Economics of Pumping Systems...

Introduction...

Every engineering frsicion must consider economics. An unprofitable venture must be guarded against to avoid the collapse of an engineering effort. It is important to consider both the capital outlay as well as the time value of money. A dollar borrowed for investment in a plant must be paid off in the future at the market value of the interest rate. Each subsystem in a plant, such as pumping arrangement, is subject to the same economic rules which apply to the entire project.

Economic Factors...

There are three major costs which have to be considered in an economic evaluation ; ( a ) direct, ( b ) indirect and ( c ) operating. Each of the basic costs is made up of items which are inherent in their meaning ; these may be summarized as follows ;

Direct costs ( material and labor ) :

- Pump, drive, and driver
- Freight
- Foundations
- Piping
- Controls

Indirect costs ( material and labor ) :

- Overhead
- Headquarters office ( Engineering, Design inspection, Estimating, Purchasing )
- Office work ( Supervision, Accounting, Field office )

Distributable cost items :

- Insurance
- Temporary construction
- Construction equipment
- Cleanup

Operating costs :

- Power : steam, electricity
- Lubrication
- Cooling water
- Maintenance

To the total direct and indirect costs must be added local taxes and an engineering fee. The total direct and indirect costs, including local taxes and the engineering fee, represent the capital outlay for the equipment or plant, whereas the total operating costs must be evaluated on the basis of the time value of money. In developing the economic factors covering the operating costs after determining the cost for each of the items listed under operating costs, it is necessary to establish the following factors ;

- Plant life expectancy ( n )
- Annual interest rate ( i )
- Annual fixed - charge rate ( AFC )
- Present - worth factor ( PWF )
- Capital - recovery factor ( CRF )
- Annual levelized cost ( ALC )
- Operating factor ( OF )

It is the annual levelized cost ( ALC ) which is required for addition to the total capital cost to determine the comparative investment value of alternate arrangements. For a determination of ALC we have ;

ALC = [ ( Present worth ) ( CRF ) ] / ( AFC )

where ;

Present worth = ( Hourly operating costs ) ( 8,760 ) ( OF ) ( PWF )

CRF = 1 / PWF

PWF = [ ( 1 + i ) n - 1 ] / [ ( i ) ( 1 + i ) n ]

To determine the values for PWF one may use logarithms, a desk calculator, or published tables, where listing are given for varying interest rates at differing periods. Plant life expectancy depends upon the industrial and the total investment for the facility. An electric power generating station may vary from 30 to 50 years for plant life, depending on its being fossil - or nuclear - fueled. A petrochemical plant may vary from 15 to 20 years plant life, depending on size of facility and competitive market of the produced product. The annual interest rate is dependent on the charge for borrowing money. Bank charge rates vary with available funds, size of loan, and period over which the payment is to be made. Each successful industry has developed its own profit rate after taxes to defray operating costs and satisfy its shareholders. The electric power generating industry is goverment - regulated as to its profitability ; therefore, the annual fixed charge rate AFC is set by regulation. Other industries, regulated by a competitive market, establish their profit margins by competition. The operating factor is dependent on a plant's design load and operating expectancy of the plant. These conditions are developed with the plant owner's cooperation so as to obtain realistic performance requirements.

Pump Availability...

Every manufacturer designs his equipment to operate over its full life span without difficulty or mechanical problems. In spite of the manufacturer's intent, there are small items such as seals, packing, bearings, etc. which may develop an unexpected problem while operating, thus causing an unscheduled shutdown. These shutdowns for repairs are fortunately short in duration but must be allowed for in the design of a plant. The tabulation in table given below is presented as an example for evaluating unscheduled centrifugal pump failures.

Type of failure Hours per outage Estimated failures per year Hours outage per year
Packing 4 4.0 16.0
Seals 16 1.0 16.0
Bearings 16 0.5 8.0
Unbalance 48 0.2 9.6
Total 49.6

From the tabulated estimated values, we deduce that centrifugal pumps may be expected to result in an availability of 99.3 percent. It is not enough to consider the pump alone ; its driver must also be included, and since most pumps are driven by electric motors, whose availability is as good as or better than the pumps , 99.3 percent may be taken as a value for the combined assembly.

Pump Operating Range...

Rating vs. Operation...

A pump is sized to include margins for capacity and head. Figure given below defines the pump margin as it affects the characteristics of a centrifugal pump. It is important to inform a pump supplier where the expected operation is to be so as to obtain its best efficiency within the operating range.



The energy capacity margin is added to ensure operability at the desgin value. The head margin results from the capacity margin to fit the system resistance. Other allowances for pump performance are left to the supplier because they are subject to manufacturing tolerances.

Power at Varying Loads...

