The Kirkwood superposition approximation is used for the study of many-particle effects in the bimolecular reaction (energy transfer from donors A to unsaturable sinks B). Several spatial distributions of sinks B are considered. It is shown that the theory presented reproduces exact results obtained earlier for particular cases of a random distribution (using the Wigner - Seitz model) and the sink-concentration correction obtained for particle accumulation by means of the mean-field theory.