AGITATION IN BENCH SCALE EXPERIMENTATION
I
ROBERT L. BATES Chemineer, Inc., Dayton, Ohio
As early as 1500 A.D., Leonard0 da Vinci argued, "Vitruvius says that small models are not confirmed in any operation by the effect of large ones. As to this, I propose.. .that his conclusion is false." Fortunatel da Vinci proved his point and our tecknology has progressed to the stage where it now makes good use of model work to predict plant-scale performance
4 Dynamometer for experimental agitator provides power data with non-Newtonian fluids and gasliquid applicairions
AGITATION
is probably the most abused unit operation when processes are miniaturized for bench scale studies. Certainly it is one of the least-understood unit operations, and straightforward relationships are seldom applicable. At the same time the role of agitation in small scale work and its significance in plans for scale-up cannot be underestimated. Development of a casual acquaintance with this subject will pay dividends in every system where an agitator is employed as a tool. Worth pointing out, too, is that the
bench model may be the only step intermediate to a full-scale plant. Pilot plants are becoming quite expensive, and there is an increasing tendency to by-pass them. Approach to a Study The realization that the essential justification of bench scale work is to provide data for extrapolation dictates the need for careful advance planning, and the importance of long range thought before any work is done cannot be over emphasized. Before designing a laboratory
setup, the full scale process should be evaluated in as much detail as possible and with particular attention to two categories.
Careful Choice of Components
Will Save Time and Money The time spent in collecting and orienting the components of a bench scale system can be completely recouped during the actual experimental work if the system is well arranged. If the reVOL. 51, NO. 10
*
OCTOBER 1959
1245
quired characteristics of the various components are not realized, it is probable that a good deal of useless data will result. Some thought and a few capital dollars invested here will minimize frustration and man-hours in the actual experimentation. T h e physical requirements of the system can be divided into five areas : Drive. Today small variable speed drives abound, but only a few have all of the desirable features. The essential requirements are : wide speed range; power characteristic of at least constant torque quality; good speed regulation under varying load; availability with an explosion proof motor; and compactness and ease in mounting. Impellers. I t is here that much bench scale work goes awry-with the nonchalant use of some piece of twisted metal or glass which has no resemblance to the impeller to be used in the prototype. Do use conventional impeller forms with the geometry of the larger commercially available ones. In propellers the common style is three-blade, left-hand, with a pitch equal to the diameter. Turbines should have more than two blades, preferably six, of the flat, pitched, or curved blade style. Ratio of blade width to diameter should follow standard practice. Paddles, a last
resort. will be two-bladed, flat, or pitched. Vessel. Some of the design features of the vessel will be stipulated by the process-pressure rating or material of construction. The agitator, though, depends on dimensional and shape features. Unless the prototype dictates otherlvise, try to work with a ratio of liquid depth to tank diameter in the range of 1 to 1 to 1.25 to 1. This allows the economy of a single impeller. Where a flow pattern is difficult to establish or maintain, or in solids suspension operations, the shape of the tank bottom should be conducive to streamlining flow. A fairly universal answer here is a standard dished bottom. Flow Pattern Control. T o maintain control of both dynamic and kinematic relationships, it is absolutely essential to do the bench scale work with a method of controlling swirl. Use baffles with turbine impellers. With propellers, use baffles or a n off-center and angled shaft entrance. The impeller location should be equivalent to that anticipated in the prototype. Power Measurement. Obtaining power data may not be necessary if the fluid has a loiv viscosity and is Newtonian. But, if not or if a gas phase exists, pobver should be recorded. If
Use This Chart in Selecting Impeller Type The first step i n assaying a mixing problem is to make a tentative selection of impeller type, based on the full-scale working volume. It is possible to adjust any mixer element, whether propeller, turbine, or paddle to satisfy any service. However, high horsepower, higher cost, or a loss of performance will result from incorrect selection of the impeller. Happily, the selection of the proper impeller for the great majority of applications is based on two specifications-fluid viscosity and batch volume. This chart shows the interrelationship of these two variables as they affect agitator type. The chart is purely a guide for preliminary selection, and the limitsfor each type can be shifted by other variables and considerable overlapping of ranges can occur. Generally, any style will amply handle the requirements of the ranges below it. Obviously, use of a type occurring above that required will yield a more expensive design because of its lower shaft speed. However, selection of impeller cannot ignore the process requirement. For blending, the selection can be made on the basis of economics, which leads to an impeller with a high flow characteristic and, i n turn, generally means a propeller. Most applications other than blending or easy solids suspension with batch sizes above 1000 gallons will require an impeller with an appreciable head or shear characteristic-which is usually satisfied by a turbine impeller. I n this category would be heat transfer, mass transfer, and heavy solids suspension.
b Impeller selection chart shows interrelationship of fluid viscosity and batch volume as they affect agitator type
1 246
INDUSTRIAL AND ENGINEERING CHEMISTRY
possible, avoid any electrical methodoperation may be below the “no-load” current rating of the motor and also losses in transmission components in the system may be included. To obtain shaft horsepower data the best l o ~ - c o smethod t is to use a d) namometer arr anqement on either the drive or the vessel. A typical bench scale system is shown on page 1245. Note that the drive here is free to rotate and the torque is registered on a platform scale.
