Business process management is especially challenging when crossing organisational boundaries. Inter-organisational business relationships are considered as a first-class citizen in BPMN collaboration diagrams, where multiple participants interact via messages. Nevertheless, proper carrying out of such interactions may be difficult due to BPMN lack of formal semantics. In particular, no formal studies have been specifically done to cope with complex BPMN interaction scenarios unified under the name of Service Interaction Patterns. In this work the depiction of the service interaction patterns in BPMN collaboration diagrams is revisited and fully formalised via a direct semantics for BPMN multi-instance collaborations, thus leaving no room for ambiguity and validating the BPMN semantics. To make the formalisation more accessible, a visualisation of the patterns execution by means of a BPMN model animation tool is provided.