The majority of (business) processes described in literature are discrete, i.e., they result in an identifiable and distinct outcome such as a settled customer claim or a produced part. However, there also exists a plethora of processes in process and control engineering that are continuous, i.e., processes that require real-time control systems with constant inlet and outlet flows as well as temporally stable conditions. Examples comprise chemical synthesis and combustion processes. Despite their prevalence and relevance a standard method for modeling continuous processes with BPMN is missing. Hence, the paper provides BPMN modeling extensions for continuous processes enabling an exact definition of the parameters and loop conditions as well as a mapping to executable processes. The BPMN modeling extensions are evaluated based on selected use cases from process and control engineering and interviews with experts from three groups, i.e., process engineers and two groups of process modelers, one with experience in industrial processes and one without. The results from the expert interviews are intended to identify (i) the key characteristics for the representation of continuous processes, (ii) how experts evaluate the current usability and comprehensibility of BPMN for continuous processes, and (iii) potential improvements can be identified regarding the introduced BPMN modeling extensions.