Pumps vs. agitators for tank mixing, classic case of CAPEX vs OPEX: white paper

By Gregory T. Benz, Benz Technology International, Inc.

Though most process tanks are agitated by means of a mechanical agitator, comprised of a rotating shaft and one or more impellers, occasionally process engineers will ask, Why can’t we just use a pump, instead of an expensive agitator? This paper attempts to answer that question by comparing capital and operating costs, as well as relative performance, of both systems, based on real-world installations. The reader is cautioned to use his own actual capital, installation and power cost figures, as they will not always match those used in this report.

Comparison basis

When comparing two fundamentally different kinds of equipment, the normal approach is to use a basis of equal process performance. For an agitated tank, that can be complex. Do we use equal flow, equal blend time, equal solids suspension, or some other criterion? While exploring the data for this paper, it became apparent that equal process performance is, for all practical purposes, impossible to attain with a pump, when compared to an agitator.

As an example, if the pump were required to produce as much flow as a typical agitator in a given service, it would require approximately 50-100 times as much power as the agitator, depending on the particulars of both the pump and the agitator design. This is because of the well-known relationship, power = flow*head. (Agitators produce orders of magnitude lower head, by virtue of not having to pump through a pipe.)

Similarly, to achieve equal blend time to that produced by an agitator, a pump would require about 100-150 times as much power.

Based on such huge differences in power required for equal process result, it would seem that pumps would never be used. However, they are used in spite of that. But, on close investigation, it appears that the level of process performance demanded of pumps, where they are used successfully, is much, much less than that typically demanded of agitators in similar service. So, for this paper, we will compare, not on the basis of equal process performance, but on the basis of an actual installation using a pump sized to deliver “acceptable” or “good enough” results, versus normal sizing for an agitator proven to give full motion and a clean tank bottom in similar service.

Application description

The application chosen for this comparison is a beverage ethanol fermenter in a distillery. The results would be equally applicable to fuel ethanol, or any application requiring modest agitation with either no solids or only slowly settling solids present (settling rate less than 2.5 mm/s). It should be noted that, during the early stages of fermentation, there is vigorous evolution of CO₂, which serves to provide considerable agitation. However, at the end of the batch, CO₂ evolution almost stops, so the pump or agitator must blend the tank and keep solids in suspension to the extent possible.

The tank size is 198” (5.03m) diameter, shallow bottom, with a working volume of 40,800 gallons (154 m³). Tank contents have an average specific gravity of 1.0

Pump Description

Installed on the above tank is a pump-around loop with two tangential nozzles. The pump produces a flow rate of 524 GPM (0.033 m³/s), and has a 15 Hp (11kW) motor. It is a simple centrifugal pump.

Agitator description

Though some agitators used in ethanol fermenters are sized below the level needed to produce complete suspension when CO₂ evolution stops, the hypothetical agitator used in this article is based on past experience as being the appropriate size to produce complete suspension throughout the batch cycle. It is based on a Scale of Agitation nominally equal to 3, calculated using the methods of reference 1.

The impeller is a 3-blade hydrofoil, 86” (2.18m) diameter, rotating at 30 rpm. The motor size is 3 Hp (2.2kW). Impeller flow is calculated by using the definition of pumping number, a dimensionless group used to characterize impeller pumping performance:

1) N_Q = Q/ND³

Using a pumping number of 0.5 (specific vendor impellers may have a slightly different value), we get a flow produced of 41300 gpm (2.61 m³/s):

2) Q = N_QND³ = 0.5*30*(86”/(12”/ft))^3 = 5521 ft³/min = 41300 gpm

Impeller power is calculated from the definition of power number, a dimensionless group used to correlate impeller power draw characteristics:

3) N_P = P/(ρN³D⁵)

Using a power number of 0.3 (specific vendor impellers may have a slightly different value), we get:

4) P = N_PρN³D⁵ = 0.3*(1000kg/m³)*(30rpm/60s/min)^3(86 in*0.0254m/in)^5 = 1865 watts = 2.5 Hp.

Process performance comparison

As previously stated, we are comparing on the basis of an actual pump system to a best practice hypothetical agitator system, not on the basis of equal performance, but on very different performance standards based on current industrial practice. Table 1 summarizes the two systems.

Table 1 Pump vs. Agitator Process Performance Comparison
	Pump	Agitator
Motor size, kW	11.2	2.2
Shaft speed, rpm	1450	30
Impeller size, in.	13	86
Flow produced, GPM	524	41300
Tank diameter, in.	198	198
Tank SS, in.	312	312
Working volume, gal.	40800	40800
Liquid level, in.	306	306
Scale of Agitation	N/A	3
Turnover time, min.	77.86	0.99
Turnovers/min.	0.013	1.012
99% blend time, min	234	1.8
Full tank motion?	No	Yes
Clean tank bottom?	No	Yes
Metabolic enhancement?	Unlikely	Likely

Some quantitative comparisons are readily evident. For example, although the pump requires 5 times as much motor power as the agitator, the agitator pumps almost 80 times as much, and blends13 times as fast.  Blend time for the agitator is calculated using a formula from a private communication, where

5) θ_b = 16.4/(N*(D/T)^1.7(Z/T)^0.5) = 16.4/(30*(86/198)^1.7*(306/198)^0.5 = 1.8 minutes.

