In wireless ad hoc networks, energy expenditure is a major performance bottleneck as almost all nodes rely on batteries. When identical data has to be sent to multiple receivers, a group communication model reduces the network communication cost, and hence, saves energy resource. In this paper we address the problem of minimizing the communication overhead associated with realizing secure group communications in energy-constrained wireless ad hoc networks. We observe that the communication overhead, defined as number of messages in wired networks, is not a suitable measure of the energy expenditure in wireless networks and introduce a novel metric to incorporate the energy parameter. We argue that great energy savings can occur when node location information is exploited in the construction of the key management scheme. We develop a location-aware key management scheme that takes into account the heterogeneity of the medium and vastly improves the energy efficiency. We present simulation studies that demonstrate the improvements achieved using our algorithms.