Clinical trials constitute large, complex, and resource intensive activities for pharmaceutical companies. Accurate prediction of patient enrollment would represent a major step forward in optimizing clinical trials. Currently models for patient enrollment that are both accurate and fast are not available. We present a discrete event model of the patient enrollment process that is accurate and uses relatively small CPU times. This model is now being used on a regular basis to predict the enrollment of patients for large trials with around 13,000 patients and has led to significant reduction in the time it takes to make these predictions.