This article introduces a breakthrough in the accuracy of geothermal simulations by allowing the fluid properties to change over time, leading to more accurate and feasible geothermal borefields. These changes are now the default in GHEtool Cloud and available to everyone.
A long story short
In order to understand the important changes that were made to the software, we need to summarise quite a lot of content from previous articles. Below, we will repeat some of the main ideas from these articles so you can follow the story, but we will reference the original articles if you want more background information.
Borehole thermal resistance
The effective borehole thermal resistance (find the article hier) describes how easily energy can be transferred from the fluid to the ground. We discussed earlier that this resistance consists of different sub-resistances, each representing a boundary the energy must pass through in order to reach the ground. This is shown in the figure below.
Although (almost) all these parameters can be changed by the designer, the convective fluid-to-pipe thermal resistance is typically the one that draws most of the attention, as it is of major importance. How easily the fluid exchanges energy with the pipe depends on the fluid regime (laminar, transitional or turbulent), which is described by the Reynolds number.
Reynolds number
The Reynolds number is a dimensionless quantity that indicates the flow regime of the fluid. (If you have not read our article on the subject, you can find it hier). The figure below shows the different fluid regimes, ranging from laminar to turbulent flow.
When the flow rate is rather low, all the different fluid particles move parallel to each other in what is called a laminar flow regime. This makes it difficult to exchange heat with the pipe boundary, as the fluid particles in the centre are more or less insulated. When the flow rate increases, the fluid transitions into a turbulent flow, where the fluid particles are constantly being mixed. This leads to better heat transfer (at the cost of higher pump energy consumption).
The transition between laminar and transitional, and transitional and turbulent flow, is governed by the Reynolds number, which depends not only on the flow velocity, but also on fluid properties such as density and dynamic viscosity. This brings us to the final step in the story.
Fluid properties
Not all fluids behave the same. You can imagine that it is easier to pump water through a system than it is to pump honey through a pipe. This has to do with the viscosity of the fluid: a higher viscosity means it is harder for the fluid to transition to a turbulent phase. Therefore, the more viscous your fluid is, the higher the dynamic viscosity and the lower your Reynolds number.
The key point is that these fluid properties are not constant — they depend on the temperature of the fluid. This is shown in the figure below for two water-glycol mixtures of 20% and 30% MPG.
The colder the fluid gets, the harder it is to bring it into a turbulent regime. The figure above shows that when your water-glycol (30%) mixture is around 0 degrees, you are far from the turbulent regime, whereas at a temperature of 15°C, your Reynolds number is almost double, bringing you much closer to the advantageous transient flow regime.
This temperature dependence of the fluid properties and its impact on the Reynolds number is essential for understanding the behaviour of geothermal systems and was overlooked for decades.
A little bit of history
Historically, geothermal borefields were invented as a stable and relatively high temperature source for ground source heat pumps. The only temperature of importance in this case is the (long-term) minimum average fluid temperature. Since borefields were always sized to cope with this minimum average fluid temperature, the fluid properties were simply calculated for this worst-case situation (or even lower, at the freezing point of the water-antifreeze mixture).
It is only more recently that more and more borefields are also being used for cooling, increasing the range of possible fluid temperatures. As shown in the graph above, the fluid properties when extracting heat from the borefield (at, say, around 0°C) are quite different from those when injecting heat into the ground during cooling (around 15°C). If the same borehole thermal resistance is used for both heating and cooling, the heat exchange in cooling is underestimated, sometimes leading to oversized or seemingly infeasible systems.
A leap in accuracy
With GHEtool, starting today, we have broken with this decades-old assumption. From now on, by default, all your geothermal simulations will take into account the temperature dependency of the fluid properties. Every month, in both heating and cooling—down to every hour if needed—we will recalculate the borehole effective thermal resistance for the specific temperature at that time, so you get the most accurate results possible. This also means that from now on, you will have two Reynolds numbers (for both heat injection and extraction) and two thermal resistances for every simulation.
This major change brings two practical benefits: it reduces the risk of oversizing when a borefield is designed primarily for cooling (i.e. heat injection), and it lowers the likelihood of receiving a gradient error when calculating the required borehole depth. Both of these will be explained further below.
!Caution
When using this new, more accurate simulation method, it may be difficult to compare your current simulations with those done previously (or with other software). If you wish to simulate a scenario for comparison purposes, you can set the ‘Temperature dependent fluid properties’ option to ‘No’.
Avoid oversizing for cooling
Below is a project that was simulated with the traditional assumption of a single worst-case effective borehole thermal resistance. The Reynolds number was 2043, giving a resistance of 0.2265 mK/W (single U-tube with 30% MPG). The temperature profile is shown below.
Based on this result, you would in the past have suggested drilling another borehole so that the fluid temperature stays below the limit of 17°C. However, with the varying fluid properties, we now have the temperature profile shown below.
Since our Reynolds number during injection is 4214, which is turbulent, our effective borehole thermal resistance is 0.1305 mK/W during cooling. This causes the peak fluid temperature during cooling to drop, leading to a feasible solution.
!Hinweis
Although this new model is always beneficial for your cooling demand, it will not always result in such a significant difference as shown above. If your fluid regime remains laminar in both heating and cooling, for example, the difference will be smaller.
Less frequent gradient error
As discussed in a previous article (which you can find hier), an error can sometimes occur when calculating the required borehole depth. This was due to the fact that the ground temperature increases with depth, causing problems in passive cooling. With this update, the heat transfer during cooling is now calculated much more accurately, leading to lower peak fluid temperatures. This counteracts the effect of the increasing ground temperature, resulting in fewer gradient errors and more feasible system designs.
Schlussfolgerung
This article outlines a major leap forward in the accuracy of geothermal simulations. By accounting for the temperature dependence of fluid properties over time, we can now calculate the effective borehole thermal resistance at every timestep—both during heat extraction and injection. As a result, the simulations are significantly more accurate, systems are more likely to be feasible, and the occurrence of gradient errors is reduced.
We hope you embrace this innovation and continue designing borefields with confidence using GHEtool Cloud.
Literaturverzeichnis
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