The most efficient optimization algorithms are gradient-based search methods.9, 10, 11, 12 These methods evaluate the complex interaction of design parameters and identify the combinations of parameters that yield the lowest cost. If the system is small enough, genetic algorithm methods can be used. The use of genetic algorithm methods in conjunction with gradient-based methods is advantageous in some cases. A comparison of these methods for piping system design is given by a company's user's guide.13
The "sweet spot"
Every piping system with at least one pump has a "sweet spot" ," the optimal tradeoff in pipe, pump and, optionally, energy and maintenance costs. This also is referred to as the optimal pumping system operating point, or OPSOP.14
If a system's pump is sized away from the system's sweet spot, the system will cost more than is necessary to meet the design requirements. And once the piping system is specified and installed, most opportunities for cost reductions are lost forever.
Therefore, it is important for the engineer to find the sweet spot before committing to hardware. Unfortunately, conventional design methods cannot do this. However, a piping system optimization design tool can accomplish this feat.
Putting the tool to the test
A typical cooling system is shown in Fig. 2. In this case, the design requirement is to supply 15,000 gallons per minute (gpm) to each condenser and 700 gpm to each lube oil cooler. When all combinations of potential pipe sizes are considered, the size of the search space grows exponentially.
For example, the system shown in Fig. 2 has more than 40 quadrillion design possibilities. Obviously, it is not practical for even an experienced designer to look at even a fraction of these possibilities.
Using steel pipe with standard costs and cost data for pumps, the piping system optimizer can identify the sweet spot from among all the potential designs. Fig. 3 shows the costs for optimal designs with different pump head rise and power usage values for a 10-year life-cycle design.
Although the piping system optimizer can find the sweet spot in a single run, the graph helps show the impact of different pump selections. Keep in mind that Fig. 3 shows only optimized designs, representing the lowest-possible cost systems that meet the design requirements. Traditional methods do not find such optimums; therefore, they will cost significantly more.
For the cooling system shown here, the design requirement is to supply 15,000 gpm to each condenser and 700 gpm to each lube oil cooler.
The cost data can be nonrecurring or recurring (e.g., energy use over time), allowing optimization to be performed for first or life-cycle cost. Table 2 shows a cost comparison of optimization runs in which the goal was to minimize first cost and 10-year life-cycle cost of the cooling system. It can be seen that an optimal life-cycle design would save $2 million over 10 years, but would require an initial design that costs $400,000 more.
First or life-cycle cost?
The decision on whether to optimize for minimum first cost or life-cycle cost can be difficult, and is frequently driven by other business considerations. However, a piping system optimization tool can make this decision easier.
Once a case has been set up to minimize the first cost, the additional effort to optimize for life-cycle cost is minimal. With results in hand for low first-cost designs and low life-cycle cost designs of different design lifetimes, decision-makers will have more information with which to make the best choice.
Designing for multiple scenarios
Another powerful capability of a piping system optimizer is the ability to intelligently size the system for multiple design cases. These cases could be, for example, normal and standby operation, different load requirements between summer and winter, and multiple pump-duty points. Multiple design case requirements are included as additional design constraints, and the optimum design is found to satisfy all design cases for the lowest cost.
Adding margin to designs
One occasional negative comment about piping system optimization is that it removes margin from the design and thus leaves no room for growth in the installed system. This is a misconception.
When using traditional design methods, margin comes from one of two sources. The first is an intentional margin that is included in the design requirements. The second is an unintentional margin that is a byproduct of the imperfect design methods in common use.
Unintentional margin is not quantifiable and is randomly spread around the system. One part of the system might have a 5 percent margin (and possibly even a negative margin) while another part has a 40 percent margin.
By using piping system optimization engineers can reduce the unintentional margin to zero; therefore, all margin is intentional. With optimization, the design margin can be assigned as desired around the system.
With a piping system optimizer, the engineer also can ask questions that previously went unasked. For example, if the engineer wanted to design with a 30 percent margin, the impact on first cost and life-cycle cost could be quantified and compared to designs of 0 percent, 10 percent and 20 percent margins. With this information in hand, the plant might decide that a 30 percent margin is too expensive, and opt for a different margin.
A final thought
It is important to note that new engineering design tools rarely, if ever, can replace engineers. Instead, engineers use the new tools to produce higher-quality designs within budget and time constraints.
Piping system optimization is simply a tool that helps engineers do their jobs better than they could before. It frees up some of the time spent on the manual aspects of piping-system design, allowing engineers to focus on creative alternatives to company problems.
In the author's opinion, computer software will never replace the human engineer. It just makes the engineer better equipped ," and more necessary than ever.
Walters is president and director of software development at Applied Flow Technology Corp., Woodland Park, Colo. He can be reached at firstname.lastname@example.org.
1. Hodgson, J. and T. Walters. "Optimizing Pumping Systems to Reduce First or Life-Cycle Cost," Proceedings of the 19th International Pump Users Symposium, Houston, February 2002.
2. Applied Flow Technology. AFT Mercury 5.0 User's Guide, Woodland Park, Colo., 2001.
3. Schmit, L. A. "Structural Design by Systematic Synthesis," Proceedings of the 2nd Conference on Electronic Computation, American Society of Civil Engineers, New York, 1960, pp. 105,"122.
4. Vanderplaats, G. N. "Structural Design Optimization ," Status and Direction," AIAA Journal Aircraft, 1999, Vol. 13, No. 1, pp. 11,"20.
5. Frenning, L, et al. Pump Life Cycle Costs: A Guide to LCC Analysis for Pumping Systems, Hydraulic Institute and Europump, Parsippany, N.J., 2001.
6. Hovstadius, G. "The Real Price of Pumping," Pumps and Systems, Randall Publishing, January 2002, pp. 6,"7.
7. Hodgson, J. and T. Walters, February 2002.
8. Applied Flow Technology, 2001.
9. Hodgson, J. and T. Walters, February 2002.
10. Applied Flow Technology, 2001.
11. Vanderplaats, G. N., 1999.
12. Vanderplaats, G. N. Numerical Optimization Techniques for Engineering Design, 3rd Ed., Vanderplaats Research & Development Inc., Colorado Springs, Colo., 1999.
13. Applied Flow Technology, 2001.
14. Hodgson, J. and T. Walters, February 2002.