direction of flow; backward-tracked particles trace flow back to its source.
- Boundary particles released from the domain edges show which portions of the boundary contribute water to specific regions of the aquifer.
Mouse Interaction
Move the cursor over the canvas at any time to see the real-time Location/Velocity readout showing cursor coordinates (X, Y) and interpolated velocity components (Vel. X, Vel. Y).
- While in Insert Well mode: click to place a well and open the Well Attributes dialog.
- While in Insert Part. mode: click to place a single particle at that point.
- Double-click an existing well symbol to re-open its Attributes dialog and edit properties.
Tip: Use Plot Options to narrow the X/Y axis ranges and zoom into a region of interest, then re-click Compute to refresh.
4 Flow Direction Compass
The circular direction compass at the left of the controls row sets the direction of the uniform regional groundwater flow gradient.
N
↻
↻
Click anywhere inside the compass circle to set the direction of regional flow. The angle is also shown in the text field below the compass and can be typed directly.
0° = flow toward the right (+x direction); angles increase counter-clockwise. 90° = flow toward the top (+y direction).
Tip: After changing the flow direction, click Compute to update the head and velocity fields.
5 Aquifer Properties
The Aquifer Prop. panel in the controls row sets the physical properties of the aquifer used in all calculations:
| Parameter | Symbol | Description | Typical Default |
|---|---|---|---|
| Reg. Flow | q | Regional (background) Darcy flux magnitude. Set to 0 for no regional flow. | varies by demo |
| Porosity | n | Aquifer porosity. Converts Darcy specific discharge to pore-water seepage velocity used for particle tracking. | 0.35 |
| Thickness | b | Saturated aquifer thickness (m). Used to compute volumetric flow rates from the 2D areal model. | varies by demo |
Tip: After editing any aquifer property, click Compute to recalculate the flow field.
6 Wells & Particles
Well Controls
Insert Well
Remove Well
Compute
Refresh
| Button | Action |
|---|---|
| Insert Well | Activates well-placement mode. Click the canvas to place a well; the Well Attributes dialog opens to set its properties. |
| Remove Well | Activates removal mode. Click on an existing well symbol to delete it from the domain. |
| Compute | Solves the superposition equations and redraws head contours and all particle pathlines. Must be clicked after any change to wells, aquifer properties, or the flow direction. |
| Refresh | Redraws the canvas without resolving — useful if the display becomes cluttered after repeated particle insertions. |
Well Attributes Dialog
When inserting or double-clicking a well, a dialog lets you configure:
| Field | Description |
|---|---|
| X, Y | Well center coordinates in the domain |
| Pumping Rate (Q) | Volumetric flow rate. Positive Q = injection (adds water); negative Q = extraction (removes water). |
| Num. Particles | For injection wells: number of particles released from the wellbore in a ring pattern after Compute. |
| Particle Start Angle | Angle (degrees from +x) for the first injected particle; remaining particles are distributed evenly. |
| Well Symbol | Color, shape (circle/square/triangle/cross), and size of the well marker on the canvas. |
| Particle Symbol | Color, shape, and size of this well's associated particles. |
Particle Controls
Insert Part.
Remove Part.
- Insert Part. — click on the canvas to place individual particles. In Polyline mode (set in Particle Options), click multiple points and double-click to finish; particles are released evenly along the drawn line.
- Remove Part. — click near an existing particle or group to delete it.
Q Totals Bar
The dark bar below the controls row displays:
- Total Q INJ — sum of all injection well rates (m³/s or consistent units)
- Total Q EXT — sum of all extraction well rates (shown as a positive magnitude)
Tip: For a closed system at steady state, Total Q INJ should approximately equal Total Q EXT. Imbalances indicate net flow across the domain boundary due to regional flow.
7 Options Panels
Plot Options
Tracking Options
Particle Options
Contour Options
Clear All
| Button | Opens… |
|---|---|
| Plot Options | Set the X and Y axis ranges to zoom or pan the domain. Click "Compute Max Y" to auto-size the vertical range to match the canvas aspect ratio. |
| Tracking Options | Control particle path integration — time step size, number of steps, time-marking options. See §8. |
| Particle Options | Choose between Point (single click) or Polyline (multi-click line) placement mode; set particle spacing, default color, shape, and size. |
| Contour Options | Toggle head contours on/off; set number of contour levels and grid resolution. See §9. |
| Clear All | Removes all wells and particles and resets the domain to a blank state. Aquifer properties are retained. |
8 Tracking Options
The Tracking Options dialog controls how particle trajectories are integrated:
| Parameter | Description |
|---|---|
| Time Step Length | Duration of each integration step. Smaller values give smoother, more accurate pathlines but are slower to compute. |
| Number of Time Steps | Total number of steps each particle is advanced. Increase to extend pathlines further into the domain. |
| Autoscale TS Length | When checked, the time step is automatically scaled to the local velocity magnitude so that each step advances the particle by a consistent spatial distance. |
| Maximum Pixel Distance | Caps the per-step displacement in screen pixels, preventing jumps and graphical artifacts near high-velocity zones around wells. |
| Contouring mode |
No Contouring — draw continuous smooth pathlines. Fixed Incremental — place a dot on the pathline at each fixed time increment to indicate travel time. Specific Times — mark particle positions at up to four user-specified times. |
Tip: Leave Autoscale TS Length enabled for most scenarios. Disable it and set a very small fixed step only when paths are erratic very close to well bores.
9 Contour Options
Head contours show the hydraulic head distribution and help visualize the shape of the flow field. In the Contour Options dialog:
| Parameter | Description |
|---|---|
| Show Head Contours | Toggle contour line display on or off. Disabling contours speeds up rendering when only pathlines are of interest. |
| Number of Contours | How many equally-spaced contour levels to draw between the minimum and maximum head in the domain. |
| Grid Density | Resolution of the internal grid used to evaluate the head field. Fine (5 px) gives the smoothest contours; Coarse (25 px) is faster for interactive exploration when many wells are present. |
Tip: Use Fine grid density for clean plots. Switch to Coarse while adjusting well positions to keep the display responsive.