CHE 415 - Agitation Final Report 2007

Experiment #7, Agitation Section #1, Group #5 Experiment #7, Agitation Section #1, Group #5 Experiment #7, Agitation Section #1, Group #5 Experiment #7, Agitation Section #1, Group #5 Experiment #7, Agitation Section #1, Group #5 Ryerson University Department of Chemical Engineering CHE 415 Unit Operations II Lab Report Experiment #7: Agitation Experiment Performed on September 25th, 2007 Report Submitted to Dr. Ginette Turcotte / Kiran Shah 1. /Leader By Group # 5 Section # 1 2. /Inspector 3. /Data Reporter October 2nd, 2007 Date Report Submitted Marking Scheme Formatting Answered all 6 questions in each Report Section / 10 General Appearance; Grammar and Spelling / 5 Complete and Informative Tables and Graphs / 15 Contents Accuracy and Precision of Results / 20 Comparison with Literature Data / 10 Discussion on Influence of Procedural Design on Results / 10 Logic of Argumentation / 20 Sample Calculations / 10 _____ Total: / 100 Abstract The purpose of this experiment was to investigate the effect of power on various impeller shapes and sizes in an agitation unit. Also, to investigate the analytical relationship between power and the factors of diameter and number of revolutions, and to determine the scale-up requirements for a 5000L tank of similar geometry to that used within the experimental. This was achieved by measuring the torque experienced by multiple impellers with various revolutions per minute (R.P.M.) and correlating it to the power consumed. The impellers used were a flat-blade, slanted-blade and curved-blade, each at three diameters, 2.5”, 3.0” and 4.0”. It was determined that the blade type should be accounted for in the power number equation. Also, the amount of power required was largest for the flat-blade and the least for the curved-blade. Lastly, the power required for scale up to a 5000L tank, of similar geometric configuration to that used in the experiment, utilizing a flat-blade impeller was found to be 16HP. In conclusion, the experiment was successful at demonstrating the effects of various shapes and sizes of impeller qualitatively. Table of Contents 22 55 55 1010 1111 1111 1212 1313 1515 1717 1717 17 List of Figures 55 66 99 99 2020 2121 21 List of Tables 1212 1313 1313 1414 1515 1818 1919 19 Objectives and Experimental Design The objectives of this experiment were to investigate the effect of impeller shape and size on the power required to achieve successful agitation of a fluid in a tank. An analytical relationship between the power and the factors of diameter and number of revolutions were also investigated. The final objective of the experiment was to determine the power requirement for a scaled-up equipment, a mixing vessel with a capacity for 5000L, with the same geometric configuration as the equipment used in the laboratory. In this experiment, impellers of various shapes and sizes (flat-blade, slanted-blade and curved-blade at 2.5”, 3” and 4” diameters each) were used to agitate a vessel filled with water. The torque experienced on each impeller was measured at various R.P.M. Introduction and Theoretical Background The process whereby two or more substances enter into a compartment where they blend together is termed mixing. The type of compartments typically utilized include: hoppers, tanks, extruder barrels and pipes. Further, the method used to blend the substances together is called agitation and is typically accomplished with the use of a rotary arm powered by a motor. The level of mixing, agitation speed, and elapsed time depend on the type of substances being mixed. For effective mixing to take place for liquids, it is essential that multiple flow patterns be created in the fluid. Three components in the fluid flow are: radial flow, axial flow, and angular flow. The first two types of flow are central to effective mixing whereas angular flow is unwanted because of little mixing actually occurring, even thought the fluid is traveling around the agitator. Furthermore, liquid flow can be defined as either laminar or turbulent. In laminar flow, layers of fluid particles slide past each other and the flow is considered predictable. In turbulent flow, on the other hand, the flow is random making it more effective for mixing but can waste energy if utilized in excess. Figure 1: Liquid Mixing Tank [3] There are many different types of impellers currently used in industry today. The shape of the impeller affects the types of fluid flow that can be achieved. For flat-blade impellers, there