36Case Study 1: Economic Optimization of a Pipe System
36.1 Process and Analysis
Figure 36.1 illustrates a fluid transport example. Fluid starts in a tank on the left and is pumped through a long pipe to a receiver on the right. The question is “What is the right pipe diameter?” Here the pipe diameter is the single decision variable (DV), and we will use net present value (NPV) as the objective function (OF).
Figure 36.1 Process illustration. Determine the optimum pipe diameter.
The smaller the pipe diameter, the lower the cost of the pipe. Also it lowers the cost of the product inventory to fill the pipe. Both are good. However, too small D makes the pressure drop () large, requiring an excessively sized pump and drive (high capital), also with excessive energy expense to operate (annual cash flow). By contrast, a larger D leads to less expensive pump and reduced energy expense; however, it increases both pipe cost and the investment in in‐process inventory. Basically, energy expense is proportional to power consumption, and capital cost is proportional to capacity to the six‐tenths power.
As a helpful artifice, I like qualitatively sketching the mechanisms to be modeled. Figure 36.2 reveals the impact of the decision variable, diameter, on the key economic factors.
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) large, requiring an excessively sized pump and drive (high capital), also with excessive energy expense to operate (annual cash flow). By contrast, a larger D leads to less expensive pump and reduced energy expense; however, it increases both pipe cost and the investment in in‐process inventory. Basically, energy expense is proportional to power consumption, and capital cost is proportional to capacity to the six‐tenths power.