Since a pump rarely, if ever, is called upon to operate at one condition during the life of a plant, it is necessary to define the expected operating range. Taking into account the power consumption and operating factor at different loads allows the determination of power consumption over the plant life. Curves similar to figure given above for a specific pump application are referred to for the determination of power consumption.

Multipump Selection...

The threat of an unscheduled shutdown with the resulting loss of productivity requires the consideration of equipment availability. By comparing the value of lost production with the additional cost of spare pump units or multiple pump selection, an economic basis is set to guide a desicion. A multipump selection cuts back the shutdown loss to a fraction of what it would be for a single unit. A full spare pump results in total protection but requires investment and maintenance without affecting production except in an emergency. For the determination of loss in production due to unscheduled shutdowns, we calculate the following for centrifugal pumps ;

Net annual loss = ( Net product value ) ( Annual production capacity ) ( 0.007 )

The factor 0.007 results from the pump availability of 99.3 percent. The net product value is the difference between the sale price of the product and the cost of production. The net annual loss may be totally or in part reduced by installing a spare pump, which would be placed into service during an unscheduled shutdown, or multiple parallel pumps, only one of which would be shutdown while the others remained in operation.

Pump Duty...

Petrochemical plant pumps may be expected to operate over a cycle similar to table given below.

% operating factor for % plant load
Operating years 100 50 0
1 - 2 90 8 2
3 - 12 95 3 2
13 - 14 90 8 2
15 - 16 80 10 10

A centrifugal pump service which will be evaluated over the operating cycle of table for the purpose of determining multiple pump service is presented as follows ;

* Service : Demethanizer reflux
* Plant elevation : Sea level
* Maximum discharge : 509 lb / in 2 abs
* Operating temperature : - 143 O F
* Vapor pressure : 450 lb / in 2 abs
* Sp gr : 0.30
* Available NPSH : 14 ft
* Driver : Electric motor ( 440 V, 3 - phase, 60 Hz )

The demethanizer pump duty is specified on figure given below, which includes the duties for two 50 percent capacity units and three 33 1/3 percent capacity units as well as the 100 percent capacity unit. The peak pump efficiency is required for the 100 percent capacity for each pump selection.



Pumps in an electric power generating plant may be expected to operate over a cycle similar to table given below.

% operating factor for % plant load
Operating years 100 75 50 0
1 - 5 60 0 30 10
6 - 10 55 0 30 15
11 - 15 40 5 32.5 22.5
16 - 20 25 10 35 30
21 - 25 10 15 37.5 37.5
26 - 35 0 0 20 80

A centrifugal pump service, which will be evaluated over the operating cycle of table given above for the purpose of determining economic piping size, is presented as follows ;

* Service : Boiler feed
* Plant elevation : Sea level
* Maximum discharge : 5,520 lb / in 2 abs
* Suction temperature : 323 O F
* Discharge temperature : 329 O F
* Sp gr : 0.905
* Available NPSH : 115 ft
* Driver : Steam turbine ( inlet 172 lb / in 2 abs and 677 O F, exhaust 2 1/2 in Hg )

Economic Evaluation...

Multipump Selection...

The service conditions and operating cycle stated for a demethanizer relux pump will be used to evaluate multipump selection. The direct and indirect costs for each pump arrangement are summarized in table shown below.

Direct and indirect costs
( $ )		 ( 1 )
100 % capacity		 ( 2 )
100 % capacity		 ( 3 )
50 % capacity		 ( 4 )
33 1/3 % capacity
Pump 4,900 9,800 9,100 10,200
Piping 20,210 25,920 24,870 27,910
Total 25,110 35,720 33,970 38,110

The data for evaluating operating costs are as follows ;

* Plant life : n = 16 yr
* Annual interest rate : i = 8 %
* Profit rate after taxes : AFC = 11.9 %
* Charge for electric power : 7.8 cent / kWh
* Charge for lubrication : 70 cent / gal
* Charge for cooling water : 7.5 cent / 1,000 gal
* Charge for maintenance : 1.50 $ / hp - year

To evaluate loss in production resulting from unscheduled pump shutdowns, it is necessary to determine a value for the losses ;

* Annual production = ( 60 ) ( 10 6 lb / yr )
* Unit sale price = 76.3 cent / lb
* Unit production cost =18.1 cent / lb
* Net unit loss = 58.2 cent / lb

Net annual loss = ( 0.582 ) ( 60 ) ( 10 6 ) ( 0.007 ) = 244,000 $

The sum of evaluated pump cost and annual loss for each pump arrangement yields a total cost for comparision to determine the lowest sum as the economic choice. For needed calculations, it is convenient to determine the product of operating factor ( OF ) and present - worth factor ( PWF ) over the life of the plant. Table given below summarizes the calculations for each plant load.



Table given below summarizes the required power for each selected pump arrangement for the demethanizer pump service.