is a large resistance to the fluid as the impeller rotates within it. This results in a system that consumes more power. In comparison, pitch-blade impellers or slanted-blade are similar to the flat-blade type except that each blade is at an angle, usually 45º from the shaft, and experience less resistance to the fluid flow. This, in turn, would require less power from the motor to agitate the same fluid. Impeller size is a design parameter to consider in an agitator system. If the impeller is too large in diameter, power may be wasted in rotating it through the fluid. On the other hand, if the diameter is too small, there may be turbulence around the impeller itself as it rotates, but near the edges of the mixing vessel there may be little disturbance in the flow, resulting in inefficient mixing. In this experiment, both the shape and the size of the impeller are investigated for their effect on the power required to achieve sufficient agitation of a fluid. Baffles are obstacles placed into the vessel to aid mixing. If there are no baffles, there is a tendency for the fluid to flow in a vortex. Very little shear is achieved in a vortex, and there is, therefore, inefficient mixing. In a typical mixing vessel, four baffles are usually employed. The flow patterns are shown in figure 2 below. Figure 2: Flow Pattern with Baffles [3] Mixing and fluid flow properties are also affected by the nature of the liquid [2]. The properties of interest include: fluid viscosity, temperature, pressure, and density. These properties can be related through the Reynolds Impeller Number, Reimp, defined in equation (1). (1) Where N = revolutions of impeller per second (s-1) D = Diameter of the impeller (m) ? = Density of the fluid medium (kg/m3) µ = Viscosity of the fluid medium (kg/m.s) The Reynolds Impeller Number also defines the type of fluid flow being experienced in the mixing vessel [5]. The ranges are as follows: Reimp<10 is laminar flow, Reimp>104 is turbulent flow. Between these values, there is transitional flow, where the fluid can be observed to experience turbulence at the impeller, but laminar flow at other regions in the vessel. In the design of a liquid agitator, the power requirement of the turbine motor, P, is an important variable to consider. The type and size of motor chosen would depend greatly on this information [1]. The power required cannot usually be determined theoretically, and therefore, empirical correlations are usually relied upon. For the system being used in this experiment, the following correlation is to be used: (2) In equation (2), the term “scale reading” is analogous to the torque experienced by the impeller. The units of this correlation are horsepower. Also, RPM is defined as the revolutions per minute. The power consumption of the impeller can be related to a variety of parameters of the system, such as fluid density, by the use of the plots of the power number, Np, versus Reynolds Impeller number [5]. The power number is another dimensionless number, and is defined as in equation (3). (3) Where Np = Power number (dimensionless) P = Power supplied (J/s or W) D = Diameter of the impeller (m) N = revolution of impeller per second (s-1) ? = density of fluid (kg/m3) Scale-up from laboratory-scale to an industrial scale is a very important process. These operations are mostly dependant on similarity [4]. There are three main sectors to consider similarity between systems; geometric, kinematic and dynamic. If the shape of the equipment is kept the same, but the sizes of the equipment have been enlarged, i.e. scaled up, the systems are considered geometrically similar. Kinematic similarity can only be achieved if there is geometric similarity, and the ratios of the velocities between certain points of the system are kept constant. Further, dynamic similarity can only be achieved, if there is both geometric and kinematic similarity between the systems, and the ratios of forces at specified points of the systems are kept the same [6]. In order to successfully scale-up the equipment, the first step is usually to calculate a scale-up ratio, R [5]. The original mixing vessel for this experiment is a cylinder, with DT1=H1. The subscript 1 indicates the original vessel, while 2 indicates the scaled-up vessel. The volume of the original tank can be calculated as follows: (4) The ratio of the volumes can then be calculated by: (5) From this relationship, the scale-up ratio can be defined as: (6) The second step involves the scaling of each of the parameters, such