Remove the battery for several hours and check if it will drain out. If the battery still charged, it should be healthy.
One possible trouble maker could be any USB port or other device that still powered while the system is shut down.
Extra powered USBs are feature for some laptops. Usually these ports are yellow colored. Port as this could be troublemaker especially if something is plugged in this port. In most cases this feature could be disabled via the BIOS settings.
Recently I've discovered that the new batteries should be charged to 100%. Unfortunately I can't find the source of this statement but this solve my problem with my new battery jump drain from ~35% to 5%.
Within Ubuntu the package
tlp (apply laptop power management settings) could be helpful. It is capable to handle the power management of the devices (USB, PCI, etc.) at kernel level.
TLP  brings you the benefits of advanced power management for Linux
without the need to understand every technical detail. TLP comes with
a default configuration already optimized for battery life, so you may
just install and forget it. Nevertheless TLP is highly customizable to
fulfil your specific requirements.
Please note: TLP runs on every laptop brand. Setting the battery
charge thresholds is available for IBM/Lenovo ThinkPads only.
TLP is a pure command line tool with automated background tasks. It
does not contain a GUI.
TLP  (TLP - Linux Advanced Power Management) is more progressive
management utility battery-for Linux, which applies different settings
automatically when you log on and every time you change the power
source, depending on your distro and hardware.
Basic usage of
Install the package:
sudo apt update && sudo apt install tlp.
If you are using
tp-smapi the better way to install the package is:
sudo add-apt-repository ppa:linrunner/tlp
sudo apt-get update
sudo apt-get install tlp tlp-rdw
sudo apt-get install tp-smapi-dkms acpi-call-dkms
There are two services installed
sudo tlp stat to check the current settings.
nano /etc/default/tlp to tweak the configuration.
sudo tlp start to apply the configuration.
Another useful tool is
powertop, that is not just a monitoring tool, but has also a calibrating option: