Tutorial 17: Monte Carlo Transport

1Multi-Realization Flow & Transport

Step 1 — Enter Synthetic Mode

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

Step 2 — Add River Boundaries

Click to add river zones on left (prescribed head = 0 m) and right (prescribed head = -10 m) edges.

Step 3 — Add a Continuous Contaminant Source

Add a rectangular zone near the left edge representing a continuous source of 1000 ppm. This source maintains constant concentration throughout the simulation — mimicking an ongoing industrial discharge or a persistent contaminant like PFAS. In each realization, the plume will follow a different path through the random K field.

Step 4 — Add a Monitoring Well with Probability Tracking

Click to add a monitoring well near the right edge. Check 'Monitoring Probability' — this records the concentration at this location for every realization, building a probability distribution of breakthrough concentrations and arrival times.

Step 5 — Assign K as a Random Field

Click the 'Zone=DM' button to create a domain-wide zone. Assign hydraulic conductivity as a random field with the desired statistical parameters.

Step 6 — Enable Monte Carlo Simulation

Click to open Solver Options. Check 'Monte Carlo Simulation' with the default 10 realizations.

Step 7 — Configure Transport Time Settings

Still in Simulation Settings, adjust the time parameters for contaminant transport:

Time step: 50 days
Simulation length: 1100 days (~3 years)

This gives enough time for the plume to migrate from the source toward the monitoring well across the domain.

Step 8 — Enable Input Display

Click to check 'Input Display' and select Conductivity. This shows the random K field for each realization alongside the flow and transport results — you see the cause (K heterogeneity) and the consequence (plume shape) simultaneously.

Step 9 — Run Monte Carlo Transport

Click to submit. Each realization proceeds in three phases: (1) generate a random K field, (2) solve flow, (3) simulate transport for 1100 days. You see the K field, flow vectors, and evolving plume for each realization in real time. Each realization produces a different plume — different shape, different extent, different arrival time at the monitoring well.

Step 10 — View Individual Realization Results

Watch each realization's K field, flow field, and concentration field unfold. Notice how the plume follows different high-K channels in each realization — sometimes arriving at the monitoring well quickly, sometimes slowly, sometimes not at all within the simulation period.

Step 11 — View Statistics at the Monitoring Well

Click 'Display Charts' under Analysis during or after the simulation. The charts show the probability distribution of concentration at the monitoring well and breakthrough curves from each realization — revealing the range of possible outcomes.

Step 12 — View Mean Concentration Field

Access Display Settings. Check 'MCS Display', then check 'Mean Conc'. The map now shows the mean concentration field — the expected plume averaged across all realizations. The mean plume is smoother and wider than any single realization's plume — this is macrodispersion in action. The effective spreading of the ensemble plume is larger than the local dispersion in any individual realization.

Step 13 — View Concentration Variance Field

Under MCS Display, check 'Conc Variance' and uncheck 'Mean Conc'. The map shows the concentration variance — where the plume is most uncertain. High variance at the plume fringe means "the plume might or might not reach here, depending on the K field." Low variance at the source means "the concentration is always high here, regardless of heterogeneity."

Monte Carlo transport setup showing synthetic domain with river boundaries, continuous source (1000 ppm) near left edge, monitoring well near right edge with probability tracking, domain-wide random K zone, and solver/time settings configured for 10 realizations over 1100 days — Figure 2-3: Complete setup — river boundaries, continuous source (1000 ppm), monitoring well with probability tracking, random K zone, Monte Carlo enabled for 10 realizations, transport over 1100 days.

Display settings showing Input Display with Conductivity selected and MCS Display options — Figure 3 (settings): Display configuration — Input Display shows the K field, MCS Display options control mean/variance visualization.

Single realization results showing the random K field (colored patches), flow vectors, and contaminant plume migrating from source toward right edge — the plume follows high-K channels and avoids low-K barriers, producing an irregular, channelized shape — Figure 4: One realization — the K field (background colors), flow vectors, and contaminant plume. The plume channels through high-K zones, producing an irregular shape unique to this particular K arrangement. The next realization will look completely different.

Multiple realization comparison showing how the same source produces different plume shapes in different K fields — some plumes reach the monitoring well quickly, others are diverted or delayed — Figure 5: Realization-by-realization view — the same source, the same statistics, but different K fields produce different plumes. This is why deterministic predictions of contaminant fate are inherently incomplete.

Probability distribution and breakthrough curves at the monitoring well showing the range of concentration outcomes across realizations — some realizations show high concentration arrivals, others show little or no arrival — Figure 6: Monitoring well statistics — concentration probability distribution and breakthrough curves across realizations. The spread quantifies plume arrival uncertainty: "There's X% probability that concentration exceeds the MCL at this well within 3 years."

Monte Carlo summary showing mean concentration field (smooth, wide plume representing the expected outcome) and concentration variance field (high variance at the plume fringe showing where uncertainty is greatest, low variance at the source and far field) — Figure 7: Mean concentration (top) and concentration variance (bottom). The mean plume is wider and smoother than any individual realization — this is macrodispersion. The variance map highlights the plume fringe: maximum uncertainty about whether contamination reaches that location.

Key Concepts

Macrodispersion: The mean plume from Monte Carlo is wider than any single realization's plume. This excess spreading — caused by the ensemble of different flow paths across realizations — is called macrodispersion. It's a fundamental property of heterogeneous aquifers and cannot be captured by a deterministic model with uniform or zoned K.

Concentration variance = plume uncertainty map: High variance at the plume fringe means "contamination might or might not be here." Near the source, variance is low (always contaminated). Far ahead of the plume, variance is low (always clean). The transition zone — the plume fringe — is where decisions are hardest and uncertainty is highest.

Breakthrough probability: At a monitoring well with probability tracking, you get breakthrough curves from every realization. Some show early, high-concentration arrivals (plume channeled through a fast pathway). Others show late, low-concentration arrivals (plume diverted by low-K barriers). The ensemble gives the probability of exceeding any concentration threshold at any time — the foundation of risk-based remediation design.

Three fields per realization: IGW-NET displays K, flow, and concentration simultaneously for each realization. This cause-mechanism-consequence linkage is educational gold: you see WHY the plume went where it did (K field), HOW it got there (flow field), and WHAT it looks like (concentration field). No other tool makes this connection so visually explicit.

2What's Next

With Monte Carlo transport mastered, continue the learning path:

Tutorial 18: Probabilistic Capture Zone — apply Monte Carlo to wellhead protection area delineation
Tutorial 19: Automatic Parameter Estimation — optimize model parameters systematically
Tutorial 20: Theis Solution — verify your stochastic model against analytical solutions

This tutorial covers