The attached worksheet (in PDF form) determines the optimum design for a gas transmission pipeline. There were four independent variables to optimize, all discrete. The worksheet describes the problem in more detail. In this note, I want to explain some of the methodology used.
The netback price is the price that a transmission company (or the pipeline division of an integrated company) can afford to "buy" the gas from the supplier. The price differential between the market price at the outlet and the netback price will cover all investment, operating costs and return on investment needed to deliver the gas to a customer at the market price. In an integrated energy company, the exploration and production division would look at this netback price and decide if they could make a profit producing the gas from a discovery.
Reverse order to netback at supply end
The calculations start at the "market" or outlet end of the pipeline and work toward the source, or supply end. Both the value of gas and the amount of gas change along the line due to consumption for fuel and for the investment costs between source and market. With the market price and amount of gas given, it is convenient to start the calculations at the market end of the line.
I chose functions as opposed to nested arrays for the variables. I only used three of the variables in the functions, leaving the number of booster stations as a separate variable set at the start of a calculation...I don't remember why. The value of the booster function variable can be changed interactively, giving a quick answer for the global optimum.
Compressor complexity included
Economics for compressors are somewhat complicated. There are break point pressure and pressure ratio levels where costs change. There are maximum pressure constraints. There is a maximum horsepower constraint for the turbines. These are all included in the model. A process simulation package may only provide simple, generic economics for compressors without the detail included in this model.
Some approximations used
I used approximations for the compressibility factor. The program may be improved if an equation of state were used. If this program were to be used frequently, further automation of the determination of the compressibility factor would be advised. In the example, the compressibility factor was not greatly affected by the changing conditions.
Please note the disclaimer and the warning about the economic data in the worksheet. It is being provided as an example of Mathcad applicability for chemical engineering problems, NOT as a proven design program.
The input data (design requirements) were changed from the original application to make the example non-proprietary.
How to obtain the Mathcad worksheet
I have not attached the Mathcad worksheet due to the current lack of copyright protection on this site. If you would like the worksheet for your personal, non-commercial use, please send a private message to me via this planetPTC site. I will reply with a download link to the file.