Blend time for the pumped system is based on reference 2, which states that pump blend time is 3 times turnover time. This author believes that may be an overly optimistic estimate of pump-around loop tank blend time.

In addition to these quantitative comparisons, performance is likely different in other, less easily quantified ways. For example, we know that the agitator design described is the minimum required to keep a clean tank bottom. Actual field experience with corn-based ethanol fermenters reveals that less agitation will require periodic shoveling out of the tank bottom; less agitation would not be sufficient to keep the bottom clean. Though the pump design includes tangential nozzles to try to at least keep the bottom clean, we suspect there will be cases where periodic manual cleanout of the tank is required. The cost of such cleanout, including downtime, is not included in the cost comparison in the following section.

It is unlikely that the pump design will produce motion throughout the tank. It is unclear what effect stagnant areas will have on the process. The agitator design listed will provide complete motion of tank contents.

In a very interesting paper presented by Galindo et al. (3), it was found that higher levels of agitation in an alcohol fermenter could increase rate of production, yield and maximum titer. Though the agitation level proposed here is modest compared to some of Galindo’s conditions, it is still much higher than the pump produces. Thus, there may be a higher effective metabolic rate produced under mechanically agitated conditions than with the pump system. However, we lack actual field comparisons to verify this.

Life cycle cost comparison

Table 2 summarizes the total life cycle comparisons. Most assumptions are included in the table.

Table 2 Pump vs. Agitator Life Cycle Cost Comparison
	Pump	Agitator
Installed cost	25000	75000
Present Replacement Cost	22000	50000
Useful life, years	7	20
Interest rate used, annual fraction	0.1	0.1
Capitalized cost	48189.21	83729.81
Motor power, kW	11.2	2.2
Electricity Cost/kwh	0.07	0.07
Motor load, %	90	90
Hours/year	8000	8000
efficiency x power factor	0.8	0.8
annual power cost	7056	1386
Facility life used, years	20	20
Present worth of power cost	60071.71	11799.8
Annual maintenance cost	700	300
Present worth of maintenance costs	5959.495	2554.069
Total lifecycle cost*	114220.4	98083.68
* does not include process downtime

Capital and maintenance costs are based on reference 4, adjusted for currency and inflation, plus private communications from pump users. Electricity costs are based on reference 5. The reader should adjust these figures according to his own capital, maintenance and electricity costs. Interest rate and equipment life can also be adjusted. The reader is also encouraged to add the costs of downtime, which could be very significant. Such downtime differences could be caused by the more frequent repairs required of pumps, as well as possible downtime for tank cleanout.

Summary

Though a pump loop can be much lower in capital cost than an agitator for tank mixing, the user should include all power and maintenance costs in the overall decision analysis. Based on capital and operating costs alone, it appears that the mechanically agitated system, in most cases, will have a lower total lifecycle cost. When differences in process performance and downtime are factored in, it is unlikely that a pump system would look favorable compared to a mechanically agitated system. If compared on the basis of equal process performance, the total lifecycle costs for pump-agitated systems would be much higher, mainly due to exorbitantly higher power requirements.

Nomenclature

D Impeller diameter, in. or m, typical; N Shaft speed, rpm or rev/s; N_P Power number (dimensionless); N_Q Pumping number (dimensionless); Q Flow rate, volume/time, e.g. gpm or m³/s; T Tank diameter, e.g. in. or m; Z Liquid level, e.g., in. or m

Greek letters

Ρ Fluid density, e.g., Kg/m^3; θ_b Blend time, s or min, typical

References 

1) “How to design agitators for desired process response”, R. Hicks, J. Morton and J. Fenic, Chemical Engineering Magazine, April 26, 1976, pp 98-104

2) ABS, Inc. Drawing No. DS-M01-137   (blend time = 3*turnover time)

3) “Effect of Mechanical Agitation on Alcoholic Fermentation”, E. Galindo, M. Salvador and B. Romain, AIChE 1992 Annual Meeting, Nov. 2-6, 1992, Miami, FL

4) “Reducing Life-Cycle Costs of Centrifugal Pumps”, K.Ost, Technical paper 1-2, Pump Users International Forum, 10-12 October, 2000.

5) U.S. Energy Information Administration, Table 5.3. Average Retail Price of Electricity to Ultimate Customers: Total by End-Use Sector, 2003 – July 2013 (Cents per Kilowatt-hour)

About the author

Gregory T. Benz is President of Benz Technology International. Phone 937-289-4504; e-mail [email protected]; URL:  www.benz-tech.com. He received his BSChE from the University of Cincinnati in 1976, and has taken a course on Fermentation Biotechnology from The Center for Professional Advancement. A registered Professional Engineer in Ohio, he has over 37 years’ experience in the design of agitation systems. Currently his company does general mixing consultation, including pilot plant protocol, equipment specification and bid evaluation. Current activity includes several cellulosic ethanol, single-cell protein and biomass projects.