In this paper we propose a novel model for the uplink in heterogeneous cellular networks. Opposed to previous works, we accurately account for the mutual interference caused by other users' connections, and we pose an optimization problem that can be straightforwardly solved to establish the minimum required transmission power that satisfies the minimum Signal-to-Interferenceplus-Noise Ratio (SINR) constraint. We assess the validity of the proposed approach by comparing the observed results with those obtained with a traditional closed-loop power control scheme. The main benefit of our solution is that it does not require any iteration to find the transmission power, while legacy approaches usually need a number of steps before finding it. Finally, we study the behavior of the uplink for different access selection strategies, and we compare the SINR and transmission power of open-loop and closed-loop power control solutions.