The quantum well solar cell (QWSC) has been proposed as a route to higher efficiency than that attainable by homojunction devices. Previous studies have established that carriers escape the quantum wells with high efficiency in forward bias and contribute to the photocurrent. Progress in resolving the efficiency limits of these cells has been dogged by the lack of a theoretical model reproducing both the enhanced carrier gen- eration and enhanced recombination due to the quantum wells. Here we present a model which calculates the incremental generation and recombination due to the QWs and is verified by modelling the experimental light and dark current-voltage characteristics of a range of III-V quantum well structures. We find that predicted dark currents are significantly greater than experiment if we use lifetimes derived from homostructure devices. Successful simulation of light and dark currents can be obtained only by introducing a parameter which represents a reduction in the quasi-Fermi level separation.