Numerical modeling of geothermal processes has received increased attention in recent years. The process of installing geothermal heating systems in residential homes and cottages is one application of numerical models. These systems typically involve drilling between one and three wells on a particular property. Heat exchangers then act as a pump and remove heat from the ground in order to heat the residential structure. Such systems have significant potential benefit in reducing long-term heating costs, but they raise the question of what impact they have on the geothermal systems in the ground over the long term.
Brad Ford recently contacted SoilVision Systems Ltd. to perform numerical modeling of an existing geothermal heating system under an acreage-type property. Known parameters for this scenario included:
- Six geothermal wells drilled to accommodate the geothermal heat-exchange process
- Heat pumping rates for each of the wells
- Air temperature for the area
- General geo-strata geometry and thermal properties
- Water table elevations for the area
The site has an overall flow of water in an aquifer across the property and down to a river, which is located a few hundred meters from the property. The aquifer flows through all six drilled geothermal wells and therefore the correct numerical modeling must include the convective heat transfer as the 'coldness' surrounding the geothermal wells is carried downstream by flow from the aquifer.
The system may be represented as shown in Figure 1, above, which illustrates the dimensions of the property as well as the direction of flow of the aquifer and the six geothermal wells.
The system was modeled with the coupled SVHeat and SVFlux finite element software packages. These packages offer fully coupled convective and conductive heat flow analysis and can also model the transition between frozen and unfrozen zones. These aspects of numerical modeling are important for this type of application, as the temperature regime around the installed geothermal wells is influenced by both conductive and convective heat movement.
The difficulty with numerical modeling of this type of system are the sharp gradients directly adjacent to each well. These sharp gradients require a significantly refined mesh adjacent to the geothermal wells. Such a system is difficult to model in a finite difference type of structure such as MODFLOW and efforts to model this system in a finite difference system were attempted but were ultimately unsuccessful.
Once the system is set up in the SVHeat / SVFlux coupled software, the model may be run in a steady-state (infinite time) or transient state manner. This would determine if:
- Enough heat would be drawn from the ground so as to create a permanent frozen zone, and
- What would be the influence of the flowing aquifer on the thermal zone around the wells.
The 3D plotting of the temperature contours can be seen in Figure 2, below. This model takes into account both conductive and convective heat flow. The iso-surface for a temperature of zero degrees is plotted in the model to show the growth of the freezing front after 50 days. It can be seen that the influx of 'warm' aquifer water causes a reduction in the frozen zone deeper in the wells. It is therefore possible to quantify the potential influence of the heat contribution from an aquifer, as opposed to only having ground conductance.
'Warm' water from the aquifer flows across the lower portions of the geothermal wells and carries the lower temperature water away from the wells. The aquifer has the net effect of increasing the amount of heat that can be pumped from the ground in this situation.
This application illustrates the use of SVFlux and SVHeat to model geothermal systems. Numerical modeling is a useful tool which can answer the following questions regarding geothermal systems:
- To what extent will a geothermal system impact the surrounding temperature regime?
- How will local groundwater flows influence the system?
- How large of a frozen zone will be created in northern locations?
- How many wells should there be and what should be the reasonable spacing between wells?