We examine the deployment of a large multi-user multiple-input multiple-output (MIMO) system and the resulting Energy Efficiency (EE) considering a 2D rectangular array with increasing antenna elements within a fixed physical space. The resulting increasing mutual coupling and correlation among the base station (BS) antennas are incorporated by deriving a practical mutual coupling matrix which considers coupling among all antenna elements. We also provide a realistic analysis of the energy consumption using a new model, taking into account the circuit power consumption as a function of the number of BS antennas and then present a performance analysis of the system with respect to EE. Our analysis shows that while spectral efficiency increases with increasing number of BS antennas in a massive MIMO system, EE does not increase boundlessly when the increasing number of antennas are to be accommodated within a fixed physical space and the total power consumed is considered to be a function of the BS antennas. Accordingly, analytic expressions for the optimum number of antennas to attain maximum EE are obtained.