What is a model? A beautiful person who struts down a run way, a scaled down sculpture of the Empire State Building, or a series of equations that describe some phenomenon? Did you guess all of the above? Gold star! Models come in many different shapes and sizes.
In the environmental consulting and remediation industry, the word “model” often refers to a numerical model. Numerical models are tools that we use to better understand a system. They can be used to make predictions and to test hypotheses. The thermal models that we customize and construct in house at TerraTherm are a type of numerical model that implement a series of equations to simulate the physics of energy and water transfer in the subsurface during a thermal remediation project.
Similarly to how there are several different forms of models, there are also several different types of numerical models ranging from steady-state single-equation box models to multi-dimensional partial differential equation transient models with over one-hundred equations. Regardless of its complexity every model makes assumptions. Assumptions are made to simplify the system being modeled in some way in order to represent it mathematically. As we all know, the “real-world” is complicated and varied. Reducing the world to a string of variables and coefficients requires making assumptions about how the system works in order to represent it simply with mathematics. It’s these assumptions that make modeling a risky business. If you assume too much, too little, or make the wrong assumptions you risk creating a model that is a false representation of a system. That’s why all numerical models should be considered with caution. A model is not a representation of reality, it is someone’s hypothesis as to how a system works, and that hypothesis can very easily be false.
So why trust the TerraTherm thermal models? We’ve proven that they work! TerraTherm has developed, implemented, and revised its numerical models over several years of applied use and our project results show good matches to what our models predict.
Examples from two different projects of modeled vs observed temperature. Note that the observed temperatures do not perfectly match the modeled but come very close. (Click to enlarge)
Our models are used during the design phase to setup the site energy and water balance, test operational parameters such as injection and extraction rates, provide treatment system design parameters, and estimate utility usage. We implement a multi-layered, multi-equation, transient box model to track how the water and energy balance within the subsurface is expected to change throughout thermal remediation. A box model is one that simplifies a system to inputs and outputs.
Steady state assumes that what goes in equals what goes out, such that the net flux is zero, whereas transient assumes that the net flux through the system can change. Transient models are generally more complicated than steady state, but also a better representation of reality. A multi-layered box model allows for discrete portions of the box to be examined more carefully. Each layer is treated as its own box through which energy and water can transfer and layers can pass energy and water to other layers. This type of model instinctively lends itself to in-situ thermal remediation because we work in the subsurface, which is naturally divided into layers according to its geologic and hydrogeologic characteristics. This is what is investigated during the conceptual model phase of thermal modeling, arguably the most important phase of thermal modeling.
During the conceptual model phase we use the data on the concentration and distribution of site contaminants and the site geologic data provided to us by the client to define the dimensions and geometry of the TTZ. Some of this data includes:
- Soil Bore Logs
- Analytical Lab Data
- Contaminant Distribution Maps
- Geological Cross Sections
- Slug Tests
- Potentiometric Surface (Water Table) Maps
We use the natural hydrogeologic boundaries in the subsurface to subdivide the TTZ into layers to be simulated in the numerical model.
Example of how a complex geologic cross-section is transformed into a simplified conceptual model (Click to enlarge)
It is during the conceptual modeling phase when simplifying assumptions about the system are made. The output is an energy and water balance for each layer that was modeled as well as the TTZ as a whole, a prediction for what the average TTZ temperature will be throughout the duration of the project, and an estimate of what the project utility use and cost will be. All of these components are crucially influential to the project design and they are used to track the progress of a project during operations.
Additionally, the models are useful for investigating potential challenges, such as ground water flow at certain depths, the importance of the R-value of a vapor cover, and sensitivity to starting groundwater levels and saturation. By simulating high and low values of key factors, we develop sensitivity studies that teach us where to focus and optimize. The figure below is an example, where the upward flow of groundwater and a poor vapor cover lead to less than optimal temperature profiles.
Temperature profiles modeled for a site (left), along with two scenarios where groundwater flow (middle) and a poor vapor cover (right) causes less than ideal heating. Sensitivity studies are used to optimize the design and to prevent realizing these challenges during heating. (Click to enlarge)
The thermal model outputs provide a solid baseline for our clients and engineers to know what to expect during a project and when operations are not going according to plan. Thus the thermal model is useful during all phases of a project. It is used to verify and inform the design, to track the progress of a project during operations, and to reflect on how a project performed relative to the expectations throughout its operation. The thermal model is a very important tool used during thermal remediation and understanding how it works is beneficial for all those involved in a thermal project.