Experimental Techniques Peculiar to agitation studies, there are many well established miscellaneous “ground rules.’‘ Utilizing them will save needless digression. .4 few of these generalizations are as follo\vs : Fluid Properties. The various other properties of a fluid can, in the interest of brevity, be ignored here to emphasize the importance of defining the apparent viscosity. The frequency with which non-Newtonian liquids are encountered requires examination of the fluid for pseudoplasticity, thixotropy, or dilatancy in advance of any actual runs. T h e easiest way to evaluate the viscosityshear characteristic is by use of a rotational viscometer. A log-log plot of viscosity 2s. some shear index such as
BENCH SCALE EXPERIMEWTATIOW
Set Values for Linear Dimensions of the Laboratory Set-Up Vessel geometry. Because geometric similitude is the basis for most scale-up, the linear dimensions of the laboratory setup must be stipulated. If no physical design exists in the plant then these values must be set and the data made a part of the final analysis. There are three areas of geometry. For the vessel, diameter, liquid level, and type of bottom must be known. With the impeller, diameter, number of blades, blade width, and location in the vessel are needed. The presence and description of accessories such as baffles and coils should be indicated.
m 0
b
0
Geometry of the laboratory setup must be determined Cc. Coil clearance cd. Coil diameter C,. Coli spacing D. Impeller diameter H. Impeller location
spindle tip speed will result in a straight ine. The extent to which the slope deviates from zero is the indicator of the degree of non-Newtonianism. SingIe us. Dual Impellers. While it often makes little difference in performance, the choice of a single or dual impeller system does affect the economics of an installation. With normal batch geometry, as discussed earlier, a single propeller or turbine will almost always suffice. The desirability of a single impeller where liquid level is very low or where aeration is deleterious is obvious. Multiple impellers will be demanded in deep tanks or by very viscous or very non-Newtonian fluids. Impeller Location. The location of the impeller, in a vertical sense, is sometimes dictated by the minimum batch to be handled. Otherwise, there are some general rules to follow. Propellers should be far enough off the tank bottom to prevent dampening of the axial discharge-one propeller diameter is an absolute minimum. Turbines are frequently located improperly because of a misconception of flow producing character. The induced flow to the “eye” of the turbine is essentially equal on top and bottom, and it is not necessary to locate the impeller near the tank bottom just to control that area. Even on severe suspension jobs it is seldom necessary to locate the impeller any closer than one diameter from the average bottom. Turbine Diameter. The selection of
ALW 17-
liquid level T. l a n k diameter Tb. Baffle width The. Baffle clearance W. Blade width 1.
,diameter is on the basis of tank diameter and viscosity. Most frequently used is a D I T of 1/3 (which is optimum for a viscosity of 1500 cp.). Ratios range from 0.2 to 0.6 for the viscosity range of 200 to 90,000 cp.
Use These Ground Rules
Fluid Properties: apparent viscosity is the most important Impellers: single with normal batch geometry, dual with very deep tanks or viscous liquids Impeller location: one propeller diameter from the bottom is the minimum Turbine diameter: determine from tank diameter and viscosity Turbine speed: 600 to 800 feet per minute tip speed Propeller speed: 1750 to 420 r.p.m. range Flow controlled applications: if log-log plot of blend time US. NDs has -1 slope, then problem is flow-controlled r unit volume: use this as Power an in ex of conditions required to give a constant process result Dimensionless groups: use these to reveal the effect of a number of variables
B”
Turbine Speeds. Operating speed for a turbine should be selected, initially, to give a tip speed in the range of 600 to 800 feet per minute. Higher or lower values may be required but only in the unusual application. Propeller Speeds. For reasons of commercial convention, experimental work should be in the speed range of 1750 to 420 r.p.m. If the problem is pure blending, lower speed and a larger propeller will yield the most gallons per minute per unit horsepower. For example, at constant power, the circulating capacity of a 420 r.p.m. system is about three times that of a 1750 r.p.m. design.
