In the paper, we propose a model to guarantee the privacy of patient data in critical processes in the healthcare sector through the application of process mining. Process mining is a discipline that discovers process models by analyzing event logs in order to identify bottlenecks and establish alternatives to improve their performance. In healthcare institutions, process mining is used to improve critical processes. However, event data logs containing confidential healthcare patient data are not protected when process mining and data visualization are applied. This definitely increases the risk of theft of this sensitive data and, therefore, the risk of patients being affected. The proposed model aims to mask event logs containing sensitive data so that they are inaccessible when process mining is applied. The model comprises four main stages: 1. target definition and data transformation; 2. data masking; 3. inspection and pattern analysis; 4. application of process mining techniques and data visualization. The model was validated using data from an appointment request process of a state health organization in Lima, Peru. Preliminary results showed that complete event logs containing sensitive data were protected, flow compliance increased by 68% and average processing time increased by 89.4%.