# Lesson 3 - Conceptual Model for Simple Example

For the remainder of this Unit we will walk through and describe a simple Example model.  In order to do so, however, we first need to provide a conceptual model for the system we are going to simulate, describing the various components of the system, the system boundaries, the processes that we will represent, and the various assumptions in the model. We also need to describe the objectives of the model (i.e., what question or questions are we trying to answer with the model?).

A schematic of the system is shown below:

A small (approximately square) man-made pond sits atop a small hill.  The pond has essentially vertical (and impermeable) sides. The bottom of the pond has a layer of sediments. Water is added to the pond via runoff and direct rainfall. Water is lost from the pond via evaporation and seepage through the sediment layer.  The inflows and outflows are such that the pond volume stays relatively constant through time. The pond is shallow and is assumed to always be well-mixed.

A pipeline adds high concentration effluent containing a contaminant for 100 days (the flow rate is small compared to other inflows such that it does not appreciably affect the pond volume). This contaminates the pond.  The contaminated water leaves the pond via seepage through the sediments and enters an unsaturated zone (the contaminant is not volatile so there is no need to explicitly model an air phase).  The water leaving the pond flows vertically downward (horizontal flow and dispersion in the unsaturated zone is assumed to be negligible). It subsequently flows into a sandy aquifer and forms a shallow plume.  The contaminant is sorbed onto the sediment strongly, and to a lesser extent, onto the sand in the unsaturated zone and aquifer. The entire plume eventually discharges to a stream and is quickly mixed across the width and depth of the stream.

In this simple system, the seepage rate from the pond, the flow through the unsaturated zone and the flow rate through the aquifer are assumed to be at steady state (they do not change with time). The stream, however, is assumed to have a flow rate that is seasonal. Hence, the stream flow is the only transient feature of the flow system.

Our objective is to predict the peak concentration of the contaminant just downgradient of where the groundwater plume discharges into the stream (at the point it is well-mixed).

The various input parameters describing this system are summarized below:

Variable Value
Pond Width and Length 100 m
Pond Depth 2 m
Pipeline Contaminant Discharge Rate 250 g/day for first 100 days of simulation (starting 1/1/2021)
Dispersivity Fraction (Sediments, Unsaturated Zone and Saturated Zone) 10%
Sediment Thickness 30 cm
Sediment Hydraulic Conductivity 7E-8 m/s
Sediment Porosity 0.25
Sediment Partition Coefficient 0.2 m3/kg
Sand Saturated Hydraulic Conductivity 5E-3 m/s
Sand Porosity 0.3
Sand Partition Coefficient 0.002 m3/kg
Unsaturated Zone Thickness 5 m
Unsaturated Zone Saturation Level 50%
Distance to Stream 1 km
Plume Thickness 10 m
Stream Flow Rate Varies seasonally from a low of 120,000 m3/day in September to a high of 510,000 m3/day in April

The boundaries of the system are clear. Contamination is added to the system via the pipeline. We are only tracking contaminant mass through five components: the pond, the sediments, the unsaturated zone, the aquifer between where the contaminated water from the unsaturated zone enters and the stream, and the stream itself (just downgradient of where the plume discharges). Other than the pipeline, all water entering the system is clean (i.e., coming from an upstream boundary).  We stop tracking the mass just past the point where the plume discharges.

The mass is introduced to the system on 1 January 2021, so we will start the simulation at that time.  We will need to continue the simulation until we see the peak concentration appear in the stream (because the mass is introduced as a 100-day pulse, it will move through the system as a pulse).

Let’s open the model now so we can begin to look at it. Go to the “Examples” subfolder of the “Contaminant Transport Course” folder you should have downloaded and unzipped to your Desktop, and open a model file named ExampleCT2_ContaminatedPond.gsm.  The model will look like this:

First, let’s take a quick look at the Time Settings (F2):

As can be seen, we are running the model for 10 (calendar) years, with a 1 day timestep. As we shall see, the 10-year timeframe is required in order to capture the peak concentration as the mass moves through the various components of the system. Given the processes active in the system, we can guess that a 1 day timestep is likely small enough to capture the dynamics accurately (but we will revisit this issue in Lesson 10).

Note that the model is organized into five Containers.  The Inputs Container collects all of the inputs listed in the table above.

The model itself is contained in the Material, Flows and Contaminant_Transport Containers.  The Results Container simply collects the key simulation results.  We will explore all of these in the remaining Lessons.