The absorption voltage should be in the Mid 14's depending on battery manufacturer recommendation.
When charging, battery voltage rises until absorption voltage is reached. Then the amps required to hold the battery at absorption voltage decreases.
A regular charger would call the time until the Absorption voltage is reached the bulk charge/Stage and it is be constant current charging. The battery can take all the charging source can provide until Absorption voltage is reached. Solar is a bit different since the amount of current varies throughout the day.
Absorption charging is a constant voltage stage. Batteries need to be held at absorption voltage for about 2 hours after a deep cycle. If the battery was not cycled deeply then the battery does not need to spend 2 hours at this absorption voltage. Some controllers allow an amperage threshold to be set. When only x amount of amps or less is required to hold absorption voltage, then the controller reverts to float voltage. This prevents unnecessary time at absorption voltages when the battery was not cycled, and on a deeply cycled battery allows absorption voltage to be held long enough to get the battery into the 96%+ range, if programmed correctly for the battery.
Float voltage(~13.2v) is basically just to prevent battery discharge, and significantly slows down any charging. Many/Most solar controllers and revert to float voltage way too early, well before the battery has absorbed everything it wants. It is like slapping the water glass out of a dehydrated persons hand.
In such an instance, then some recharging still occurs at float voltage, but at a mere fraction of the rate at which charging would have continued at absorption voltages.
Battery monitors need to be programmed correctly and reset occasionally, in addition to being wired correctly. Many people do none of this and just believe the numbers to be 100% accurate, or believe the flashing green lights telling them when the battery is full.
The Blinking green lights Lie often and arguably, always. They only indicate the charging source has decided absorption voltage has been held as long as it was designed to do so. It does not mean the battery is actually fully charged. Fine tuning the absorption voltages and duration of absorption voltage is key to Ideal maximum battery longevity.
Blindly believing the flashing green light full charge indicators can lead to premature battery failure.
If the goal is maximizing battery longevity, or just preventing premature demise due to chronic undercharging, then some tinkering with absorption voltage and duration with a Hydrometer on a flooded battery is required.
When i first got solar I killed my first set of batteries in a year with 14.4 absorption voltage and 13.2 float voltage. It was only spending 30 minutes at 14.4 before reverting to 13.2v. The flashing green lights were soothing, but lying. Ultimately the batteries needed 14.8 and to be held there for 2+ hours a day after a deeper discharge cycle. They did not get this, and were murdered with one Wally world battery failing at 13 months of shallow cycles and then second failed at 22 months even after absorption voltage was raised and lengthened.
A solar charge controller which allows one to adjust absorption voltages and durations is Key, as every battery is slightly different, requires slightly different parameters in different discharge situations, and changes as it ages. One can hope a happy preprogrammed medium yields acceptable battery life, or one can take it to another level and experiment with voltages and a hydrometer to fine tune the system to best recharge the petulant battery, which might need more or less Absv and duration than which the manufacturer lists.
It all depends on what is acceptable to the battery depleter.
Reaching a true 100% recharge after each discharge is the key to maximizing battery longevity.
A blinking green light does not equal a 100% recharge.
