Transient Analysis with Time-Decoupled Pumping Station

An explicit numerical approximation of the inertial equation governing pump speed changes is shown to have many computational advantages over the conventional implicit approach when modeling complex pumping stations. The pump boundary condition is numerically decoupled from the transient time step by solving the first-order differential torque equation explicitly. A step-by-step finite difference method is used to integrate the torque equation, but the energy equation is solved separately by Newton's method. The explicit approach is demonstrated on a simple forcemain and shows good agreement with the conventional implicit approach. Applications show the ease with which complex and variable speed pumping arrangements are efficiently modeled using the explicit approach. In particular, the explicit approach does not require: (1) contraction of the system of equations as a decelerating pump is eliminated upon pump check valve closure; (2) expansion of the system of equations as an accelerating pump comes up to speed; or (3) dedicated code for combinations of operating, failing, or speed-changing pumps.