Scale-up Methods An initial difficulty arises from the lack of a basic “yardstick” to gage results, but the problem can be resolved by admitting that agitation is the one unit operation which is just a tool to enhance the performance of another unit operation. Thus, the index used to stipulate performance in a particular process can be the one measured and held constant in scale-up. I t may be a direct result, such as blend time or over-all heat transfer coefficient, or an indirect parameter, such as pH or iodine number. Scale-up based on some constant dimensionless group is meaningless, but the process result which is to be held constant may be, for convenience, a part of a dimensionless group. VOL. 51, NO. 10
OCTOBER 1959
1247
Flow Controlled Applications. These are the blending problems in which time is the best index of performance. Then, circulation rate is scaled-up to maintain a constant number of tank turnovers per unit time. Used mainly with propellers, this method requires only the knowledge of their pumping characteristics, which is generally available. If it is desired to establish definitely that a particular problem is flow controlled, this is done by a plot of blend time us. n’O3 on log-log paper. A slope of - 1 confirms this category of problem. Power per Unit Volume. Horsepower per unit volume as an index of the conditions required to give a constant process result is one of the most useful methods available. I t serves \vel1 for the broad range of applications where a reasonable ratio of f l o ~ v and shear is demanded in the system. I t does require geometric similarity in scale-up and, because not all applications are constant horsepower,’volume, necessitates experimental runs in t\ro or more batch sizes. A log-log plot (Figure 1) is then used to relate the two variables, horsepower per unit volume being the ordinate and batch size the abcissa. The extent to which this plot may be extrapolated is a function of the accuracy of the slope, which is dependent upon the incrernent of batch volume it is possible to obtain. Naturally, too, confidence in extrapolation decreases as the slope departs from zero (constant horsepower ’volume). I n Figure 1, curves B and B’ are typical deviations. Curves C and C’ would be considered in wide variation from constant horsepower, volume and would indicate a process demanding more detailed study. Dimensionless Groups. For the systems where the balance of flo~vand turbulence in the regime is critical, and this includes most mass transfer and many heat transfer problems, a method must be used which will reveal the effect of a number of variables. Dimensionless groups are very useful here, and the procedure is as follows: Include the rate coefficient in a dimensionless group. Correlate with another dimensionless group which describes the motions and forces involved. From the slope of the curve obtain the exponent of the second dimensionless group. Solve for the effect on the process result in terms of some convenient parameter such as poirer. I n Figure 2> 2 is the conventional dimensionless form for mass transfer where k is the rate coefficient, D a linear dimension, and B the diffusivity. Equation 1 then shows the general form of the correlation, using Reynolds number as the motion coefficient.
1248
10
5
tn 2 Q c3
I
0 0 0 -
.5
I
.2
\ a
.I
.O6
0 BATCH SIZE (GALS.) Figure 1.
Power per unit volume for equal process result
Confident extrapolation depends c n accuracy of the slope
B,B’. Typical deviations C,C’. Indicates need for more detailed process study
“D R
c
( P 3 ) “
(1)
Assuming that temperature is constant, viscosity. density, and diffusivity terms drop out, leaving
k NaD2a-I (2) I n scale-up, it \rould be assumed that the mass transfer rate is to be held constant. hfanipulations to the relationship in Ayr= DrPa-1) - a (3) Equation 3 hvould follow, which gives the behavior of diameter with respect to speed. r indicating the ratio of the quantities. Equation 4 is a \veil-
established fact for operation in a baffled Pr = AVr?.;-3Dr5
(4)
turbulent regime, and Equation 5 simply states that the I’r
= Dr3
(5)
batch volume varies as the cube of a linear dimension. Combining, pr =
L;(5-6a)/3a
(6)
Equation 6 states the effect on the p o w c ~ ratio as the process is scaled-up to larger batches. If the slope, a, is 0.75 then scale-up is on a constant horsepower,/unit volume basis. Pr = Vr, a = 0.75
(7)
larger a gives a lower ( P / V ) ?in scalrup, and thus all variations in environment and method of power investment will be made irith the goal of a n increased slope.
2
/ P N D~ LOG /u
Figure 2.
Rate coefficient correlation
If a = 0.75, scale-up is on a constant horsepower/unit volume basis
INDUSTRIAL AND ENGINEERING CHEMilSTRY
References (1) Clark, E. L., Chem. Eng. 6 5 , 119-24 (June 2, 1958). (21 Ibid.,129-40 (Oct. 6, 1958). ( 3 ) Johnstone, R. E., Thring, M. W.,
‘.Pilot Plants, Models and Scale-up Methods in Chemical Engineering,” SlcGraw-Hill, New York, 1957. (4) Jordan, D. G., “Chemical Pilot Plant Practice,” Interscience, New York, 1955. (5) Rushton, J. H., Chem. Eng. Progr. 47, 485-8 (1951).
RECEIVED for review May 4, 1959 ACCEPTED August 5, 1959
