Our dependent variables, the outcome of our research, would be aggression.
We would need to further define aggression so that it is something we can test such as speeding or cutting other people off in traffic. We now have the basics of our very simple experiment and can write our Hypothesis: People who drive sports cars drive over the speed limit more frequently than people who drive other types of cars.
Before we can continue, however, we need to be aware of some aspects of research that can contaminate our results. In other words, what could get in the way of our results in this study being accurate.
The Experimental Method
These aspects are called research biases, and there are basically three main biases we need to be concerned with. In other words, if I believe the new medication will help me feel better, I may feel better even if the new medication is only a sugar pill. After carefully reviewing our study and determining what might effect our results that are not part of the experiment, we need to control for these biases.
To control for the placebo effect, subjects are often not informed of the purpose of the experiment. This is called a Blind study, because the subjects are blind to the expected results. To control for experimenter biases, we can utilize a Double-Blind study, which means that both the experimenter and the subjects are blind to the purpose and anticipated results of the study.
We have our hypothesis, and we know what our subject pool is, the next thing we have to do is standardize the experiment.
Experimental methods in chemical engineering: Reactors—fluidized beds
Standardization refers to a specific set of instructions. The reason we want the experiment to be standardized is twofold. Particle density , , is the basis of correlations to characterize fluidized bed hydrodynamics, including: bed void fraction , particle terminal velocity , minimum fluidization velocity, and slip velocity. The particle density is: 9. Skeletal density , , is the true density of the material without intra and interparticle voids and we calculate it from the bulk density and intra particle void fraction, : 10 This is the true density of the solid and we measure it with Hg and gas porosimetry.
High pressure forces Hg into connected channels and pores: 11 where is the pores diametre, is the surface tension of Hg, is the contact angle, and is the applied pressure: Hg penetrates 3 nm pores at 40 MPa. Hausner ratio , , is the quotient of the poured density to the tapped density,. Values greater than 1. Angle of repose , , is another measure of flowability. When powder piles up on a flat surface, it forms a cone and the angle it forms with respect to the horizontal plane is called the angle of repose. The coefficient of static friction, , equals.
In this test, powder poured out of a graduated cylinder a couple of cm from the table top until the diameter of the circle it formed reached mm. The angle of repose of the FCC was higher than for the sand with a similar standard deviation, so we expect that the FCC would flow better. PSD, particle size and distribution , is a parameter equally important as density to classify powders. Sphericity , , is a coefficient we apply to a particle diameter that represents how much its geometry deviates from a perfect sphere: for spheres and for cubes.
Catalysts in fluidized beds become rounded with time, but in experimental reactors with short run times, they are more often angular polyhedrons cuboids. Researchers synthesize catalysts, form pellets, then break up the pellets to 60— m.
FCC catalyst is spray dried and so its shape is spherical and approaches 1 Figure 4 a , while the sand is a mixture of angular chunks and rounded particles, so is less than 0. The crushed particles have angular shapes and a full characterization considers sphericity, surface texture, and particle corner roundness. Surface area , , is the property that researchers maximize to ensure that molecules from the gas phase adequately contact the active phase. Bulk catalysts have lower surface than catalysts grafted to zeolites and other high surface area supports.
Changes in surface area with time correlate with changes in the catalyst performance. Pore volume , , like surface area is an excellent indicator of how micro pores change with conditions as well as. These characteristics are measured in parallel with the surface area. The analytical techniques to study the hydrodynamic conditions include Table 2 : Optical probes inserted in the bed measure reflected or transmitted light intensity.
When the probe is larger than the particle, it detects all particles and evaluates solids concentration. When the probe is smaller than the particle diameter, it estimates velocity. Pressure measurements are easy, inexpensive, and widely applied in experimental and commercial facilities. Time averaged pressure difference at two heights assesses bed density, while sampling at high frequency determines fluidization quality. The principle is based on discriminating between the physical properties of the phases.
Aims of Experimental Research
Electric capacitance tomography ECT differentiates the solids phase from the gas based on the powder's dielectric constant: electrodes around the bed circumference measure capacitance. Particle tracking identifies the position of tracer particles with time. Tracers match either the fluid properties continuous phase or the particle properties dispersed phase.
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To construct images from data generated with phosphorescent, optical, or magnetic particles requires digital image analysis DIA software. Particle image velocimetry PIV : Ultrafast high resolution cameras record images of an illuminated bed. DIA software identifies particles and bubbles displacement from one image to the next. The analysis includes pattern recognition algorithms to treat the data statistically to derive the hydrodynamic parameters. The three top cited manuscripts were reviews of lignocellulosic biomass pyrolysis with citations , 48 then methanation citations , 49 and ash generated from biomass combustion 98 citations.
The solids phase in fluidized beds is perfectly backmixed to some extent, radial concentration gradients are negligible, and the bed operates isothermally. These characteristics simplify interpreting kinetic data compared to fixed beds, which have thermal, axial, and radial concentration gradients. Gas passes through the bed as bubbles at velocities, , several times greater than the superficial gas velocity Figure 6.
Bubbles are formed near the distributor, grow, coalesce, collapse, and erupt at the bed surface. They drag a wake of solids upward and reacting species traverse a cloud of circulating gas around the bubble. Bubbles, gas bypassing, and the notion that the gas phase is backmixed have limited the adoption of fluid bed reactors as a tool to measure catalytic reaction kinetics, despite their superior solids mass transfer and heat transfer characteristics. High throughput tandem reactors test hundreds of compositions and reaction conditions in a matter of a week. In reactors, from 5—21 mm in diameter, the gas phase is close to plug flow in shallow beds with an expanded bed height of 20 mm.
The fluidization characteristics—bed expansion, bubble size, and flow characteristics—are superior with rounded particles, which are produced in spray dryers. More binder ensures the integrity of the catalyst when the bed operates above. Heating the gas to reaction conditions is a limiting factor, and so solids backmixing and higher gas velocities heat the atomized droplets faster.
Because of the degrees of freedom, researchers adapt fluidized bed geometry, particle properties, and gas and solids injection to suit the needs of the process.
Most of the work in fluidized beds is dedicated to pyrolysis, combustion, gasification, and reduction, which require adding solids to the bed as it operates. Pulsating the air flow changes the size and number of the bubbles and decreases solids backmixing while increasing bed density. A pneumatic actuator lifts the reactor or grid up at a frequency to suspend the bed and thus also operates at high slip velocities.
For any function, , the uncertainty, , is: When is a product of factors, : 21 and when it is a sum of factors, For the reaction, A B, conversion, , is: 23 24 where is the molar fraction of species. The resulting uncertainty in conversion, , is: The uncertainty in of repeated measurements is the product of the coverage factor value at a significance level and a confidence level of , which we usually assume 0.
Assuming the reaction is first order in species concentration A, the rate constant, at reference temperature at a contact time is: 27 and the corresponding uncertainty is: The reaction rate, , at any temperature with respect to and uncertainty are: 29 The contribution to is greater for temperature and conversion compared to. To derive kinetics in fixed beds, researchers dilute catalyst with inert solids, operate in long narrow reactors and , for example , 80 and dilute the reactants.
Whereas, operating at low conversion facilitates interpreting the data from the point of view of hydrodynamics, it introduces error with respect to uncertainty. A standard set of boundary conditions assumes at and at.