as the impeller diameter. This is done by simply multiply the parameter by the ratio. The third step requires the agitator speed to be scaled. This can be done using equation (7). (7) The parameter n in the above equation is dependant on the type of mixing desired. For example, n=1 for equal fluid motion, while n= ¾ for equal suspension of solids. Equal fluid motion occurs when agitation is desired for only a fluid, while suspension of solids is used only when solids are being mixed into a liquid, but the solids are not soluble in the liquid, and equal dispersion is desired. The final step would be to determine the power number, which can be determined using equation (1) to find the Reynolds Impeller Number, and then using figure 3 below to find the corresponding power number. Equation 3 can be rearranged to calculate the power required to be supplied by the motor. Figure 3: Reimp vs. P0 [5, page 145] Experimental Set-up Figure 4: Schematic diagram of agitation unit Experimental Procedure The mixing vessel was filled with ordinary tap water, assumed to be around 20ºC, to a level equal to the diameter of the tank. That is, because the diameter of the tank was 11”, the vessel was filled up to 11” of water. A flat-blade impeller of 2.5” diameter was securely attached to the shaft, using Allan keys to tighten the hold. The shaft was then inserted into position and again Allan keys were used to tighten the connection securely. The power to the motor was then activated. At each R.P.M, the system was allowed to equilibrate itself. A digital tachometer was then employed to measure the actual R.P.M. experienced. The torque meter was next attached to the housing, which freely rotates. Subsequently, the torque readings were recorded off the gauge. The “dial” was used to increase the R.P.M. of the rotating shaft/impeller component. The procedure was repeated for flat-blade, slanted-blade and curved-blade with diameters of 2.5”, 3.0” and 4.0”. Safety and Environmental Concerns during the Experiment: The impellers used in this experiment had typically sharp edges and attention was taken when handling them. The shaft was also handled with care because any scratches and dents on the shaft would affect the results obtained. In this experiment, an electrically powered motor was in close proximity to a large tank of water. Laboratory occupants were aware of the danger of electrocution if for any reason there was contact between the motor and the water. The motor rotated the impellers at high speeds, and care was taken to ensure that no loose objects, such as long hair or lab coats, were close to the shaft or impeller while rotating. These objects were unwanted to avoid them catching on the shaft and being wound around it, pulling the individual or other objects attached to it towards the rotating impeller. The impellers were also fastened tightly to the shaft to avoid them being released from the rotating shaft and causing damage to either the vessel or any individuals in close proximity. Also, when reading the tachometer, caution was used when taking the reading, as the laser can damage the occupant’s eyes. Safety and Environmental Concerns in Industrial Applications: There are many industrial applications in agitation, ranging from wastewater treatment plants to the food industry. In wastewater, flocculation aids in the removal of phosphate and the elimination of BOD (biochemical oxygen demand) by a flocculants (flocculating agent) [6]. The agents attach to the unwanted chemicals forming colloids, where later on filtration removes the chemicals [6]. Agitation machinery is used in flocculation to ensure that the agents are attaching to all the unwanted chemicals. Typically, it is divided into four parallel zones each with an A- impeller [6]. In the food industry, agitation machines are widely used to blend all necessary components together in the same consistency. For example, the process of manufacturing chocolate milk involves combining vitamin A and D, chocolate syrup, artificial flavouring, colour, glucose solids, and other additives to the pasteurized and homogenized milk [7]. Results and Discussion While keeping the number of revolutions per minute constant and varying the diameter of the blade, the power required increased with diameter size for each of the blade types, as seen in Table 1. As the blade diameter increased, regardless of the blade type, there was a larger surface area in contact with the water in the tank. Therefore, there was a larger amount of power