Composite services are often long-running, loosely coupled, and cross-platform, so they bring additional complexity to the system in the presence of failures. Transaction is a basic concept in building reliable distributed system. However, Web transaction cannot be easily rolled back as conventional ACID transactions, so a main problem that remains is how to cancel a long-running Web transaction. This paper introduces a calculus based on pi-calculus, which deals with the faults of Web service composition in long-running business processes. The calculus is equipped with operational semantics to guarantee both appropriate installation and activation of compensation of Web Transaction.