Convolutional Neural Networks (CNNs) are currently one of the most widely used predictive models in machine learning. Recent studies have demonstrated that hardware faults induced by radiation fields, including cosmic rays, may significantly impact the CNN inference leading to wrong predictions. Therefore, ensuring the reliability of CNNs is crucial, especially for safety-critical systems. In the literature, several works propose reliability assessments of CNNs mainly based on statistically injected faults. This work presents a software emulator capable of injecting real faults retrieved from radiation tests. Specifically, from the device characterisation of a DRAM memory, we extracted event rates and fault models. The software emulator can reproduce their incidence and access their effect on CNN applications with a reliability assessment precision close to the physical one. Radiation-based physical injections and emulator-based injections are performed on three CNNs (LeNet-5) exploiting different data representations. Their outcomes are compared, and the software results evidence that the emulator is able to reproduce the faulty behaviours observed during the radiation tests for the targeted CNNs. This approach leads to a more concise use of radiation experiments since the extracted fault models can be reused to explore different scenarios (e.g., impact on a different application).