Tutorial 15: Single Realization Stochastic Flow Tutorial

1Building the Stochastic Model

Step 1 — Enter Synthetic Mode

Click 'Go to Synthetic Case Area' under Utilities to create a blank domain.

Step 2 — Add River Boundaries

Click to add rectangular zones along the left and right edges of the domain representing rivers/streams. These drive the regional flow:

Left edge: Prescribed head = 0 m
Right edge: Prescribed head = -10 m

The 10 m head difference drives flow from left to right — through whatever heterogeneous K field the random generator creates.

Step 3 — Add a Particle Line

Click to add a particle line near the left-edge river. Particles will be released along this line and tracked through the heterogeneous K field — revealing how the random structure affects flow paths.

Step 4 — Assign K as a Random Field

Click the 'Zone=DM' button to create a zone covering the entire aquifer. In the zone properties, assign hydraulic conductivity as a random field rather than a constant value. Configure the probability distribution parameters: mean K, variance (or standard deviation of log-K), and correlation scales (how far the spatial pattern extends before becoming uncorrelated). The random field generator produces a spatially correlated K field — not random noise, but a realistic pattern with connected high-K and low-K structures.

Step 5 — Display the K Field

Click to access Display Settings in the Domain Attributes menu. Check 'Input Display' and select Conductivity from the dropdown. The map now shows the generated random K field — a patchwork of high and low conductivity zones that represents one possible realization of aquifer heterogeneity.

Step 6 — Simulate and View Results

Click to submit for simulation. Watch the flow field respond to the heterogeneous K: head contours become irregular, flow vectors bend around low-K zones and concentrate through high-K channels. Particle paths are no longer smooth parallel lines — they twist, diverge, and channel through the random structure.

Synthetic model setup showing rectangular domain with prescribed head boundaries on left (0m) and right (-10m), particle line near left boundary, and zone covering entire domain configured for random field K assignment — Figure 2: Model setup — river boundaries drive flow left to right, particle line placed for tracking, and the entire domain assigned random field K. The zone properties dialog shows the random field configuration.

Generated random hydraulic conductivity field showing spatially correlated patterns of high-K (warm colors) and low-K (cool colors) zones across the model domain, with connected structures reflecting the correlation scale — Figure 3: The generated random K field — spatially correlated heterogeneity with connected high-K channels and low-K barriers. This is one realization — one possible arrangement that honors the specified statistical parameters. A different random seed would produce a different pattern with the same statistics.

Simulation results showing head contours distorted by the heterogeneous K field, flow vectors bending around low-K zones and channeling through high-K zones, and particle paths showing tortuous, irregular trajectories through the random field — dramatically different from the smooth parallel paths in a uniform model — Figure 4: Flow and particle tracking through the random K field — head contours are irregular, flow vectors channel through high-K zones, and particle paths are tortuous. Compare this to the smooth, parallel paths you'd get with uniform K. This is the reality of groundwater flow in heterogeneous aquifers — and it profoundly affects contaminant transport predictions.

Key Concepts

Realization vs. reality: A single realization is one possible version of the aquifer that's consistent with the available statistics. It's not "the truth" — it's a hypothesis. The actual K field in the ground is different. That's why Monte Carlo simulation (Tutorial 16) runs many realizations: to explore the range of possible outcomes and quantify the uncertainty.

Correlation scale: Controls the "grain size" of the heterogeneity. Large correlation scale → broad, smooth K variations (like regional geological trends). Small correlation scale → fine, patchy variations (like local sand/clay lenses). The grid must be fine enough to resolve the correlation structure — rule of thumb: cell size ≈ 1/3 of the correlation scale.

Channeling and macrodispersion: In a heterogeneous K field, flow preferentially follows high-K pathways — this is called "channeling." The result: particles spread much faster than diffusion or local dispersion would predict. This enhanced spreading is called "macrodispersion" — it's an emergent property of heterogeneity that can only be captured by explicitly modeling the spatial variability of K.

From single realization to Monte Carlo: This tutorial shows what happens in ONE possible aquifer. But how confident are you in that result? Tutorial 16 runs hundreds of realizations — each with a different random K field — to build statistical distributions of outcomes. That's how you go from "the plume might go here" to "there's a 95% probability the plume stays within this boundary."

2What's Next

With single-realization stochastic modeling mastered, continue the learning path:

Tutorial 16: Monte Carlo Flow Simulation — run hundreds of realizations and accumulate flow statistics
Tutorial 17: MC Transport Simulation — Monte Carlo for contaminant plumes — plume uncertainty
Tutorial 18: Probabilistic Capture Zone — capture zone uncertainty from stochastic realizations

This tutorial covers