Optimal design of piping systems for district heating

First, a method for determining the optimal size for a single pipe segment in a district heating system is developed. The method is general enough to allow for any set of economic or physical parameter values. In addition, any form of load management, i.e., temperature or flow modulation, or both, can be accommodated by the integral form of the coefficients in the cost equation. An example is presented that shows a 17% savings in life cycle costs over a design based on a common rule of thumb. Next the heat consumer and his effects on the piping system are studied. A new model is developed for the consumer's heat exchanger that uses the geometric mean temperature difference as an approximation for the logarithmic mean temperature difference. The new consumer model is integrated into the previous single pipe model and, for a sample case, its effect is determined. For systems having multiple pipes and consumers, the constraints are first developed and then the general solution strategy. The method makes use of the solution to the unconstrained problem as a starting point for the constrained solution. Monotonicity analysis is then used to prove activity of some of the constraints, and thus simplify the problem. Finally, the branch-and-bound technique is shown to be suitable for finding a design with discrete values for all the pipe diameters. A simple example is provided. In addition, a method is also demonstrated for further refinement of the pipe network to eliminate excessive throttling losses in the consumer's control valves. The method developed here should be feasible for designing the piping networks for district heating systems of moderate size, and its major advantage is its flexibility. (MM)