En el capítulo anterior se explicó el concepto de caída de presión y su importancia. En este capítulo profundizaremos en este concepto, examinaremos cómo evoluciona la pérdida de carga con el tiempo y estudiaremos cómo puede definirse la pérdida de carga crítica. También se introducirán los conceptos de potencia y energía de la bomba.
Deepening insights in pressure drop
En Parte 4.1, the concept of pressure drop was defined using the hydraulic configuration (length, depth, local losses), as well as the fluid and flow properties. However, as discussed in the previous part, the fluid properties and even the flow rate are not constant over the simulation period. The consequences of this are detailed below.
Propiedades variables de los fluidos
En Parte 3.2, the importance of using variable fluid properties was explained, focusing on the thermal design of the borefield. However, there is also a hydraulic aspect to this, since when the fluid properties vary over time, the pressure drop also changes. In the graph below, the pressure drop is shown for different flow rates with 25 v/v% MPG during both extraction and injection.
It is clear that the flow enters a turbulent regime sooner during injection, as shown by the sharp increase in pressure drop around 0.5 l/s, whereas the transition occurs later during extraction. Therefore, depending on the flow rate, either the pressure drop during extraction or during injection will be critical. For example, for a design flow rate of 1 l/s, the injection pressure drop of around 40 kPa will be limiting, whereas at a flow rate of 0.5 l/s, the 18 kPa during extraction will be limiting.
Therefore, when selecting the critical pressure drop (required for pump design), both extraction and injection conditions should be considered.
In the graph below, an hourly pressure drop profile is shown for a borefield with 4 boreholes of 120 m depth, a double DN32 probe, 25 v/v% MPG, and a constant flow rate of 0.8 kg/s through the borefield.
In the graph above, sharp jumps are visible during the winter periods, whereas the pressure drop follows a more smooth behaviour during summer. This is because the fluid temperatures in summer are higher and, therefore, the flow remains turbulent (Re > 2300). However, in winter, the temperature fluctuates significantly and the flow frequently switches between laminar and turbulent regimes.
When the hourly temperature profile above is compared with the pressure drop graph, this behaviour becomes clearer. The sharp drop in temperature around 25 January is also clearly visible in the pressure drop graph, indicating that the flow is indeed in a laminar regime at that moment.
When the flow rate is doubled, so that the system remains fully turbulent, these jumps in pressure drop disappear and a smooth curve, similar to that observed during the summer period, is obtained.
Variable flow rate
Besides having variable fluid properties, the flow rate is also no longer constant, as was discussed in Parte 3.3. The pressure drop for the same 4 boreholes of 120 m depth, with a constant temperature difference of 4 °C during extraction and injection (and a minimum flow percentage of 30%), is shown below.
When the graph above, with a variable flow rate, is compared to the one with a constant flow rate, it is immediately clear that, on average, the pressure drop is lower in the variable flow rate case. This is especially noticeable in summer, where the pressure drop was always high in the constant flow rate case (due to the turbulent flow regime), which is not the case here. Due to the lower peak powers (as can be seen in the building demand below), the flow rate is significantly lower, and consequently the pressure drops are also lower.
Given these insights into how the pressure drop evolves over time, the concepts of pump power and pump energy will now be explained.
Pump power
Once the pressure drop is known at a given moment, it is relatively straightforward to calculate the required hydraulic power for the pump using the following relationship:$$P_h=\dot{Q}\cdot \Delta P$$where$P_h$ the hydraulic power in (kW), $\dot{Q}$ the flow rate in (m³/s) and $\Delta P$ the pressure drop in (kPa).
It is important to note that the hydraulic power represents the theoretical minimum power a pump must deliver to transport a given amount of fluid at a certain pressure. However, since pumps are neither mechanically nor electrically ideal, the overall efficiency typically ranges between 50% and 90%, as shown in the graph below.
The electrical power of the system can be easily calculated, given an average pump efficiency $\eta$, as:$$P_e=\frac{P_h}{\eta}$$
Energía de bombeo
With the electrical power of the circulation pump known, the pump electricity consumption can be calculated. The method used, however, depends on whether the borefield has been simulated with an hourly or a monthly load profile. For both cases, the pump energy calculation is explained below.
