Design of a Water Transmission Pipeline with an Analytical Probabilistic Model

A challenge that utilities face is to design new water transmission systems with incomplete information concerning future water demand. With an increase in water demand caused by population and economic growth, a design chosen today may deliver inadequate operating pressures to meet higher-than-expected demands in the future. This paper presents an analytical probabilistic model that evaluates the expected level and uncertainty of pressure head at the end of a design period (e.g., $20\mathrm{year}$ ) linked to pipe-diameter decisions in a new water transmission pipeline subject to uncertainty in water demand. The model is developed by deriving a cumulative distribution function (CDF) of pressure head from a probability density function of peak demand. The CDF of pressure head is used to compute measures of central tendency and variability in pressure head and is validated with Monte Carlo simulation (MCS). The model is applied to the design of a new transmission pipeline with pipe break and pump outage scenarios. The results indicate that increasing pipe diameter increases median pressure head, decreases standard deviation, and lowers uncertainty associated with pressure head predictions. Pressure head percentiles generated with the analytical probabilistic model closely match those generated with MCS.