GermanJoel,
you seem to have skipped over the bit in the intro to B 41.4 as noted below which summarise it better than I ever could.
B31.3 Process Piping: piping typically found in petroleum refineries; chemical, pharmaceutical,
textile, paper, semiconductor, and cryogenic plants; and related processing plants
and terminals.
B31.4 Pipeline Transportation Systems for Liquids and Slurries: piping transporting products
that are predominately liquid between facilities, plants, and terminals, and
within terminals, pumping, regulating, and metering stations.
In your section the key words are "building service piping". You are talking about a 13km buried PIPELINE. B 31.4 covers that better than B 31.3, but as noted above by me and others, it (B31.4) is predominantly used in hydrocarbon and chemical service, whereas water, as a low hazard substance, has its own set of codes specific to water only which are even more specific and ultimately more attuned to water pipelines than even B 31.4 - hence cheaper.
You haven't given us:
Diameter of your pipe
Pressure of your pipe
Flow rate of the water
Your planned pipe material (if you already know it)
Where in the world you are building this.
All these will have an impact on which design code is "best" for your application.
Remember - More details = better answers
Also: If you get a response it's polite to respond to it.