We utilize a time-dependent drift-diffusion model incorporating electron trapping and field-dependent charge separation to explore the device physics of organic bulk-heterojunction solar cells based on blends of poly(3-hexylthiophene) (P3HT) with a red polyfluorene copolymer. The model is used to reproduce experimental photocurrent transients measured in response to a step-function excitation of light of varied intensity. The experimental photocurrent transients are characterized by (i) a fast rise of order 1 μ s followed by (ii) a slow rise of order 10–100 μ s that evolves into a transient peak at high intensity, (iii) a fast decay component after turn-off and (iv) a long-lived tail with magnitude that does not scale linearly with light intensity or steady-state photocurrent. The fast rise and decay components are explained by the transport of mobile carriers while the slow rise and decay components are explained by slower electron trapping and detrapping processes. The transient photocurrent peak at high intensities with subsequent decay to the steady-state value is explained by trap-mediated space-charge effects. The build-up of trapped electrons in the device produces reduction in the strength of the electric field near the transparent anode that increases the likelihood of bimolecular recombination, and lowers the overall efficiency of charge dissociation in the device. Notably the model demonstrates that a reduction in free charge generation rate by space-charge effects is as significant as bimolecular recombination in this device assuming Langevin-type bimolecular recombination. The model is also used to explore the dynamics of charge separation with an upper bound of 50 ns set for the lifetime of electron-hole pairs, and to provide an estimate of the trap density of 1.3×10²² m ^-3 .