required to achieve successful agitation of the fluid. Further, the power required was greatest for the flat-blade and the least for the curved-blade. The power requirement for the flat-blade is greatest due to the shape of the blade. The flat-blade sits at 90° to the shaft and therefore creates the greatest amount of friction in the fluid as it rotates, and this needs to be overcome to achieve successful agitation. For the curved-blade, the power input required is the least, as seen in Table 1. This can be explained by the fact that the curved-blade does not lie horizontally in the water but wraps around the shaft similar to a propeller. Therefore, it creates less resistance to fluid flow that is required to be overcome, by an increase in the amount of power applied, to achieve successful agitation to the fluid. The slanted-blade is the middle ground between the flat and curved-blades in terms of power requirement. This may be because even through its blades are flat in nature, they lie at 45º from the shaft. HP Type of blade Diameter (in) 200 RPM 400 RPM 600 RPM flat 2.50 0.0001 0.0015 0.0035 flat 3.00 0.0007 0.0027 0.0050 flat 4.00 0.0030 0.0080 0.0284 slant 2.50 0.0005 0.0017 0.0030 slant 3.00 0.0005 0.0021 0.0055 slant 4.00 0.0015 0.0071 0.0217 curve 2.50 0.0005 0.0012 0.0020 curve 3.00 0.0005 0.0013 0.0026 curve 4.00 0.0007 0.0026 0.0059 Table 1: Power Required for various blades with various diameters The analytical relationship for the power used in the motor is P = Np?NaDb (equation 3), where a is three and b is 5. Therefore, P is directly proportional to the number of revolutions to the third power for a constant diameter of the impeller. Also, P is directly proportional to the diameter to the fifth power for a constant number of revolutions, R.M.P. Figure 5 (in the appendix) shows the relationship of log P vs. log N. This established the values of a (from the general power equation) for a specific impeller blade type and a specified diameter as summarized in Table 2. Similarly, the value of b (from the general power equation) for a specific impeller blade type and a specified RPM from figure 6 is summarized in Table 3. Flat Blade Slanted Blade Curved Blade Average 2.5” 2.38 1.66 1.53 1.86 3.0” 1.75 1.90 1.65 1.77 4.0” 2.63 2.57 2.04 2.41 Average 2.25 2.04 1.74 Table 2: The value of “a” for each type of blade and its corresponding diameter Flat Blade Slanted Blade Curved Blade Average 200rpm 7.04 2.47 0.76 3.42 400rpm 3.58 3.15 1.71 2.81 600rpm 4.60 4.26 2.35 3.74 Average 5.07 3.29 1.61 Table 3: The value of “b” for each type of blade and a set value of RPM The flat blade 4.0” diameter impeller at 600rpm has the closest value to the theoretical power coefficients. Therefore, it should be used when scaling up as it contains the least amount of error. According to the power equation, the type of blade should not affect the value the power coefficients. However, this was not the case as the value of “a” were different. From table 2, the average values of “a” in the power equation was 2.25, 2.04 and 1.74 for flat, slanted, and curved blade respectively. The average “a” values should be approximately the same. Also, from table 3, the average value of “b” was 5.07, 3.29, and 1.61 for a flat, slanted, and curved blade for specific revolution per minute readings. Because of the differences observed, the type of blade should be accounted for in the general power number equation. The variations could be due to friction experienced as the blade rotates within the water. For example, the slanted had less friction, which resulted in a more turbulent flow, and the curved blade had even higher Reynold’s numbers, indicating even more turbulence. From the three types of blade used, the flat blade had the closest “a” and “b” value. The slanted and curved blade did not have values that resembled the power coefficients. Therefore, the flat blade should be used when studying the power equation. Scale-Up As discussed before, it was desired to scale-up the mixing vessel to accommodate for 5000L capacity. The experimental mixing vessel had a volume of 17.1L. This resulted in a scale-up factor of 6.63 using equation (6). The 4” flat-blade impeller at 600 R.P.M. was used for the scale-up because it yielded the closest to the exponent terms of the power number correlation. The experimental impeller, the diameter of the scale-up impeller to be used would be 0.674m. For a 600 R.P.M. experimental rotational speed, the speed required for the larger vessel, using equation (7) was