The smaller the
batch_size is, the larger number of batches is processed per one epoch.
On one hand, since one makes more steps per epoch, one can think, that less epochs are required to achieve the same level of accuracy.
On the other side, smaller
batch size leads to more noisy and stochastic estimates of the gradient, therefore, convergence would not be as steady most likely.
I think it is difficult to give a definite answer about the exact relation on the number of epochs - since say, to achieve a certain level of accuracy use of small batch may be more beneficial since it allows for more exploration and is more likely to escape from local minima and saddles, but when one reaches the approximation limit of the network and is in the vicinity of the good optimum - large batch would descend better to the extremum.
Good strategy usually is to start from smaller batches to find wide and plain minima, which are better from the generalization point of view, and then increase batch size for steadier convergence.