Using natural variables to reduce algorithmic complexity of some hydraulic calculations

Hydraulic calculations play an important role in a variety of engineering software in many areas, including oil and gas production. Increasing the efficiency of their numerical implementations is important for solving practical inverse problems of recovering unknown parameters of many processes. The purpose of this work is to reduce the algorithmic the complexity of calculating the time-varying pressure drop of slurry on its way through the tubing, given the slurry and the tubing parameters. Hydrostatic pressure and frictional pressure loss are being calculated as functions of specific friction pressure losses, tubing geometry and slurry pumping schedule. The correct choice of variables, introduced in this paper, allows to reduce the algorithmic complexity of the friction pressure loss to linear while hydrostatic pressure to linear-logarithmic complexity on the input data dimensions.