In opportunistic networks data dissemination is an important, although not widely explored, topic. Since opportunistic networks topologies are very challenged and unstable, data-centric approaches are an interesting direction to pursue. Data should be proactively and cooperatively disseminated from sources towards possibly interested receivers, as sources and receivers might not be aware of each other, and never get in touch directly. In this paper we consider a utility-based cooperative data dissemination system in which the utility of data is defined based on the social relationships between users. Specifically, we study the performance of this system through an analytical model. Our model allows us to completely characterise the data dissemination process, as it describes both its stationary and transient regimes. After validating the model, we study the system's behaviour with respect to key parameters such as the definition of the data utility function, the initial data allocation on nodes, the number of users in the system, and the data popularity.