COST/CAPACITY RELATIONSHIPS from first principles: Part 2

In Part 1 of this feature (page 16, March 1998), we found that E the exponent in the cost scale-up relationship defined by equation (1) can be related to the base case costs of individual items of equipment and Q, the ratio of throughputs for two different sizes of the same plant.

{{Equation (7) derived last month is:

E = Swmnm/Swm (7)m m}}

where w is a weighting factor, assumed constant for each main plant item m, and equal to the ratio of the cost of that item to the cost of a standard item (eg, a specific pump) sized for the same representative throughtput. Typical values of nm and wm are listed here in Table 1.

Thus, if the cost of main plant items (MPIs) has been evaluated for a new process at a given throughput and a single estimate completed by factors equations (1) and (6) show how capital cost varies with capacity. If, on the other hand, a predesign estimate which does not require or provide individual MPI costs has been carried out, equations (1) and (7) indicate the plant's cost-capacity variation. Table 2 gives a simple example of the use of this quite powerful technique for the latter case.

The illustration yields an exponent (E) of 0.64+/-0.02, which is in the range we would have expected. Thus, a quick and easy calculation gives a reasonably accurate scale-up relation for this, or any other, proposed plant.

{{TABLE 1: Main plant item capacity exponents and relative base costs

Equipment description Capacity exponent Relative base nm cost, wm

Blowers and fans 0.68 9.5Boilers, packaged unit 0.7 60Boilers (industrial), 15psig 0.5 92Boilers (industrial), 150psig 0.5 101.2Boilers (industrial), 300psig 0.5 115Boilers (industrial), 600psig 0.5 138Column with trays 0.73 33.5Column with packing 0.65 35.2Compressor, air, 125psig 0.28 36.5Compressor, process gas, 1000psig 0.82 85Cooling tower facilities 0.6 9.9Crushers, cone 0.85 12Crushers, gyratory 1.2 3Crushers, jaw 1.2 4.7Crushers, pulverisers 0.35 23.4Crystallisers, growth 0.65 385Crystallisers, forced circulation 0.55 276.5Crystallisers, batch 0.7 32.5Dryers, drum 0.45 30Dryers, pan 0.38 12.5Dryers, rotary vacuum 0.45 43.4Evaporators, forced circulation 0.7 270Evaporators, vertical tube 0.53 37.2Evaporators, horizontal tube 0.53 30.4Evaporators, jacketted vessel 0.6 32Filters, plate and frame 0.58 4.3Filters, pressure leaf (wet) 0.58 5.3Filters, pressure leaf (dry) 0.53 15.1Filters, rotary drum 0.63 17.5Filters, rotary disc 0.78 31Furnace, process 0.85 135Heat exchangers, cooler 0.66 6.8Heat exchangers, kettle reboiler 0.65 8.8Heat exchangers, shell and tube 0.65 6.5Heat exchangers, U-tube 0.65 5.5Heater, direct fired 0.85 103.5Hoppers, conical 0.68 0.1Hoppers, silos 0.9 0.4Mills, ball 0.65 4.4Mills, roller 0.65 40Mills, hammer 0.85 8Pumps, centrifugal/motor 0.52 1.5Pumps, centrifugal/turbine 0.52 1.5Pumps, reciprocating/motor 0.7 6Pumps, reciprocating/steam 0.7 1.1Pressure vessels, vertical 0.65 7.6Pressure vessels, horizontal 0.6 5Tanks, horizontal pressure storage 0.65 4.8Tanks, spherical pressure storage 0.7 8Tanks, storage 0.3 6}}

{{Table 2: Calculation of cost/capacity function at predesign

Main plant item No of items Capacity Relative Product Product m m exponent base cost mwm mwmnm nm wmTray column 1 0.73 33.5 33.5 24.46Packed column 1 0.65 35.2 35.2 22.88Heat exchangers 4 0.65 6.5 26.0 16.90(shell and tube)Kettle reboilers 2 0.65 8.8 17.6 11.44Heat exchanger 1 0.66 6.8 6.8 4.49(cooler)Centrifugal pumps 6 0.52 1.5 9.0 4.68Storage tanks 4 0.30 6.0 24.0 7.20

Swmnm 97.17Swm 152.1

E = 97.17/152.1 = 0.64 and C1 = C2Q0.64 (where C1 is known capitalcost, C2 unknown cost, Q ratio of throughputs)}}