Lubricating oil consumption is based on 0.02 gal / 100 hp - hr for each pair of bearings. A motor driven centrifugal pump results in 0.04 gal / 100 hp - hr total. Hence, gal / hr = 0.04 bhp / 100. Cooling water requirements are based on 10 O F temperature rise and 2 percent energy loss to the water for each pair of bearings. Because the demethanizer serviceis at - 143 O F it will not be necessary to furnish cooling water for the pumps ; it will, however, be necessary to furnish cooling water for the motor bearings. Therefore, gpm = bhp / 100. The annual operating costs associated with each pump arrangement in demethanizer service are developed from the following ;

* Power = ( 0.078 ) ( kWh ) ( 8,760 )
* Lubricating oil = ( 0.7 ) ( 0.04 ) ( bhp per 100 ) ( 8,760 )
* Cooling water = ( 0.075 ) ( per 1,000 ) ( bhp per 100 ) ( 60 ) ( 8,760 )
* Maintenance = ( 1.50 ) ( bhp )

From the data listed in table just given above, combined with the cost values listed above, table shown below summarizes the total annual operating costs.



From the total annual operating costs listed in table given just abovei we determine the annual levelized costs ( ALC ) as follows ;

ALC = [ ( Total operating cost ) ( OF ) ( PWF ) ( CRF ) ] / ( AFC )

where the product ( OF ) ( PWF ) ( CRF ) has been determined in table given above for 100 and 50 percent of plant load. Table shown below summarizes all the costs associated with the alternate demethanizer pump arrangements.



Note that the annual loss which was calculated to be $ 244,000 is listed as zero for two 100 percent capacity units because one of the units is a spare to be placed in operation during an unscheduled shutdown. For the multiple parallel units, it is considered that only one of the pumps may be shutdown during an unscheduled mishap ; therefore, the loss is proportionately less. Thus it may be seen that most economic pump arrangement ( the lowest comparative sum ), is two 100 percent capacity units.

Optimum Piping Size...

The service conditions and operating cycle stated for a boiler feed pump will be used to evaluate optimum piping size. Only changes in discharge piping will be considered for study because the suction piping is subject to NPSH restrictions and, therefore, not subject to economic considerations. Table given below summarizes the direct and indirect costs associated with the boiler feed pump service.



The data for evaluating operating costs are as follows ;

* Plant life : n = 35 yr
* Annual interest rate : i = 7 %
* Annual fixed - charge rate, AFC = 13 %
* Charge for steam : 80 cent / 1,000
* Charge for lubrication : 70 cent / gal
* Charge for cooling water : 7.5 cent / 1,000 gal
* Charge for maintenance : 1.50 $ / hp - year

Since an electric generating system is made up of multiple units which permit minor unscheduled shutdowns, it is not generally necessary to consider the availability of a centrifugal pump requiring more than a one 100 percent capacity unit. For needed calculations, it is convenient to determine the product of operating factor ( OF ) and present worth factor ( PWF ) over the life time of the plant. Tablo given below summarizes the calculations for each plant load.



Table given below summarizes the steam consumption for the varying discharge piping size and the differing capacity of the boiler feed pump. From steam tables or an H - S diagram ;





Lubricating oil consumption, based on 0.02 gal / 100 hp - hr for each pair of bearings, results in 0.04 gal / 100 hp - hr for a steam - turbine - driven centrifugal pump. Hence ;

gal / hr = ( 0.04 ) ( bhp / 100 )

Cooling water, based on 10 O F temperature rise and 2 percent energy loss to the water for each pair of bearings, results in ;

gpm = ( bhp ) / ( 50 )

The annual operating costs associated with the boiler feed pump and the alternate piping size are developed from the following ;

* Steam = ( 0.80 ) ( 1,000 lb per hr ) ( 8,760 )
* Lubricating oil = ( 0.7 ) ( 0.04 ) ( bhp per 100 ) ( 8,760 )
* Cooling water = ( 0.075 ) ( per 1,000 ) ( bhp per 50 ) ( 60 ) ( 8,760 )
* Maintenance = ( 1.50 ) ( bhp )

From the data listed in table just given above, combined with the cost values listed above, table shown below summarizes the total operating costs.



From the total annual operating costs listed in table just given above, we determine the annual levelized costs as follows ;

ALC = [ ( Total operating cost ) ( OF ) ( PWF ) ( CRF ) ] / ( AFC )

where the product ( OF ) ( PWF ) ( CRF ) has been determined in table given above for 100, 75, and 50 percent load. Table shown below summarizes all the costs associated with the alternate piping sizes for the boiler feed pump.



From a plot of the total evaluated costs shown on figure given below, one can see that the minimum piping size is 10 in. This conclusion may have been reached from the tabulated data in table just given above, but it is cautioned that it is not safe to reach a desicion until a plot is made.