  In realistic situations, physical systems can not be completely isolated from
its environment. Its inevitable interaction with the environment can influence
the working process of the device. In this paper, we consider two-qubit quantum
batteries where one qubit of the battery is successively interacting with the
spins present in the surrounding environment. We examine the effect of the
interaction on the maximum amount of energy that can be extracted from the
battery using unitaries. In this context, we use the notion of locally passive
states. In particular, we examine the behavior of the amount of extractable
work from the noisy battery, initially prepared in a locally passive or
ordinary pure state, having a fixed initial entanglement, with the number of
interactions the qubit has gone through. We also examine the amount of locally
extractable work from the noisy battery. We realize though the amount of
extractable energy, be it global or local, as a whole will decrease with the
number of spins of environment it interacted with, but if we increase the time
interval of the interaction with each spin, after a cut off value of the
interval, the small time behavior shows a peculiarity, i.e., the extractable
energy within a single interaction starts to increase with time. The cut-off
time indicates the Markovian-to-non-Markovian transition of the interaction. We
also observe a non-Markovian increase in extractable energy from the Markovian
scenario.
