We present a simulation tool for transient events in complex hydraulic networks. The code includes modelling of the transport of suspended cuttings in near-vertical wells. An unstructured finite volume formulation with implicit time integration has been chosen. The unconditional stability of the integrator makes the method suitable for the simulation of transient events over a wide range of characteristic time scales. It handles both very fast transients (e.g. fluid hammer events) as well as the long-term evolution of the well (e.g. hole cleaning operations). The software has been developed to address the need of the oil industry for a robust and efficient predictive tool allowing effective well control in managed pressure drilling operations. The physical modelling follows the standard practices accepted by the industry (e.g. mud rheology computations). The mathematical foundation of the algorithm is described followed by validation cases that illustrate its capabilities and accuracy. Finally, a practical industrial application example is provided to demonstrate the real-world performance of the software.