estimated to be 90.5 R.P.M. The power required to be supplied to the impeller to achieve this speed was then estimated to be 16HP, using figure 3 and described in the sample calculations. As mentioned in the introduction, scale-up can be performed on an experiment using a variety of similarities. This scale-up was performed using the geometric similarity. When sizing power requirements, this may not be the only similarity to depend upon. Dynamic similarity is also important for power sizing as it accounts for all the forces of the system [6]. There are four major forces that must be considered; the input force from the mixer, viscosity, gravity and surface tension. It is the input force, or inertia force that is being investigated. For dynamic similarity, instead of using the dimensionless Reynolds Impeller Number, another dimension number, the Weber number, should be used. (8) where all the parameters are defined as before, but ? is the surface tension of the fluid. Error Analysis Tables 4 and 5 below displays the errors experienced with the measurements taken during this experiment. Flat Blade Slanted Blade Curved Blade Average 2.5” 20.7% 44.7% 49% 38.1% 3.0” 41.7% 36.7% 45% 41.1% 4.0” 12.3% 14.3% 32% 19.5% Average 24.9% 31.9% 42% Table 4: Percent error of the value of “a” for each type of blade and its corresponding diameter Flat Blade Slanted Blade Curved Blade Average 200rpm 40.8% 50.6% 98.5% 63.3% 400rpm 28.4% 37% 65.8% 43.7% 600rpm 8% 14.8% 53% 25.3% Average 25.7% 34.1% 72.4% Table 5: Percent error of the value of “b” for each type of blade and a set value of RPM During the experiment the torque meter readings were difficult to read due to their fluctuation. As the speed was increased, the fluctuations of the readings also increased. This introduced error into the experimental power calculation and therefore into all results calculated thereafter. Also, the RPM readings taken with the tachometer were inconsistent. If multiple readings were consecutively taken for the same speed the value read for the RPM would fluctuate by approximately 30-50 RPM. This too introduced discrepancies into the experimental power calculation and therefore into all calculations and plots thereafter that utilized the experimental power. Typically, in industry, the impellers are kept approximately one time the impeller diameter above the tank bottom [5]. This was not done throughout the experiment due to limitations in shaft length; the shaft was not long enough. This introduced error in the scale-up calculations as the equations for scale-up assume that the industry standard is used. Further, the lines of best fit that were drawn in all the plots produced brought inaccuracy into all results obtained from the plots. This is due to the plots not creating perfectly straight lines without the aid of creating lines of best fit. Dents that where present in the shaft and impellers during the experiment introduced inaccuracies in the recorded torque meter and tachometer values. The values obtained with the dents present vary from those that would have been recorded if there were no dents due to the dents creating slight changed in fluid flow. Conclusion In conclusion, this experiment was successful at demonstrating the effect of impeller size and shape on the power required to achieve agitation. However, it failed to resemble the general power equation for constant diameter and constant R.P.M for the three types of impellers used. The flat-blade was closest at resembling the general power equation, while the slanted-blade and curved-blade did not resemble. Therefore, this experiment could not properly correlate the power number for the slanted-blade and curved-blade. The power required for a scale up of 5000L for a flat-blade tank of the geometric configurations as this experiment was found to be 16HP. Recommendations One recommendation would be to change the screws on the impellers with newer and less rusted ones. This is to make the equipment safer to operate. Even when using the Allan keys, it was difficult to obtain a tight enough hold to the shaft as the heads of the screws used to hold it in place was worn down and difficult to turn. The impeller sometimes fell off the shaft while the motor was on. Another recommendation would be to change the spring that is attached to the torque meter. The current spring is old and has been stretched past its elastic limit, and there were many kinks. This created errors in the measurements of the torque obtained. With a new spring, the measurements