yr \ prob 20% 30% 40% 50% 60% 70% 80% 90% 100% 2 € 306,934 € 719,157 € 1,131,380 € 1,543,603 € 1,955,826 € 2,368,049 € 2,780,272 € 3,192,495 € 3,604,718 4 € 225,578 € 597,123 € 968,668 € 1,340,213 € 1,711,758 € 2,083,304 € 2,454,849 € 2,826,394 € 3,197,939 6 € 151,396 € 485,850 € 820,304 € 1,154,759 € 1,489,213 € 1,823,667 € 2,158,121 € 2,492,575 € 2,827,029 8 € 83,794 € 384,447 € 685,100 € 985,753 € 1,286,406 € 1,587,058 € 1,887,711 € 2,188,364 € 2,489,017 10 € 22,224 € 292,092 € 561,960 € 831,828 € 1,101,696 € 1,371,564 € 1,641,432 € 1,911,300 € 2,181,168 15 (€ 108,513) € 95,986 € 300,486 € 504,985 € 709,485 € 913,984 € 1,118,484 € 1,322,983 € 1,527,483 20 (€ 211,409) (€ 58,357) € 94,694 € 247,746 € 400,798 € 553,849 € 706,901 € 859,952 € 1,013,004 30 (€ 354,760) (€ 273,384) (€ 192,009) (€ 110,633) (€ 29,257) € 52,119 € 133,495 € 214,871 € 296,247 Table 1 – Expected lifetime CAPEX advantage of oversizing a 2 km backbone with 1 dimension (from DN150 to DN200), as a function of years until upgrade and probability that the upgrade is needed. Green = oversizing wins. Red = tight-sizing wins. The assumed discount rate is 3.5%, and the service life is 60 years.
The Upper Limit of the Window Of course, there is an upper limit. The example in this article illustrates the expected benefit of stepping up one pipe dimension but jumping four or five dimensions introduces a different set of problems entirely. Beyond being clearly unnecessary, available underground space also imposes a physical constraint. Finally, if the diameter is too large, low- demand periods can reduce flow velocities and cause water stagnation, increasing heat losses. On the other hand, heat loss scales with the pipe’s diameter, while the energy it carries scales with the diameter squared. So, the relative heat loss per MWh delivered actually falls as diameter grows, provided the pipe is well loaded. Oversizing only creates a heat-loss penalty while the pipe is still lightly loaded – in the early years before anticipated demand arrives. That is a transitional cost, not a permanent one. The Lower Limit of the Window Choosing too small a diameter, on the other hand, creates trouble much faster on the hydraulic side. Halving the diameter roughly quadruples the velocity. Pressure loss is hit even harder. By the Darcy–Weisbach formula, it scales roughly with the fifth power of the diameter. Go just one size too small, and pumping costs explode. This is the main reason behind the usual design limits of around 100 Pa/m and velocities under roughly 2 m/s – and why undersizing bites so quickly. Given the above, it is reasonable to assume that going up one or two dimensions does not raise OPEX – on the contrary, provided the pipe is well loaded, the relative heat loss per MWh delivered and pumping costs fall. For this reason, a CAPEX-only cost assessment, as presented in this article, should be sufficient to support a Final Investment Decision (FID). Making the Backbone Affordable Today Long-term thinking requires an investment logic that openly accepts that some pipes are paid for ahead of their local business case, because their value lies in the optionality they
This means the weighted-average extra cost of stepping up from DN150 to DN200 is only app. 13% in this case. In return, that same step-up delivers an increased capacity of app. 69% – calculated as a simple ratio between the cross-sectional areas – assuming no changes in the allowed pressure gradient or velocity of the water. Whether scenario A or B is the preferred solution financially, of course depends on the probability p that an upgrade is needed and the number of years t before it happens. For this example, T able 1 a bo ve shows the calculations. The tendency is clear: tight sizing only comes out ahead when the probability of needing more capacity is low, or when the upgrade is decades away. The table clearly shows that sizing tightly and revisiting the pipe later can easily end up being the most expensive choice – making the case for holistic planning and modest future-ready sizing clear. In addition, upgrading later means reopening a street to replace a functioning transmission line. It can disrupt supply to existing customers and delay the development, additional heat demand, or new heat source that the upgrade was meant to enable. To keep the calculation simple, these impacts are deliberately omitted. However, this does not mean every pipe should be sized for future capacity. Local distribution pipes and the connections to individual buildings are the opposite case. They are cheap and fast to install, so there is little (if any) reason to build in spare capacity up front; they can simply be extended, street by street, as new customers connect. A Practical and Technical Window The main message of this article is: “Build transmission pipes as large as reasonably possible and distribution pipes as small as practically possible”. That framing is deliberately exaggerated.
8
HOTCOOL no.5 2026
Powered by FlippingBook