Hourly load profile
In the case of an hourly simulation, the calculation of pump energy is quite straightforward. Since the pressure drop and the flow rate are known for every hour, the pump power is also known. By simply summing the required power over all hours in the year, the pump energy can be obtained. The average yearly pump energy consumption can be calculated as:$$E_e=\frac{\sum\limits_{i=0}^{8760 n}{P_e(i)}}{n}$$where $E_e$ is the required electrical energy in (kWh), $P_e$ is the electrical power at time $i$ in (kW), and $n$ is the number of years in the simulation period.
Having an hourly simulation has clear advantages not only for the thermal analysis of the borefield (as discussed in Part 3.1) but also for the calculation of pump energy. Earlier, the difference between an hourly pressure drop with a constant and a variable flow rate was explained, and it was shown that the pressure drop for the variable flow rate case is, on average, much lower. In the graph below, the cumulative pump energy consumption (assuming an efficiency of 70%) is shown for both cases.
In the graph above, it is clear that the variable flow rate results in a significantly lower pump electricity consumption on a yearly basis than the constant flow rate case, namely 17 kWh/year versus 224 kWh/year. This means that using a variable flow rate in this case reduces pump electricity consumption by 92%.
Monthly load profile
For an hourly simulation, the calculation of pump electricity consumption is relatively straightforward. For a monthly simulation, however, this is not the case. Since the flow rate is not known for every hour, certain assumptions must be made to estimate the pump energy demand. A distinction is therefore made between the case of a constant and a variable flow rate.
Constant flow
In the case of a constant flow rate, the maximum pressure drop can be calculated during extraction and injection by considering both the minimum and maximum average fluid temperatures and using these to determine the pressure drop. Once this is known, it can easily be converted into the maximum required pump power by multiplying the pressure drop by the flow rate.
Based on this maximum required power, a best estimate of the pump energy consumption can be made using the full-load hours of the circulation pump. To calculate this, the baseload extraction and injection energy in each month is divided by the extraction and injection peak power to obtain the full-load hours. By summing these values, an overall estimate of the full-load hours of the circulation pump is obtained.
For the same case as above, now using a monthly simulation, the circulation pump has an estimated 3333 full-load hours, resulting in a pump energy consumption of 100 kWh/year.
Variable flow
In the case of a monthly simulation with a variable flow rate, the maximum pressure drop and the corresponding required pump power are calculated for each month, for both injection and extraction. Instead of taking the maximum of these values and using it to calculate the pump energy demand, the monthly required pump power (for both extraction and injection) is multiplied by the full-load hours in each month (for both extraction and injection).
Although the total number of full-load hours remains the same, using different pump powers for each month results in a more optimistic pump electricity consumption of 37 kWh/year. This is again significantly lower than the constant flow rate case, 63% lower to be precise, but it is still much higher than the 17 kWh/year obtained from the hourly simulation with a variable flow rate.
Conclusión
In this chapter, the hourly variations in pressure drop were considered, taking into account both variable fluid properties and variable flow rate. Using the concepts of pump power and pump energy consumption, it was shown that using variable flow rates can reduce pump electricity consumption by 92% compared to a constant flow rate.
In the next chapter, the actual hydraulic design, including the horizontal connections between the boreholes, will be explained, together with an example in GHEtool Cloud.
Preguntas
In the graph below, the pressure drops during both heating and cooling are shown, and the transition from laminar to turbulent flow is clearly visible. As expected, the transition from laminar to turbulent flow occurs sooner during cooling, since the Reynolds number is higher. How is it possible that the pressure drop at 0.55 l/s during cooling, which is turbulent, is lower than the pressure drop during heating, which is laminar?
Why is the pressure drop in the graph below, when working with a constant flow rate, higher in winter than in summer?
Referencias
- Grundfos. Calculating pump efficiency. Available online. [last visited 24-04-2026]