validity would be improved. References: [1]. Turcotte, G. CHE415 - Unit Operations II Lab Manual – Exp 7 – Agitation, Ryerson University, Fall 2007 [2]. Rensselaer Polytechnic Institute, Dimensionless numbers, retrieved on September 21, 2007, from _http://www.rpi.edu/dept/chem-eng/Biotech-Environ/AERATION/dimnum.htm_ [3]. Rockwell Automation, Publication D-7747, Agitation and Mixing Processes, March 2007, retrieved on September 21, 2007, from _http://www.reliance.com/prodserv/standriv/appnotes/d7747.pdf_ [4]. Holland, F.A., Chapman, F.S. Liquid Mixing and Processing in Stirred Tanks. Reinhold Publishing Corporation, 1966. [5]. Geankoplis, C.J., Transport Processes and Unit Operations, Third Edition, Prentice-Hall, Inc., 1993. [6]. Oldshue, J.Y., Fluid Mixing Technology, McGraw-Hill Publiscations Co., 1983. [7] University of Guelph. Dairy Products: Overview and Fluid Milk Products. Dairy Science and Technology, University of Guelph. September 20, 2007. <_http://www.foodsci.uoguelph.ca/dairyedu/fluid.html_> Appendix: Flat Blade           Diameter (inches) Speed Dial Setting Torque Meter (lb) Speed (RPM) Diameter (meters) Speed (RPS)   P (HP) Reimp 2.5 5 0.02 188 0.0635 3.133   0.00030 7.80E+06 2.5 10 0.04 371 0.0635 6.183   0.00118 1.54E+07 2.5 15 0.07 571 0.0635 9.517   0.00317 2.37E+07 2.5 20 0.11 763 0.0635 12.717   0.00666 3.17E+07 2.5 25 0.17 916 0.0635 15.267   0.01235 3.80E+07 2.5 30 0.22 1080 0.0635 18.000   0.01885 4.48E+07 3 5 0.04 185 0.0762 3.083   0.00059 9.21E+06 3 10 0.08 350 0.0762 5.833   0.00222 1.74E+07 3 15 0.10 536 0.0762 8.933   0.00425 2.67E+07 3 20 0.11 728 0.0762 12.133   0.00635 3.63E+07 4 5 0.08 163 0.1016 2.717   0.00103 1.08E+07 4 10 0.24 351 0.1016 5.850   0.00668 2.33E+07 4 15 0.42 534 0.1016 8.900   0.01779 3.55E+07 4 20 0.98 695 0.1016 11.583   0.05403 4.62E+07                   Slanted Blade           Diameter (inches) Speed Dial Setting Torque Meter (lb) Speed (RPM) Diameter (meters) Speed (RPS)   HP Reimp 2.5 5 0.03 169 0.0635 2.817   0.00040 7.02E+06 2.5 10 0.05 343 0.0635 5.717   0.00136 1.42E+07 2.5 15 0.06 557 0.0635 9.283   0.00265 2.31E+07 2.5 20 0.07 726 0.0635 12.100   0.00403 3.01E+07 2.5 25 0.09 894 0.0635 14.900   0.00638 3.71E+07 2.5 30 0.11 1088 0.0635 18.133   0.00949 4.52E+07 3 5 0.04 150 0.0762 2.500   0.00048 7.47E+06 3 10 0.06 353 0.0762 5.883   0.00168 1.76E+07 3 15 0.10 538 0.0762 8.967   0.00427 2.68E+07 3 20 0.16 772 0.0762 12.867   0.00980 3.85E+07 3 25 0.20 901 0.0762 15.017   0.01430 4.49E+07 4 5 0.07 179 0.1016 2.983   0.00099 1.19E+07 4 10 0.19 355 0.1016 5.917   0.00535 2.36E+07 4 15 0.38 543 0.1016 9.050   0.01637 3.61E+07 4 20 0.63 718 0.1016 11.967   0.03589 4.77E+07                   Table 6: Data and Results from Experiment for the Flat and Slanted Blade Impellers Curved Blade           Diameter (inches) Speed Dial Setting Torque Meter (lb) Speed (RPM) Diameter (meters) Speed (RPS)   HP Reimp 2.5 5 0.03 189 0.0635 3.150   0.00045 7.85E+06 2.5 10 0.04 362 0.0635 6.033   0.00115 1.50E+07 2.5 15 0.04 565 0.0635 9.417   0.00179 2.35E+07 2.5 20 0.05 724 0.0635 12.067   0.00287 3.01E+07 2.5 25 0.07 932 0.0635 15.533   0.00518 3.87E+07 2.5 30 0.08 1076 0.0635 17.933   0.00683 4.47E+07 3 5 0.03 161 0.0762 2.683   0.00038 8.02E+06 3 10 0.04 352 0.0762 5.867   0.00112 1.75E+07 3 15 0.05 552 0.0762 9.200   0.00219 2.75E+07 3 20 0.07 741 0.0762 12.350   0.00412 3.69E+07 3 25 0.10 906 0.0762 15.100   0.00719 4.51E+07 4 5 0.04 190 0.1016 3.167   0.00060 1.26E+07 4 10 0.07 340 0.1016 5.667   0.00189 2.26E+07 4 15 0.11 543 0.1016 9.050   0.00474 3.61E+07 4 20 0.17 739 0.1016 12.317   0.00997 4.91E+07 Table 7: Data and Results from Experiment for the Curved Blade Impellers Figure 5: Linear relationship of log(power) vs. log(RPM) Figure 6: Linear relationship of log(power) vs. log(Diameter) Sample Calculations: Sample Calculations: Diameter of the tank = 0.2794m (measured) The revolutions per minute of the impeller can be estimated using the tachometer.. ? = 998.2kg/m3 [1] ? = 1cP = 0.001kg/m.s [1] Reynold’s Impeller Number: Power Consumption: A torque scale reading of 0.07 was achieved: Scale-up of mixing vessel [2]: Desired Volume of Mixing Vessel = 5000L Volume of Laboratory-scale Mixing Vessel, Scale-up Factor [2], Number of Revolutions of Desired Tank to achieve the same mixing, n=1[2]: Diameter of the impeller for the larger tank: D2 = R*D1 = 6.63*0.1016m = 0.674m Reynold’s Impeller Number: Power Required: From figure 3, the Power Number for this Reynold’s Number, Np, is around 0.35 - 1 - - 1 - - 1 - - 1 - - 1 -