15.066 Pump System Design MEMORANDUM To: Professor Graves From: Team 3 - Tammy Greenlaw, Chris Caballero, Aaron Raphel, Minja Penttila, Cliff Smith Date: August, 2003 Re: 15.066 - System Optimization Pump System Design: Optimizing Total Cost over System Life Cycle Executive Summary Traditionally, pump and pipe systems are designed by beginning with a given pipe design (diameter and physical layout). The pump is then selected for the pipe layout by considering the operating costs for the pump and the capital costs of the pipe. Additionally, the pumps are often designed by engineering consultants who oversize the pumps for the system to guarantee that pump is not undersized. Unfortunately, this causes poor efficiencies and, consequently, higher operating costs. We believe that an improved methodology includes: 1. Selecting the pipe design concurrently with the pump design 2. Including the capital costs of the pumps in the life cycle cost analysis during the system design The utility of this methodology was demonstrated by using a linear, integer optimization model to select optimal combinations of pipe systems and pump systems. The optimization model was then extended to assess the impact of various energy rate structures and potential (pending) tax implementations on carbon emissions. These analyses did show how certain “price-break” structures give incentives to build less-efficient pump and pipe systems. Background The total energy in a pumping system moving water from Point A to Point B in a full pipe at a constant flowrate (Q) can be calculated at any point in the pipe using the Bernoulli equation. PA + VA2/2g + ZA = PB + VB2/2g + ZB + Hf where: PX = Pressure VX = Velocity g = Gravitational constant ZX = ElevationHf = Energy lost as heat due to friction If you consider only conditions at Points A and B, one can assume that the velocity at Point A (pump) and the velocity at Point B (exit) is zero, and assume that pressure at Point B is zero (atmospheric pressure), the equation simplifies to: PA = Hf + ∆Z PA is the pressure that the pump must add to move water from Point A to Point B at flow Q. PA is usually expressed in feet (similar to inches of mercury) and referred to as System Head (H) or Total 115.066 Pump System Design Dynamic Head (TDH). ∆Z is the change is elevation from Point A to Point B. Where ∆Z is positive, water is pumped to a higher elevation and energy is stored as potential energy. Where ∆Z is negative, PA is reduced or water flows by gravity. Hf is also expressed in feet and often referred to as Frictional Loss or Headloss due to friction. Hf is the amount of energy lost as heat due to the friction of water moving along pipe walls or fittings. In industrial pumping, most pumping energy is actually spent overcoming frictional losses (Hawken, et. al, p. 115). Appendix X shows the frictional loss and elevation change calculations used to generate System Head values for each pipe diameter at flow Q. Frictional losses are calculated along straight pipe and through fittings as follows: Fittings: Hf = kV2/2g (See Appendix B1 for further details) Pipe: Hf = fLV2 / 2gD Fluid flow in full pipes can be expressed as: Q = VA where: Q = Flowrate V = Velocity A = Cross-sectional area of pipe Therefore, at a constant flowrate (Q), velocity (V) can be reduced by increasing the pipe diameter. Since frictional energy losses along straight pipe and through fittings are directly proportional to V2, increasing pipe diameter significantly reduces frictional losses. Project Summary We have created a linear, integer model to aid in the concurrent selection of a pump size and a pipe diameter. The model optimizes the pumping system design by selecting two components, pump size and pipe diameter, based on their impact on the system life cycle costs. Binary decision variables include four pump options and four pipe diameter options; the program is structured to pick one pump and one pipe option to minimize the life cycle costs (Z) as follows: Minimize Z = Cj + Ci + n x Comwhere: Cj = Capital costs to purchase and install pump, Ci = Capital costs to purchase and install pipe, fittings, and valves), Com = Operating costs due to pump energy consumed over assumed life cycle, n = Life cycle in years Preliminary engineering calculations provided performance and capital cost parameters for each piping configuration option and pump size option. Performance parameters including pump efficiency (ηp), motor efficiency (ηm), and system head are used to calculate the annual energy consumption for any combinations of pump and pipe diameter. Capital cost estimates for each pump option and each pipe option are utilized directly as part of the objective function. The main engineering assumptions made to calculate energy consumption and capital costs for each combination of pump and pipe options are: • Flow (Q) is constant at 750 gallons per minute (gpm) • The pump is centrifugal with On/Off controls • Total pipe length is 400 linear feet + fittings and valves • Pipe is Schedule 40 steel with grooved connections • Point B is 40 feet higher (elevation) than Point A 215.066 Pump System Design • The pump is running continuously (95% service factor) • Life Cycle = 20 years Four energy cost structure options are modeled to convert energy consumption (kwh) to annual operating costs. Table 1 shows the Option 1 rate structure that decreases in a step-wise fashion with increasing energy use. This option represents a simplified public utility rate structure that provides volume discounts. The unit cost function is not continuous, i.e. if a customer purchases a volume of energy that puts them in the higher consumption bracket, they pay the lower unit cost for their total energy consumption. Table 2 shows the resulting Total Cost function for Option 1. Option 1 Energy Rate Structure$0.04$0.06$0.08$0.10$0.12$0.14$0.160 500000 1000000 1500000 2000000Annual Energy Use (kwh)U nit C ost ($ /kwh) Option 1 - Price Breaks from Electric Company0200004000060000800001000001200001400001600000 500000 1000000 1500000 2000000 2500000KW H0 to 500k KWH500k to 1M KWH1M K W H + Table 1: Option 1 Unit Energy Costs Table 2: Option 1 Total Energy Cost Function Table 3 shows the Option 2 rate structure that increases in a step-wise fashion. This option represents an industrial